Exergoeconomic multiobjective optimization of an externally fired gas turbine integrated with a biomass gasifier

Applied Thermal Engineering 91 (2015) 848e859

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Applied Thermal Engineering
journal homepage: www.elsevier.com/locate/apthermeng

Research paper

Exergoeconomic multi-objective optimization of an externally fired
gas turbine integrated with a biomass gasifier
Shoaib Khanmohammadi*, Kazem Atashkari, Ramin Kouhikamali
Department of Mechanical Engineering, Faculty of Engineering, University of Guilan, P.O. Box 3576, Rasht, Iran

h i g h l i g h t s
 Apply a modified thermodynamic equilibrium modeling for a biomass gasifier.
 Apply a multi objective optimization technique based on a developed code in Matlab.
 Perform a sensitivity analysis to better understanding of decision variables change.

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 1 June 2015
Accepted 27 August 2015
Available online 5 September 2015

This study deals with thermodynamic and economic analysis of a combined gas turbine and Organic
Rankine Cycle integrated with a biomass gasifier. A modified model is used to increase the precision of
the gasifier thermodynamic model. Seven decision variables, namely, biomass gasification temperature

(Tgasif), combustion temperature (Tcomb), gas turbine inlet temperature (T3), gas turbine isentropic efficiency (hGT), compressor isentropic efficiency (hcomp), compressor pressure ration (rp) and maximum
ORC operating pressure (P3R), are selected as the main decision variables of the combined system. The
total cost rate and exergy efficiency of the system are chosen as the two main objective functions. A
group method of data handling (GMDH) type neural network and evolutionary algorithm (EAs) are used
for modeling the effects of the seven decision variables on both objective functions. The result of multiobjective optimization shows that the exergy efficiency of the system is 15.6%, which can be increase to
17.9% in the optimal state, regardless of the total cost rate of system as objective function. In addition, in
order to better illustrate the effects of decision variables change in three selected points of the Pareto
curve, a sensitive analysis is performed.
© 2015 Elsevier Ltd. All rights reserved.

Keywords:
Externally fired gas turbine
Gasification
Multi-objective optimization
Organic Rankine cycle

1. Introduction
The depletion of fossil fuels, environmental pollutions, greenhouse gas emissions, and global climate changes together with the
potential of biomass to meet a part of energy demand have converted biomass as one of promising renewable energy source [1,2].
The comprehensive energy policies adopted by governments have
developed significant research in this area and have paved the way
for utilizing such renewable energies. In general, renewable energies can further reduce the environmental impacts and enhance
energy security as well. Biomass sources such as paper, agricultural
products, forestry residues, stems, wood, and cane are examples of

* Corresponding author. Tel.: þ98 133 6690271 9.
E-mail address: (S. Khanmohammadi).
/>1359-4311/© 2015 Elsevier Ltd. All rights reserved.

the renewable sources with low heating value for energy

production.
Biomass is considered as renewable energy source because the
carbon in biomass is regarded as part of the natural carbon cycle.
The recent studies on this issue mainly focus on a more efficient
simulation this type of energy conversion and more accurate
thermodynamic modeling of biomass gasification and biomass
combustion. Generally, the efficiency of power production using
biomass is low. For example, the efficiency in small and large systems is almost 15% and 30%, respectively [3]. The use of biomass in
gas turbines has its own problems. The gas turbine is a highly
sensitive mechanical device in which require extremely clean gas
so biomass combustion product needs expensive filters in order to
prevent fuel injector and routes from blocking and preventing
turbine blades from different damages. Also, the syngas produced
with a low heating value by gasification process for use in a gas


S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

Nomenclature
A
C_
CRF
DHW
ex
HHV
i
LHV
m
m0
_

m
n
N
ORC
rp

Area (m2)
Cost rate ($/h)
Capital recovery factor
Domestic hot water heater
Exergy (kJ/kg)
Higher heating value (kJ/kg)
Interest rate
Lower heating value (kJ/kg)
Number of moles required for firing per kmole of wood
Number of mole required for complete combustion per
mole of syngas
Mass flow rate (kg/s)
function year
Annual function hour per component
Organic Rankine cycle
Pressure ratio

Subscripts
AP
Air preheater
C
Carbon
cc
Combustion chamber

ch
Chemical
comb
Combustion

turbine combustion chamber requires a large amount of air for
combustion process, which this can expose compressor to surge [4].
The above-mentioned problems could be resolved by using
external combustion of biomass and a high temperature heat
exchanger.
Datta et al. [5] discussed energy and exergy analysis for an
externally fired gas turbine including biomass gasification process
for distributed power generation. They used thermodynamic
equilibrium modeling for simulation syngas production from
biomass and carried out energy and exergy analysis. The study of
the effect of important parameters such as cold end temperature of
heat exchanger and compressor pressure ratio were parts of their
investigations. They obtained thermal efficiency of system between
16% and 34% depending on design parameters variations. Arnavat et
al. [6] considered a trigeneration system using biomass as a prime
mover. The system consisted of biomass gasification and use of
syngas to drive an internal combustion engine and utilize waste
heat to drive a double-effect absorption chiller. In their study, five
configurations for power generation, heating and cooling were
considered in which each one of them had the same investment
cost but with different power, heating and cooling output. In
another study Ahmadi et al. [7] considered a novel multi generation
biomass-based integrated energy system. They performed a multiobjective optimization method to determine the best design parameters for the system. A sensitivity analysis was conducted to
show the effect of design parameters on exergy efficiency, total cost
rate, and CO2 emission.

