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Efficiency enhancement and NOx emission reduction of a turbo-compressor gas engine by mass and heat recirculations of flue gases
Accepted Manuscript Title: Efficiency enhancement and NOx emission reduction of a turbocompressor gas engine by mass and heat recirculations of flue gases Author: Mohammad Tahmasebzadehbaie, Hoseyn Sayyaadi PII: DOI: Reference:
S1359-4311(16)30045-X http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.095 ATE 7655
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
20-9-2015 21-1-2016
Please cite this article as: Mohammad Tahmasebzadehbaie, Hoseyn Sayyaadi, Efficiency enhancement and NOx emission reduction of a turbo-compressor gas engine by mass and heat recirculations of flue gases, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.095. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Efficiency Enhancement and NOx Emission Reduction of a Turbo-
2
Compressor Gas Engine By Mass and Heat Recirculations of Flue Gases
3
Mohammad Tahmasebzadehbaie, Hoseyn Sayyaadi*
4
Faculty of Mechanical Engineering-Energy Division, K.N. Toosi University of Technology
5
P.O. Box: 19395-1999, No. 15-19, Pardis Str., Mollasadra Ave., Vanak Sq., Tehran 1999
6
143344, IRAN
7
Tel.: +98 8406 3212
8
Fax: +21 8867 4748
9
E-mail: [email protected]
10
[email protected]
11
12
Highlights:
13
heat and mass recirculation of flue gas in a turbo-compressor is proposed.
14
A plate-fin heat exchanger (PFHE) as an air pre-heater used for heat recirculation.
15
34.7% reduction in NOx and 5.8% improvement in exergy efficiency Was obtained.
16
Balance between different objectives is made in NSGA-II algorithm.
17
LINMAP, TOPSIS and fuzzy decision making methods used to select optimal solution.
18 19 1 of 42 Page 1 of 42
20
Abstract
21
A simple Turbo-Compressor model-GE MS 6001B PLTG-PLN-Sektor Tello Makassar-with 30
22
MW power generation, 27.71 % thermal efficiency and 26.07 exergy efficiency (at ISO
23
condition) considered for the efficiency enhancement and emission reduction. A cross flow
24
plate-fin heat exchanger (PFHE) as an air pre-heater (heat recirculation) along with direct
25
recirculation of a part of flue gases into the combustion chamber (mass recirculation) were
26
considered as modifications of original turbo-compressor gas engine to increase thermal
27
efficiency and reduce NOx emission. In a multi-objective optimization process, geometric and
28
thermal specifications of the plate-fin heat exchanger as well as the percentage of the recirculated
29
flue gas were obtained. The payback time for the capital investment of the heat exchanger and
30
NOx emission were minimized simultaneously while the exergetic efficiency of the gas cycle
31
was maximized and a frontier of optimal solution called as the Pareto frontier was obtained in
32
objective space. The final optimal solution was selected from the Pareto frontier using three
33
different decision-making methods, including the fuzzy Bellman-Zadeh, TOPSIS and LINMAP
34
methods. It was shown that the best results in comparison to the simple cycle led to 34.7%
35
reduction in NOx emission and 5.8% improvement in exergy efficiency (as difference).
36 37
Keywords: Decision-making; Gas turbine; Heat and Mass recirculation; Multi-objective
38
optimization; NOx emission reduction
39
2 of 42 Page 2 of 42
Nomenclature A
Area of heat transfer,
A ff
Free flow area,
BL
Booked life (years)
C
Costs (US $)
CI
Capital investment (US $)
CCL
Levelized carrying charge (US $)
c
Unit Cost (US $)
Ė
Exergy rate (kW)
e
Specific exergy (kJ.kg-1)
h
Heat transfer coefficient (W.m-2.K-1)
h
Molar enthalpy (kJ.kmol-1)
ieff
Rate of interest (cost of money)
j
jth year of operation
LHV
Molar lower heating value of fuel (kJ.kmol-1)
M
Molecular weight (kg.kmol-1)
m
Flow rate (kg.s-1)
m
m
2
2
3 of 42 Page 3 of 42
n
Molar flow rate (kmol.s-1)
P
Pressure (kPa)
Q
Rate of heat transfer (kW)
rFC
Escalation rate for the annual fuel cost
T
Temperature (K or 0C)
TRRj
Total revenue requirement for jth year (US $)
PFHE
Plate Fin Heat Exchanger
TOPSIS
Technique for Order Preference by Similarity to Ideal Situation
LINMAP
Linear Programming Technique for Multidimensional Analysis of Preference
s
Molar specific entropy (kJ.kmol-1.K-1)
Uo
Overall heat transfer coefficient (W.m-2.K-1)
W
Power (kW)
P
Drop of Pressure (kPa)
Greek Letters
Density (kg.m-3)
Efficiency
ν
Specific volume (m3. kg-1)
4 of 42 Page 4 of 42
ε
Exergetic efficiency
fuel-air ratio
Molar fuel-air ratio
ηsc
Compressor isentropic efficiency
ηsg
Gas turbine isentropic efficiency
Subscripts 1,2,3,4,5,x,y,z
States 1,2,3,4,5,x,y,z on regenerative turbo-compressor
a
Air
ac
Air compressor
cc
Combustion chamber
f
Fuel
hx
Heat exchanger
g
Gas (flue gas)
gt
Gas turbine
Dh
f
hydraulic diameter, m fanning friction factor
5 of 42 Page 5 of 42
mass flux velocity
G
2
1
h
heat transfer coefficient, W
H
height of the fin, m ; outer height of the fin,
j
Colburn factor
.m
.K
; inner height of the fin,
lance length of the fin, m
l
L
heat exchanger length, m
m
mass flow rate of fluid,
n
fin frequency, fins per meter
Na, Nb
simple
k g .s
1
number of fin layers for fluid a and b Simple gas turbine cycle
40 41
1
Introduction
42
A turbo-compressor model-GE MS 6001B PLTG-PLN-Sektor Tello Makassar [1] that works in
43
the simple Brayton cycle unit with a 30 MW power generation, 27.71 % thermal efficiency and
44
26.07 exergy efficiency at ISO condition was proposed to optimize its thermal efficiency and
45
NOx emission. The thermal and exergy efficiencies of turbo-compressor are increased by heat
46
recirculation of flue gases. In heat recirculation, the thermal and exergy efficiency of turbo-
47
compressor is enhanced by implicating air pre-heater or recuperator [2-6]. In this method, the
48
heat energy of exhaust gas is recovered by a heat exchanger called as air pre-heater or 6 of 42 Page 6 of 42
49
recuperator. Recuperators are usually in the form of cross flow plate fin heat exchanger, PFHE,
50
however, there are cases that tubular heat exchangers are used. The air-pre heating method is
51
also called as the heat recirculation. The heat recirculation is mostly used for increasing
52
combustion efficiency and therefore, increasing the cycle thermal efficiency. Another method for
53
enhancing the operation of gas turbines is mass recirculation that mostly used for emission. In
54
mass recirculation a percent of the outlet flue gas of the combustion chamber is recirculated to
55
the combustion chamber inlet and mixed with the preheated air coming from the air compressor
56
and PFHE. The mass recirculation is also called as the flue gas recirculation (FGR) or exhaust
57
gas recirculation (EGR). In this method, besides the heat recirculation caused preheating of the
58
inlet air of the combustion process, dilution of air-fuel mixture is obtained. The dilution of the
59
air-fuel leads to reduction in formation of NOx. The NOx is formed by three mechanisms. These
60
mechanisms are thermal nitrogen oxidation, prompt box and fuel NOx [7]. The FGR or mass
61
recirculation reduces N2 and O2 concentration as their contents in the mixture are substituted
62
with CO2 and H2O. On the other hand, shorter residence time of reactants due to preheating and
63
reduction of local peak temperatures caused by a better mixing are other outgoings of the mass
64
recirculation [8]. For instance, Tsolakis et al. [9] have investigated the effect of exhaust-assisted
65
fuel reforming on reaction profiles in diesel engines. Scribano et al. [10] have utilized the FGR
66
for industrial radiant tube burners.
67
Both heat recirculation [3-6, 11, 12] and mass recirculation [7-10] has been investigated by a
68
number of researchers to improve thermal efficiency and environmental emission of combustion
69
processes, respectively.
70
As is mentioned the heat recirculation is used for efficiency enhancement and mass recirculation
71
is a method for improving the environmental impact of gas turbines. Therefore, in a 7 of 42 Page 7 of 42
72
comprehensive improving approach, these criteria along with other criteria such as economics
73
would be considered, simultaneously. For improving the performance of gas turbine, several
74
criteria would be considered simultaneously. Such multi-criteria approaches for improving gas
75
cycles would be attended from the optimization viewpoint. For example, it is essential to
76
improve gas turbine efficiency while the cost of improvement and/or environmental emission of
77
the cycle to be minimized. This class of comprehensive optimization needs, employing the multi-
78
objective approach. Optimization of multi-objective was implemented by researchers to optimize
79
environmental, economic and energetic features of energy systems, simultaneously [13-19]. As
80
an energetic, economic and environmental models are in the form of the mixed integer non-linear
81
optimization problem so-called MINLP, this kind of problem is usually optimized using a class
82
of genetic algorithm called as multi-objective evolutionary algorithm, MOEA [14, 16, 19-21].
