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Modified exergy and exergoeconomic analyses of a biomass post fired hydrogen production combined cycle
Accepted Manuscript Modified exergy and exergoeconomic analyses of a biomass post fired hydrogen production combined cycle
Saeed Soltani PII:
S0960-1481(18)31144-3
DOI:
10.1016/j.renene.2018.09.074
Reference:
RENE 10614
To appear in:
Renewable Energy
Received Date:
25 October 2017
Accepted Date:
20 September 2018
Please cite this article as: Saeed Soltani, Modified exergy and exergoeconomic analyses of a biomass post fired hydrogen production combined cycle, Renewable Energy (2018), doi: 10.1016/j. renene.2018.09.074
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ACCEPTED MANUSCRIPT
1
Modified exergy and exergoeconomic analyses of a biomass post fired
2
hydrogen production combined cycle
3
Saeed Soltani
4
Faculty of Mechanical Engineering, University of Tabriz, 16471 Tabriz, Iran
5
[email protected]; [email protected]
6
Tel: +98 914 406 7078
7
Abstract
8
Biomass post fired hydrogen production combined cycle (BPFHPCC) is proposed and analyzed
9
via common exergy and exergoeconomic analyses. In order to have an objective insight and
10
especially realistic approach to the cycle’s thermodynamic and exergoeconomic performance,
11
modified approach is applied. Within common exergy analysis, the components with high exergy
12
destruction are respectively, the combustion chamber, heat recovery steam generator and gasifier
13
while with modified exergy analysis they are the gas turbine, steam turbine and post combustion
14
chamber. As far as components exergy destruction cost rate are concerned, with common
15
analysis the highest exergy destruction cost rates are for the combustion chamber, heat recovery
16
steam generator and steam turbine while with modified analysis they are the combustion
17
chamber, gas turbine, and steam turbine. In this system hydrogen is used for other units.
18
However, if we want to use it within the system, the case in which hydrogen is injected into the
19
combustion chamber is extended. The effects on the thermodynamic efficiency and system
20
product cost were negative while it decreased the system CO2 emissions, exergy destruction and
21
loss rates as well as the exergy destruction and loss cost rates.
1
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Keyword: Modified exergy; Modified exergoeconomic; Hydrogen; Post firing; Biomass
23
gasification
24
1. Introduction
25
Recently, biomass has become a significant source of energy in many countries. It can be an
26
advantageous substitute for non-renewable energy sources such as fossil fuels. Rising the energy
27
consumption, greenhouse gas emissions [1], acid precipitation and ozone depletion have fostered
28
much research on alternatives to non-renewable energy. One disadvantage for renewable energy
29
is that its availability is intermittent, varying throughout the day and year. One means of
30
addressing this problem is to use two or more sources of renewable energies with fossil fuels.
31
Using renewable energy also can help mitigate the harmful environmental effects of fossil fuels.
32
Biomass is a renewable energy form which can be used directly or indirectly after conversion
33
into a biofuel. Various approaches have been demonstrated for utilizing biomass energy, a
34
common one being gasification [2]. Biomass can also be used as a fuel in an externally fired gas
35
turbine [3]. Gnanapragasam et al. [4] have examined the most appropriate conditions in which
36
natural gas is used in a combined cycle power plant as a primary fuel and biomass as a secondary
37
fuel. Gholami et al. [5] compared two types of biomass, and showed that wood has 1 point
38
percent higher energy efficiency and higher CO2 emissions than paper in a cogeneration system.
39
Ahmadi et al. [6] optimized a multi-generation energy system which has a gas turbine to generate
40
multiple products such as the electricity, heating, cooling and domestic hot water. The authors
41
assessed many design parameters to determine the most important to consider for enhancing the
42
exergy efficiency and the total cost of the system. Ghenai and Hachicha [7] examined a 10 MW
43
biomass-fired steam power plant, considering various biomass fuels blended with sub-
44
bituminous coal and fractions varying from 0 to 100%. It was shown that, by increasing the 2
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biomass fraction from 6 to 100%, the annual energy production increases while CO2 emissions
46
decrease. Moharamian et al. [8] investigated various biomass cycles based on organic Rankine
47
cycles and evaluated several working fluids for the system. R141b was identified as the most
48
effective for that system.
49
Hydrogen may become an important energy carrier in the near future because it is a clean fuel,
50
and it can be utilized in chemical and petrochemical processing [9]. The production of hydrogen
51
from renewable energies is described in [10, 11, 12]. As an energy carrier, hydrogen can
52
facilitate the use of renewable energies. For instance, Iribarren et al. [13] examined a hydrogen
53
production system based on biomass gasification. One method of hydrogen production uses
54
electrolysis. Bhandari et al [14] showed that in many studies electrolysis technology was utilized,
55
and global warming potential considered for assessing the environmental impacts. In a water
56
electrolyzer, electric energy is employed to separate water into hydrogen and oxygen. There are
57
several types of electrolysis, including alkaline, solid oxide and proton exchange membrane
58
(PEM) [15]. For increasing the lifetime of an electrolyzer, a solid electrolyte is utilized in the
59
PEM electrolyzer. The PEM electrolyzer has advantages over an alkaline electrolyzer, such as
60
higher hydrogen quality and lower energy waste. Corradetti and Desideri [16] techno-
61
economically compared biomass utilization in two applications: electric power generation and
62
hydrogen production. The authors showed that hydrogen can be generated from wood with an
63
energy efficiency of 66%, and the efficiency of a biomass integrated gasification combined cycle
64
was about 44%. As a result, it was suggested that biomass can be beneficially utilized both for
65
producing the electric power and hydrogen. Parametric analyses have been performed to
66
investigate the effect of important design and operating parameters on the plant energy
67
conversion efficiency by Ni et al [17]. This study has quantified how much the energy efficiency 3
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can decreases by increasing the operating temperature, lowering the current density, reducing the
69
electrolyte thickness, and increasing the electrode catalytic activity. In addition, for high
70
hydrogen production levels, a PEM electrolyzer has some drawbacks, such as high temperature
71
operating conditions and scale up demands while an alkaline electrolyzer can be a suitable choice
72
since it has a higher efficiency than a PEM electrolyzer [18, 19].
73
Many scientists indicate that, apart from a comprehensive thermodynamic analysis based on
74
exergy, exergy costing is also a significant principle for providing an exergoeconomic
75
perspective. Such a perspective can be utilized to compare the input fuel costs and capital
76
expenditures for determining the product unit costs, which plays an important role in
77
performance optimizing [20]. Taheri et al. [21] have examined a novel integrated biomass
78
multigeneration system. They found that fuel mass flow rate is the most important operating
79
parameter affecting the energy efficiency and the total cost rate. By increasing the fuel mass rate
80
from 4 kg/s to 10 kg/s, energy efficiency decreased by 8% and total cost rate increased by
81
122.8%.
82
Tsatsaronis and Park [22] proposed the avoidable and unavoidable exergy destruction and
83
investment costs in thermal systems with the name of modified exergy and modified
84
exergoeconomic analyses. They concluded in order to evaluate the thermodynamic performance
85
and cost effectiveness of thermal systems and to estimate the potential for improvements, it is
86
useful to know the avoidable part of both exergy destruction and component’s investment costs.
87
They applied this approach on a cogeneration system and concluded that modified
88
exergoeconomic analysis considers the air compressor, gas turbine, and heat recovery steam
89
generator (HRSG) for investment cost reduction. Finally, they showed modified exergy and
90
exergoeconomic analyses are more realistic than normal exergy and exergoeconomic analyses. 4
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In this study, a biomass post fired hydrogen production combined cycle (BPFHPCC) is proposed
92
and evaluated with thermodynamic, exergoeconomic, modified exergy and modified
93
exergoeconomic analyses. Modified exergy and exergoeoconomic analyses are applied to obtain
94
the realistic potentials for system performance improvement. Hydrogen is produced by the PEM
95
electrolyzer and steam turbine output power is the running power for the hydrogen production.
96
The prominent aspects of this system are co-combustion of natural gas and biomass as a
97
renewable energy which makes this system technically flexible for various amount of power
98
production with lesser environmental impacts. Meanwhile, recovery of gas turbine’s heat energy
99
discharge paves the way for existence of the hydrogen production unit by which makes the
100
system to be linked to industrial, commercial or residential areas. For example, product hydrogen
101
can be sold to the mentioned places. As another alternative, when there is no use in
102
aforementioned units, hydrogen is injected into the combustion chamber for ascertaining the
103
results, especially for the environmental impacts.
104
2. System description
105
The BPFHPCC is shown in Fig. 1. The cycle includes: gas turbine (GT), compressor (Comp),
106
post combustion chamber (PCC), combustion chamber (CC), pump, HRSG, condenser (Cond),
107
steam turbine (ST), biomass gasification unit (Ga), heat exchanger (HE), oxygen separator, and
108
PEM electrolyzer. Air enters to the compressor and is compressed until a desired compressor
109
pressure ratio (rp) and then combusts with the natural gas and oxygen in the air until a desired gas
110
turbine inlet temperature (TIT). The combusted gas enters the gas turbine and expands. The
111
expanded gas enters the post combustion chamber and again burns by gasified biomass and after
112
heating the water in the HRSG extracts to the atmosphere. The heated water enters the steam
113
turbine at point 3. The electrical power of the steam turbine in the combined cycle is used in the 5
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electrolyzer section, which is investigated here for the first time. The hot water which is needed
115
in the PEM electrolyzer is supplied by a heat exchanger. Hydrogen is produced at the cathode of
116
the electrolyzer, and oxygen at the anode is separated in the (water/oxygen) mixer, where the
117
hydrogen and oxygen are both cooled to the environment temperature. For later hydrogen
118
production, the remaining hot water is returned to the PEM inlet.
119 19
26
1 2
Pump
20
Cond 4
HRSG
18
Water O2 Separator
29 14
17 ST
HE
28
21
13
27
O2
25 PEM
Gen
H2
15
3 Fuel 24
Tank CC
6
7
22
Comp
GT
23
Gen
5
Air
8 12 PCC
Biofuel 11
Ga
Air 10
120 121 122
9 Biomass
Fig. 1 Biomass post fired hydrogen production combined cycle (BPFHPCC) 3. System analysis
123 6
16
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124
3.1.
Thermodynamic analysis
125
A thermodynamic analysis framework is represented for the combined system, which has three
126
main parts: steam and gas turbine, PEM electrolyzer and biomass gasifier. The combined cycle
127
operation is steady-state and the net electric power output is 10,000 kW.
128
The following assumptions are brought in Table 1:
129
Table 1
130
Assumptions and data for the components of the BPFHPCC Component or condition
Ambient parameters
Compressor, turbines, pump [23]
Assumptions and data
P=1.01 bar T=298 K The air composition by volume is 79% nitrogen and 21% oxygen η is,Comp=0.87 η is,GT=0.89 η is,ST=0.9 η is,Pump= 0.8 TIT is 1500 K
The dry biomass (wood) has a gravimetric composition of C: 50%, H: 6% and O: 44%, and a calorific value (on a dry Gasifier [24]
basis) of 449,568 kJ/kmol
The biomass moisture content is 20% on a mass basis
The equivalence ratio for gasification is 0.4188
7
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HRSG
Combustion and postcombustion chamber [23]
The maximum pressure of the steam cycle is 8000 kPa The pinch point temperature difference in the boiler is 10°C
Complete combustion occurs in the combustion
chambers
The combustion chambers are adiabatic and have a
pressure drop of 1% PEM electrolyzer [17]
TPEM = 353 K
J aref =1.7×105 A/m2
J cref =4.6×103 A/m2
D = 50 μm
F = 96486
λ a =14
λ c =10
E act,a = 76 kJ/mol
E act,c = 10 kJ/mol
131 132
For all components of the system, mass and energy balances can be written respectively as
133
follows [25]:
134
∑ṁin=∑ṁout
(1)
135
E + ∑ṁinhin= Ẇ +∑ṁouthout
(2)
136 137
For the system, the energy efficiency is written based on the net output power of cycle and the
138
amount of hydrogen which is available is accounted for the energy efficiency. In the 8
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139
denominator since we have input energy at point 26 it also should be accounted for the energy
140
efficiency of cycle.