Soltani et al. [8] performed a thermodynamic analysis of an
externally fired gas turbine with biomass gasification. They
considered three cases based on the variations in compressor
pressure ratio and temperature difference of the cold end of the
heat exchanger to find the impact of parameter variations on three
cases. Their results indicated that gasifier and combustion chamber
have the highest rate of irreversibility.
In another study, Soltani et al. [9] carried out exergy analysis for
a system with co-firing of natural gas and biomass. Their analysis

comp
Cond, R
Ev, R
f
G
gasif
GT
h
K
LM
Ph
prod
Pump, R
R
React
T
Tur, R
w
Z
o

849

Compressor
Organic condenser
Organic evaporator
Formation
Gasifier
Gasification
Gas turbine
Enthalpy (kJ/kg)
Equilibrium constant
Logarithm
Physical
Product
Organic pump
Universal gas constant (kJ/kg K)
Reactant
Temperature
Organic turbine
Amount of water per kmol of biomass
Cost of component
Reference state

Greek symbols
b
Biomass exergy coefficient
4
Operation and maintenance factor
j

Exergy efficiency

included a review of the effects of compressor pressure ratio and
compressor isentropic efficiency and the effects of mass ratio of
natural gas to biomass flow rate for a system with 80 MW power
output. Soltani et al. [10] also compared performance of two
combined cycle configurations included co-firing of natural gas and
biomass. Their study included an assessment of the exergoeconomic of these two systems and the effects of various parameters on their performance. Their analysis showed that the
configuration with co-firing of natural gas and biomass show a
better performance than the pure biomass configuration in terms of
lower economic factors and lower cost of biomass. The results show
that energy and exergy efficiencies of the configuration with cofiring of natural gas and biomass were 2% and 4% higher than
pure biomass. Ahmadi et al. [11] carried out an multi-objective
optimization for a new multi-generation energy system including
power, heating, cooling, hot water and hydrogen. They merge the
new environmental cost function with the thermoeconomic cost
objective and introduce a useful thermoenvironomic function. The
results of multi objective optimization suggest the best values for
the design parameters. In other research, Ahmadi et al. [12] presented an exergo-environmental analysis for an integrated organic
Rankine cycle for tirgeneration purpose. The results show that
exergy efficiency and sustainability index increase with increasing
compressor pressure ratio and gas turbine inlet temperature.
A review of the above studies indicates that most of the investigations examine the performance variations in different configurations of system. Given that the results of the studies must
finally result in the selection of the optimal cycle in terms of economic and thermodynamic performance, the optimization of the
relevant systems is necessary both in terms of economic and
thermodynamic considerations. Regarding the lack of investigations in thermoeconomic and optimization of the previous
studies, the present work concentrates firstly to develop models of
thermodynamic and economics of an organic Rankine cycle and an
externally fired gas turbine integrated with a biomass gasifier. The
second part of this work is to apply multi-objective optimization

850

S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

procedure to find the optimum working conditions and to show
sensitivity of the optimum performances in terms of decision variables. The overall objectives of this study can be summarized as
follows:
 Applying a modified model of thermodynamic equilibrium for
the gasification system.
 Exergy analysis of the proposed system to obtain the first
objective function.
 Development of economic model of the system to obtain the
second objective function.
 Multi objective optimization procedure using evolutionary genetic algorithm for producing Pareto front.

2. System modeling
A schematic of combined gas turbine and Rankine cycle integrated with the syngas producer shown in Fig. 1. The system consists of a hot air driven gas turbine. The gasifier in the system
produces syngas using gasification of dry biomass. The product of
combustion exiting combustion chamber is at 1177 C as shown
in Fig. 1. The products enter the ceramic heat exchanger to increase
exiting air from the compressor. This type of high temperature
ceramic heat exchanger is capable of raising the air temperature up
to 1350 C . The airside can handle air at pressures from 1 bar to
13 bar, which makes this exchanger ideal for using clean air to drive
a gas turbine. In the ceramic heat exchanger, exiting a part of the
combustion products is removed to the evaporator of organic
Rankine cycle. The reminder of combustion products enters into
another heat exchanger to produce domestic hot water. Finally,

products of combustion discharges into the ambient at 130 C .
Furthermore, the initial designing state of the system is listed
in Table 1.
The thermodynamic properties of streams and system performance are evaluated with EES (Engineering Equation Solver). In
addition, a code developed in Matlab software program using an
evolutionary algorithm is used to perform multi-objective optimization method.