83
In a most relevant work, the multi-objective optimization of gas turbines using the heat
84
recirculation approach was performed by Sayyaadi and Aminian [22, 23]. They found the
85
optimal configuration of the regenerative gas with a special type of vertical shell and tube
86
recuperator, while objective functions were the cost of recuperator, exergy efficiency, and
87
environmental impact of the gas turbine.
88
In previous research [22, 23], heat recirculation was performed using a special type of vertical
89
shell and tube recuperator. As plate fin heat exchangers have a higher thermal efficiency for gas
90
stream, in this paper, heat recirculation was considered based on this type of heat exchanger
91
along with the mass recirculation. There is several research dedicated to optimization of the
92
structure PFHEs as a standalone thermal system [24-39]. However, in some cases, tubular
93
recuperator was proposed for heat recirculation in gas turbines [23, 24, 40]. Babaelahi et al.
8 of 42 Page 8 of 42
94
considered optimal design of a cross-flow heat exchanger using minimization of entropy
95
generation using the genetic algorithm [24].
96
The integration of PFHEs as recuperator was used in this paper for heat recirculation of a turbo-
97
compressor gas engine; however, as addressed previously there are cases that tubular recuperator
98
are implemented for heat recirculation [23, 24, 40]. Therefore, in this paper, the combination of
99
the PFHE air pre-heater into the turbo-compressor for heat recirculation along with mass
100
recirculation of flue gas for efficiency enhancement and NOx emission reduction of the proposed
101
turbo-compressor gas turbine was studied. Geometric and thermal specifications of the
102
recuperative heat exchanger and the percentage of flue gas for mass recirculation were obtained
103
in a multi-objective optimization process while the exergy efficiency, NOx emission, and
104
payback time of the investment of the recuperator were three objective functions of optimization.
105
Further, three decision-making approaches, including the fuzzy Bellman-Zadeh [41], Linear
106
Programming Technique for Multidimensional Analysis of Preference (LINMAP) [42, 44] and
107
Technique for Order Preference by Similarity to Ideal Situation (TOPSIS) [42, 44] were utilized
108
for selecting a final optimum solution from the Pareto frontier at the ISO condition.
109 110
2
111
The proposed simple turbo-compressor [1] with 30 MW power generation and 27.71 % thermal
112
efficiency and 26.07 exergy efficiency at ISO condition (25˚C ambient air temperature with
113
101.325kPa atmospheric pressure) was considered for a modification in this paper. General
114
specifications of the proposed turbo-compressor gas turbine were presented in Table 1.
115
Problem definition:
[Insert Table 1 here] 9 of 42 Page 9 of 42
116
In the present study, the exergetic efficiency of the proposed turbo-compressor was increased by
117
the integration of a PFHE recuperative heat exchanger as an air pre-heater and the NOx emission
118
of the proposed gas turbine was reduced by mass recirculation of a part of flue gas from the
119
outlet of the combustion chamber to its inlet. Fig. 1 shows a schematic arrangement of the
120
proposed regenerative turbo-compressor cycle with a PFHE as an air pre-heater while it
121
illustrates the mass recirculation of a part of flue gases into the combustion chamber. Inlet air to
122
the Combustion chamber is preheated using the flue gas exhausts from the turbo-compressor
123
with a plate fin heat exchanger and intermixes with the recirculated stream of the flue gas at the
124
inlet of the combustion chamber.
125
[Insert Fig. 1 here]
126
In analyzing the PFHE, the compressed air at the compressor outlet was called as the fluid ′b′. It
127
is preheated by the outlet flue gas from the turbine that called as the fluid ′a′ in the PFHE
128
analysis. The preheated air exits from the PFHE mixes the recirculated flue gas and directed to
129
the intake of the combustion chamber. More detail about proposed recuperative heat exchanger
130
can be found in [24].
131 132
3
Modeling of system:
133
3.1 Thermodynamic modeling:
134
The thermodynamic model of the regenerative turbo-compressor cycle was built based on the
135
following assumptions [40]
136
1. Steady state processes were assumed.
137
2. The air and combustion products were assumed to be an ideal-gas mixture. 10 of 42 Page 10 of 42
138 139 140 141 142 143 144 145
3. The natural gas as the fuel of the gas turbine was ideal gas and it was composed of 100% CH4. 4. Heat loses from the combustion chamber was considered as 2% of the LHV of the fuel. Adiabatic process was supposed for all other components. 5. A constant value for pressure drops were considered for all components except the airpreheater. In the PFHE, hydraulic model was used to determine the pressure drop. 6. The properties of combustion products and air were calculated based on the ideal gas mixture model.
146
7. Mole fractions of the inlet air are 0.7748N2, 0.2059 O2, 0.019 H2O and 0.0003 CO2.
147
Based on aforementioned assumptions the thermodynamic model for the simple and
148
regenerative gas cycles were presented in the following sections,
149 150 151
3.1.1
Air compressor
Power consumption of the compressor is:
152
(1)
153
In Eq. (1), the outlet temperature of air compressor was calculated as a function of the
154
isentropic efficiency,
, and isentropic outlet temperature,
155
, as follows: (2)
156
The isentropic efficiency,
, was assumed to be 0.87 and
157
compressor compressed ratio (=9.78), as follows:
was calculated based on
11 of 42 Page 11 of 42
158
159
(3)
where
is the adiabatic constant of the air (
).
160 161 162
3.1.2
Combustion process
Chemical reaction equation of the combustion process can be formulated as follows,
163 164 165
(4)
166
where
167
air ratio
168
is the molar fuel to air ratio and a is the molar portion of the recirculated flue gas to
,
169
,
170
,
171
(5)
172
In Eq. (5) subscripts 'a', 'z' and 'g' were dedicated to molar properties of the air, recirculated
173
flue gas and flue gas, respectively. From the balance of energy of combustion chamber we
174
have:
175
(6)
12 of 42 Page 12 of 42
176
where subscripts ‘f’’, ‘a’, ‘z’ and ‘p’ stand for the fuel, air, recirculated flue gas, and the
177
combustion products, respectively. As mentioned previously, it was assumed that the heat
178
loss
179
therefore,
180
chamber there is no power transfer i.e.
181
follows,
from
the
combustion
chamber
is
2%
of
of
the
fuel,
. On the other hand, in combustion , therefore, Eq. (6) could be rewritten as
182 183
LHV
(7) for the methane is 3124 kJ.kmole-1. Furthermore, we have:
184
(8a)
185
(8b)
186
(8b)
187
Hence
was calculated from the above equations. Then, the fuel mass flow rate was
188
calculated as, (9a)
(9b)
(9c)
(9d)
13 of 42 Page 13 of 42
(9e) 189
where
and
are fuel and air molecular weights, respectively.
190
Thermodynamic specifications of the recirculated flue gas depend on the outlet condition of
191
the flue gas from the combustion chamber, hence: (10a) (10b) (10c) (10d) (10e) (10f)
192 193 194
3.1.3
Gas turbine
In a similar manner to the air compressor we have:
195 196
(11a) where
197
(11b)
198
where
and
are the gas turbine expansion ratio (=9.2) and the turbine isentropic
199
efficiency (= 0.89), respectively.
200
14 of 42 Page 14 of 42
201 202
3.1.4
Overall exergetic efficiency of the turbo-compressor
The overall exergetic efficiency of the turbo-compressor cycle is,
203
(12)
204
where
is the net generated power and
205
53155.8 kJ.kg-1 for methane.
is the fuel chemical exergy assumed as
206 207
3.2 Hydraulic and Thermal design of the cross flow PFHE
208
A PFHE is consisting of a block of alternating layers of various fins and flat separators known as
209
partitioning plates [45, 46]. A simple cross flow PFHE was depicted in Fig. 2.
210
[Insert Fig. 2 here]
211
In the PFHE, heat is transferred from the hot gas into the cold gas stream. The hot and cold gas
212
flows were nominated as fluids 'a' and 'b' are outlet flue gas from the turbine and the outlet
213
compressed air from the compressor, respectively.
214
The following assumptions were considered for thermohydraulic modeling of the PFHE [24]:
215
1- Both hot and cold sides’ flows were steady state.
216
2- Properties of fluids were not dependent to the variation of temperatures.
217
3- The thermal resistance of the separators between two streams was ignored.
218
4- Both hot and cold sides had similar geometry of offset-strip fins.
219
5- The heat transfer coefficients and heat transfer areas were distributed uniformly along the
220
heat exchanger. 15 of 42 Page 15 of 42
221
6- Number of fins layers of stream 'b' were one layer less than the number of fins layers of
222
stream 'a'.
