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

Seven decision variables, namely, biomass gasiﬁcation temperature Tgasif, combustion temperature Tcomb, gas turbine inlet temperature T3, gas turbine isentropic efﬁ-ciency hGT, compresso

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Research paper

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

Article history:

Received 1 June 2015

Accepted 27 August 2015

Available online 5 September 2015

Keywords:

Externally ﬁred gas turbine

Gasiﬁcation

Multi-objective optimization

Organic Rankine cycle

a b s t r a c t

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 effi-ciency (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 multi-objective 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

1 Introduction

The depletion of fossil fuels, environmental pollutions,

green-house gas emissions, and global climate changes together with the

potential of biomass to meet a part of energy demand have

con-verted 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

en-ergies 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

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

combustion Generally, the efﬁciency of power production using biomass is low For example, the efﬁciency in small and large sys-tems 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 expensiveﬁlters 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

* Corresponding author Tel.: þ98 133 6690271 9.

E-mail address: khshoaib@phd.guilan.ac.ir (S Khanmohammadi).

Contents lists available atScienceDirect Applied Thermal Engineering

j o u r n a l h o me p a g e : w w w e l s e v i e r c o m / lo c a t e / a p t h e r m e n g

http://dx.doi.org/10.1016/j.applthermaleng.2015.08.080

Applied Thermal Engineering 91 (2015) 848e859

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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

externallyﬁred 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

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

multi-objective optimization method to determine the best design

pa-rameters for the system A sensitivity analysis was conducted to

show the effect of design parameters on exergy efﬁciency, total cost

rate, and CO2emission

considered three cases based on the variations in compressor

pressure ratio and temperature difference of the cold end of the

heat exchanger toﬁnd 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

included a review of the effects of compressor pressure ratio and compressor isentropic efﬁciency and the effects of mass ratio of

combined cycle conﬁgurations included co-ﬁring of natural gas and biomass Their study included an assessment of the exer-goeconomic of these two systems and the effects of various pa-rameters on their performance Their analysis showed that the

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 co-firing 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] pre-sented 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 in-vestigations examine the performance variations in different con-ﬁgurations of system Given that the results of the studies must ﬁnally result in the selection of the optimal cycle in terms of eco-nomic and thermodynamic performance, the optimization of the relevant systems is necessary both in terms of economic and

in-vestigations in thermoeconomic and optimization of the previous studies, the present work concentratesfirstly to develop models of thermodynamic and economics of an organic Rankine cycle and an externallyfired gas turbine integrated with a biomass gasifier The second part of this work is to apply multi-objective optimization

Nomenclature

mole of syngas

Subscripts

Cond, R Organic condenser

Pump, R Organic pump

Greek symbols

S Khanmohammadi et al / Applied Thermal Engineering 91 (2015) 848e859 849

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procedure toﬁnd the optimum working conditions and to show

sensitivity of the optimum performances in terms of decision

var-iables 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

ge-netic algorithm for producing Pareto front

2 System modeling

A schematic of combined gas turbine and Rankine cycle

inte-grated with the syngas producer shown inFig 1 The system

con-sists of a hot air driven gas turbine The gasiﬁer in the system

produces syngas using gasiﬁcation of dry biomass The product of

inFig 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

inTable 1

The thermodynamic properties of streams and system

perfor-mance 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

optimi-zation method

2.1 Thermodynamic model

Before proceeding to the development of each components

thermodynamic model, the assumptions for the system are given as

follow:

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

com-pounds as: 50% carbon, 6% hydrogen, 44% oxygen[14]

The cost of biomass (wood) is considered 2 $/GJ[15]

The wood chemical formula based on one carbon atom could be

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:

CHxOyNzþ wH2Oþ mðO2þ 3:76N2Þ/x1H2þ x2COþ x3CO2

þ x4H2Oþ x5CH4þ x6N2

(1)

Here, CHxOyNzdenotes the biomass chemical formula and w is the amount of water per kmol of biomass All coefﬁcients x1to x6 are obtained by performing atomic balance and using equilibrium constant equations The procedures are given as follows:

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

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

K1¼PCH 4

P2H2 ¼x5

K2¼PCO 2PH2

PCOPH2O¼x3x1

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

hf;biomassþ whf;H2O¼ x1hf;H2þ Dhþ x2hf;COþ Dh

þ x3

hf;CO2þ Dhþ x4

hf;H2Oþ Dh

þ x5

hf;CH4þ Dhþ x6

hf;N2þ Dh

(10)

where, hf;iis the formation enthalpy in terms of kJ/kmol, and its value for all the chemical compositions is zero in the reference state and Dh is enthalpy difference value for the given state with 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:

x1H2þ x2COþ x3CO2þ x4H2Oþ x5CH4þ x6N2þ m0ðO2

þ 3:76N2Þ/aCO2þ bH2Oþ cO2þ dN2

(11)

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The coefﬁcients x1to x6have already been calculated and m0is

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 m0is calculated

X

j¼react

hf;j¼ X

j¼Prod

ni

hf;iþ DhTcomb;i (12)

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]

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 inﬂow systems, most notably in heat exchangers The

LMTD is a logarithmic average of the temperature difference be-tween 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 constantﬂow rate and ﬂuid thermal properties For the ceramic heat exchanger LMTD can be express as:

LMTDHE¼ðT6 T2Þ ðT5 T3Þ

ln

T 6 T 2

T 5 T 3

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

X in

_minexin¼X

out

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

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

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

exch¼Xxiexcho;iþ RT+

X

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

Table 1

Initial performance parameter of the integrated system.

Gas turbine inlet temperature 877 C

Air gasiﬁcation mass ﬂow rate 1.09 kg/s

ﬂow rate

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here xiis molar fraction of ith component and exch

o;i is standard

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

coefﬁcientbwhich is calculated as follows[5,8]:

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

21:1ASH

(20)

b ¼

1:044 þ 016Z H

Z C :34493Z O

Z C

1þ :0531Z H

Z C

1 0:4124Z O

Z C

(21)

Here ZC, ZHand ZOare 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

hfg¼ 2258 kJ/kg[18]

LHVðkJ=kgÞ ¼ HHV hfg

9H

100

(22)

where H is the percent of hydrogen and M is the percent of

mois-ture in biomass fuel In order to accurate evaluation of the system

and obtain the parameters, which play critical roles in the

exergy losses in the components of the cycle under study

The organic Rankine cycle (ORC) has the principles of the steam

Rankine cycle, but uses organicﬂuid with lower boiling point to

recover energy from a lower temperature heat sources The

work-ing ﬂuids play an important role in the performance of organic

cycle The organicﬂuid selection directly affects the efﬁciency of the

system, operating parameters, environmental impacts, and

eco-nomic factors There are several studies conducted by different

workingﬂuids (e.g Ammonia[19], R11 and R134a[20], and R152a

[21]) depending on a low-grade temperature energy source,

avail-ability and material limitation Concerning the heat source

tem-perature and the lower pressure of organic Rankine cycle

(condenser pressure)ﬁve types of organic ﬂuid selected for organic

cycle.Table 3shows some properties of these ﬂuids and

perfor-mance parameters of system for mentioned organicﬂuids

Also,Fig 2show the TeS diagram for these four organic working

ﬂuids In addition, two bounds temperature for heat source

tem-perature (Tmax) and cold temperature (Tmin) is illustrated in this

ﬁgure

As shown inTable 3the exergy efﬁciency of system for R123,

show a higher value Furthermore, the higher value of critical

temperature offers a distinct advantage over other workingﬂuids

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

regula-tions (Kyoto and Montreal Protocols), and regards to the above

mentioned characteristics of workingﬂuids the R123 is used as

organic workingﬂuid in this study

4 Group method of data handling (GMDH) According to literature, there has been ample research conducted

on optimization using evolutionary method tools for system

iden-tiﬁcation 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 ( _Ctotal) of the system, known as the Pareto front

5 Optimization 5.1 The deﬁnition of objective functions Two objective functions in multi objective optimization

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:

j ¼Ex_ Q;domesticþ __Wnet;ORCþ _Wnet;GT

_Ctotal¼ _Ztotalþ _Cbiomass (24) _Ztotal¼ _ZCompþ _ZGTþ _ZAPþ _ZCCþ _ZDHWþ _ZGþ _ZPump;Rþ _ZEv;R

þ _ZTur;Rþ _Zcond;R

(25)