2.1.1. Gasifier
Thermodynamic equilibrium procedure has been used for
modeling the process in the gasifier [39]. The chemical reaction in
the gas producer system is assumed as:

CHx Oy Nz þ wH2 O þ mðO2 þ 3:76N2 Þ/x1 H2 þ x2 CO þ x3 CO2
þ x4 H2 O þ x5 CH4 þ x6 N2
(1)
Here, CHxOyNz denotes the biomass chemical formula and w is
the amount of water per kmol of biomass. All coefficients x1 to x6
are obtained by performing atomic balance and using equilibrium
constant equations. The procedures are given as follows:

x2 þ x3 þ x5 ¼ 1

(2)

2x1 þ 2x4 þ 4x5 ¼ x þ 2w

(3)

x2 þ 2x3 þ x4 ¼ y þ w þ 2m

(4)

x6 ¼ z þ 3:76 Â 2m

(5)

To obtain the rest of equations two equilibrium equations are
derived. As it is expected that pyrolysis products before reaching
reduction region are fired and prior to emitting from gasifier achieve equilibrium state, the reactions can be written as follows:

C þ 2H2 /CH4

(6)

CO þ H2 O/CO2 þ H2

(7)

The above reactions are known as methanation reaction and
gasewater shift reaction, which the equilibrium constants for them
are given as follows:

K1 ¼

K2 ¼

PCH4

x5
x21

(8)

PCO2 PH2
x x
¼ 3 1
PCO PH2 O x2 x4

(9)

P2H2

¼

2.1. Thermodynamic model

Finally, for the calculation of gasification temperature (Tgasif) the
energy balance is applied as:

Before proceeding to the development of each components
thermodynamic model, the assumptions for the system are given as
follow:

 
 




hf;biomass þ whf;H2 O ¼ x1 hf;H2 þ Dh þ x2 hf;CO þ Dh

 
 


þ x3 hf;CO2 þ Dh þ x4 hf;H2 O þ Dh
 
 


þ x5 hf ;CH4 þ Dh þ x6 hf;N2 þ Dh

 The molar compositions of standard air are taken 79% nitrogen,
21% oxygen in 101.325-kPa and 25 C [10].
 The biomass moisture content for the system under study is
considered 16%.
 The gas turbine isentropic efficiency is 89% [13].
 The isentropic compressor efficiency 87% [10].
 The pressure drop in the combustor chamber is 0.5% of inlet
pressure [13].
 The isentropic efficiency of the turbine and pump with organic
fluid is 85% and 70% respectively [10].
 The pressure drop in hot and cold fluid of heat exchanger is 3%
and 1.5% of inlet pressure respectively [13].
 The ultimate analysis of dry biomass (wood) shows the compounds as: 50% carbon, 6% hydrogen, 44% oxygen [14].
 The cost of biomass (wood) is considered 2 $/GJ [15].

and Dh is enthalpy difference value for the given state with
reference state.

The wood chemical formula based on one carbon atom could be

written in the form of CH1.44O0.66 [14].

(11)

(10)


where, hf ;i is the formation enthalpy in terms of kJ/kmol, and its
value for all the chemical compositions is zero in the reference state


2.1.2. Combustion chamber
A complete combustion process is assumed in the combustion
chamber of the system. As given by the following:

x1 H2 þ x2 CO þ x3 CO2 þ x4 H2 O þ x5 CH4 þ x6 N2 þ m0 ðO2
þ 3:76N2 Þ/aCO2 þ bH2 O þ cO2 þ dN2


S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

851

Fig. 1. A schematic of the modeled cycle with the external combustion of the syngas produced from wood biomass and organic Rankine cycle.

The coefficients x1 to x6 have already been calculated and m0 is
the number of mole required for complete combustion per mole of
syngas. Applying atoms balance and using energy equation similar
to equation (10) for the combustion chamber m0 is calculated.

X



hf ;j ¼

j¼react

X

 


ni hf;i þ DhTcomb;i

(12)

j¼Prod

LMTD is a logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe
exchanger. The larger the LMTD, the more heat is transferred. The
use of the LMTD arises straightforwardly from the analysis of a heat
exchanger with constant flow rate and fluid thermal properties. For
the ceramic heat exchanger LMTD can be express as:

LMTDHE ¼

2.1.3. Ceramic heat exchanger
Considering energy balance equation between hot and cold
stream, it is possible to achieve the following equation for the heat

exchanger [40].

_ air ðh3 À h2 Þ
_ prod ðh5a À h6 Þ ¼ m
m

(13)

It should be mentioned that heat loss to environment is
neglected.
The concept of logarithmic mean temperature difference
(LMTD) is used to determine the temperature deriving force for
heat transfer in flow systems, most notably in heat exchangers. The

ðT6 À T2 Þ À ðT5 À T3 Þ


2
ln TT65 ÀT
ÀT3

2.2. Exergy analysis
Mass, energy and exergy balance for each component of the
system are applied. The following equation is used to obtain irreversibility in each component [16].

X

_ in exin ¼
m

X

_ out exout þ I_
m

Parameter

Value

Unit

Gasification temperature
Combustion temperature
Gas turbine inlet temperature
Compressor pressure ratio

827
1177
877
9



Biomass flow rate
Biomass moisture content
ORC maximum pressure
Air gasification mass flow rate
Air combustion mass flow rate

0.8

16
1000
1.09
6.24




C
C
C

e
kg/s
%
kPa
kg/s
kg/s

(15)

out

in

The exergy of each stream is composed of two parts including
chemical and physical one.

ex ¼ exph þ exch
Table 1

Initial performance parameter of the integrated system.