223
Heat balance between two fluids of the PFHE is,
224 225
(13) On the other hand, we have,
226 227
(14) The LMTD was defined as,
228 229
(15)
where (16a) (16b)
230
The effective heat transfer area and the overall heat transfer coefficient are [47],
231
232
(17)
Flow areas related to fluids a and b were calculated as follows,
233
(18a)
234
(18b)
235
The finned channel’s hydraulic diameter was calculated as follows,
16 of 42 Page 16 of 42
236
237
(19)
where
238 239
(20) Heat transfer areas on both sides (Aa and Ab) were obtained as follows,
240
(21a)
241
(21b)
242
On the other hand, the Colburn factor (j) was defined as,
243
(22)
244
Where
,
and
are Stanton number, Prandtl number, and mass flux and
245
transfer coefficient. The Colburn factor, j, depends on the type and geometry of fins, the
246
geometric parameters of the PFHE and the Reynolds number [46]. Moreover, heat transfer
247
coefficient was determined according the Colburn factor. Hence, placing A and h to the equations
248
of heat balance lead to the following expression:
249 250
is the heat
(23)
On the other hand, Colburn factor was obtained as [30]:
251
(24)
17 of 42 Page 17 of 42
252
Hot and cold side pressure losses of the PFHE were calculated based on friction factor, f, as
253
follows:
254
(25a)
255
(25b)
256
Friction factor was calculated as follows [30]:
(26)
257
258
In Eqs. (24) and (26), Reynolds number was defined as follows,
259
(27)
260 261
3.3 Economic modeling
262
The capital investment of the PFHE consisting of the capital and operating costs was formulated
263
as follows [24, 48]:
264 265 266
(28) where Atot is heat transfer area (m2). Parameters used in Eq. (28) were presented in Table 2. [Insert Table 2 here]
18 of 42 Page 18 of 42
267
The payback period for the return of the capital investment as one objective function in this
268
paper was determined according to the levelized capital investment, the levelized annual saving
269
on the fuel cost (due to increasing the thermal efficiency) and levelized cost due to the annual
270
reduction of the generated power (due to the mass recirculation). The formulation of the payback
271
period objective function was obtained as follows:
272
(29)
273
where
is operating time per year,
274
system operation (dedicated to the recuperator only),
275
and sold electricity, respectively. In addition,
276
generated power,
277
In Eq. (29),
278
as follows:
and
is the total revenue requirement of jth year of the
and
and
are the levelized price of fuel
are fuel mass flow rate and the net
indexes imply to simple Brayton and recuperative gas cycles.
denotes to the booked system life (Assumed to be 20 years) and
was calculated
279
280
(30)
where ri is the inflation rate (0.205 in Iran). ieff is the interest rate, which was obtained as,
281
(31)
282
In the above equation, i is the rate of return for the money or interest rate, which was taken as
283
0.185 in Iran.
284
In Eq. (29),
285
following expression [40]:
is the levelized cost per cubic meter of the natural gas. It was calculated from the
19 of 42 Page 19 of 42
286
cf
L
cf CELF cf 0
k
FC
0
(1 k
(1 k
FC
BL FC
)
(32)
CRF
)
287
where
is the fuel cost in the first year of the system operation and
288
follows [40]:
289
k FC
290
The terms
291
the capital-recovery factor obtained as follows:
was obtained as
1 rFC
(33)
1 i eff
and CRF denote the annual inflation rate for the fuel cost (assumed to be 5%) and
i e f f (1 i e f f )
BL
292
CRF
293
In a similar manner to
294
The average cost of the natural gas,
295
$.m-3 and 0.0.2152 $.kwhr-1 based on the Iran energy market.
296
In Eq. (29), total revenue requirement of the system operation at jth of the system operation,
297
TRRj, was simply calculated based on the capital investment of the PFHE as follows [13]:
298
TRR
299
j
where
(34)
(1 i e f f ) 1 n
, the levelized value of selling electricity, , and electricity,
, was obtained.
, in the first year was taken as 0.032
CI
(35)
BL
is the capital investment of the PFHE obtained from Eq. (28).
300 301
3.4 Emission modeling
20 of 42 Page 20 of 42
302
Emission from the combustion process (grams per kilogram of fuel) was determined based on a
303
semi-analytical correlation presented by Rizk and Mongia [49] as follows:
304
(36)
305
(37)
306
(38)
307
where
and
are NOx and CO emission in ppm, respectively.
,
,
are the primary
308
zone combustion temperature, the pressure of the inlet stream to the combustion chamber, and
309
the non-dimensional pressure drop (assumed to be 0.05), respectively. In addition,
310
residence time in the combustion zone . It depends on the percentage of recirculated flue gas and
311
when it is 0%, equals to 0.002 s [14, 50].
is the
312 313 314
4. Objective functions, decision variables and constraints 4.1.Definition of the objectives
315
The exergy efficiency of the turbo-compressor, the payback period for the return of the
316
investments of the PFHE and NOx emissions as represented by Eqs. (12), (29), and (38),
317
respectively. The multi-objective optimization aimed at making the balance between
318
simultaneous maximization of the thermal efficiency and minimization of the payback period
319
and NOx emission.
320 21 of 42 Page 21 of 42
321
4.2.Choice of decision variables
322
Decision variables in the current study were design parameters of the PFHE along with mass
323
recirculation parameter as follows,
324
Fin height (Hb and Ha)
325
Fin thickness (tb and ta)
326
Fin frequency (nb and na)
327
Number of fin layers of stream a (Na)
328
Heat exchanger dimensions (La, Lb and Lc)
329
Fin dimension (lfa and lfb).
330
Percentage of the recirculated flue gas (a)
331
Decision variables that are geometrical specifications of PFHE were illustrated in Fig. 3.
332 333
[Insert Fig. 3 here] 4.3. Constraints and limitations
334
Following constraints were considered in the multi-objective optimization of proposed turbo-
335
compressor gas engine: (m)
(39a)
(m)
(39b)
(m)
(39c)
(m)
(39d) (39e) (39f)
22 of 42 Page 22 of 42
(39g) (m)
(39h)
(m)
(39i) (39j)
(m) (m)
(39k)
(m)
(39l) (39m)
(%) 336
Following additional limitations were considered on operating variables of the gas cycle [40]: (40a)
(K) 337
(40b)
338
(40c) (40d)
339
Since the pressure drop in PFHE may cause reduction of the exergy following additional
340
constraints was imposed to prevent such unsatisfactory condition [40]:
341
(41)
342
where
and
343
compressor, respectively.
are exergetic efficiencies of the regenerative and simple turbo-
344
23 of 42 Page 23 of 42
345
5. Multi-objective optimization and decision making methods
346
In this study, a class of genetic algorithm called as NSGA-II (non-dominated sorting genetic
347
algorithm), was employed. Details of the working principle of NSGA-II was given in [22, 23]. In
348
multi-objective optimization, instead of a single optimal solution obtained in conventional
349 350 351
single-objective optimization, a frontier of optimal solution called as Pareto frontier is obtained. Therefore, we have a set of optimal solutions, hence, a process of decision making is required to select a single final solution from potential optimal solutions located on the Pareto frontier. In
352
this paper, three decision making methods were examined to select the final optimal solution
353
[51]. These methods are the LINMAP, TOPSIS and fuzzy Bellman-Zadeh decision making
354
methods. Since, dimension of various objectives in a multi-objective optimization problem might
355
be different (for example, in our case the exegetic objective has no dimension while the
356
dimension of the NOx emissions is in kg/year and the dimension of the payback time is in
357
years), therefore, before any decision, dimension and scales of objective space should be unified.
358
In this paper, objectives vectors should be non-dimensioned before decision-making. There are
359
some methods of non-dimensioning utilized in decision making including linear, Euclidian and
360
fuzzy non-dimensioning [40]. The fuzzy Bellman-Zadeh method utilizes the fuzzy-non-
361
dimensioning, while LINMAP and TOPSIS method employ Euclidian non-dimensioning. The
362
following sections are presented here in order to describe these decision-making algorithms. In
363
the LINMAP method, an ideal solution which has all objectives in their best values is defined
364
and Euclidian distances of solutions from this ideal solution in normalized objective space are
365
measured. Then, a solution with minimum distance to the ideal point is selected as the final
366
selected optimal solution. In TOPSIS, beside the ideal solution a non-ideal solution is defined
367
and the final solution is selected based on its distance from the ideal and non-ideal points in
24 of 42 Page 24 of 42
368
Euclidian normalized space of objectives. The fuzzy Bellman-Zadeh is developed based on fuzzy
369
membership functions of solutions and the final optimal solution is a solution which has a
370
maximum membership function. Details of the LINMAP, TOPSIS and FUZZY decision making
371
methods were given in [40].
372
373
6. Results and discussion
374
The simple turbo-compressor was modeled at the ISO condition. Table 3 summarizes thermal
375
specifications of the simple turbo-compressor prior to any modification at ISO condition.