141
W net,cycle =WGT -WComp +WST -WPump -WPEM
142
η=
143
When hydrogen is not available as the final product the energy efficiency becomes:
144
η=
145
Thermomechanical and chemical exergy are considered in the analysis. The specific
146
thermomechanical flow exergy at a state i is [25]:
147
ex i h i h 0 T0 s i s 0
148
where 0 is the restricted dead state condition.
149
Chemical exergy is calculated respect to the unrestricted dead state, which relates to the chemical
150
composition of the reference environment in addition to the reference pressure and temperature
151
[26]. The chemical exergy of an ideal gas mixture at the restricted dead state is based on the
152
partial pressures of the mixture components and the partial pressures of the same components in
153
the reference environment, but the chemical exergy in a combustion process is used to obtain the
154
potential useful work [26]. Also, the specific chemical exergy of a mixture of ideal gases follows
155
[26]:
156
ch ex ch mixture u i ex 0,i RT0 u i lnu i
(3a)
W net,cycle +m15 LHVH2 fuel LHVfuel +E 26 m
(3b)
W net,cycle
(3c)
fuel LHVfuel +E 26 m
(4a)
(4b)
i
9
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157
Here, ui and ex ch 0,i denote the mole fraction and standard chemical exergy, respectively, of a
158
mixture component.
159
The exergy balance of the flows can be expressed as follows:
160
Ėxin+∑iṁiexi=∑eṁeexe+W+ĖxD
161
Conventional exergy analysis has been applied based on approach “exergy of product/exergy of
162
fuel”. Note that an efficiency based on “exergy of product/exergy of fuel” is often but not
163
always similar to an efficiency based on “product outlet streams/inlet streams” or “outlet
164
streams/inlet streams” [27].
165
Exergy of fuels and products for components are listed in Table 2.
(4c)
166
Table 2
167
Exergy of the fuels and products Component Comp GT CC PCC Ga HRSG HE ST Cond Pump PEM electrolyzer
Ė-fuel Ėx22 Ėx7-Ėx8 Ėx24 Ėx11 Ėx10+Ėx9 Ėx12-Ėx13 Ėx26 Ėx3-Ėx4 Ėx4-Ėx1 Ėx19 Ėx17
168 169
The exergy efficiency for the cycle with available hydrogen is:
10
Ė-product Ėx6-Ėx5 Ėx22+Ėx23 Ėx7-Ėx6 Ėx12-Ėx8 Ėx11 Ėx3-Ėx2 Ėx28-Ėx27 Ėx18 Ėx21-Ėx20 Ėx2-Ėx1 +Ex -Ex Ex 15
25
14
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170
ε=
W net,cycle +Ex15 +Ex +Ex Ex 10
24
(5a) 26
171
The exergy efficiency for the cycle with unavailable hydrogen is:
172
ε=
173
W net,cycle Ex +Ex +Ex 10 24 26
3.2.
(5b)
Biomass combustion
174
A downdraft type gasifier is considered and the equilibrium model presumes that all of the
175
gasifier reactions are in the thermodynamic equilibrium. The reactions in the gasification process
176
are as follows [23, 28]:
177
C+CO2 2CO
(6)
178
C+H2O CO+H2
(7)
179
C+2H2 CH4
(8)
180
The shift reaction with combination of equations 6 and 7 is:
181
CO + H2O CO2+H2
182
The overall gasification reaction can be written as:
183
CHxOyNz + μ H2O + λ (O2+3.76N2) →aCO + bN2 + cH2 + dCO2 + eCH4 + fH2O
184
Equilibrium constants, respectively, are:
185
K1 =
e c2
186
K 2=
cd af
187
By MC = (mass of water/mass of wet biomass)
188
Kilomole number of moisture content can be calculated as follows:
(9)
(10)
(11)
(12)
11
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m biomass MC 18 1-MC
189
μ=
190
where mbiomass is the mass of biomass. Applying mass and energy balances to overall reaction
191
(Eq. 10) and considering the equilibrium constants, values of “a to f” and the gasification
192
temperature T (if m is known) or m (if T is known) are obtained. [23, 28].
193
The equilibrium constants are related to the change in the Gibbs functions, as:
194
-
195
ΔG= h -Tg s
196
Assuming no heat loss from the gasifier, an energy balance for the reaction in Eq. 10 can be
197
written. The enthalpy of formation of biomass is derived from its heating value [28].
198
The gasification product constituents in the present study are compared with the results of other
199
studies in Table 3 which indicates good agreement. The comparison considers biomass having a
200
20 % moisture content, based on experimental [29] and Zainal equilibrium model [28] results at
201
800 ℃.
(13)
ΔG =lnK RT
(14)
(15)
Table 3 Comparison of mole fractions of gasification constituents Constituent Present model Experiment [29]
Zainal equilibrium model [28]
H2
18.01
15.23
21.06
CO
18.77
23.04
19.61
CH4
0.68
1.58
0.64
CO2
13.84
16.42
12.01
N2
48.7
42.31
46.68
O2
0.00
1.42
0.00
202 12
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203
The heating value of wood represents the amount of heat released by a specific quantity (at 25 ℃
204
). The detailed calculations are mentioned in [30, 31] or as a given value for wood in [28]:
205
The exergy of biomass can be defined as the maximum amount of work that can be extracted in a
206
process in which the biomass is converted to the environment conditions, i.e., to the dead state.
207
Also, exwood can be expressed as follows [32]:
208
exwood=β LHVwood M
209
(16) M
H C
M
β=
C
M
H C
(17)
O
1 ‒ 0.4124 M
210
O
1.044 + 0.016 M ‒ 0.34493 M (1 + 0.0531 M )
C
Mi is the mass fraction of the elements (hydrogen, oxygen and carbon) in the biomass. 3.3.
211
PEM electrolyzer
212
The entire energy required for the PEM can be expressed as:
213
∆H=∆G+T∆S
214
Here, ∆G is the Gibbs free energy (for electricity demand), T is the electrolyzer temperature and
215
T∆S represents the thermal demand. The molar flow rate of the hydrogen product can be
216
expressed as:
217
nH
218
Here, J and F respectively denote current density and Faraday constant. The PEM electrolyzer
219
voltage can be expressed as [33, 34, 35]:
220
V=V0 + Vact,c +Vact,a + Vohm
(20)
221
V0 =1.229-8.5 10-4 (TPEM – 298)
(21)
(18)
J
= = ,out 2F nH
2
(19)
2O,reacted
13
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222
where Vact,a, Vact,c and Vohm are the anode, cathode and Ohmic activation overpotentials,
223
respectively. The resistance of the membrane, through which hydrogen ions pass, creates the
224
Ohmic overpotential. The local ionic conductivity σPEM of the electrolyzer and the water quantity
225
at location x can be expressed as follows [36]:
226
1 1 σ PEM λ x = 0.5139λ x -326 ×exp 1268 - 303 T
227
λ(x)=
228
Here, x represents the distance into the membrane which is evaluated from the cathode
229
membrane interface, D is the membrane thickness, λa is the water quantity at the anode
230
membrane, and λc is the water quantity at the cathode membrane. The overall ohmic resistance,
231
ohmic overpotential and overall activation based on J0 can be expressed respectively as [36]:
232
D RPEM=∫0 σ
(24)
233
Vohm,PEM =JR PEM
(25)
234
Vact,i= F sinh
235
J0,i=J i exp (- RT )
236
Fig. 2 compares the J-V characteristics of the PEM for current model and the experimental
237
results by Ioroi et al. [33]. It is seen that there is a good agreement between these two results.
(22)
λa ‒ λc
x+λc
D
(23)
dx PEM[λ(x)]
RT
ref
‒1
J
(2J )
i=a,c
(26)
0,i
Eact,i
i=a,c
(27)
14
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238
239 240
Fig. 2. Comparison of results for J-V characteristics of PEM for current model and experimental
241
work [33]
242
3.4.
Exergoeconomics
243
Exergoeconomics is a significant part of cycle analysis which is utilized to give economic and
244
thermodynamic insights simultaneously by applying the cost concepts to the exergy, which
245
accounts for the quality of energy. In this study, the specific exergy costing method is used in the
246
exergoeconomic analysis. The relevant cost balance equations and required auxiliary equations
247
are described below and are employed for each of the component of the integrated system [23,
248
37]. The exergy costing principles lead to the cost rate balance, as follows:
249
+Z=c c F Ex F P Ex P
(28)
15
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250
C=cEx
(29)
251
Here c is the cost per unit exergy of each stream. Equation (28) indicates that the sum of cost
252
rates associated with all exergy streams entering a component and the cost rates associated with
253
CI OM the capital investment as well as operation and maintenance ( Z Z Z ) is equal to the sum
254
of cost rates associated with the exiting exergy streams. The cost data for each component of the
255
system (Zk) is taken from appropriate references [23, 38] and brought in Table 5. The cost data
256
provided in the literature are for different years and in the present work they are brought to the
257
reference year, 2017, using the Marshall and Swift equipment cost index through the following
258
relation [39]:
259
Reference year cost =
260
Table 5
261
Components’ cost equations [23, 38]:
(Original cost) (Reference cost index) Original year cost index
Components Comp
CC and PCC
Cost equations c m P ZComp = 11 air out c -η 12 is,Comp Pin c11 =75$/(kg/s),c12 =0.9
Pout ln Pin
air(gas) . 1+exp(c 22 Tout -c 23 ) . ZCC&PCC =c 21.m
1 0.995-
c 21 =48.64$/(kg/s),c 22 =0.018K -1 ,c 23 =26.4
GT
c m P ZGT = 31 gas out 1+exp(c33Tin -c34 ) c -η 32 is,GT Pin c31 =1536$/(kg/s),c32 =0.92, c33 =0.036K -1 16
Pout Pin
ACCEPTED MANUSCRIPT
dry-biomass kg/h )0.67 ZGa =1600.(m
Ga ST
0.05 ZST =c51.W 1+ 1-ηis,ST 0.7 ST
3
× 1+5.exp Tin -866K 10.42K
c51 =3880.5$.kW -0.7
Q Cond CW +70.5.Q +c62 .m Cond × -0.6936.ln TCW -TWB +2.1898 2.2.LMTD c61 =280.74$.m -2
Cond
ZCond =c61.
c62 =746$.(kg.s)-1 Pump
0.71 1+ 0.2 ZPump =c71.W Pump 1-μ is,Pump c71 =705.48$.(kg.s)-1
HRSG
0.8 Q i steam,j +c 43 .m 1.2 ZHRSG =c 41. f p,i .f T.steam,i .f T.gas,i . +c 42 . f p,j .m gas i j LMTDi p f p,i =0.0971. i +0.9029 30bar -830K T f T.steam,i =1+exp out,steam,i 500K
-990K T f T.gas,i =1+exp out,gas,i 500K c 41 =4131.8$.(kW.K)0.8 c 42 =13380$.(kg.s)-1 c 43 =1489.7$.(kg.s)-1.2 *PEM
262
ZPEM=1000 W PEM ($)
electrolyzer * Costs
of the heat exchanger and O2 separator are included
263
The costs of natural gas and biomass respectively are 9.08 $/GJ and 2 $/GJ [23, 40].
264
The annual levelized capital investment for the k th component can be calculated as [23]:
265
CRF Z CI k = Zk τ
(30)
17
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266
where CRF and τ are the capital recovery factor and the annual plant operation hours,
267
respectively. The capital recovery factor is a function of the interest rate, ir, and the number of
268
years of the plant operation, n, as follows:
i r 1+i r
n
(31)
269
CRF=
270
For the k th component, the annual levelized operation and maintenance cost can be expressed as
271
[23]:
272
1+i r
n
-1
ZOM k =γ k Z k +ω k E p,k +R k
(32)
273
Here, γ k and ωk account for the fixed and variable operation and maintenance costs,
274
respectively, associated with the k th component and R k includes all other operation and
275
maintenance costs, which are independent of investment cost and product exergy. The last two
276
terms on the right side of Eq. (32) are neglected in the present work as they are small compared
277
to the first term [23].