(14)

(16)

The physical exergy of each stream depends on its temperature
and pressure and is given as follows:

exph ¼ ðh À ho Þ À To ðs À so Þ

(17)

where o is reference state. In addition, the chemical exergy of gas
mixture could be obtained through the following equation [41]:

exch ¼

X
i

xi exch
o;i þ RT+

X
i

xi Lnxi

(18)

852

S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

here xi is molar fraction of ith component and exch
is standard
o;i
exergy of ith pure material [17]. To obtain the fuel chemical exergy,
it is required to calculate the lower heating value of fuel and the
coefficient b which is calculated as follows [5,8]:

exbiomass ¼ bLHVwood

Table 2
Exergy destruction rate and exergy efficiency for different components.
Component

Exergy destruction rate
Exergy efficiency

Compressor

_ D ¼ Ex
_ þW
_ À Ex
_
Ex
1

C
2
WC

_ À Ex
_ þ Ex
_ 5a À Ex
_
_ D;HE ¼ Ex
Ex
2
3
6

Heat exchanger

_

b¼



1:044 þ 016 ZZHC À :34493 ZZOC 1 þ :0531 ZZHC
1 À 0:4124 ZZOC

LHVðkJ=kgÞ ¼ HHV À hfg

9H
M
þ

100 100

jGT ¼

W_ GT
_ 4
_ 3 ÀEx
Ex

_
_
_
_
Ex
D;CC ¼ Ex4 þ Exb1 À Ex5

Combustion chamber

_

_

jGT ¼ Ex5_ÀEx4
Exb1

_
_
_
_
Ex

D;gasif ¼ Exbiomass þ Exair À Exb1

Gasifier

(21)

_

_

jgasif ¼ Ex5_ÀEx4
Exb1

_ D;DHW ¼ Ex
_ À Ex
_ 7 þ Ex
_
_
Ex
6
W1 À ExW2

Domestic hot water

Here ZC, ZH and ZO are the mass elements of carbon, hydrogen
and oxygen in biomass. For the wood with the given chemical
formula and the above equation, higher heating value of the fuel
19,980 kJ/kg is obtained. Also, the lower heating value of biomass
can be calculated in the following equation and given that
hfg ¼ 2258 kJ/kg [18].



Ex3 ÀEx2

_
_
_
_
Ex
D;GT ¼ Ex3 À W GT À Ex4

Gas turbine

(20)

_

6
jHE ¼ Ex_ 5a ÀEx
_

HHVðkJ=kgÞ ¼ 349:1C þ 1178:3H þ 100:5S À 103:4O À 15:1N
À 21:1ASH

_

_

Ex1

jcomp ¼ Ex2 À
_

(19)

Ex6 ÀEx7

_
_
_
_ D;pmp ¼ Ex
Ex
1R À Ex2R þ W pmp

Organic pump

W pump

_ D;eva ¼ Ex
_
_
_
_
Ex
5b À Ex5c þ Ex2R À Ex3R

Organic evaporator

_

3. Working fluid selection
The organic Rankine cycle (ORC) has the principles of the steam
Rankine cycle, but uses organic fluid with lower boiling point to
recover energy from a lower temperature heat sources. The working fluids play an important role in the performance of organic
cycle. The organic fluid selection directly affects the efficiency of the
system, operating parameters, environmental impacts, and economic factors. There are several studies conducted by different
working fluids (e.g. Ammonia [19], R11 and R134a [20], and R152a
[21]) depending on a low-grade temperature energy source, availability and material limitation. Concerning the heat source temperature and the lower pressure of organic Rankine cycle
(condenser pressure) five types of organic fluid selected for organic
cycle. Table 3 shows some properties of these fluids and performance parameters of system for mentioned organic fluids.
Also, Fig. 2 show the TeS diagram for these four organic working
fluids. In addition, two bounds temperature for heat source temperature (Tmax) and cold temperature (Tmin) is illustrated in this
figure.
As shown in Table 3 the exergy efficiency of system for R123,
show a higher value. Furthermore, the higher value of critical
temperature offers a distinct advantage over other working fluids.
R123 with a low life cycle in the atmosphere dose not contributes to
the greenhouse gas effect responsible for global warming as GWP
index indicate too. In addition, the value of ozone depletion ratio
for R123 is a reasonable value. Following the International regulations (Kyoto and Montreal Protocols), and regards to the above
mentioned characteristics of working fluids the R123 is used as
organic working fluid in this study.

_

3R ÀEx2R
jpump ¼ Ex
_
_

Ex5b ÀEx5c

_
_
_
_ D;tur ¼ Ex
Ex
3R À Ex4R þ W tur
jtur ¼

(22)

where H is the percent of hydrogen and M is the percent of moisture in biomass fuel. In order to accurate evaluation of the system
and obtain the parameters, which play critical roles in the performance, exergy loss calculation and exergy efficiency of each
component is necessary. Table 2 shows exergy efficiencies and
exergy losses in the components of the cycle under study.

_

_

jpump ¼ Ex2R_ ÀEx1R

Organic turbine



_

_

W1
jDHW ¼ Ex_W2 ÀEx
_

W_ tur
_ 4R
_ 3R ÀEx
Ex

_
_
_
_
_
Ex
D;cond ¼ Ex4R À Ex1R þ ExC1 À ExC2

Organic condenser

jtur ¼

_ 1R
_ 4R ÀEx
Ex
_ C2
_ C1 ÀEx
Ex

4. Group method of data handling (GMDH)

According to literature, there has been ample research conducted
on optimization using evolutionary method tools for system identification. Among these methodologies, the Group Method of Data
Handling (GMDH) has proven itself as a self-organizing approach by
which complicated models are generated based on the evolution of
their performances. In this paper, groups of 2500 data series are
selected for the training and test purpose, from which 1500 are used
for training while the remaining 1000 data are merely used for the
model evaluation. The obtained polynomial models are then used in
a Pareto based multi-objective optimization approach to determine
the best possible combination of exergy efficiency (j) and total cost
rate (C_
) of the system, known as the Pareto front.
total