376
[Insert Table 3 here]
377
At this stage, the heat and mass circulation of flue gases were considered for exergetic efficiency
378
improvement and emission reduction of the original simple turbo-compressor gas turbine. For
379
heat recirculation, a PFHE was integrated into the gas cycle and the mass recirculation of flue
380
gas was considered for emission reduction. In this regards, the optimized values of thermal and
381
geometric specifications of the PFHE and the percentage of recirculated mass were determined
382
using the multi-objective optimization. multi-objective optimization process with three objective
383
functions expressed by Eqs. (15), (29) and (38) and constraints specified by Eqs. (39)-(41).
384
Multi-objective optimization was performed and the Pareto frontier was obtained at ISO
385
condition. The final optimal solution from the Pareto frontier was selected using three
386
aforementioned decision-making methods. The Pareto optimal frontier was depicted in Fig. 4.
387
[Insert Fig. 4 here]
388
The final optimal solution was selected using LINMAP, TOPSIS and fuzzy and selected points
389
were indicated in Fig. 4. As is clear, TOPSIS and LINMAP selected a same final optimal 25 of 42 Page 25 of 42
390
solution. Specifications of the modified turbo-compressor that recommended by the LINMAP,
391
TOPSIS and fuzzy decision-makers were indicated in Table 4.
392
[Insert Table 4 here]
393
Table 4 shows that, the LINMAP and TOPSIS decision-maker, leads to the lowest payback time
394
of the recuperator investment. Therefore, it seems that in this case, TOPSIS&LINMAP provide
395
more desirable final optimal solution.
396
Table 5 indicates specifications of the selected final optimal regenerative gas cycle. Furthermore,
397
Figs 5a, 5b and 5c compare the fuel consumption, NOx emission and exergetic efficiency of the
398
simple gas cycle with the improved regenerative gas cycle, respectively.
399
[Insert Table 5 here]
400
[Insert Fig. 5 here]
401
As is found from Table 5 and Figs. (5a, b) the fuel consumption, exergy efficiency and NOx
402
emission of the modified cycle were improved 34.8%, 5.8% (as difference) and 34.7%,
403
respectively. The net generated power of the modified cycle was 19.5% lower than the simple
404
turbo-compressor gas engine. The reduction in generating power was due to recirculation of part
405
of flue gas which leads to reduction in mass flow rate of the working fluid entering the turbine
406
section. If optimization was a single- objective optimization with NOx emission objective
407
function, it would lead to 100% mass recirculation i.e. zero output power of the gas turbine. The
408
multi-objective optimization of this study with conflicting objectives, prevent obtaining such in
409
practical result.
26 of 42 Page 26 of 42
410
Aforementioned improvement requires an investment of approximately 579960US $.
411
investment will be paid back within 2.84 years with the current domestic cost of the natural gas
412
fuel in Iran. It is required mentioning that since optimization was performed based on the local
413
natural gas price in Iran, which is very cheap in comparison to the international market, the
414
payback time for the optimized cycle is relatively high. Based on the international price of the
415
natural gas, the return on investment will be very short in a few months.
416
At various ambient temperatures in the range of 5 to 40 ºC, the exergetic efficiency and NOx
417
emission of the modified cycle were compared to the original simple gas turbine in Figs 6a and 6b,
418
respectively. According to Figs. 6a and 6b at the all of ambient temperatures, optimized model
419
was better than the original cycle.
420
This
[Insert Fig. 6 here]
421
7. Conclusions
422
A simple gas turbine was improved using mass and heat recirculation of flue gas. A plate fin heat
423
exchanger was designed via genetic algorithm optimizer. For mass recirculation, 19.5% of flue
424
gas was recirculated from the outlet of the combustion chamber to its inlet. The total cost of the
425
modification was estimated to be 579960 US $ and the payback period for the return of this
426
investment 2.84 years. The modification led to 34.7% reduction in the NOx emission and +5.8%
427
improvement in the exergetic efficiency.
428
27 of 42 Page 27 of 42
429
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554 555
Fig. 1: Scheme of the modified turbo-compressor cycle
556
34 of 42 Page 34 of 42
557 558
Fig. 2: Typical cross flow plate fin heat exchanger [45, 46]
559 560
561 562
Fig. 3: Schematic view of decision variables that are considered for the PFHE
563
35 of 42 Page 35 of 42
564 565
Fig. 4: Pareto optimal frontier
566
36 of 42 Page 36 of 42
(a)
(b)
(c)
567
Fig. 5: Comparison of the present turbo-compressor cycle with the modified cycle for (a) fuel
568
consumption; (b) Exergy efficiency; (c) NOx emissions
37 of 42 Page 37 of 42
(a)
(b)
569
Fig. 6: Comparison of modified and original cycles at various ambient temperatures (a) exergy
570
efficiency (b) NOx emission
571
38 of 42 Page 38 of 42
572
Table 1: Specifications of the case study simple turbo-compressor Parameter
Value
Number of turbine stages Speed of rotor (RPM) Air flow rate at ISO condition (kg s-1) Flue Gas flow rate with natural gas at ISO condition (kg s-1) Turbine inlet temperature of the base load operation at rated output (°C) Turbine inlet temperature of the peak load operation at rated output (°C) Air flow rate of the compressor at the ISO condition (kg s-1) Compressor compression ratio at the ISO condition Turbine compression ration at the ISO condition Compressor isentropic efficiency Turbine isentropic efficiency Combustion chamber type Number of combustors Pressure drop in the combustion chamber
4 3000 125 127.1736 1025 1050 125 9.78 9.2 0.87 0.89 Vertical silo type 4 5% of the inlet pressure
573 574 575
Table 2: Cost coefficient of a PFHE heat exchanger [48]
576 Parameter
Value
578
Af [m2]
0.322
579
Ca [US $]
30 000
580
Cb
750
581
c
0.8
577
582 583 584
39 of 42 Page 39 of 42
585
Table 3: Specifications of the base case existing regenerative turbo-compressor cycle Parameter
Value
Mass flow rate of the air (kg/s)
125
Mass flow rate of the fuel (kg/s)
2.17
Mass flow rate of the flue gas (kg/s)
127.17
Gas turbine pressure ratio
9.2
Compressor pressure ratio
9.78
Net generated power (MW)
30
Isentropic efficiency of the gas turbine
0.89
Isentropic efficiency of the compressor
0.87
Thermal efficiency (%)
27.71
Exergetic efficiency (%)
26.97
NOx emission (ppm)
29.66
586 587
40 of 42 Page 40 of 42
588
Table 4: Specifications of the PFHE and the regenerative gas cycle with heat and mass
589
recirculations Parameters
Fuzzy
LINMAP & TOPSIS
Ha,Hb(m)
0.0706
0.0871
ta,tb(m)
0.0012
0.0011
na(1/m)
71.641
68.869
nb(1/m)
53.713
61.472
Na
28
27
Nb
27
26
(m)
3.395
2.941
(m)
7.104
7.592
(m)
3.881
4.617
(m)
0.0527
0.0586
(m)
0.0244
0.0252
19.5
19.5
1.415
1.417
24.15
24.15
33.80
33.88
31.81
31.87
19.35
19.38
529650
579960
3.57
2.84
(%) (kg/s) (MW) (%) (%) (ppm) ($) Payback (year) 590
41 of 42 Page 41 of 42
591
Table 5: The final specifications of the modified turbo-compressor with mass and heat
592
recirculations Parameter Symbol Value
Symbol
Value
Fin height(m) Fin thickness(m) Fin frequency for stream a(1/m) Fin frequency for stream b(1/m) Number of fin layers for stream a Number of fin layers for stream b Width (m) Length (m) Height (m) Length of fin (m) Width of heat fin (m) Percentage of mass recirculation (%) Fuel mass flow rate (kg/s) Net generated power (MW) Thermal efficiency (%) Exergetic efficiency (%) NOx emission (ppm) Total cost ($) Payback (year) Net generated power reduction (%) Exergetic efficiency improvement (%) Fuel consumption reduction (%) NOx emission reduction (%)
Ha,Hb ta,tb na nb Na Nb
0.0871 0.0011 68.869 61.472 27 26 2.941 7.592 4.617 0.0586 0.0252 19.50 1.42 24.01 33.88 31.87 19.38 579960 2.84 19.50 5.8 35.10 34.65
a
Ctot tpb -
593 594 595 596
42 of 42 Page 42 of 42
S1359-4311(16)30045-X http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.095 ATE 7655
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
20-9-2015 21-1-2016
Please cite this article as: Mohammad Tahmasebzadehbaie, Hoseyn Sayyaadi, Efficiency enhancement and NOx emission reduction of a turbo-compressor gas engine by mass and heat recirculations of flue gases, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.01.095. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Efficiency Enhancement and NOx Emission Reduction of a Turbo-
2
Compressor Gas Engine By Mass and Heat Recirculations of Flue Gases
3
Mohammad Tahmasebzadehbaie, Hoseyn Sayyaadi*
4
Faculty of Mechanical Engineering-Energy Division, K.N. Toosi University of Technology
5
P.O. Box: 19395-1999, No. 15-19, Pardis Str., Mollasadra Ave., Vanak Sq., Tehran 1999
6
143344, IRAN
7
Tel.: +98 8406 3212
8
Fax: +21 8867 4748
9
E-mail: [email protected]
10
[email protected]
11
12
Highlights:
13
heat and mass recirculation of flue gas in a turbo-compressor is proposed.