278
With the Fuel and Product theory [37], which are commonly used for analyzing exergy, the cost
279
rate related to the costs of fuel and product, and exergy destruction rate (i.e., CFuel,k, CP,k, CD,k),
280
we can write:
281
ĊP,k=cP,kĖxP,k
(33)
282
ĊFuel,k=cFuel,kĖxFuel,k
(34)
283
ĊD,k=cD,kĖxD,k
(35)
284
The total unit product cost (TUPC) can be expressed as follows: 18
ACCEPTED MANUSCRIPT
285
TUPC=
∑nk Ż + ∑nfuelc k Fuel ĖFuel i=1
i=1
i
i
(36)
n
∑ p Ė i=1 P
i
286
The exergoeconomic factor indicates the contribution of the component’s capital investment cost
287
to the total cost in terms of costs related to the exergy destruction plus capital investment cost of
288
the component. The exergoeconomic factor can be expressed as
289
f=
290
Table 6 shows the primary equations for exergoeconomic analysis of the NFBPC-HI.
Z k Z +C k D,k
(37)
Table 6 Exergy cost rate balances and auxiliary equations of the BPFHPCC Components Auxiliary equation
Cost balance
Comp
-
Ċ6 = Ċ5+ ŻComp+ Ċ22
CC
-
Ċ6+Ċ24+ŻCC = Ċ7
GT
c22 = c23
PCC
-
Ċ8+ ŻPCC + Ċ11 = Ċ12
Ga
-
Ċ9+ ŻGa + Ċ10 = Ċ11
HE
-
Ċ26+Ċ27+ ŻHE = Ċ28
ST
c18 = c19
Ċ3+ ŻST = Ċ4+ Ċ18
Cond
c1 = c4
Pump
-
HRSG
c12 = c13
Ċ2+ ŻHRSG+Ċ12 = Ċ3+ Ċ13
PEM electrolyzer
c14 = c 25
Ċ14+ ŻPEM+Ċ17 = Ċ15+ Ċ25
Ċ7+ ŻGT = Ċ8+ Ċ23 + Ċ22
Ċ4 + Ċ20+ Ż Cond = Ċ1+ Ċ21 Ċ1+ŻPump+Ċ19 = Ċ2
291 292
3.5 Modified exergy analysis
293
Technological and economic design limitations determine a minimum value of the exergy
294
destruction. The part of the exergy destruction that cannot be avoided with technologically
19
ACCEPTED MANUSCRIPT
295
feasible design modifications is the unavoidable exergy destruction [22]. The unavoidable exergy
296
destruction is calculated by considering each component in isolation, separated from the system,
297
assuming the most favorable operating conditions. These conditions refer to minimum exergy
298
destruction and are associated with very low temperature differences and thermal/pressure losses
299
within the components. The assumptions for simulating unavoidable conditions depend on the
300
decision maker and are arbitrary to some extent. In this paper these assumptions have been
301
selected based on the authors’ knowledge and experience on plant operation and by considering
302
the maximum improvement potential that could be achieved for each plant component in the
303
foreseeable future. Table 7 lists the assumptions which are used.
304
The modified exergy efficiency of the system is defined based on the realistic definition for
305
exergy efficiency, since unavoidable exergy destruction should not be accounted in the exergy
306
efficiency:
307
ε* =
Ex P,k Ex -Ex UN F,k
(38)
D,k
308
Table 7
309
Assumptions for the unavoidable exergy destruction of the components of the BPFHPCC Component Comp GT
CC, PCC
Unavoidable conditions ηis,Comp = 0.98 ηis,GT = 0.99
Δp = 0 Qloss = 0 λ=1
Ga ST Pump HRSG
ER = 0.3632 ηis,ST = 0.97 ηis,Pump = 0.95
Tpp = 7 K 20
ACCEPTED MANUSCRIPT
TPEM = 150 oC
PEM 310
3.6 Modified exergoeconomic analysis
311
In modified exergoeconomic analysis, Z UN =Z -Z AV is the unavoidable capital investment, where
312
Z UN is related to the case in which the cost of the component is low [22]. Therefore, poor
313
characteristics are considered for components. In this paper the values are based on Table 8.
314
Note that, as for the unavoidable exergy destruction rate, the assumptions for simulating the
315
unavoidable conditions depend on the decision maker and are arbitrary to some extent.
316
Meanwhile, the cost rates related to the unavoidable exergy destruction rate can be expressed as [22]:
317
UN UN C D,k,A =cf,k Ex D,k,A
318
Avoidable exergy destruction costs are calculated by [17]
319
UN C AV D,k,A =C D,k,A -C D,k,A
320
Finally the modified exergoeconomic factor based on the avoidable cost rates is [22]:
321
f k* =
(39)
(40)
Z AV k AV Z AV +C k
(41)
D,k
322
Table 8
323
Assumptions for the unavoidable capital investment cost rate of the components of the BPFHPCC Component Comp GT CC
Unavoidable conditions ηis,Comp = 0.7 ηis,GT = 0.76
TCC = 1273K
PCC
TPCC = 1062 K
Ga ST Pump
ER = 0.3632 ηis,ST = 0.7 ηis,pump = 0.7 21
ACCEPTED MANUSCRIPT
324
HRSG PEM 4. Results and discussion
Tpp = 20 K
325
Parametric analyses are applied to show the effects of the various design and operating
326
conditions on the performances of the cycle considered in this study. The analyses focus on the
327
effects of varying the gas turbine inlet temperature and pressure ratio since these are the key
328
inputs in power plants. Meanwhile, the hydrogen injection flow rate into the combustion
329
chamber when there is hydrogen injection is an input parameter. The output parameters
330
considered include hydrogen production rate, energy and exergy efficiencies, exergy destruction
331
and loss rates, CO2 emissions rate, exergy destruction and loss cost rates, total unit product cost
332
and exergoeconomic factor.
333
Table 9 lists the thermodynamic values for flows of the BPFHPCC, when the net power output is
334
10,000 kW, the gas turbine inlet temperature is 1500 K, and the heat recovery steam generator
335
(HRSG) inlet temperature is 1050 K.
ηis,ST = 0.7
336 337
Table 9
338
Thermodynamic values for flows of the BPFHPCC State
ṁ (kg/s)
P (bar)
T (K)
h (kJ/kmol)
1 2 3 4 5 6
3.61 3.61 3.61 3.61 14 14
0.08 80 80 0.08 1.01 9.09
314.7 315.4 850 314.7 298 589.9
3132 3314 64600 41742 -4.366 8673
10.67 10.79 125.3 133.4 198.6 200.6
6.461 35.96 5489 417 0 3990
7
14.33
8.99
1500
5340
234.8
15158
8
14.33
1.02
964.3
-13789
237.3
5101
22
s (kJ/(kmol K))
Ėx (kW)
ACCEPTED MANUSCRIPT
11
0.4228
1.02
1073
-67564
227.5
1648
12 13 14 15 20 21 24 25
14.75 14.75 0.6925 0.0390 185.22 185.22 0.323 0.6541
1.01 1.01 1.01 1.01 1.01 1.01 9.09 1.01
1050 322.7 353.2 353.2 308.1 318.15 298.15 353.2
-15411 -38982 6035 1596 1889 2642 -74595 -4563
240.6 203 19.37 135.5 6.61 9.069 168 85.97
6399 15.19 378.6 4557 0 131 16901 190.6
339 340
Fig. 3 shows the variations of the hydrogen production rate in the BPFHPCC with rp and TIT.
341
Increasing rp leads to a minimum hydrogen rate at rp=12 and increasing TIT decreases the
342
hydrogen production rate. These variations are affected by the variation of the steam turbine
343
power output with either rp or TIT, since the hydrogen is produced using the steam turbine output
344
power. For example, increasing TIT increases the gas turbine output power and for the constant
345
=10000 kW ), steam turbine power decreases. Therefore, by TIT total output power ( W net
346
increase, hydrogen production decreases.
23
ACCEPTED MANUSCRIPT
347 348
Fig. 3 Variations of hydrogen production rate with rp and TIT
349
Variations for the energy and exergy efficiencies of the BPFHPCC plant with rp and TIT are
350
shown in Fig.4. Increasing rp leads to an optimum point for energy efficiency, at a value of
351
around rp=11, while exergy efficiency decreases. Raising TIT increases the energy and exergy
352
efficiencies.
24
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353
354 355 356
Fig. 4 Variations for the BPFHPCC of the energy and exergy efficiencies with rp and TIT
357
Fig. 5 shows the variations with TIT and rp for the BPFHPCC plant of the exergy destruction and
358
loss rates. Increasing rp raises the exergy destruction rate. While increasing TIT decreases the
359
exergy destruction rate. Increasing TIT reduces the exergy loss rate while increasing rp at TIT=
360
1500 K leads to an optimum point for the exergy loss rate, approximately at a compressor
361
pressure ratio of 12.
25
ACCEPTED MANUSCRIPT
362
363 364
Fig. 5 Variations for the BPFHPCC plant of exergy destruction and loss rates with rp and TIT
365
Fig. 6 presents the variations of the exergy destruction and loss cost rates with rp and TIT for the
366
BPFHPCC plant. Increasing rp decreases the exergy destruction cost rate. Meanwhile, increasing
367
rp reduces the exergy loss cost rate. Increasing TIT decreases the exergy destruction cost rate in
368
the BPFHPCC plant. Furthermore, increasing TIT raises the exergy loss cost rate, which is
369
opposite to the variation of exergy loss rate with TIT. The reason is the natural gas flow rate
370
increases with TIT, so the high cost of natural gas is the determining factor.
26
ACCEPTED MANUSCRIPT
371
372 373 374
Fig. 6 Variations for the BPFHPCC plant of the exergy destruction and loss cost rates with rp and
375
TIT
376 377
Fig. 7 displays the variations for the BPFHPCC plant of the total unit product cost and
378
exergoeconomic factor with rp and TIT. Increasing rp reduces the total unit product cost.
379
However, the total unit product cost increases with TIT. For the BPFHPCC plant, a higher TIT is
380
advantageous only thermodynamically. Furthermore, increasing rp raises the exergoeconomic
381
factor, showing that component purchase and maintenance costs increase more with rp than does
382
the exergy destruction cost. Note also that, at all values of rp, the component purchase and
27
ACCEPTED MANUSCRIPT
383
maintenance costs are higher than the exergy destruction cost. As TIT rises, the component
384
purchase and maintenance costs are optimized, with the optimal rp value of 14 (TIT= 1500 K).
385
386 387 388
Fig. 7 Variations for the BPFHPCC plant of the total unit product cost and exergoeconomic
389
factor with rp and TIT
390
Until now, the analysis was based on the hydrogen production for other units. However, suppose
391
we want to exploit hydrogen in the BPFHPCC. In the following figures these effects on the
392
energy efficiency, CO2 emissions rate, exergy destruction and loss rates, exergy destruction and
393
loss cost rates, total unit product cost and exergoeoconomic factor, will be shown.
28
ACCEPTED MANUSCRIPT
394
Variations for the BPFHPCC plant of the energy efficiency and CO2 emissions rate with
395
hydrogen injection rate into the combustion chamber are shown in the Fig. 8. Energy efficiency
396
decreases by hydrogen injection around 0.15 points. Increasing the hydrogen injection decreases
397
the natural gas flow rate in the combustion chamber with the expense of lower available
398
hydrogen, the latter effect leads to lower energy efficiency. An appealing result is shown for the
399
CO2 emissions rate in which the emissions decrease by hydrogen injection.