5. Optimization
5.1. The definition of objective functions
Two objective functions in multi objective optimization
considered in this work are exergy efficiency of the combined
system (to be maximized) and the total cost rate of combined
system (to be minimized). The objective functions in this study can
be written as follows:

j¼

_
_
_
Ex
Q ;domestic þ Wnet;ORC þ Wnet;GT
_

Ex

(23)

biomass

C_ total ¼ Z_ total þ C_ biomass

(24)

Z_ total ¼ Z_ Comp þ Z_ GT þ Z_ AP þ Z_ CC þ Z_ DHW þ Z_ G þ Z_ Pump;R þ Z_ Ev;R
þ Z_ Tur;R þ Z_ cond;R
(25)


S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

853

Table 3
Thermodynamic properties and some characteristics of organic fluids [22,23].
Working fluid

Molecular weight

Critical temperature (K)

Critical pressure (MPa)

GWPa

ODPb

Second law efficiency of system (%)

Output work of ORC (kW)

R123
R600
R245fa
R11
R141b

152.93
58.12
134.05
137.37
116.95

456.83
425.13
427.2
425.12
479.96

3.66
3.8
3.64
4.408
4.46

120
725
950
4600
700

0.012
0.12
0
1
0.086

12.98
12.96
11.8
12.72
11.85

256.6
254.3
235
242.4
236

a
b

GWP: Global Warming Potential (GWP) for 100 years integration.
ODP: Ozone Depletion Potential, relative to R11.

In addition, it is assumed that the cost of wood biomass and
transportation are 40 $/ton.
5.2. Decision variables
Given the performance data of the modeled system and the
design process of the system under study, seven variables influencing the system performance are taken into account based on
previous investigator results [8e10]. These parameters include
biomass gasification temperature (Tgasif), combustion temperature
(Tcomb), inlet gas turbine temperature (T3), gas turbine isentropic
efficiency (hGT), compressor isentropic efficiency (hcomp) and
compressor pressure ration (rp) and maximum organic Rankine
cycle performance pressure (P3R) as decision variables. Table 5
shows reasonable variations interval for the above parameters.
Fig. 2. TeS diagram for organic working fluids.

5.3. Evolutionary genetic algorithm

Several varieties of methods are proposed to calculate purchase
equipment cost in terms of design parameters. Here, the functions
used by Bejan et al. [24], Ahmadi [25], Soltani et al. [10] and
Khanmohammadi et al. [26] and the variations corresponding to
local conditions and Iran interest rate are applied.

Z CRF4
Z_ K ¼ K
N Â 3600

(26)

Here ZK is the purchase cost of each component which is presented in the Appendix A, CRF is capital recovery factor, N is the

annual function hour per component, and 4 is operation and
maintenance factor which is regarded usually as 1.06 [16]. The
capital recovery factor has a relationship with interest rate and
operation years as follows:

CRF ¼

ið1 þ iÞn
ð1 À iÞn À 1

(27)

where i is interest rate and n is function year. Table 4 shows the
required parameters for the calculations relevant to purchase
equipment cost and economic factors.
Biomass fuel cost calculation is mainly dependent upon the type
of raw material, and collection and processing methods. For
instance, forest waste has a higher purchase cost and a lower
processing cost. On the contrary, industrial and municipal waste
has a much lower and even negative cost; but a higher processing
cost. Collection method and transportation distance of such material also affect the finished cost. The overall fuel cost as a function
of internal energy can be written as follows [27]:


biomass cost ¼

Genetic algorithm as a repetitive algorithm with random search
strategy and biological evolution modeling attempts to find optimal
solutions [28]. The main feature of evolutionary algorithms is a
population in which individuals are a series of design parameters

and decision variables and the optimal solution is found among
them [29]. More detail about genetic algorithm and multi objective
optimization can be found in Refs. [30e33].

 

cost=ton
3:6
Â
1000
LHV

(28)

6. Results and discussion
6.1. The model validation
Thermodynamic modeling of syngas production through
biomass gasification is the most important part of the modeling of
the system under study. To validate the modified equilibrium
thermodynamic model, the results were compared to those of other
studies. It should be noted that to make the results and modeling
more accurate, the modified equilibrium thermodynamic model
was used in this study, i.e. by multiplying variable coefficients to
equilibrium constants and minimizing the error root mean square
of the model and the experimental results to enhance the accuracy
of preceding models [34]. It should be mentioned that a and b are
two constants applied to equilibrium constants to enhance the
model precision.

Table 4

Economic factors.
Economic parameters

Value

Interest rate (%)
Function year (Year)
Operation and maintenance coefficient
Hours of the system function annually (Hour)
Biomass fuel higher heating value (kJ/kg)

12
20
1.06
8000
19,980


854

S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

Table 5
Decision variables and their reasonable range.

Table 6
Parameter values resulting from exergy and energy analysis of the system.