14
A plate-fin heat exchanger (PFHE) as an air pre-heater used for heat recirculation.
15
34.7% reduction in NOx and 5.8% improvement in exergy efficiency Was obtained.
16
Balance between different objectives is made in NSGA-II algorithm.
17
LINMAP, TOPSIS and fuzzy decision making methods used to select optimal solution.
18 19 1 of 42 Page 1 of 42
20
Abstract
21
A simple Turbo-Compressor model-GE MS 6001B PLTG-PLN-Sektor Tello Makassar-with 30
22
MW power generation, 27.71 % thermal efficiency and 26.07 exergy efficiency (at ISO
23
condition) considered for the efficiency enhancement and emission reduction. A cross flow
24
plate-fin heat exchanger (PFHE) as an air pre-heater (heat recirculation) along with direct
25
recirculation of a part of flue gases into the combustion chamber (mass recirculation) were
26
considered as modifications of original turbo-compressor gas engine to increase thermal
27
efficiency and reduce NOx emission. In a multi-objective optimization process, geometric and
28
thermal specifications of the plate-fin heat exchanger as well as the percentage of the recirculated
29
flue gas were obtained. The payback time for the capital investment of the heat exchanger and
30
NOx emission were minimized simultaneously while the exergetic efficiency of the gas cycle
31
was maximized and a frontier of optimal solution called as the Pareto frontier was obtained in
32
objective space. The final optimal solution was selected from the Pareto frontier using three
33
different decision-making methods, including the fuzzy Bellman-Zadeh, TOPSIS and LINMAP
34
methods. It was shown that the best results in comparison to the simple cycle led to 34.7%
35
reduction in NOx emission and 5.8% improvement in exergy efficiency (as difference).
36 37
Keywords: Decision-making; Gas turbine; Heat and Mass recirculation; Multi-objective
38
optimization; NOx emission reduction
39
2 of 42 Page 2 of 42
Nomenclature A
Area of heat transfer,
A ff
Free flow area,
BL
Booked life (years)
C
Costs (US $)
CI
Capital investment (US $)
CCL
Levelized carrying charge (US $)
c
Unit Cost (US $)
Ė
Exergy rate (kW)
e
Specific exergy (kJ.kg-1)
h
Heat transfer coefficient (W.m-2.K-1)
h
Molar enthalpy (kJ.kmol-1)
ieff
Rate of interest (cost of money)
j
jth year of operation
LHV
Molar lower heating value of fuel (kJ.kmol-1)
M
Molecular weight (kg.kmol-1)
m
Flow rate (kg.s-1)
m
m
2
2
3 of 42 Page 3 of 42
n
Molar flow rate (kmol.s-1)
P
Pressure (kPa)
Q
Rate of heat transfer (kW)
rFC
Escalation rate for the annual fuel cost
T
Temperature (K or 0C)
TRRj
Total revenue requirement for jth year (US $)
PFHE
Plate Fin Heat Exchanger
TOPSIS
Technique for Order Preference by Similarity to Ideal Situation
LINMAP
Linear Programming Technique for Multidimensional Analysis of Preference
s
Molar specific entropy (kJ.kmol-1.K-1)
Uo
Overall heat transfer coefficient (W.m-2.K-1)
W
Power (kW)
P
Drop of Pressure (kPa)
Greek Letters
Density (kg.m-3)
Efficiency
ν
Specific volume (m3. kg-1)
4 of 42 Page 4 of 42
ε
Exergetic efficiency
fuel-air ratio
Molar fuel-air ratio
ηsc
Compressor isentropic efficiency
ηsg
Gas turbine isentropic efficiency
Subscripts 1,2,3,4,5,x,y,z
States 1,2,3,4,5,x,y,z on regenerative turbo-compressor
a
Air
ac
Air compressor
cc
Combustion chamber
f
Fuel
hx
Heat exchanger
g
Gas (flue gas)
gt
Gas turbine
Dh
f
hydraulic diameter, m fanning friction factor
5 of 42 Page 5 of 42
mass flux velocity
G
2
1
h
heat transfer coefficient, W
H
height of the fin, m ; outer height of the fin,
j
Colburn factor
.m
.K
; inner height of the fin,
lance length of the fin, m
l
L
heat exchanger length, m
m
mass flow rate of fluid,
n
fin frequency, fins per meter
Na, Nb
simple
k g .s
1
number of fin layers for fluid a and b Simple gas turbine cycle
40 41
1
Introduction
42
A turbo-compressor model-GE MS 6001B PLTG-PLN-Sektor Tello Makassar [1] that works in
43
the simple Brayton cycle unit with a 30 MW power generation, 27.71 % thermal efficiency and
44
26.07 exergy efficiency at ISO condition was proposed to optimize its thermal efficiency and
45
NOx emission. The thermal and exergy efficiencies of turbo-compressor are increased by heat
46
recirculation of flue gases. In heat recirculation, the thermal and exergy efficiency of turbo-
47
compressor is enhanced by implicating air pre-heater or recuperator [2-6]. In this method, the
48
heat energy of exhaust gas is recovered by a heat exchanger called as air pre-heater or 6 of 42 Page 6 of 42
49
recuperator. Recuperators are usually in the form of cross flow plate fin heat exchanger, PFHE,
50
however, there are cases that tubular heat exchangers are used. The air-pre heating method is
51
also called as the heat recirculation. The heat recirculation is mostly used for increasing
52
combustion efficiency and therefore, increasing the cycle thermal efficiency. Another method for
53
enhancing the operation of gas turbines is mass recirculation that mostly used for emission. In
54
mass recirculation a percent of the outlet flue gas of the combustion chamber is recirculated to
55
the combustion chamber inlet and mixed with the preheated air coming from the air compressor
56
and PFHE. The mass recirculation is also called as the flue gas recirculation (FGR) or exhaust
57
gas recirculation (EGR). In this method, besides the heat recirculation caused preheating of the
58
inlet air of the combustion process, dilution of air-fuel mixture is obtained. The dilution of the
59
air-fuel leads to reduction in formation of NOx. The NOx is formed by three mechanisms. These
60
mechanisms are thermal nitrogen oxidation, prompt box and fuel NOx [7]. The FGR or mass
61
recirculation reduces N2 and O2 concentration as their contents in the mixture are substituted
62
with CO2 and H2O. On the other hand, shorter residence time of reactants due to preheating and
63
reduction of local peak temperatures caused by a better mixing are other outgoings of the mass
64
recirculation [8]. For instance, Tsolakis et al. [9] have investigated the effect of exhaust-assisted
65
fuel reforming on reaction profiles in diesel engines. Scribano et al. [10] have utilized the FGR
66
for industrial radiant tube burners.
67
Both heat recirculation [3-6, 11, 12] and mass recirculation [7-10] has been investigated by a
68
number of researchers to improve thermal efficiency and environmental emission of combustion
69
processes, respectively.
70
As is mentioned the heat recirculation is used for efficiency enhancement and mass recirculation
71
is a method for improving the environmental impact of gas turbines. Therefore, in a 7 of 42 Page 7 of 42
72
comprehensive improving approach, these criteria along with other criteria such as economics
73
would be considered, simultaneously. For improving the performance of gas turbine, several
74
criteria would be considered simultaneously. Such multi-criteria approaches for improving gas
75
cycles would be attended from the optimization viewpoint. For example, it is essential to
76
improve gas turbine efficiency while the cost of improvement and/or environmental emission of
77
the cycle to be minimized. This class of comprehensive optimization needs, employing the multi-
78
objective approach. Optimization of multi-objective was implemented by researchers to optimize
79
environmental, economic and energetic features of energy systems, simultaneously [13-19]. As
80
an energetic, economic and environmental models are in the form of the mixed integer non-linear
81
optimization problem so-called MINLP, this kind of problem is usually optimized using a class
82
of genetic algorithm called as multi-objective evolutionary algorithm, MOEA [14, 16, 19-21].
83
In a most relevant work, the multi-objective optimization of gas turbines using the heat
84
recirculation approach was performed by Sayyaadi and Aminian [22, 23]. They found the
85
optimal configuration of the regenerative gas with a special type of vertical shell and tube
86
recuperator, while objective functions were the cost of recuperator, exergy efficiency, and
87
environmental impact of the gas turbine.
88
In previous research [22, 23], heat recirculation was performed using a special type of vertical
89
shell and tube recuperator. As plate fin heat exchangers have a higher thermal efficiency for gas
90
stream, in this paper, heat recirculation was considered based on this type of heat exchanger
91
along with the mass recirculation. There is several research dedicated to optimization of the
92
structure PFHEs as a standalone thermal system [24-39]. However, in some cases, tubular
93
recuperator was proposed for heat recirculation in gas turbines [23, 24, 40]. Babaelahi et al.