400 401 402
Fig. 8 Variations for the BPFHPCC plant of the energy efficiency and CO2 emissions rate with hydrogen injection rate into the combustion chamber
29
ACCEPTED MANUSCRIPT
403
Fig. 9 shows the variations for the BPFHPCC plant of the exergy destruction and exergy loss
404
rates with hydrogen injection rate into the combustion chamber. Exergy destruction rate
405
decreases in the plant. The reason is by hydrogen injection the combustion chamber exergy
406
destruction decreases and overall exergy destruction of system decreases. The effect of hydrogen
407
injection on the exergy loss of the system is negligible.
408 409
Fig. 9 Variations for the BPFHPCC plant of the exergy destruction and exergy loss rates with
410
hydrogen injection rate into the combustion chamber
411
Fig. 10 shows the variations for the BPFHPCC plant of the exergy destruction and exergy loss
412
cost rates with hydrogen injection rate into the combustion chamber. The effects are similar with
413
the exergy destruction and loss rates.
30
ACCEPTED MANUSCRIPT
414 415
Fig. 10 Variations for the BPFHPCC plant of the exergy destruction and exergy loss cost rates
416
with hydrogen injection rate into the combustion chamber
417
Fig. 11 shows the variations for the BPFHPCC plant of the total unit product cost and
418
exergoeconomic factor with hydrogen injection rate into the combustion chamber. Both the total
419
unit product cost and exergoeconomic factor increases by the hydrogen injection.
420
31
ACCEPTED MANUSCRIPT
421 422
Fig. 11 Variations for the BPFHPCC plant of the total unit product cost and exergoeconomic factor with
423
hydrogen injection rate into the combustion chamber
424 425
Table 10 shows the results for modified exergy analysis of the BPFHPCC plant. Modified exergy
426
efficiency ( ε* ) has an advantage over common exergy efficiency ( ε ) since it accounts the
427
avoidable exergy destruction and unavoidable part due to non-realistic definition is discarded.
428
The highest exergy efficiencies, in the rank order, are: the PEM, GT, Comp, ST, HRSG, Pump,
429
PCC, Ga and CC. However, from the modified perspective, they are: the HRSG, PEM, GT,
430
Comp, ST, CC, pump and PCC. This shows how a realistic definition of exergy efficiency
431
changes the interpretation across the components. For example, the gasifier, CC and HRSG with
32
ACCEPTED MANUSCRIPT
432
common exergy analysis have low efficiencies but with modified exergy analysis have high
433
efficiencies.
434
Table 10
435
Results for the modified exergy analysis of the BPFHPCC
Component
Ex
F
Ex
P
Ex D
UN Ex D
AV Ex D
UN Ex P
ε
ε*
(kW)
(%)
(%)
(kW)
(kW)
(kW)
(kW)
(kW)
Comp
4213
3927
286
38.24
247.76
4174.76
93.22
94.06
GT
10057
9674
383
32.21
350.79
10024.79 96.19
96.50
CC
16901
11168
5733
4076
1657
12825
66.08
87.08
PCC
1648
1298
350
11.89
338.11
1636.11
78.79
79.33
HRSG
6384
5437
947
917
30
5467
85.16
99.45
Pump
36.33
29.41
6.92
1.49
5.43
34.84
80.96
84.41
ST
5057
4575
482
139.5
342.5
4917.5
90.48
93.03
PEM
4919
4755
164
69.55
94.45
4849.45
96.66
98.05
Ga
2296
1648
648
593
55
1703
71.79
96.77
436 437
Table 11 shows the results of the modified exergoeconomic analysis for the BPFHPCC. The
438
exergoeconomic factor ( f k ) indicates the contribution of component capital investment cost to
439
the total costs related to that component. A comparison of the exergoeconomic factor with the
440
modified exergoeconomic factor ( f *k ), which is the contribution of component avoidable capital
441
investment cost on the total avoidable costs of that component, gives interesting results. Based
442
on the conventional exergoeconomic factor, the components that should be considered for
443
reduction of capital investment cost are: the PEM, ST, GT, Pump, and Comp, while from the
444
modified perspective they are replaced by the HRSG, GT, PEM, ST, and Comp. Like modified
445
exergy analysis, modified exergoeconomic analysis is a better and realistic benchmark for
33
ACCEPTED MANUSCRIPT
446
engineers and in this plant the modified exergoeconomic analysis and conventional
447
exergoeconomic analysis give completely different recommendations for the pump. This is
448
because, within the modified analysis, the PCC, and the pump should be considered for quality
449
betterment. But conventional analysis gives apposite results. Also with conventional analysis, the
450
HRSG should be considered for the quality improvement but modified analysis gives apposite
451
result.
452
Table 11
453
Results for the modified exergoeconomic analysis of the BPFHPCC
AV Z K
C D,k
C D,k UN
C D,k AV f k (%)
($/h)
($/h)
($/h)
($/h)
3.75
18.55
15.66
2.04
13.62
58.75
57.66
86.71
19.26
67.45
20.2
1.70
18.50
81.10
78.47
9.33
12.38
5.29
7.09
192.6
136.90
55.70
6.15
11.29
PCC
2.78
4.49
4.43
0.06
3.50
0.12
3.38
56.17
1.74
HRSG
12.38
38.06
29.76
8.30
42.22
40.87
1.35
46.29
86.01
Pump
16.1
0.75
0.69
0.06
0.40
0.09
0.31
65.37
16.22
ST
14.57
138.5
111.8
26.70
25.25
7.32
17.93
84.58
59.82
PEM
16.1
137.6
118.9
18.70
9.55
4.03
5.52
93.51
77.21
Ga
2
3.014
2.98
0.034
4.66
4.27
0.39
39.25
8.02
c F,k
Z k
($/GJ)
($/h)
Comp
15.22
22.3
GT
14.64
CC
Component
UN Z k ($/h)
f *k (%)
454 455 456
5. Conclusions
457
The BPFHPCC is analyzed with two set of approaches namely conventional energy, exergy and
458
exergoeconomic analyses as well as the modified exergy and modified exergoeconomic analyses.
459
The latter focusses on the real and practical potentials for system performance improvement via
460
the avoidable and unavoidable exergy destruction and cost rates. That is to say, it discards the
34
ACCEPTED MANUSCRIPT
461
margins for improvement which is not aligned with the engineering applications since there are
462
technology limitations for absolute elimination of inefficiencies. The results for both approaches
463
are brought below:
464
Increasing the rp leads to a minimum point for hydrogen production (rp=12), an optimum point
465
for the energy efficiency and the exergy loss rate (rp=12), decreases the exergy efficiency, the
466
exergy destruction and loss cost rates, the product cost and increases the exergy destruction, and
467
the exergoeconomic factor. Furthermore, increasing the TIT leads to the decrease in the
468
hydrogen production cost, the exergy destruction and loss rates, the exergy destruction and loss
469
cost rates and increase in the energy and exergy efficiencies, the product cost, and an optimum
470
point for the exergoeconomic factor (rp=14). Overall, rp has some contradictory effects while
471
TIT increase is almost always favorable for thermodynamic performance except for the
472
exergoeconomic and the hydrogen production. In case hydrogen is injected to the CC the
473
benefits are: lower CO2 emissions, lower exergy destruction and loss rates and their
474
corresponding cost rates and the other results are not favorable. Finally, modified exergy and
475
modified exergoeconomic analyses give almost opposite results compared with conventional
476
analyses in which with the modified exergy analysis highest and lowest exergy efficiencies of the
477
components are the HRSG and the PCC, respectively, while with conventional analysis they are
478
the PEM electrolyzer and the CC. Moreover, with modified exergoeconomic analysis, the
479
highest and lowest exergoeconomic factor are, respectively, the HRSG and the PCC while with
480
conventional analysis they are the PEM and the CC.
481
Nomenclature
482
c
Cost per unit exergy, $/GJ
483
CRF
Capital recovery factor 35
ACCEPTED MANUSCRIPT
484
Ċ
Cost rate, $/h
485
D
Membrane thickness, µm
486
ex
Specific exergy, kJ/kg
487
Ė
Energy rate, kW
488
Ėx
Exergy rate, kW
489
Eact,a
Activation energy of anode, kJ/mol
490
Eact,c
Activation energy of cathode, kJ/mol
491
F
Faraday constant, C/mol
492
G
Gibbs free energy, J/mol
493
Ga
Gasifier
494
h
Specific enthalpy, kJ/kg
495
H
Enthalpy, kJ
496
HE
Heat exchanger
497
ir
Interest rate
498
J
Current density, A/m2
499
J0
Exchange current density, A/m2
500
Ja
501
ref
Pre-exponential factor of anode, A/m2
Jc
ref
Pre-exponential factor of cathode, A/m2
502
LHV
Lower heating value, kJ/kg
503
MC
Moisture fraction of wet biomass
504
Mi
Mass fraction
505
ṁ
Mass flow rate, kg/s 36
ACCEPTED MANUSCRIPT
506
Pi
Pressure at state i, bar
507
rp
Compressor pressure ratio
508
RPEM
Proton exchange membrane resistance, Ω
509
Rk
Independent operation and maintenance cost, $
510
s
Specific entropy, kJ/(kg.K)
511
S
Entropy, kJ/K
512
T
Temperature, K
513
Tg
Gasification temperature, K
514
TIT
Gas turbine inlet temperature, K
515
TUPC
Total unit product cost, $/GJ
516
Ẇ
Electrical power, kW
517
W PEM
Electrical power required to split water in the electrolyzer (kW)
518
V0
Reversible potential, V
519
Vact,a
Anode activation over potential, V
520
Vact,c
Cathode activation overpotential, V
521
VOhm
Ohmic overpotential, V
522
Z
Investment cost of component, $
523
Ż
Investment cost rate of component, $/h
524
Greek letters
525
γ
Fixed operation and maintenance cost
526
η
Energy efficiency
527
ηis,Comp
Isentropic efficiency of compressor
37
ACCEPTED MANUSCRIPT
528
ηis,GT
Isentropic efficiency of gas turbine
529
ηis,ST
Isentropic efficiency of steam turbine
530
ηis,Pump
Isentropic efficiency of pump
531
ε
Exergy efficiency
532
ε*
Modified exergy efficiency
533
f
Exergoeconomic factor
534
f*
Modified exergoeconomic factor
535
σ (x)
Local ionic PEM conductivity, S/m
536
σ PEM
Proton conductivity in PEM, S/m
537
τ
Annual plant operation hours, h
538
λc
Water content at cathode-membrane interface
539
λa
Water content at anode-membrane interface
540
λ (x)
Water content in location x in membrane
541
β
Ratio of the chemical exergy to the LHV of the organic fraction of biomass
542
ω
Variable operation and maintenance cost, $/kW
543
Subscripts
544
a
Anode
545
act
Activation
546
HRSG
Heat recovery steam generator
547
C
Cathode
548
Comp
Compressor
549
CC
Combustion chamber
550
CI
Capital investment 38
ACCEPTED MANUSCRIPT
551
Cond
Condenser
552
CW
Cooling water
553
D
Destruction
554
F
Fuel
555
Ga
Gasifier
556
GT
Gas turbine
557
HE
Heat exchanger
558
i
Index for thermodynamic state point
559
in
Inlet condition
560
is
Isentropic
561
k
Index for component
562
K
Equilibrium constant
563
P
Product
564
PEM
Proton exchange membrane
565
PCC
Post combustion chamber
566
ohm
Ohmic
567
out
Outlet condition
568
ST
Steam turbine
569
WB
Wet bulb
570
0
Reference
571
Superscripts
572
AV
Avoidable
573
CI
Capital investment
574
OM
Operation and maintenance 39
ACCEPTED MANUSCRIPT
575
UN
Unavoidable
576 577
Acronyms and Abbreviations
578 579
BPFHPCC
Biomass post fired hydrogen production combined cycle
580
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581
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582
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583
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586
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588
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589
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43
ACCEPTED MANUSCRIPT Highlights
Biomass post fired hydrogen production cycle is proposed Modfied exergy and exergoeconomic analyses are applied Hydrogen is injected into the combustion chamber Modified exergy and exergoeconomic analyses yield more realistic results
Saeed Soltani PII:
S0960-1481(18)31144-3
DOI:
10.1016/j.renene.2018.09.074
Reference:
RENE 10614
To appear in:
Renewable Energy
Received Date:
25 October 2017
Accepted Date:
20 September 2018
Please cite this article as: Saeed Soltani, Modified exergy and exergoeconomic analyses of a biomass post fired hydrogen production combined cycle, Renewable Energy (2018), doi: 10.1016/j. renene.2018.09.074
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ACCEPTED MANUSCRIPT
1
Modified exergy and exergoeconomic analyses of a biomass post fired
2
hydrogen production combined cycle
3
Saeed Soltani
4
Faculty of Mechanical Engineering, University of Tabriz, 16471 Tabriz, Iran
5
[email protected]; [email protected]
6
Tel: +98 914 406 7078
7
Abstract
8
Biomass post fired hydrogen production combined cycle (BPFHPCC) is proposed and analyzed
9
via common exergy and exergoeconomic analyses. In order to have an objective insight and
10
especially realistic approach to the cycle’s thermodynamic and exergoeconomic performance,
11
modified approach is applied. Within common exergy analysis, the components with high exergy
12
destruction are respectively, the combustion chamber, heat recovery steam generator and gasifier
13
while with modified exergy analysis they are the gas turbine, steam turbine and post combustion
14
chamber. As far as components exergy destruction cost rate are concerned, with common
15
analysis the highest exergy destruction cost rates are for the combustion chamber, heat recovery
16
steam generator and steam turbine while with modified analysis they are the combustion
17
chamber, gas turbine, and steam turbine. In this system hydrogen is used for other units.