Restriction

Cause

Parameters

Values

950 K < Tgasif < 1150 K
1300 K < Tcomb < 1450 K
1250 K < T3 < 1350 K
0.78 < hcomp < 0.89
0.78 < hGT < 0.91
7 < rp < 11
800 < P3R < 1200

Thermodynamic limitation
Metallurgical limitation
Heat transfer limitation in heat exchanger
Cost limitation
Cost limitation
Cost limitation
Thermodynamic limitation

_ net (kW)
Net Power output, W
Exergy efficiency of system, j (%)
Energy efficiency of system, h (%)
_ D;tot (kW)
Total exergy destruction rate, Ex
Heating load, Q_
(kW)

16.13
24.15
13,357

_ DWH (kg/s)
Hot water mass flow rate, m

21.9

1961.3

2569

DWH

47.0%

aK1 ¼

x5
x21

(29)

bK2 ¼

x3 x1
x2 x4

(30)

29.8%

The results indicate that in terms of the values a ¼ 2.89 and
b ¼ 1, the model has a good consistency with previous works. The

11.5%

compositions are shown in Fig. 3 [35,36].

6.8%
1.3%

2.2%

0.6%

0.1%

0.3%

0.4%

6.2. The results of exergy and economic analysis
The results of thermodynamic analysis are presented here.
Table 6 shows the main output of the system for the initial performance parameters.
To find the locations where the main exergy destruction take
place, for each component the exergy destruction rate is calculated.
Fig. 4 illustrates the percent of exergy destruction for the components of the studied system. The results indicate that the maximum

exergy destruction rate is related to gasifier, combustion chamber,
organic Rankine cycle evaporator, and domestic hot water heat
exchanger. The main reason of exergy destruction in gasifier and
combustion chamber is the presence of a high temperature difference between flows entering and exiting such components, which
enhance the intensity of irreversibility in these components.
On the other hand, in organic Rankine cycle evaporator, as high
temperature stream (combustion products) transfers its heat to
organic working fluid, it could be said that high quality energy
converts into low quality energy and this is the main reason of high
rate of exergy destruction in such component. Similarly, domestic
hot water generator allocates a main part of the system exergy loss
to itself.

60
50

Fig. 4. The percent of exergy loss for each component of the cycle.

In addition, Table 7 shows the exergy efficiency of each components of the cycle.
Fig. 5 show the exergy and energy efficiency for three modes of
the system. As it can be seen, the exergy and energy efficiency in
the combined heat and power mode has the highest value because
a larger part of primary energy converts to useful products. In this
case, the gas turbine output is 1669 kW; the ORC output is
292.3 kW and domestic water heater produces 2569 kW hot water.
It can be found that the energy efficiency in the combined heat
and power mode is higher than exergy efficiency for the same case.
Since the exergy of produced hot water is lower than its energy for
a determined mass flow rate and temperature, the energy efficiency
is more than exergy efficiency in combined heat and power mode.

The results of the economic analysis of the system under study
are shown in Table 8. The cost of each component is compared to
the equations of different references and is given in the Appendix A.

Present Study
Experimantal (Alaudin Z.A.[36])

Percent (%)

40
30

Experimental (Jayah T.H.[37])
Zainal model [16]

20
10
0

Fig. 3. A comparison of the present study results with experimental results and previous research.

Table 7
Exergy efficiency for each component of the cycle in: Tcomb ¼ 1177 (C ),
rp ¼ 9, Tgasif ¼ 827 (C ), Moisture content ¼ 0.16, Biomass flow rate ¼ 0.8 kg/
s.
Component

Exergy efficiency (%)

Compressor

Heat exchanger
Gas turbine
Combustion chamber
Gasifier
Domestic hot water
Organic pump
Organic evaporator
Organic turbine
Organic condenser

91.4
91.4
97
64.4
61.3
26.6
88.5
23.1
15
60.7


S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

855

30
Energy efficiency (%)

Exergy efficiency (%)

25
Effeciency (%)

20
15
10
5
0
GT

GT+ORC

GT+ORC+DWH

Fig. 5. Comparison of energy and exergy efficiency for different types of system.

6.3. Optimization results
The optimization results of the system based on selected decision variables and objective functions are shown in the Fig. 6. This
figure shows the optimal point for the system based on the
objective functions defined in the equations (22) and (23).
It can be seen that the final cost of the system increases steadily
with an increase in the system exergy efficiency. The results indicate that by an increase in efficiency from 14.5% to 16.5%, the final
cost increases from 75 $/h to 77 $/h which is an optimal value.
However, higher increase in efficiency from 16.5% to 17.9% can exert
a higher cost to the system.
As shown in Fig. 6, although the design point C has a maximum
efficiency of 17.9%, the system cost rate in this point will reach
maximum value of 87 $/h. However, design point A has the minimum design cost in which the system cost rate is 75 $/h. Therefore,
the design point C is the optimal design point when it is regarded as

the only objective function of the system efficiency, and the point A
is the optimal design point when the cost function is considered as
the only objective of the system optimization.
In general, in multi-objective optimization and Pareto diagram,
all points are considered as the optimal solutions of problem, and
ultimately system designers and decision makers attempt to select
a point as the optimal solution by considering some designing
consideration. Table 9 presents the value of decision variables in the
selected design points A, B and C.
In order to obtain a diagram through which it is possible to
obtain the system cost in terms of exergy efficiency, the Pareto
frontier diagram is depicted in Fig. 7.

Fig. 6. The optimized points based on the defined objective functions.

Table 9
The characteristics of the selected design points A, B, C.
Optimum point

Tcomb (K) rp

P3R (kPa) hcomp

hGT

Tgasif (K) GTIT (K)

A
B
C

1449
1449
1449

800.5
800.5
1171

0.78
0.78
0.78

1114.6
1065.7
987.2

7.08
8.6
9.97

0.9
0.9
0.9

1266
1269.6
1266.4

To predict the system behavior and find a correlation between

exergy efficiency and final cost of system a relation derived based
on Pareto frontier diagram.