8 of 42 Page 8 of 42
94
considered optimal design of a cross-flow heat exchanger using minimization of entropy
95
generation using the genetic algorithm [24].
96
The integration of PFHEs as recuperator was used in this paper for heat recirculation of a turbo-
97
compressor gas engine; however, as addressed previously there are cases that tubular recuperator
98
are implemented for heat recirculation [23, 24, 40]. Therefore, in this paper, the combination of
99
the PFHE air pre-heater into the turbo-compressor for heat recirculation along with mass
100
recirculation of flue gas for efficiency enhancement and NOx emission reduction of the proposed
101
turbo-compressor gas turbine was studied. Geometric and thermal specifications of the
102
recuperative heat exchanger and the percentage of flue gas for mass recirculation were obtained
103
in a multi-objective optimization process while the exergy efficiency, NOx emission, and
104
payback time of the investment of the recuperator were three objective functions of optimization.
105
Further, three decision-making approaches, including the fuzzy Bellman-Zadeh [41], Linear
106
Programming Technique for Multidimensional Analysis of Preference (LINMAP) [42, 44] and
107
Technique for Order Preference by Similarity to Ideal Situation (TOPSIS) [42, 44] were utilized
108
for selecting a final optimum solution from the Pareto frontier at the ISO condition.
109 110
2
111
The proposed simple turbo-compressor [1] with 30 MW power generation and 27.71 % thermal
112
efficiency and 26.07 exergy efficiency at ISO condition (25˚C ambient air temperature with
113
101.325kPa atmospheric pressure) was considered for a modification in this paper. General
114
specifications of the proposed turbo-compressor gas turbine were presented in Table 1.
115
Problem definition:
[Insert Table 1 here] 9 of 42 Page 9 of 42
116
In the present study, the exergetic efficiency of the proposed turbo-compressor was increased by
117
the integration of a PFHE recuperative heat exchanger as an air pre-heater and the NOx emission
118
of the proposed gas turbine was reduced by mass recirculation of a part of flue gas from the
119
outlet of the combustion chamber to its inlet. Fig. 1 shows a schematic arrangement of the
120
proposed regenerative turbo-compressor cycle with a PFHE as an air pre-heater while it
121
illustrates the mass recirculation of a part of flue gases into the combustion chamber. Inlet air to
122
the Combustion chamber is preheated using the flue gas exhausts from the turbo-compressor
123
with a plate fin heat exchanger and intermixes with the recirculated stream of the flue gas at the
124
inlet of the combustion chamber.
125
[Insert Fig. 1 here]
126
In analyzing the PFHE, the compressed air at the compressor outlet was called as the fluid ′b′. It
127
is preheated by the outlet flue gas from the turbine that called as the fluid ′a′ in the PFHE
128
analysis. The preheated air exits from the PFHE mixes the recirculated flue gas and directed to
129
the intake of the combustion chamber. More detail about proposed recuperative heat exchanger
130
can be found in [24].
131 132
3
Modeling of system:
133
3.1 Thermodynamic modeling:
134
The thermodynamic model of the regenerative turbo-compressor cycle was built based on the
135
following assumptions [40]
136
1. Steady state processes were assumed.
137
2. The air and combustion products were assumed to be an ideal-gas mixture. 10 of 42 Page 10 of 42
138 139 140 141 142 143 144 145
3. The natural gas as the fuel of the gas turbine was ideal gas and it was composed of 100% CH4. 4. Heat loses from the combustion chamber was considered as 2% of the LHV of the fuel. Adiabatic process was supposed for all other components. 5. A constant value for pressure drops were considered for all components except the airpreheater. In the PFHE, hydraulic model was used to determine the pressure drop. 6. The properties of combustion products and air were calculated based on the ideal gas mixture model.
146
7. Mole fractions of the inlet air are 0.7748N2, 0.2059 O2, 0.019 H2O and 0.0003 CO2.
147
Based on aforementioned assumptions the thermodynamic model for the simple and
148
regenerative gas cycles were presented in the following sections,
149 150 151
3.1.1
Air compressor
Power consumption of the compressor is:
152
(1)
153
In Eq. (1), the outlet temperature of air compressor was calculated as a function of the
154
isentropic efficiency,
, and isentropic outlet temperature,
155
, as follows: (2)
156
The isentropic efficiency,
, was assumed to be 0.87 and
157
compressor compressed ratio (=9.78), as follows:
was calculated based on
11 of 42 Page 11 of 42
158
159
(3)
where
is the adiabatic constant of the air (
).
160 161 162
3.1.2
Combustion process
Chemical reaction equation of the combustion process can be formulated as follows,
163 164 165
(4)
166
where
167
air ratio
168
is the molar fuel to air ratio and a is the molar portion of the recirculated flue gas to
,
169
,
170
,
171
(5)
172
In Eq. (5) subscripts 'a', 'z' and 'g' were dedicated to molar properties of the air, recirculated
173
flue gas and flue gas, respectively. From the balance of energy of combustion chamber we
174
have:
175
(6)
12 of 42 Page 12 of 42
176
where subscripts ‘f’’, ‘a’, ‘z’ and ‘p’ stand for the fuel, air, recirculated flue gas, and the
177
combustion products, respectively. As mentioned previously, it was assumed that the heat
178
loss
179
therefore,
180
chamber there is no power transfer i.e.
181
follows,
from
the
combustion
chamber
is
2%
of
of
the
fuel,
. On the other hand, in combustion , therefore, Eq. (6) could be rewritten as
182 183
LHV
(7) for the methane is 3124 kJ.kmole-1. Furthermore, we have:
184
(8a)
185
(8b)
186
(8b)
187
Hence
was calculated from the above equations. Then, the fuel mass flow rate was
188
calculated as, (9a)
(9b)
(9c)
(9d)
13 of 42 Page 13 of 42
(9e) 189
where
and
are fuel and air molecular weights, respectively.
190
Thermodynamic specifications of the recirculated flue gas depend on the outlet condition of
191
the flue gas from the combustion chamber, hence: (10a) (10b) (10c) (10d) (10e) (10f)
192 193 194
3.1.3
Gas turbine
In a similar manner to the air compressor we have:
195 196
(11a) where
197
(11b)
198
where
and
are the gas turbine expansion ratio (=9.2) and the turbine isentropic
199
efficiency (= 0.89), respectively.
200
14 of 42 Page 14 of 42
201 202
3.1.4
Overall exergetic efficiency of the turbo-compressor
The overall exergetic efficiency of the turbo-compressor cycle is,
203
(12)
204
where
is the net generated power and
205
53155.8 kJ.kg-1 for methane.
is the fuel chemical exergy assumed as
206 207
3.2 Hydraulic and Thermal design of the cross flow PFHE
208
A PFHE is consisting of a block of alternating layers of various fins and flat separators known as
209
partitioning plates [45, 46]. A simple cross flow PFHE was depicted in Fig. 2.
210
[Insert Fig. 2 here]
211
In the PFHE, heat is transferred from the hot gas into the cold gas stream. The hot and cold gas
212
flows were nominated as fluids 'a' and 'b' are outlet flue gas from the turbine and the outlet
213
compressed air from the compressor, respectively.
214
The following assumptions were considered for thermohydraulic modeling of the PFHE [24]:
215
1- Both hot and cold sides’ flows were steady state.
216
2- Properties of fluids were not dependent to the variation of temperatures.
217
3- The thermal resistance of the separators between two streams was ignored.
218
4- Both hot and cold sides had similar geometry of offset-strip fins.
219
5- The heat transfer coefficients and heat transfer areas were distributed uniformly along the
220
heat exchanger. 15 of 42 Page 15 of 42
221
6- Number of fins layers of stream 'b' were one layer less than the number of fins layers of
222
stream 'a'.