18
However, if we want to use it within the system, the case in which hydrogen is injected into the
19
combustion chamber is extended. The effects on the thermodynamic efficiency and system
20
product cost were negative while it decreased the system CO2 emissions, exergy destruction and
21
loss rates as well as the exergy destruction and loss cost rates.
1
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22
Keyword: Modified exergy; Modified exergoeconomic; Hydrogen; Post firing; Biomass
23
gasification
24
1. Introduction
25
Recently, biomass has become a significant source of energy in many countries. It can be an
26
advantageous substitute for non-renewable energy sources such as fossil fuels. Rising the energy
27
consumption, greenhouse gas emissions [1], acid precipitation and ozone depletion have fostered
28
much research on alternatives to non-renewable energy. One disadvantage for renewable energy
29
is that its availability is intermittent, varying throughout the day and year. One means of
30
addressing this problem is to use two or more sources of renewable energies with fossil fuels.
31
Using renewable energy also can help mitigate the harmful environmental effects of fossil fuels.
32
Biomass is a renewable energy form which can be used directly or indirectly after conversion
33
into a biofuel. Various approaches have been demonstrated for utilizing biomass energy, a
34
common one being gasification [2]. Biomass can also be used as a fuel in an externally fired gas
35
turbine [3]. Gnanapragasam et al. [4] have examined the most appropriate conditions in which
36
natural gas is used in a combined cycle power plant as a primary fuel and biomass as a secondary
37
fuel. Gholami et al. [5] compared two types of biomass, and showed that wood has 1 point
38
percent higher energy efficiency and higher CO2 emissions than paper in a cogeneration system.
39
Ahmadi et al. [6] optimized a multi-generation energy system which has a gas turbine to generate
40
multiple products such as the electricity, heating, cooling and domestic hot water. The authors
41
assessed many design parameters to determine the most important to consider for enhancing the
42
exergy efficiency and the total cost of the system. Ghenai and Hachicha [7] examined a 10 MW
43
biomass-fired steam power plant, considering various biomass fuels blended with sub-
44
bituminous coal and fractions varying from 0 to 100%. It was shown that, by increasing the 2
ACCEPTED MANUSCRIPT
45
biomass fraction from 6 to 100%, the annual energy production increases while CO2 emissions
46
decrease. Moharamian et al. [8] investigated various biomass cycles based on organic Rankine
47
cycles and evaluated several working fluids for the system. R141b was identified as the most
48
effective for that system.
49
Hydrogen may become an important energy carrier in the near future because it is a clean fuel,
50
and it can be utilized in chemical and petrochemical processing [9]. The production of hydrogen
51
from renewable energies is described in [10, 11, 12]. As an energy carrier, hydrogen can
52
facilitate the use of renewable energies. For instance, Iribarren et al. [13] examined a hydrogen
53
production system based on biomass gasification. One method of hydrogen production uses
54
electrolysis. Bhandari et al [14] showed that in many studies electrolysis technology was utilized,
55
and global warming potential considered for assessing the environmental impacts. In a water
56
electrolyzer, electric energy is employed to separate water into hydrogen and oxygen. There are
57
several types of electrolysis, including alkaline, solid oxide and proton exchange membrane
58
(PEM) [15]. For increasing the lifetime of an electrolyzer, a solid electrolyte is utilized in the
59
PEM electrolyzer. The PEM electrolyzer has advantages over an alkaline electrolyzer, such as
60
higher hydrogen quality and lower energy waste. Corradetti and Desideri [16] techno-
61
economically compared biomass utilization in two applications: electric power generation and
62
hydrogen production. The authors showed that hydrogen can be generated from wood with an
63
energy efficiency of 66%, and the efficiency of a biomass integrated gasification combined cycle
64
was about 44%. As a result, it was suggested that biomass can be beneficially utilized both for
65
producing the electric power and hydrogen. Parametric analyses have been performed to
66
investigate the effect of important design and operating parameters on the plant energy
67
conversion efficiency by Ni et al [17]. This study has quantified how much the energy efficiency 3
ACCEPTED MANUSCRIPT
68
can decreases by increasing the operating temperature, lowering the current density, reducing the
69
electrolyte thickness, and increasing the electrode catalytic activity. In addition, for high
70
hydrogen production levels, a PEM electrolyzer has some drawbacks, such as high temperature
71
operating conditions and scale up demands while an alkaline electrolyzer can be a suitable choice
72
since it has a higher efficiency than a PEM electrolyzer [18, 19].
73
Many scientists indicate that, apart from a comprehensive thermodynamic analysis based on
74
exergy, exergy costing is also a significant principle for providing an exergoeconomic
75
perspective. Such a perspective can be utilized to compare the input fuel costs and capital
76
expenditures for determining the product unit costs, which plays an important role in
77
performance optimizing [20]. Taheri et al. [21] have examined a novel integrated biomass
78
multigeneration system. They found that fuel mass flow rate is the most important operating
79
parameter affecting the energy efficiency and the total cost rate. By increasing the fuel mass rate
80
from 4 kg/s to 10 kg/s, energy efficiency decreased by 8% and total cost rate increased by
81
122.8%.
82
Tsatsaronis and Park [22] proposed the avoidable and unavoidable exergy destruction and
83
investment costs in thermal systems with the name of modified exergy and modified
84
exergoeconomic analyses. They concluded in order to evaluate the thermodynamic performance
85
and cost effectiveness of thermal systems and to estimate the potential for improvements, it is
86
useful to know the avoidable part of both exergy destruction and component’s investment costs.
87
They applied this approach on a cogeneration system and concluded that modified
88
exergoeconomic analysis considers the air compressor, gas turbine, and heat recovery steam
89
generator (HRSG) for investment cost reduction. Finally, they showed modified exergy and
90
exergoeconomic analyses are more realistic than normal exergy and exergoeconomic analyses. 4
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91
In this study, a biomass post fired hydrogen production combined cycle (BPFHPCC) is proposed
92
and evaluated with thermodynamic, exergoeconomic, modified exergy and modified
93
exergoeconomic analyses. Modified exergy and exergoeoconomic analyses are applied to obtain
94
the realistic potentials for system performance improvement. Hydrogen is produced by the PEM
95
electrolyzer and steam turbine output power is the running power for the hydrogen production.
96
The prominent aspects of this system are co-combustion of natural gas and biomass as a
97
renewable energy which makes this system technically flexible for various amount of power
98
production with lesser environmental impacts. Meanwhile, recovery of gas turbine’s heat energy
99
discharge paves the way for existence of the hydrogen production unit by which makes the
100
system to be linked to industrial, commercial or residential areas. For example, product hydrogen
101
can be sold to the mentioned places. As another alternative, when there is no use in
102
aforementioned units, hydrogen is injected into the combustion chamber for ascertaining the
103
results, especially for the environmental impacts.
104
2. System description
105
The BPFHPCC is shown in Fig. 1. The cycle includes: gas turbine (GT), compressor (Comp),
106
post combustion chamber (PCC), combustion chamber (CC), pump, HRSG, condenser (Cond),
107
steam turbine (ST), biomass gasification unit (Ga), heat exchanger (HE), oxygen separator, and
108
PEM electrolyzer. Air enters to the compressor and is compressed until a desired compressor
109
pressure ratio (rp) and then combusts with the natural gas and oxygen in the air until a desired gas
110
turbine inlet temperature (TIT). The combusted gas enters the gas turbine and expands. The
111
expanded gas enters the post combustion chamber and again burns by gasified biomass and after
112
heating the water in the HRSG extracts to the atmosphere. The heated water enters the steam
113
turbine at point 3. The electrical power of the steam turbine in the combined cycle is used in the 5
ACCEPTED MANUSCRIPT
114
electrolyzer section, which is investigated here for the first time. The hot water which is needed
115
in the PEM electrolyzer is supplied by a heat exchanger. Hydrogen is produced at the cathode of
116
the electrolyzer, and oxygen at the anode is separated in the (water/oxygen) mixer, where the
117
hydrogen and oxygen are both cooled to the environment temperature. For later hydrogen
118
production, the remaining hot water is returned to the PEM inlet.
119 19
26
1 2
Pump
20
Cond 4
HRSG
18
Water O2 Separator
29 14
17 ST
HE
28
21
13
27
O2
25 PEM
Gen
H2
15
3 Fuel 24
Tank CC
6
7
22
Comp
GT
23
Gen
5
Air
8 12 PCC
Biofuel 11
Ga
Air 10
120 121 122
9 Biomass
Fig. 1 Biomass post fired hydrogen production combined cycle (BPFHPCC) 3. System analysis
123 6
16
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124
3.1.
Thermodynamic analysis
125
A thermodynamic analysis framework is represented for the combined system, which has three
126
main parts: steam and gas turbine, PEM electrolyzer and biomass gasifier. The combined cycle
127
operation is steady-state and the net electric power output is 10,000 kW.
128
The following assumptions are brought in Table 1:
129
Table 1
130
Assumptions and data for the components of the BPFHPCC Component or condition
Ambient parameters
Compressor, turbines, pump [23]
Assumptions and data
P=1.01 bar T=298 K The air composition by volume is 79% nitrogen and 21% oxygen η is,Comp=0.87 η is,GT=0.89 η is,ST=0.9 η is,Pump= 0.8 TIT is 1500 K
The dry biomass (wood) has a gravimetric composition of C: 50%, H: 6% and O: 44%, and a calorific value (on a dry Gasifier [24]
basis) of 449,568 kJ/kmol
The biomass moisture content is 20% on a mass basis
The equivalence ratio for gasification is 0.4188
7
ACCEPTED MANUSCRIPT
HRSG
Combustion and postcombustion chamber [23]
The maximum pressure of the steam cycle is 8000 kPa The pinch point temperature difference in the boiler is 10°C
Complete combustion occurs in the combustion
chambers
The combustion chambers are adiabatic and have a
pressure drop of 1% PEM electrolyzer [17]
TPEM = 353 K
J aref =1.7×105 A/m2
J cref =4.6×103 A/m2
D = 50 μm
F = 96486
λ a =14
λ c =10
E act,a = 76 kJ/mol
E act,c = 10 kJ/mol
131 132
For all components of the system, mass and energy balances can be written respectively as
133
follows [25]:
134
∑ṁin=∑ṁout
(1)
135
E + ∑ṁinhin= Ẇ +∑ṁouthout
(2)
136 137
For the system, the energy efficiency is written based on the net output power of cycle and the
138
amount of hydrogen which is available is accounted for the energy efficiency. In the 8
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139
denominator since we have input energy at point 26 it also should be accounted for the energy
140
efficiency of cycle.