À817:7h3ex þ 1:464 Â 104 h2ex þ 1722hex þ 132:9
C_ tot ðhex Þ ¼ 4
hex À 56:98h3ex þ 898:6h2ex À 3589hex þ 815:8
(31)
As it shown in Fig. 7, the optimized values for exergy efficiency
on the Pareto frontier valid in the range between 14% and 18% and
the equation (31) are valid for the same range.

Table 8
The results of the economic analysis of the system under study in: Tcomb ¼ 1177 (C ),
rp ¼ 9, Tgasif ¼ 827 (C ), Moisture content ¼ 0.16, Biomass flow rate ¼ 0.8 kg/s.
Component

Cost ($)

Cost rate ($/h)

Biomass fuel (wood)
ORC turbine
ORC pump
ORC condenser
ORC evaporator
Compressor
Gas turbine
Heat exchanger
Combustion chamber
Gasifier

Domestic hot water

2 ($/GJ)
341,175
3686
55,103
6969
219,468
164,414
305,161
33,390
332,593
6546

117
6.05
0.065
0.97
0.12
3.89
2.91
5.41
0.59
5.9
0.11

Fig. 7. The Pareto frontier diagram: the optimal approximations for the objective
functions.

856

S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

6.4.2. Combustion temperature
One of the most significant design parameters in this study is
combustion temperature, which directly affects gas turbine performance and organic Rankine cycle. Fig. 9 shows the behavior of
objective functions with variations of this parameter.
Based on the behavior of the above diagram for the selected
points, it could be inferred that an increase in the combustion
temperature leads to an increase in the exergy efficiency of the
studied system and has a positive economic impact on the system
cost reduction.
With a close analysis of such variations, it could be seen that by
an increment in the combustion temperature, the cost of hightemperature heat exchanger, which plays significant roles in the
system cost, reduces significantly. In addition, considering the cost
function of the high temperature heat exchanger, it could be seen
that the cost of heat exchanger reduces as combustion temperature
increases due to the increased logarithm mean temperature difference. Therefore, the system overall cost will be decreased. It
must be noted that even though increased combustion temperature
improve both objective functions, metallurgical and physical
Fig. 8. The impacts of gasification temperature variation from 950 K to 1150 K on the
system objective functions in the optimized points A, B and C.

6.4. Sensitivity analysis
In order to better understand the system behavior and the
impact of the decision variables on the thermodynamic and economic performance of studied system, in the optimal points A, B
and C, sensitivity analysis is extracted on these variables.
6.4.1. Gasification temperature
The diagram in Fig. 8 indicates that by an increase in gasification

temperature, the overall cost as well as the system exergy efficiency
will be reduced. As it can be seen from the results, in the design
point C, with a decrement in the gasification temperature the
exergy efficiency has no sensitive change while the system cost rate
experiences a severe increment. This fact reveals that by selecting
the point C as the design point, changing the gasification temperature, as a parameter for enhancing efficiency is not cost-effective
and therefore the points A and B show a more reasonable
behavior from cost rate point of view.

Fig. 9. The effects of combustion temperature variation from 1300 K to 1450 K on the
objective functions in the optimized points A, B, and C.

Fig. 10. The effects of the parameters variation (a) the compressor isentropic efficiency
from 0.78 to 0.89 (b) the gas turbine isentropic efficiency from 0.78 to 0.91 in the
optimized points A, B and C on objective functions.


S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

857

limitations allows increase in combustion temperature to a limited
extent [37].
6.4.3. Isentropic efficiency of compressor and gas turbine
Fig. 10 shows the effect of changes in the efficiency of isentropic
compressor and turbine efficiencies on the objective functions. An
Increment in the compressor isentropic efficiency and gas turbine
isentropic efficiency has a different effect on the objective functions. Fig. 10(a) shows that in the optimal points, more increase in
isentropic efficiency leads to a higher cost and higher exergy efficiency for the system.
The results indicate that the higher isentropic efficiency of

compressor means reduced work exerted on compressor, and in
turn, an increase in the system exergy efficiency. On the other hand,
this effect can increase the final cost of compressor, and by keeping
fuel cost and purchase equipments cost constant, the system total
cost rate will be increased.
In addition, results indicate that an increase in isentropic efficiency of gas turbine can both positively affect the system total
exergy efficiency and final cost rate of system. Increased output
working of the system due to an increase in isentropic efficiency is
one main reason for the enhancement of the system thermodynamic performance. Moreover, although increase in turbine isentropic efficiency from 87 to 91% leads to an increase in gas turbine
purchase cost, decrease in fuel cost in output constant power can
reduce total cost rate, which the results of the Fig. 10(b) refers to
this issue.
6.4.4. Compressor pressure ratio
The diagram in Fig. 11 shows the impact of the compressor
pressure ratio on two objective functions in the selected optimal
points. As it could be seen, for a higher-pressure ratios, exergy efficiency is high and the system overall cost increases. It can be
found that with an increment in the compressor pressure ratio the
outlet compressor temperature will be increased which resulted in
a reduction of heat transfer from hot stream (combustion products)
to cold stream (air). Consequently, a slight reduction in heat
exchanger purchase cost, and increase in the price of some installations such as compressor and gas turbine lead to the increase

Fig. 11. The effects of the compressor pressure ratio variation from 7 to 11 on objective
functions in the optimized points A, B and C.