223
Heat balance between two fluids of the PFHE is,
224 225
(13) On the other hand, we have,
226 227
(14) The LMTD was defined as,
228 229
(15)
where (16a) (16b)
230
The effective heat transfer area and the overall heat transfer coefficient are [47],
231
232
(17)
Flow areas related to fluids a and b were calculated as follows,
233
(18a)
234
(18b)
235
The finned channel’s hydraulic diameter was calculated as follows,
16 of 42 Page 16 of 42
236
237
(19)
where
238 239
(20) Heat transfer areas on both sides (Aa and Ab) were obtained as follows,
240
(21a)
241
(21b)
242
On the other hand, the Colburn factor (j) was defined as,
243
(22)
244
Where
,
and
are Stanton number, Prandtl number, and mass flux and
245
transfer coefficient. The Colburn factor, j, depends on the type and geometry of fins, the
246
geometric parameters of the PFHE and the Reynolds number [46]. Moreover, heat transfer
247
coefficient was determined according the Colburn factor. Hence, placing A and h to the equations
248
of heat balance lead to the following expression:
249 250
is the heat
(23)
On the other hand, Colburn factor was obtained as [30]:
251
(24)
17 of 42 Page 17 of 42
252
Hot and cold side pressure losses of the PFHE were calculated based on friction factor, f, as
253
follows:
254
(25a)
255
(25b)
256
Friction factor was calculated as follows [30]:
(26)
257
258
In Eqs. (24) and (26), Reynolds number was defined as follows,
259
(27)
260 261
3.3 Economic modeling
262
The capital investment of the PFHE consisting of the capital and operating costs was formulated
263
as follows [24, 48]:
264 265 266
(28) where Atot is heat transfer area (m2). Parameters used in Eq. (28) were presented in Table 2. [Insert Table 2 here]
18 of 42 Page 18 of 42
267
The payback period for the return of the capital investment as one objective function in this
268
paper was determined according to the levelized capital investment, the levelized annual saving
269
on the fuel cost (due to increasing the thermal efficiency) and levelized cost due to the annual
270
reduction of the generated power (due to the mass recirculation). The formulation of the payback
271
period objective function was obtained as follows:
272
(29)
273
where
is operating time per year,
274
system operation (dedicated to the recuperator only),
275
and sold electricity, respectively. In addition,
276
generated power,
277
In Eq. (29),
278
as follows:
and
is the total revenue requirement of jth year of the
and
and
are the levelized price of fuel
are fuel mass flow rate and the net
indexes imply to simple Brayton and recuperative gas cycles.
denotes to the booked system life (Assumed to be 20 years) and
was calculated
279
280
(30)
where ri is the inflation rate (0.205 in Iran). ieff is the interest rate, which was obtained as,
281
(31)
282
In the above equation, i is the rate of return for the money or interest rate, which was taken as
283
0.185 in Iran.
284
In Eq. (29),
285
following expression [40]:
is the levelized cost per cubic meter of the natural gas. It was calculated from the
19 of 42 Page 19 of 42
286
cf
L
cf CELF cf 0
k
FC
0
(1 k
(1 k
FC
BL FC
)
(32)
CRF
)
287
where
is the fuel cost in the first year of the system operation and
288
follows [40]:
289
k FC
290
The terms
291
the capital-recovery factor obtained as follows:
was obtained as
1 rFC
(33)
1 i eff
and CRF denote the annual inflation rate for the fuel cost (assumed to be 5%) and
i e f f (1 i e f f )
BL
292
CRF
293
In a similar manner to
294
The average cost of the natural gas,
295
$.m-3 and 0.0.2152 $.kwhr-1 based on the Iran energy market.
296
In Eq. (29), total revenue requirement of the system operation at jth of the system operation,
297
TRRj, was simply calculated based on the capital investment of the PFHE as follows [13]:
298
TRR
299
j
where
(34)
(1 i e f f ) 1 n
, the levelized value of selling electricity, , and electricity,
, was obtained.
, in the first year was taken as 0.032
CI
(35)
BL
is the capital investment of the PFHE obtained from Eq. (28).
300 301
3.4 Emission modeling
20 of 42 Page 20 of 42
302
Emission from the combustion process (grams per kilogram of fuel) was determined based on a
303
semi-analytical correlation presented by Rizk and Mongia [49] as follows:
304
(36)
305
(37)
306
(38)
307
where
and
are NOx and CO emission in ppm, respectively.
,
,
are the primary
308
zone combustion temperature, the pressure of the inlet stream to the combustion chamber, and
309
the non-dimensional pressure drop (assumed to be 0.05), respectively. In addition,
310
residence time in the combustion zone . It depends on the percentage of recirculated flue gas and
311
when it is 0%, equals to 0.002 s [14, 50].
is the
312 313 314
4. Objective functions, decision variables and constraints 4.1.Definition of the objectives
315
The exergy efficiency of the turbo-compressor, the payback period for the return of the
316
investments of the PFHE and NOx emissions as represented by Eqs. (12), (29), and (38),
317
respectively. The multi-objective optimization aimed at making the balance between
318
simultaneous maximization of the thermal efficiency and minimization of the payback period
319
and NOx emission.
320 21 of 42 Page 21 of 42
321
4.2.Choice of decision variables
322
Decision variables in the current study were design parameters of the PFHE along with mass
323
recirculation parameter as follows,
324
Fin height (Hb and Ha)
325
Fin thickness (tb and ta)
326
Fin frequency (nb and na)
327
Number of fin layers of stream a (Na)
328
Heat exchanger dimensions (La, Lb and Lc)
329
Fin dimension (lfa and lfb).
330
Percentage of the recirculated flue gas (a)
331
Decision variables that are geometrical specifications of PFHE were illustrated in Fig. 3.
332 333
[Insert Fig. 3 here] 4.3. Constraints and limitations
334
Following constraints were considered in the multi-objective optimization of proposed turbo-
335
compressor gas engine: (m)
(39a)
(m)
(39b)
(m)
(39c)
(m)
(39d) (39e) (39f)
22 of 42 Page 22 of 42
(39g) (m)
(39h)
(m)
(39i) (39j)
(m) (m)
(39k)
(m)
(39l) (39m)
(%) 336
Following additional limitations were considered on operating variables of the gas cycle [40]: (40a)
(K) 337
(40b)
338
(40c) (40d)
339
Since the pressure drop in PFHE may cause reduction of the exergy following additional
340
constraints was imposed to prevent such unsatisfactory condition [40]:
341
(41)
342
where
and
343
compressor, respectively.
are exergetic efficiencies of the regenerative and simple turbo-
344
23 of 42 Page 23 of 42
345
5. Multi-objective optimization and decision making methods
346
In this study, a class of genetic algorithm called as NSGA-II (non-dominated sorting genetic
347
algorithm), was employed. Details of the working principle of NSGA-II was given in [22, 23]. In
348
multi-objective optimization, instead of a single optimal solution obtained in conventional
349 350 351
single-objective optimization, a frontier of optimal solution called as Pareto frontier is obtained. Therefore, we have a set of optimal solutions, hence, a process of decision making is required to select a single final solution from potential optimal solutions located on the Pareto frontier. In
352
this paper, three decision making methods were examined to select the final optimal solution
353
[51]. These methods are the LINMAP, TOPSIS and fuzzy Bellman-Zadeh decision making
354
methods. Since, dimension of various objectives in a multi-objective optimization problem might
355
be different (for example, in our case the exegetic objective has no dimension while the
356
dimension of the NOx emissions is in kg/year and the dimension of the payback time is in
357
years), therefore, before any decision, dimension and scales of objective space should be unified.
358
In this paper, objectives vectors should be non-dimensioned before decision-making. There are
359
some methods of non-dimensioning utilized in decision making including linear, Euclidian and
360
fuzzy non-dimensioning [40]. The fuzzy Bellman-Zadeh method utilizes the fuzzy-non-
361
dimensioning, while LINMAP and TOPSIS method employ Euclidian non-dimensioning. The
362
following sections are presented here in order to describe these decision-making algorithms. In
363
the LINMAP method, an ideal solution which has all objectives in their best values is defined
364
and Euclidian distances of solutions from this ideal solution in normalized objective space are
365
measured. Then, a solution with minimum distance to the ideal point is selected as the final
366
selected optimal solution. In TOPSIS, beside the ideal solution a non-ideal solution is defined
367
and the final solution is selected based on its distance from the ideal and non-ideal points in
24 of 42 Page 24 of 42
368
Euclidian normalized space of objectives. The fuzzy Bellman-Zadeh is developed based on fuzzy
369
membership functions of solutions and the final optimal solution is a solution which has a
370
maximum membership function. Details of the LINMAP, TOPSIS and FUZZY decision making
371
methods were given in [40].
372
373
6. Results and discussion
374
The simple turbo-compressor was modeled at the ISO condition. Table 3 summarizes thermal
375
specifications of the simple turbo-compressor prior to any modification at ISO condition.
376
[Insert Table 3 here]
377
At this stage, the heat and mass circulation of flue gases were considered for exergetic efficiency
378
improvement and emission reduction of the original simple turbo-compressor gas turbine. For
379
heat recirculation, a PFHE was integrated into the gas cycle and the mass recirculation of flue
380
gas was considered for emission reduction. In this regards, the optimized values of thermal and
381
geometric specifications of the PFHE and the percentage of recirculated mass were determined
382
using the multi-objective optimization. multi-objective optimization process with three objective
383
functions expressed by Eqs. (15), (29) and (38) and constraints specified by Eqs. (39)-(41).
384
Multi-objective optimization was performed and the Pareto frontier was obtained at ISO
385
condition. The final optimal solution from the Pareto frontier was selected using three
386
aforementioned decision-making methods. The Pareto optimal frontier was depicted in Fig. 4.
387
[Insert Fig. 4 here]
388
The final optimal solution was selected using LINMAP, TOPSIS and fuzzy and selected points
389
were indicated in Fig. 4. As is clear, TOPSIS and LINMAP selected a same final optimal 25 of 42 Page 25 of 42
390
solution. Specifications of the modified turbo-compressor that recommended by the LINMAP,
391
TOPSIS and fuzzy decision-makers were indicated in Table 4.