141
W net,cycle =WGT -WComp +WST -WPump -WPEM
142
η=
143
When hydrogen is not available as the final product the energy efficiency becomes:
144
η=
145
Thermomechanical and chemical exergy are considered in the analysis. The specific
146
thermomechanical flow exergy at a state i is [25]:
147
ex i h i h 0 T0 s i s 0
148
where 0 is the restricted dead state condition.
149
Chemical exergy is calculated respect to the unrestricted dead state, which relates to the chemical
150
composition of the reference environment in addition to the reference pressure and temperature
151
[26]. The chemical exergy of an ideal gas mixture at the restricted dead state is based on the
152
partial pressures of the mixture components and the partial pressures of the same components in
153
the reference environment, but the chemical exergy in a combustion process is used to obtain the
154
potential useful work [26]. Also, the specific chemical exergy of a mixture of ideal gases follows
155
[26]:
156
ch ex ch mixture u i ex 0,i RT0 u i lnu i
(3a)
W net,cycle +m15 LHVH2 fuel LHVfuel +E 26 m
(3b)
W net,cycle
(3c)
fuel LHVfuel +E 26 m
(4a)
(4b)
i
9
ACCEPTED MANUSCRIPT
157
Here, ui and ex ch 0,i denote the mole fraction and standard chemical exergy, respectively, of a
158
mixture component.
159
The exergy balance of the flows can be expressed as follows:
160
Ėxin+∑iṁiexi=∑eṁeexe+W+ĖxD
161
Conventional exergy analysis has been applied based on approach “exergy of product/exergy of
162
fuel”. Note that an efficiency based on “exergy of product/exergy of fuel” is often but not
163
always similar to an efficiency based on “product outlet streams/inlet streams” or “outlet
164
streams/inlet streams” [27].
165
Exergy of fuels and products for components are listed in Table 2.
(4c)
166
Table 2
167
Exergy of the fuels and products Component Comp GT CC PCC Ga HRSG HE ST Cond Pump PEM electrolyzer
Ė-fuel Ėx22 Ėx7-Ėx8 Ėx24 Ėx11 Ėx10+Ėx9 Ėx12-Ėx13 Ėx26 Ėx3-Ėx4 Ėx4-Ėx1 Ėx19 Ėx17
168 169
The exergy efficiency for the cycle with available hydrogen is:
10
Ė-product Ėx6-Ėx5 Ėx22+Ėx23 Ėx7-Ėx6 Ėx12-Ėx8 Ėx11 Ėx3-Ėx2 Ėx28-Ėx27 Ėx18 Ėx21-Ėx20 Ėx2-Ėx1 +Ex -Ex Ex 15
25
14
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170
ε=
W net,cycle +Ex15 +Ex +Ex Ex 10
24
(5a) 26
171
The exergy efficiency for the cycle with unavailable hydrogen is:
172
ε=
173
W net,cycle Ex +Ex +Ex 10 24 26
3.2.
(5b)
Biomass combustion
174
A downdraft type gasifier is considered and the equilibrium model presumes that all of the
175
gasifier reactions are in the thermodynamic equilibrium. The reactions in the gasification process
176
are as follows [23, 28]:
177
C+CO2 2CO
(6)
178
C+H2O CO+H2
(7)
179
C+2H2 CH4
(8)
180
The shift reaction with combination of equations 6 and 7 is:
181
CO + H2O CO2+H2
182
The overall gasification reaction can be written as:
183
CHxOyNz + μ H2O + λ (O2+3.76N2) →aCO + bN2 + cH2 + dCO2 + eCH4 + fH2O
184
Equilibrium constants, respectively, are:
185
K1 =
e c2
186
K 2=
cd af
187
By MC = (mass of water/mass of wet biomass)
188
Kilomole number of moisture content can be calculated as follows:
(9)
(10)
(11)
(12)
11
ACCEPTED MANUSCRIPT
m biomass MC 18 1-MC
189
μ=
190
where mbiomass is the mass of biomass. Applying mass and energy balances to overall reaction
191
(Eq. 10) and considering the equilibrium constants, values of “a to f” and the gasification
192
temperature T (if m is known) or m (if T is known) are obtained. [23, 28].
193
The equilibrium constants are related to the change in the Gibbs functions, as:
194
-
195
ΔG= h -Tg s
196
Assuming no heat loss from the gasifier, an energy balance for the reaction in Eq. 10 can be
197
written. The enthalpy of formation of biomass is derived from its heating value [28].
198
The gasification product constituents in the present study are compared with the results of other
199
studies in Table 3 which indicates good agreement. The comparison considers biomass having a
200
20 % moisture content, based on experimental [29] and Zainal equilibrium model [28] results at
201
800 ℃.
(13)
ΔG =lnK RT
(14)
(15)
Table 3 Comparison of mole fractions of gasification constituents Constituent Present model Experiment [29]
Zainal equilibrium model [28]
H2
18.01
15.23
21.06
CO
18.77
23.04
19.61
CH4
0.68
1.58
0.64
CO2
13.84
16.42
12.01
N2
48.7
42.31
46.68
O2
0.00
1.42
0.00
202 12
ACCEPTED MANUSCRIPT
203
The heating value of wood represents the amount of heat released by a specific quantity (at 25 ℃
204
). The detailed calculations are mentioned in [30, 31] or as a given value for wood in [28]:
205
The exergy of biomass can be defined as the maximum amount of work that can be extracted in a
206
process in which the biomass is converted to the environment conditions, i.e., to the dead state.
207
Also, exwood can be expressed as follows [32]:
208
exwood=β LHVwood M
209
(16) M
H C
M
β=
C
M
H C
(17)
O
1 ‒ 0.4124 M
210
O
1.044 + 0.016 M ‒ 0.34493 M (1 + 0.0531 M )
C
Mi is the mass fraction of the elements (hydrogen, oxygen and carbon) in the biomass. 3.3.
211
PEM electrolyzer
212
The entire energy required for the PEM can be expressed as:
213
∆H=∆G+T∆S
214
Here, ∆G is the Gibbs free energy (for electricity demand), T is the electrolyzer temperature and
215
T∆S represents the thermal demand. The molar flow rate of the hydrogen product can be
216
expressed as:
217
nH
218
Here, J and F respectively denote current density and Faraday constant. The PEM electrolyzer
219
voltage can be expressed as [33, 34, 35]:
220
V=V0 + Vact,c +Vact,a + Vohm
(20)
221
V0 =1.229-8.5 10-4 (TPEM – 298)
(21)
(18)
J
= = ,out 2F nH
2
(19)
2O,reacted
13
ACCEPTED MANUSCRIPT
222
where Vact,a, Vact,c and Vohm are the anode, cathode and Ohmic activation overpotentials,
223
respectively. The resistance of the membrane, through which hydrogen ions pass, creates the
224
Ohmic overpotential. The local ionic conductivity σPEM of the electrolyzer and the water quantity
225
at location x can be expressed as follows [36]:
226
1 1 σ PEM λ x = 0.5139λ x -326 ×exp 1268 - 303 T
227
λ(x)=
228
Here, x represents the distance into the membrane which is evaluated from the cathode
229
membrane interface, D is the membrane thickness, λa is the water quantity at the anode
230
membrane, and λc is the water quantity at the cathode membrane. The overall ohmic resistance,
231
ohmic overpotential and overall activation based on J0 can be expressed respectively as [36]:
232
D RPEM=∫0 σ
(24)
233
Vohm,PEM =JR PEM
(25)
234
Vact,i= F sinh
235
J0,i=J i exp (- RT )
236
Fig. 2 compares the J-V characteristics of the PEM for current model and the experimental
237
results by Ioroi et al. [33]. It is seen that there is a good agreement between these two results.
(22)
λa ‒ λc
x+λc
D
(23)
dx PEM[λ(x)]
RT
ref
‒1
J
(2J )
i=a,c
(26)
0,i
Eact,i
i=a,c
(27)
14
ACCEPTED MANUSCRIPT
238
239 240
Fig. 2. Comparison of results for J-V characteristics of PEM for current model and experimental
241
work [33]
242
3.4.
Exergoeconomics
243
Exergoeconomics is a significant part of cycle analysis which is utilized to give economic and
244
thermodynamic insights simultaneously by applying the cost concepts to the exergy, which
245
accounts for the quality of energy. In this study, the specific exergy costing method is used in the
246
exergoeconomic analysis. The relevant cost balance equations and required auxiliary equations
247
are described below and are employed for each of the component of the integrated system [23,
248
37]. The exergy costing principles lead to the cost rate balance, as follows:
249
+Z=c c F Ex F P Ex P
(28)
15
ACCEPTED MANUSCRIPT
250
C=cEx
(29)
251
Here c is the cost per unit exergy of each stream. Equation (28) indicates that the sum of cost
252
rates associated with all exergy streams entering a component and the cost rates associated with
253
CI OM the capital investment as well as operation and maintenance ( Z Z Z ) is equal to the sum
254
of cost rates associated with the exiting exergy streams. The cost data for each component of the
255
system (Zk) is taken from appropriate references [23, 38] and brought in Table 5. The cost data
256
provided in the literature are for different years and in the present work they are brought to the
257
reference year, 2017, using the Marshall and Swift equipment cost index through the following
258
relation [39]:
259
Reference year cost =
260
Table 5
261
Components’ cost equations [23, 38]:
(Original cost) (Reference cost index) Original year cost index
Components Comp
CC and PCC
Cost equations c m P ZComp = 11 air out c -η 12 is,Comp Pin c11 =75$/(kg/s),c12 =0.9
Pout ln Pin
air(gas) . 1+exp(c 22 Tout -c 23 ) . ZCC&PCC =c 21.m
1 0.995-
c 21 =48.64$/(kg/s),c 22 =0.018K -1 ,c 23 =26.4
GT
c m P ZGT = 31 gas out 1+exp(c33Tin -c34 ) c -η 32 is,GT Pin c31 =1536$/(kg/s),c32 =0.92, c33 =0.036K -1 16
Pout Pin
ACCEPTED MANUSCRIPT
dry-biomass kg/h )0.67 ZGa =1600.(m
Ga ST
0.05 ZST =c51.W 1+ 1-ηis,ST 0.7 ST
3
× 1+5.exp Tin -866K 10.42K
c51 =3880.5$.kW -0.7
Q Cond CW +70.5.Q +c62 .m Cond × -0.6936.ln TCW -TWB +2.1898 2.2.LMTD c61 =280.74$.m -2
Cond
ZCond =c61.
c62 =746$.(kg.s)-1 Pump
0.71 1+ 0.2 ZPump =c71.W Pump 1-μ is,Pump c71 =705.48$.(kg.s)-1
HRSG
0.8 Q i steam,j +c 43 .m 1.2 ZHRSG =c 41. f p,i .f T.steam,i .f T.gas,i . +c 42 . f p,j .m gas i j LMTDi p f p,i =0.0971. i +0.9029 30bar -830K T f T.steam,i =1+exp out,steam,i 500K
-990K T f T.gas,i =1+exp out,gas,i 500K c 41 =4131.8$.(kW.K)0.8 c 42 =13380$.(kg.s)-1 c 43 =1489.7$.(kg.s)-1.2 *PEM
262
ZPEM=1000 W PEM ($)
electrolyzer * Costs
of the heat exchanger and O2 separator are included
263
The costs of natural gas and biomass respectively are 9.08 $/GJ and 2 $/GJ [23, 40].
264
The annual levelized capital investment for the k th component can be calculated as [23]:
265
CRF Z CI k = Zk τ
(30)
17
ACCEPTED MANUSCRIPT
266
where CRF and τ are the capital recovery factor and the annual plant operation hours,
267
respectively. The capital recovery factor is a function of the interest rate, ir, and the number of
268
years of the plant operation, n, as follows:
i r 1+i r
n
(31)
269
CRF=
270
For the k th component, the annual levelized operation and maintenance cost can be expressed as
271
[23]:
272
1+i r
n
-1
ZOM k =γ k Z k +ω k E p,k +R k
(32)
273
Here, γ k and ωk account for the fixed and variable operation and maintenance costs,
274
respectively, associated with the k th component and R k includes all other operation and
275
maintenance costs, which are independent of investment cost and product exergy. The last two
276
terms on the right side of Eq. (32) are neglected in the present work as they are small compared
277
to the first term [23].