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

Component Exergy destruction rate

Exergy efﬁciency Compressor _Ex D ¼ _Ex 1 þ _ W C _Ex 2

j comp ¼_Ex2 _Ex 1

_

W C Heat exchanger _ExD;HE¼ _Ex 2 _Ex 3 þ _Ex 5a _Ex 6

j HE ¼_Ex5a _Ex 6

_Ex 3 _Ex 2 Gas turbine _ExD;GT¼ _Ex 3 _ W GT _Ex 4

j GT ¼ W_GT

_Ex 3 _Ex 4 Combustion chamber _ExD;CC¼ _Ex 4 þ _Ex b1 _Ex 5

j GT ¼_Ex5 _Ex 4

_Exb1

Gasiﬁer _ExD;gasif¼ _Ex biomass þ _Ex air _Ex b1

j gasif ¼_Ex5 _Ex 4

_Exb1

Domestic hot water _ExD;DHW¼ _Ex 6 _Ex 7 þ _Ex W1 _Ex W2

j DHW ¼_ExW2 _Ex W1

_Ex 6 _Ex 7 Organic pump _ExD;pmp¼ _Ex 1R _Ex 2R þ _ W pmp

j pump ¼_Ex2R _Ex 1R

_

W pump Organic evaporator _ExD;eva¼ _Ex 5b _Ex 5c þ _Ex 2R _Ex 3R

j pump ¼_Ex3R _Ex 2R

_Ex 5b _Ex 5c Organic turbine _ExD;tur¼ _Ex 3R _Ex 4R þ _ W tur

j tur ¼ W_tur

_Ex3R _Ex4R

Organic condenser _ExD;cond¼ _Ex 4R _Ex 1R þ _Ex C1 _Ex C2

j tur ¼_Ex4R _Ex 1R

_Ex C1 _Ex C2

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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

local conditions and Iran interest rate are applied

_ZK¼ ZKCRF4

Here ZKis the purchase cost of each component which is

pre-sented in theAppendix A, CRF is capital recovery factor, N is the

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:

CRF¼ ið1 þ iÞn

where i is interest rate and n is function year.Table 4shows 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

ma-terial also affect theﬁnished cost The overall fuel cost as a function

of internal energy can be written as follows[27]:

biomass cost¼

cost=ton 1000

3:6 LHV

(28)

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 in ﬂu-encing 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

cycle performance pressure (P3R) as decision variables Table 5

shows reasonable variations interval for the above parameters

5.3 Evolutionary genetic algorithm Genetic algorithm as a repetitive algorithm with random search strategy and biological evolution modeling attempts toﬁnd 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]

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

thermodynamic model, the results were compared to those of other studies It should be noted that to make the results and modeling

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 thataandbare two constants applied to equilibrium constants to enhance the model precision

Table 3

Thermodynamic properties and some characteristics of organic ﬂuids [22,23]

Working ﬂuid Molecular weight Critical temperature (K) Critical pressure (MPa) GWP a ODP b Second law efﬁciency of system (%) Output work of ORC (kW)

a GWP: Global Warming Potential (GWP) for 100 years integration.

b ODP: Ozone Depletion Potential, relative to R11.

Fig 2 TeS diagram for organic working ﬂuids.

Table 4 Economic factors.

Operation and maintenance coefﬁcient 1.06 Hours of the system function annually (Hour) 8000

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bK2¼x3x1

The results indicate that in terms of the valuesa ¼ 2.89 and

b¼ 1, the model has a good consistency with previous works The

compositions are shown inFig 3 [35,36]

6.2 The results of exergy and economic analysis

The results of thermodynamic analysis are presented here

Table 6shows the main output of the system for the initial

per-formance parameters

place, for each component the exergy destruction rate is calculated

Fig 4illustrates the percent of exergy destruction for the

compo-nents 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

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

In addition,Table 7shows the exergy efﬁciency of each com-ponents of the cycle

Fig 5show 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 massﬂow 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 inTable 8 The cost of each component is compared to the equations of different references and is given in theAppendix A

Table 5

Decision variables and their reasonable range.