Fig. 12. The effects of the inlet gas turbine temperature variation from 1250 K to
1350 K on objective functions in the optimized points A, B and C.

of overall cost of system. In addition, it could be inferred that in the
design point C, by an increase in exergy efficiency, the total cost has

a drastic increase.
6.4.5. Gas turbine inlet temperature
Fig. 12 shows the effects of variation in gas turbine inlet temperature parameter on two objective functions. The results indicate
that an increase in this parameter can affect the system performance to a limited extent and improve both objective functions. By
a closer look at the gas turbine purchase cost equation, an increment in gas turbine inlet temperature can increase gas turbine
purchase cost, however, it can significantly reduce high temperature heat exchanger purchase cost, which in turn decreases overall
cost. It must be noted that considering the limited variation range
of this parameter in Fig. 12 and the designing limitations of the
desired cycle, the parameter cannot be regarded as an influencing
parameter for efficiency increase.

Fig. 13. The effects of the maximum pressure of the organic Rankine cycle variation
from 800 kPa to 1200 kPa on objective functions in the optimized points A, B and C.


858

S. Khanmohammadi et al. / Applied Thermal Engineering 91 (2015) 848e859

6.4.6. Maximum pressure of organic Rankine cycle
Two main variables influencing the organic Rankine cycle are
the type of organic fluid and maximum organic fluid temperature.
The variation in the maximum organic Rankine cycle pressure,
which follows the maximum cycle temperature, is shown in the
Fig. 13.
Concerning the fact that the working fluid critical temperature is
456.8 K, the maximum pressure variations interval of organic
Rankine cycle is considered from 800 kPa to 1200 kPa. The results
indicate that by an increment in the maximum pressure of organic
Rankine cycle, the power output of organic Rankine cycle will be

increased, which in turn, it increases the overall cycle efficiency. Of
course, it must be noted that by an increase in the cycle pressure,
more work is consumed in pump. However, a higher increase will
be occurred in organic cycle turbine, and these can lead to an increase in working of the organic cycle. On the other hand, an
escalation in the maximum cycle pressure due to an increase in
organic Rankine purchase cost and lack of variation in purchase
cost of other components can lead to an increase in the overall
system cost rate.

Appendix A. Cost function for system elements [16,24,25,38].

Air compressor :
C11


ZCC ¼

 The system efficiency based on the lower heating value of the
wood in the initial designing state was 15.6%, which this efficiency could be improved to 17.9% in the optimal state, regardless of the cost objective function.
 The optimization results indicate that the final system cost could
be reduced to 75 $/h, regardless of the exergy efficiency as an
objective function.
 The system sensitivity analysis in the optimal points A, B and C
shows that reduction in gasification temperature in the determined interval can positively affect efficiency, and can steadily
increase the system costs.
 An increase in compressor isentropic efficiency in selected
optimal points leads to a drastic increase in total cost of system
as well as a mild increase in exergy efficiency of system.
Finally, it can be concluded that variegation each decision variables in reasonable range has different effects on exergy efficiency
and total cost of system. Selecting the optimal point and considering the effect of variation performance parameters in optimal

point is one of important issue which should be considered in an
energy system design.

Acknowledgement
I would like to acknowledge National Iranian Gas Company
(NIGC) for their helpful support (Gr. No. 930201).


_a
C21 m
C22 À 0:98

Âð1 þ expðC32 Tcomb À C24 ÞÞ

Combustion chamber :

C21 ¼ 46:08; C22 ¼ 0:995;
C23 ¼ 0:018; C24 ¼ 26:4

Gas turbine :

ZGT ¼

  
_g
C31 m
P
ln 4 ð1 þ expðC33 T3 À C34 ÞÞ
C32 À hGT
P3

C31 ¼ 479:34; C32 ¼ 0:92; C33 ¼ 0:036; C34 ¼ 54:4


7. Conclusion
In the present study, a comprehensive thermodynamic and
economic modeling for an externally fired combined system integrated with Syngas produced from biomass (wood) as a prime
mover is presented. The system exergy analysis results indicated
that gasifier, combustion chamber and organic Rankine cycle have
the maximum exergy destruction rate in the system under study. In
addition, organic turbine, organic evaporator and hot water
generator for domestic use are the most ineffective components of
a system with 15%, 23.1% and 26.6%exergy efficiency, respectively.
Other study results are as follows:


À Á
C11
rp ln rp
C12 À hsc

.
C12 ¼ 0:9
¼ 71:1 $ kgsÀ1


ZC ¼

ZAP ¼ C41

Air preheater :


_ 5 ðh5 À h6 Þ 0:6
m
UDTLM

U ¼ 6; C41 ¼ 4122
Gasifier :

_ biomass Þ0:67
ZG ¼ 1600ð3600 Â m

Domestic hot water heater :
ORC evaporator :

_ DHW
ZDHW ¼ 0:3m

ZEv;R ¼ 309:14ðAEv Þ0:85

ORC pump :


0:65
_ Pump
ZPump;R ¼ 200 W

ORC turbine :

0:75

_ tur
ZTur;R ¼ 4750 W

ORC condenser :

ZCond;R ¼ 516:62ðACondnser Þ0:6

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