278
With the Fuel and Product theory [37], which are commonly used for analyzing exergy, the cost
279
rate related to the costs of fuel and product, and exergy destruction rate (i.e., CFuel,k, CP,k, CD,k),
280
we can write:
281
ĊP,k=cP,kĖxP,k
(33)
282
ĊFuel,k=cFuel,kĖxFuel,k
(34)
283
ĊD,k=cD,kĖxD,k
(35)
284
The total unit product cost (TUPC) can be expressed as follows: 18
ACCEPTED MANUSCRIPT
285
TUPC=
∑nk Ż + ∑nfuelc k Fuel ĖFuel i=1
i=1
i
i
(36)
n
∑ p Ė i=1 P
i
286
The exergoeconomic factor indicates the contribution of the component’s capital investment cost
287
to the total cost in terms of costs related to the exergy destruction plus capital investment cost of
288
the component. The exergoeconomic factor can be expressed as
289
f=
290
Table 6 shows the primary equations for exergoeconomic analysis of the NFBPC-HI.
Z k Z +C k D,k
(37)
Table 6 Exergy cost rate balances and auxiliary equations of the BPFHPCC Components Auxiliary equation
Cost balance
Comp
-
Ċ6 = Ċ5+ ŻComp+ Ċ22
CC
-
Ċ6+Ċ24+ŻCC = Ċ7
GT
c22 = c23
PCC
-
Ċ8+ ŻPCC + Ċ11 = Ċ12
Ga
-
Ċ9+ ŻGa + Ċ10 = Ċ11
HE
-
Ċ26+Ċ27+ ŻHE = Ċ28
ST
c18 = c19
Ċ3+ ŻST = Ċ4+ Ċ18
Cond
c1 = c4
Pump
-
HRSG
c12 = c13
Ċ2+ ŻHRSG+Ċ12 = Ċ3+ Ċ13
PEM electrolyzer
c14 = c 25
Ċ14+ ŻPEM+Ċ17 = Ċ15+ Ċ25
Ċ7+ ŻGT = Ċ8+ Ċ23 + Ċ22
Ċ4 + Ċ20+ Ż Cond = Ċ1+ Ċ21 Ċ1+ŻPump+Ċ19 = Ċ2
291 292
3.5 Modified exergy analysis
293
Technological and economic design limitations determine a minimum value of the exergy
294
destruction. The part of the exergy destruction that cannot be avoided with technologically
19
ACCEPTED MANUSCRIPT
295
feasible design modifications is the unavoidable exergy destruction [22]. The unavoidable exergy
296
destruction is calculated by considering each component in isolation, separated from the system,
297
assuming the most favorable operating conditions. These conditions refer to minimum exergy
298
destruction and are associated with very low temperature differences and thermal/pressure losses
299
within the components. The assumptions for simulating unavoidable conditions depend on the
300
decision maker and are arbitrary to some extent. In this paper these assumptions have been
301
selected based on the authors’ knowledge and experience on plant operation and by considering
302
the maximum improvement potential that could be achieved for each plant component in the
303
foreseeable future. Table 7 lists the assumptions which are used.
304
The modified exergy efficiency of the system is defined based on the realistic definition for
305
exergy efficiency, since unavoidable exergy destruction should not be accounted in the exergy
306
efficiency:
307
ε* =
Ex P,k Ex -Ex UN F,k
(38)
D,k
308
Table 7
309
Assumptions for the unavoidable exergy destruction of the components of the BPFHPCC Component Comp GT
CC, PCC
Unavoidable conditions ηis,Comp = 0.98 ηis,GT = 0.99
Δp = 0 Qloss = 0 λ=1
Ga ST Pump HRSG
ER = 0.3632 ηis,ST = 0.97 ηis,Pump = 0.95
Tpp = 7 K 20
ACCEPTED MANUSCRIPT
TPEM = 150 oC
PEM 310
3.6 Modified exergoeconomic analysis
311
In modified exergoeconomic analysis, Z UN =Z -Z AV is the unavoidable capital investment, where
312
Z UN is related to the case in which the cost of the component is low [22]. Therefore, poor
313
characteristics are considered for components. In this paper the values are based on Table 8.
314
Note that, as for the unavoidable exergy destruction rate, the assumptions for simulating the
315
unavoidable conditions depend on the decision maker and are arbitrary to some extent.
316
Meanwhile, the cost rates related to the unavoidable exergy destruction rate can be expressed as [22]:
317
UN UN C D,k,A =cf,k Ex D,k,A
318
Avoidable exergy destruction costs are calculated by [17]
319
UN C AV D,k,A =C D,k,A -C D,k,A
320
Finally the modified exergoeconomic factor based on the avoidable cost rates is [22]:
321
f k* =
(39)
(40)
Z AV k AV Z AV +C k
(41)
D,k
322
Table 8
323
Assumptions for the unavoidable capital investment cost rate of the components of the BPFHPCC Component Comp GT CC
Unavoidable conditions ηis,Comp = 0.7 ηis,GT = 0.76
TCC = 1273K
PCC
TPCC = 1062 K
Ga ST Pump
ER = 0.3632 ηis,ST = 0.7 ηis,pump = 0.7 21
ACCEPTED MANUSCRIPT
324
HRSG PEM 4. Results and discussion
Tpp = 20 K
325
Parametric analyses are applied to show the effects of the various design and operating
326
conditions on the performances of the cycle considered in this study. The analyses focus on the
327
effects of varying the gas turbine inlet temperature and pressure ratio since these are the key
328
inputs in power plants. Meanwhile, the hydrogen injection flow rate into the combustion
329
chamber when there is hydrogen injection is an input parameter. The output parameters
330
considered include hydrogen production rate, energy and exergy efficiencies, exergy destruction
331
and loss rates, CO2 emissions rate, exergy destruction and loss cost rates, total unit product cost
332
and exergoeconomic factor.
333
Table 9 lists the thermodynamic values for flows of the BPFHPCC, when the net power output is
334
10,000 kW, the gas turbine inlet temperature is 1500 K, and the heat recovery steam generator
335
(HRSG) inlet temperature is 1050 K.
ηis,ST = 0.7
336 337
Table 9
338
Thermodynamic values for flows of the BPFHPCC State
ṁ (kg/s)
P (bar)
T (K)
h (kJ/kmol)
1 2 3 4 5 6
3.61 3.61 3.61 3.61 14 14
0.08 80 80 0.08 1.01 9.09
314.7 315.4 850 314.7 298 589.9
3132 3314 64600 41742 -4.366 8673
10.67 10.79 125.3 133.4 198.6 200.6
6.461 35.96 5489 417 0 3990
7
14.33
8.99
1500
5340
234.8
15158
8
14.33
1.02
964.3
-13789
237.3
5101
22
s (kJ/(kmol K))
Ėx (kW)
ACCEPTED MANUSCRIPT
11
0.4228
1.02
1073
-67564
227.5
1648
12 13 14 15 20 21 24 25
14.75 14.75 0.6925 0.0390 185.22 185.22 0.323 0.6541
1.01 1.01 1.01 1.01 1.01 1.01 9.09 1.01
1050 322.7 353.2 353.2 308.1 318.15 298.15 353.2
-15411 -38982 6035 1596 1889 2642 -74595 -4563
240.6 203 19.37 135.5 6.61 9.069 168 85.97
6399 15.19 378.6 4557 0 131 16901 190.6
339 340
Fig. 3 shows the variations of the hydrogen production rate in the BPFHPCC with rp and TIT.
341
Increasing rp leads to a minimum hydrogen rate at rp=12 and increasing TIT decreases the
342
hydrogen production rate. These variations are affected by the variation of the steam turbine
343
power output with either rp or TIT, since the hydrogen is produced using the steam turbine output
344
power. For example, increasing TIT increases the gas turbine output power and for the constant
345
=10000 kW ), steam turbine power decreases. Therefore, by TIT total output power ( W net
346
increase, hydrogen production decreases.
23
ACCEPTED MANUSCRIPT
347 348
Fig. 3 Variations of hydrogen production rate with rp and TIT
349
Variations for the energy and exergy efficiencies of the BPFHPCC plant with rp and TIT are
350
shown in Fig.4. Increasing rp leads to an optimum point for energy efficiency, at a value of
351
around rp=11, while exergy efficiency decreases. Raising TIT increases the energy and exergy
352
efficiencies.
24
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353
354 355 356
Fig. 4 Variations for the BPFHPCC of the energy and exergy efficiencies with rp and TIT
357
Fig. 5 shows the variations with TIT and rp for the BPFHPCC plant of the exergy destruction and
358
loss rates. Increasing rp raises the exergy destruction rate. While increasing TIT decreases the
359
exergy destruction rate. Increasing TIT reduces the exergy loss rate while increasing rp at TIT=
360
1500 K leads to an optimum point for the exergy loss rate, approximately at a compressor
361
pressure ratio of 12.
25
ACCEPTED MANUSCRIPT
362
363 364
Fig. 5 Variations for the BPFHPCC plant of exergy destruction and loss rates with rp and TIT
365
Fig. 6 presents the variations of the exergy destruction and loss cost rates with rp and TIT for the
366
BPFHPCC plant. Increasing rp decreases the exergy destruction cost rate. Meanwhile, increasing
367
rp reduces the exergy loss cost rate. Increasing TIT decreases the exergy destruction cost rate in
368
the BPFHPCC plant. Furthermore, increasing TIT raises the exergy loss cost rate, which is
369
opposite to the variation of exergy loss rate with TIT. The reason is the natural gas flow rate
370
increases with TIT, so the high cost of natural gas is the determining factor.
26
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371
372 373 374
Fig. 6 Variations for the BPFHPCC plant of the exergy destruction and loss cost rates with rp and
375
TIT
376 377
Fig. 7 displays the variations for the BPFHPCC plant of the total unit product cost and
378
exergoeconomic factor with rp and TIT. Increasing rp reduces the total unit product cost.
379
However, the total unit product cost increases with TIT. For the BPFHPCC plant, a higher TIT is
380
advantageous only thermodynamically. Furthermore, increasing rp raises the exergoeconomic
381
factor, showing that component purchase and maintenance costs increase more with rp than does
382
the exergy destruction cost. Note also that, at all values of rp, the component purchase and
27
ACCEPTED MANUSCRIPT
383
maintenance costs are higher than the exergy destruction cost. As TIT rises, the component
384
purchase and maintenance costs are optimized, with the optimal rp value of 14 (TIT= 1500 K).
385
386 387 388
Fig. 7 Variations for the BPFHPCC plant of the total unit product cost and exergoeconomic
389
factor with rp and TIT
390
Until now, the analysis was based on the hydrogen production for other units. However, suppose
391
we want to exploit hydrogen in the BPFHPCC. In the following figures these effects on the
392
energy efficiency, CO2 emissions rate, exergy destruction and loss rates, exergy destruction and
393
loss cost rates, total unit product cost and exergoeoconomic factor, will be shown.
28
ACCEPTED MANUSCRIPT
394
Variations for the BPFHPCC plant of the energy efficiency and CO2 emissions rate with
395
hydrogen injection rate into the combustion chamber are shown in the Fig. 8. Energy efficiency
396
decreases by hydrogen injection around 0.15 points. Increasing the hydrogen injection decreases
397
the natural gas flow rate in the combustion chamber with the expense of lower available
398
hydrogen, the latter effect leads to lower energy efficiency. An appealing result is shown for the
399
CO2 emissions rate in which the emissions decrease by hydrogen injection.