392
[Insert Table 4 here]
393
Table 4 shows that, the LINMAP and TOPSIS decision-maker, leads to the lowest payback time
394
of the recuperator investment. Therefore, it seems that in this case, TOPSIS&LINMAP provide
395
more desirable final optimal solution.
396
Table 5 indicates specifications of the selected final optimal regenerative gas cycle. Furthermore,
397
Figs 5a, 5b and 5c compare the fuel consumption, NOx emission and exergetic efficiency of the
398
simple gas cycle with the improved regenerative gas cycle, respectively.
399
[Insert Table 5 here]
400
[Insert Fig. 5 here]
401
As is found from Table 5 and Figs. (5a, b) the fuel consumption, exergy efficiency and NOx
402
emission of the modified cycle were improved 34.8%, 5.8% (as difference) and 34.7%,
403
respectively. The net generated power of the modified cycle was 19.5% lower than the simple
404
turbo-compressor gas engine. The reduction in generating power was due to recirculation of part
405
of flue gas which leads to reduction in mass flow rate of the working fluid entering the turbine
406
section. If optimization was a single- objective optimization with NOx emission objective
407
function, it would lead to 100% mass recirculation i.e. zero output power of the gas turbine. The
408
multi-objective optimization of this study with conflicting objectives, prevent obtaining such in
409
practical result.
26 of 42 Page 26 of 42
410
Aforementioned improvement requires an investment of approximately 579960US $.
411
investment will be paid back within 2.84 years with the current domestic cost of the natural gas
412
fuel in Iran. It is required mentioning that since optimization was performed based on the local
413
natural gas price in Iran, which is very cheap in comparison to the international market, the
414
payback time for the optimized cycle is relatively high. Based on the international price of the
415
natural gas, the return on investment will be very short in a few months.
416
At various ambient temperatures in the range of 5 to 40 ºC, the exergetic efficiency and NOx
417
emission of the modified cycle were compared to the original simple gas turbine in Figs 6a and 6b,
418
respectively. According to Figs. 6a and 6b at the all of ambient temperatures, optimized model
419
was better than the original cycle.
420
This
[Insert Fig. 6 here]
421
7. Conclusions
422
A simple gas turbine was improved using mass and heat recirculation of flue gas. A plate fin heat
423
exchanger was designed via genetic algorithm optimizer. For mass recirculation, 19.5% of flue
424
gas was recirculated from the outlet of the combustion chamber to its inlet. The total cost of the
425
modification was estimated to be 579960 US $ and the payback period for the return of this
426
investment 2.84 years. The modification led to 34.7% reduction in the NOx emission and +5.8%
427
improvement in the exergetic efficiency.
428
27 of 42 Page 27 of 42
429
References
430
[1] Yusuf Siahaya, Thermoeconomic Analysis of Gas Turbine Power Plant (GE MS 6001B
431
PLTG-PLN-Sektor Tello Makassar), Journal Penelition Engineering Vol. 12 No. 2. Tahun 2009,
432
ISSN: 1411-6243, hal. 141-150
433
[2] Budzianowski W.M., Miller R, Toward improvement in thermal efficiency and reduced
434
harmful emissions of combustion process by using recirculation of heat and mass: a review,
435
Recent Patents on Mechanical Engineering 2 (2009) 228-239.
436
[3] Budzianowsky W. M., Thermal integration of combustion-based energy generators by heat
437
recirculation, Rynek Energii 91(6) (2010) 108-115.
438
[4] Budzianowsky W. M., A comparative framework for recirculating combustion of gases,
439
Archivum Combustionis 30(1-2) (2010) 25-36.
440
[5] Aldushin A. P., Matokowsky B. J., Volpert V. A., Enhancement of Gasless Combustion
441
Synthesis By Counterflow Gas Filtration, Combustion Science and Technology 103 (1994) 41-
442
61.
443
[6] Budzianowski W.M., Miller R., Superadiabatic lean catalytic combustion in a high-pressure
444
reactor, Int J Chem React Eng 7 (2009) art. no. A20.
445
[7] Paul B., Datta A., Burner development for the reduction of NO x emission from coal fired
446
electric utilities, Recent Patents on Mechanical Engineering 1 (2008) 175-189.
447
[8] Al-Ibrahim A. M., Varnhama A., A review of inlet air-cooling technologies for enhancing the
448
performance of combustion turbines in Saudi Arabia, Applied Thermal Engineering 30 (2010)
449
1879-1888.
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450
[9] Tsolakis A, Megaritis A, Golunski SE. Reaction profiles during exhaust-assisted reforming of
451
diesel engine fuels. Energy Fuels 2005; 19: 744-752.
452
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33 of 42 Page 33 of 42
554 555
Fig. 1: Scheme of the modified turbo-compressor cycle
556
34 of 42 Page 34 of 42
557 558
Fig. 2: Typical cross flow plate fin heat exchanger [45, 46]
559 560
561 562
Fig. 3: Schematic view of decision variables that are considered for the PFHE
563
35 of 42 Page 35 of 42
564 565
Fig. 4: Pareto optimal frontier
566
36 of 42 Page 36 of 42
(a)
(b)
(c)
567
Fig. 5: Comparison of the present turbo-compressor cycle with the modified cycle for (a) fuel
568
consumption; (b) Exergy efficiency; (c) NOx emissions
37 of 42 Page 37 of 42
(a)
(b)
569
Fig. 6: Comparison of modified and original cycles at various ambient temperatures (a) exergy
570
efficiency (b) NOx emission
571
38 of 42 Page 38 of 42
572
Table 1: Specifications of the case study simple turbo-compressor Parameter
Value
Number of turbine stages Speed of rotor (RPM) Air flow rate at ISO condition (kg s-1) Flue Gas flow rate with natural gas at ISO condition (kg s-1) Turbine inlet temperature of the base load operation at rated output (°C) Turbine inlet temperature of the peak load operation at rated output (°C) Air flow rate of the compressor at the ISO condition (kg s-1) Compressor compression ratio at the ISO condition Turbine compression ration at the ISO condition Compressor isentropic efficiency Turbine isentropic efficiency Combustion chamber type Number of combustors Pressure drop in the combustion chamber
4 3000 125 127.1736 1025 1050 125 9.78 9.2 0.87 0.89 Vertical silo type 4 5% of the inlet pressure
573 574 575
Table 2: Cost coefficient of a PFHE heat exchanger [48]
576 Parameter
Value
578
Af [m2]
0.322
579
Ca [US $]
30 000
580
Cb
750
581
c
0.8
577
582 583 584
39 of 42 Page 39 of 42
585
Table 3: Specifications of the base case existing regenerative turbo-compressor cycle Parameter
Value
Mass flow rate of the air (kg/s)
125
Mass flow rate of the fuel (kg/s)
2.17
Mass flow rate of the flue gas (kg/s)
127.17
Gas turbine pressure ratio
9.2
Compressor pressure ratio
9.78
Net generated power (MW)
30
Isentropic efficiency of the gas turbine
0.89
Isentropic efficiency of the compressor
0.87
Thermal efficiency (%)
27.71
Exergetic efficiency (%)
26.97
NOx emission (ppm)
29.66
586 587
40 of 42 Page 40 of 42
588
Table 4: Specifications of the PFHE and the regenerative gas cycle with heat and mass
589
recirculations Parameters
Fuzzy
LINMAP & TOPSIS
Ha,Hb(m)
0.0706
0.0871
ta,tb(m)
0.0012
0.0011
na(1/m)
71.641
68.869
nb(1/m)
53.713
61.472
Na
28
27
Nb
27
26
(m)
3.395
2.941
(m)
7.104
7.592
(m)
3.881
4.617
(m)
0.0527
0.0586
(m)
0.0244
0.0252
19.5
19.5
1.415
1.417
24.15
24.15
33.80
33.88
31.81
31.87
19.35
19.38
529650
579960
3.57
2.84
(%) (kg/s) (MW) (%) (%) (ppm) ($) Payback (year) 590
41 of 42 Page 41 of 42
591
Table 5: The final specifications of the modified turbo-compressor with mass and heat
592
recirculations Parameter Symbol Value
Symbol
Value
Fin height(m) Fin thickness(m) Fin frequency for stream a(1/m) Fin frequency for stream b(1/m) Number of fin layers for stream a Number of fin layers for stream b Width (m) Length (m) Height (m) Length of fin (m) Width of heat fin (m) Percentage of mass recirculation (%) Fuel mass flow rate (kg/s) Net generated power (MW) Thermal efficiency (%) Exergetic efficiency (%) NOx emission (ppm) Total cost ($) Payback (year) Net generated power reduction (%) Exergetic efficiency improvement (%) Fuel consumption reduction (%) NOx emission reduction (%)
Ha,Hb ta,tb na nb Na Nb
0.0871 0.0011 68.869 61.472 27 26 2.941 7.592 4.617 0.0586 0.0252 19.50 1.42 24.01 33.88 31.87 19.38 579960 2.84 19.50 5.8 35.10 34.65
a
Ctot tpb -
593 594 595 596
42 of 42 Page 42 of 42