950 K < T gasif < 1150 K Thermodynamic limitation

1300 K < T comb < 1450 K Metallurgical limitation

1250 K < T 3 < 1350 K Heat transfer limitation in heat exchanger

0.78 <hcomp < 0.89 Cost limitation

0.78 <hGT < 0.91 Cost limitation

7 < r p < 11 Cost limitation

800 < P 3R < 1200 Thermodynamic limitation

0

10

20

30

40

50

60

Present Study

Experimantal (Alaudin Z.A.[36])

Experimental (Jayah T.H.[37])

Zainal model [16]

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

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

Net Power output, _ W net (kW) 1961.3 Exergy efﬁciency of system,j(%) 16.13 Energy efﬁciency of system,h(%) 24.15 Total exergy destruction rate, _ ExD;tot(kW) 13,357

Hot water mass ﬂow rate, _m DWH (kg/s) 21.9

1.3% 2.2% 0.6%

29.8%

47.0%

6.8%

0.1%

11.5%

0.3% 0.4%

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

Table 7 Exergy efﬁciency for each component of the cycle in: T comb ¼ 1177 (C ),

r p ¼ 9, T gasif ¼ 827 (C ), Moisture content ¼ 0.16, Biomass ﬂow rate ¼ 0.8 kg/ s.

Component Exergy efﬁciency (%)

Combustion chamber 64.4

Domestic hot water 26.6

Organic evaporator 23.1

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6.3 Optimization results

The optimization results of the system based on selected

deci-sion variables and objective functions are shown in theFig 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 theﬁnal cost of the system increases steadily

with an increase in the system exergy efﬁciency The results

indi-cate 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 inFig 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

mini-mum 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 9presents 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 inFig 7

To predict the system behavior andfind a correlation between exergy efficiency and final cost of system a relation derived based

on Pareto frontier diagram

_CtotðhexÞ ¼817:7h3exþ 1:464 104h2

exþ 1722hexþ 132:9

h4

ex 56:98h3

exþ 898:6h2

ex 3589hexþ 815:8

(31)

As it shown inFig 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

0

5

10

15

20

25

30

Energy eﬃciency (%) Exergy eﬃciency (%)

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

Table 8

The results of the economic analysis of the system under study in: T comb ¼ 1177 (C ),

r p ¼ 9, T gasif ¼ 827 (C ), Moisture content ¼ 0.16, Biomass ﬂow rate ¼ 0.8 kg/s.

Component Cost ($) Cost rate ($/h)

Biomass fuel (wood) 2 ($/GJ) 117

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 T comb (K) r p P 3R (kPa) hcomp hGT T gasif (K) GTIT (K)

A 1449 7.08 800.5 0.9 0.78 1114.6 1266

B 1449 8.6 800.5 0.9 0.78 1065.7 1269.6

C 1449 9.97 1171 0.9 0.78 987.2 1266.4

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

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6.4 Sensitivity analysis

In order to better understand the system behavior and the

impact of the decision variables on the thermodynamic and

eco-nomic 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 inFig 8indicates 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

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

temper-ature, 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

6.4.2 Combustion temperature One of the most signiﬁcant design parameters in this study is combustion temperature, which directly affects gas turbine per-formance and organic Rankine cycle.Fig 9shows 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 high-temperature 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 dif-ference 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.

Fig 9 The effects of combustion temperature variation from 1300 K to 1450 K on the

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

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limitations allows increase in combustion temperature to a limited

extent[37]

6.4.3 Isentropic efﬁciency of compressor and gas turbine

Fig 10shows 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

func-tions.Fig 10(a) shows that in the optimal points, more increase in

isentropic efﬁciency leads to a higher cost and higher exergy

efﬁ-ciency 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 theﬁnal 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 ef

ﬁ-ciency 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

thermody-namic performance Moreover, although increase in turbine

isen-tropic 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 theFig 10(b) refers to

this issue

6.4.4 Compressor pressure ratio

pressure ratio on two objective functions in the selected optimal

points As it could be seen, for a higher-pressure ratios, exergy

ef-ﬁciency 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

in-stallations such as compressor and gas turbine lead to the increase

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 12shows the effects of variation in gas turbine inlet tem-perature parameter on two objective functions The results indicate that an increase in this parameter can affect the system perfor-mance to a limited extent and improve both objective functions By

a closer look at the gas turbine purchase cost equation, an incre-ment in gas turbine inlet temperature can increase gas turbine purchase cost, however, it can signiﬁcantly reduce high tempera-ture heat exchanger purchase cost, which in turn decreases overall cost It must be noted that considering the limited variation range

of this parameter inFig 12 and the designing limitations of the desired cycle, the parameter cannot be regarded as an inﬂuencing parameter for efﬁciency increase

Fig 11 The effects of the compressor pressure ratio variation from 7 to 11 on objective

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.

Fig 13 The effects of the maximum pressure of the organic Rankine cycle variation

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