400 401 402
Fig. 8 Variations for the BPFHPCC plant of the energy efficiency and CO2 emissions rate with hydrogen injection rate into the combustion chamber
29
ACCEPTED MANUSCRIPT
403
Fig. 9 shows the variations for the BPFHPCC plant of the exergy destruction and exergy loss
404
rates with hydrogen injection rate into the combustion chamber. Exergy destruction rate
405
decreases in the plant. The reason is by hydrogen injection the combustion chamber exergy
406
destruction decreases and overall exergy destruction of system decreases. The effect of hydrogen
407
injection on the exergy loss of the system is negligible.
408 409
Fig. 9 Variations for the BPFHPCC plant of the exergy destruction and exergy loss rates with
410
hydrogen injection rate into the combustion chamber
411
Fig. 10 shows the variations for the BPFHPCC plant of the exergy destruction and exergy loss
412
cost rates with hydrogen injection rate into the combustion chamber. The effects are similar with
413
the exergy destruction and loss rates.
30
ACCEPTED MANUSCRIPT
414 415
Fig. 10 Variations for the BPFHPCC plant of the exergy destruction and exergy loss cost rates
416
with hydrogen injection rate into the combustion chamber
417
Fig. 11 shows the variations for the BPFHPCC plant of the total unit product cost and
418
exergoeconomic factor with hydrogen injection rate into the combustion chamber. Both the total
419
unit product cost and exergoeconomic factor increases by the hydrogen injection.
420
31
ACCEPTED MANUSCRIPT
421 422
Fig. 11 Variations for the BPFHPCC plant of the total unit product cost and exergoeconomic factor with
423
hydrogen injection rate into the combustion chamber
424 425
Table 10 shows the results for modified exergy analysis of the BPFHPCC plant. Modified exergy
426
efficiency ( ε* ) has an advantage over common exergy efficiency ( ε ) since it accounts the
427
avoidable exergy destruction and unavoidable part due to non-realistic definition is discarded.
428
The highest exergy efficiencies, in the rank order, are: the PEM, GT, Comp, ST, HRSG, Pump,
429
PCC, Ga and CC. However, from the modified perspective, they are: the HRSG, PEM, GT,
430
Comp, ST, CC, pump and PCC. This shows how a realistic definition of exergy efficiency
431
changes the interpretation across the components. For example, the gasifier, CC and HRSG with
32
ACCEPTED MANUSCRIPT
432
common exergy analysis have low efficiencies but with modified exergy analysis have high
433
efficiencies.
434
Table 10
435
Results for the modified exergy analysis of the BPFHPCC
Component
Ex
F
Ex
P
Ex D
UN Ex D
AV Ex D
UN Ex P
ε
ε*
(kW)
(%)
(%)
(kW)
(kW)
(kW)
(kW)
(kW)
Comp
4213
3927
286
38.24
247.76
4174.76
93.22
94.06
GT
10057
9674
383
32.21
350.79
10024.79 96.19
96.50
CC
16901
11168
5733
4076
1657
12825
66.08
87.08
PCC
1648
1298
350
11.89
338.11
1636.11
78.79
79.33
HRSG
6384
5437
947
917
30
5467
85.16
99.45
Pump
36.33
29.41
6.92
1.49
5.43
34.84
80.96
84.41
ST
5057
4575
482
139.5
342.5
4917.5
90.48
93.03
PEM
4919
4755
164
69.55
94.45
4849.45
96.66
98.05
Ga
2296
1648
648
593
55
1703
71.79
96.77
436 437
Table 11 shows the results of the modified exergoeconomic analysis for the BPFHPCC. The
438
exergoeconomic factor ( f k ) indicates the contribution of component capital investment cost to
439
the total costs related to that component. A comparison of the exergoeconomic factor with the
440
modified exergoeconomic factor ( f *k ), which is the contribution of component avoidable capital
441
investment cost on the total avoidable costs of that component, gives interesting results. Based
442
on the conventional exergoeconomic factor, the components that should be considered for
443
reduction of capital investment cost are: the PEM, ST, GT, Pump, and Comp, while from the
444
modified perspective they are replaced by the HRSG, GT, PEM, ST, and Comp. Like modified
445
exergy analysis, modified exergoeconomic analysis is a better and realistic benchmark for
33
ACCEPTED MANUSCRIPT
446
engineers and in this plant the modified exergoeconomic analysis and conventional
447
exergoeconomic analysis give completely different recommendations for the pump. This is
448
because, within the modified analysis, the PCC, and the pump should be considered for quality
449
betterment. But conventional analysis gives apposite results. Also with conventional analysis, the
450
HRSG should be considered for the quality improvement but modified analysis gives apposite
451
result.
452
Table 11
453
Results for the modified exergoeconomic analysis of the BPFHPCC
AV Z K
C D,k
C D,k UN
C D,k AV f k (%)
($/h)
($/h)
($/h)
($/h)
3.75
18.55
15.66
2.04
13.62
58.75
57.66
86.71
19.26
67.45
20.2
1.70
18.50
81.10
78.47
9.33
12.38
5.29
7.09
192.6
136.90
55.70
6.15
11.29
PCC
2.78
4.49
4.43
0.06
3.50
0.12
3.38
56.17
1.74
HRSG
12.38
38.06
29.76
8.30
42.22
40.87
1.35
46.29
86.01
Pump
16.1
0.75
0.69
0.06
0.40
0.09
0.31
65.37
16.22
ST
14.57
138.5
111.8
26.70
25.25
7.32
17.93
84.58
59.82
PEM
16.1
137.6
118.9
18.70
9.55
4.03
5.52
93.51
77.21
Ga
2
3.014
2.98
0.034
4.66
4.27
0.39
39.25
8.02
c F,k
Z k
($/GJ)
($/h)
Comp
15.22
22.3
GT
14.64
CC
Component
UN Z k ($/h)
f *k (%)
454 455 456
5. Conclusions
457
The BPFHPCC is analyzed with two set of approaches namely conventional energy, exergy and
458
exergoeconomic analyses as well as the modified exergy and modified exergoeconomic analyses.
459
The latter focusses on the real and practical potentials for system performance improvement via
460
the avoidable and unavoidable exergy destruction and cost rates. That is to say, it discards the
34
ACCEPTED MANUSCRIPT
461
margins for improvement which is not aligned with the engineering applications since there are
462
technology limitations for absolute elimination of inefficiencies. The results for both approaches
463
are brought below:
464
Increasing the rp leads to a minimum point for hydrogen production (rp=12), an optimum point
465
for the energy efficiency and the exergy loss rate (rp=12), decreases the exergy efficiency, the
466
exergy destruction and loss cost rates, the product cost and increases the exergy destruction, and
467
the exergoeconomic factor. Furthermore, increasing the TIT leads to the decrease in the
468
hydrogen production cost, the exergy destruction and loss rates, the exergy destruction and loss
469
cost rates and increase in the energy and exergy efficiencies, the product cost, and an optimum
470
point for the exergoeconomic factor (rp=14). Overall, rp has some contradictory effects while
471
TIT increase is almost always favorable for thermodynamic performance except for the
472
exergoeconomic and the hydrogen production. In case hydrogen is injected to the CC the
473
benefits are: lower CO2 emissions, lower exergy destruction and loss rates and their
474
corresponding cost rates and the other results are not favorable. Finally, modified exergy and
475
modified exergoeconomic analyses give almost opposite results compared with conventional
476
analyses in which with the modified exergy analysis highest and lowest exergy efficiencies of the
477
components are the HRSG and the PCC, respectively, while with conventional analysis they are
478
the PEM electrolyzer and the CC. Moreover, with modified exergoeconomic analysis, the
479
highest and lowest exergoeconomic factor are, respectively, the HRSG and the PCC while with
480
conventional analysis they are the PEM and the CC.
481
Nomenclature
482
c
Cost per unit exergy, $/GJ
483
CRF
Capital recovery factor 35
ACCEPTED MANUSCRIPT
484
Ċ
Cost rate, $/h
485
D
Membrane thickness, µm
486
ex
Specific exergy, kJ/kg
487
Ė
Energy rate, kW
488
Ėx
Exergy rate, kW
489
Eact,a
Activation energy of anode, kJ/mol
490
Eact,c
Activation energy of cathode, kJ/mol
491
F
Faraday constant, C/mol
492
G
Gibbs free energy, J/mol
493
Ga
Gasifier
494
h
Specific enthalpy, kJ/kg
495
H
Enthalpy, kJ
496
HE
Heat exchanger
497
ir
Interest rate
498
J
Current density, A/m2
499
J0
Exchange current density, A/m2
500
Ja
501
ref
Pre-exponential factor of anode, A/m2
Jc
ref
Pre-exponential factor of cathode, A/m2
502
LHV
Lower heating value, kJ/kg
503
MC
Moisture fraction of wet biomass
504
Mi
Mass fraction
505
ṁ
Mass flow rate, kg/s 36
ACCEPTED MANUSCRIPT
506
Pi
Pressure at state i, bar
507
rp
Compressor pressure ratio
508
RPEM
Proton exchange membrane resistance, Ω
509
Rk
Independent operation and maintenance cost, $
510
s
Specific entropy, kJ/(kg.K)
511
S
Entropy, kJ/K
512
T
Temperature, K
513
Tg
Gasification temperature, K
514
TIT
Gas turbine inlet temperature, K
515
TUPC
Total unit product cost, $/GJ
516
Ẇ
Electrical power, kW
517
W PEM
Electrical power required to split water in the electrolyzer (kW)
518
V0
Reversible potential, V
519
Vact,a
Anode activation over potential, V
520
Vact,c
Cathode activation overpotential, V
521
VOhm
Ohmic overpotential, V
522
Z
Investment cost of component, $
523
Ż
Investment cost rate of component, $/h
524
Greek letters
525
γ
Fixed operation and maintenance cost
526
η
Energy efficiency
527
ηis,Comp
Isentropic efficiency of compressor
37
ACCEPTED MANUSCRIPT
528
ηis,GT
Isentropic efficiency of gas turbine
529
ηis,ST
Isentropic efficiency of steam turbine
530
ηis,Pump
Isentropic efficiency of pump
531
ε
Exergy efficiency
532
ε*
Modified exergy efficiency
533
f
Exergoeconomic factor
534
f*
Modified exergoeconomic factor
535
σ (x)
Local ionic PEM conductivity, S/m
536
σ PEM
Proton conductivity in PEM, S/m
537
τ
Annual plant operation hours, h
538
λc
Water content at cathode-membrane interface
539
λa
Water content at anode-membrane interface
540
λ (x)
Water content in location x in membrane
541
β
Ratio of the chemical exergy to the LHV of the organic fraction of biomass
542
ω
Variable operation and maintenance cost, $/kW
543
Subscripts
544
a
Anode
545
act
Activation
546
HRSG
Heat recovery steam generator
547
C
Cathode
548
Comp
Compressor
549
CC
Combustion chamber
550
CI
Capital investment 38
ACCEPTED MANUSCRIPT
551
Cond
Condenser
552
CW
Cooling water
553
D
Destruction
554
F
Fuel
555
Ga
Gasifier
556
GT
Gas turbine
557
HE
Heat exchanger
558
i
Index for thermodynamic state point
559
in
Inlet condition
560
is
Isentropic
561
k
Index for component
562
K
Equilibrium constant
563
P
Product
564
PEM
Proton exchange membrane
565
PCC
Post combustion chamber
566
ohm
Ohmic
567
out
Outlet condition
568
ST
Steam turbine
569
WB
Wet bulb
570
0
Reference
571
Superscripts
572
AV
Avoidable
573
CI
Capital investment
574
OM
Operation and maintenance 39
ACCEPTED MANUSCRIPT
575
UN
Unavoidable
576 577
Acronyms and Abbreviations
578 579
BPFHPCC
Biomass post fired hydrogen production combined cycle
580
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581
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ACCEPTED MANUSCRIPT Highlights
Biomass post fired hydrogen production cycle is proposed Modfied exergy and exergoeconomic analyses are applied Hydrogen is injected into the combustion chamber Modified exergy and exergoeconomic analyses yield more realistic results