Exergoeconomic multi-objective optimization of an externally fired gas turbine integrated with a biomass gasifier

Applied Thermal Engineering 91 (2015) 848e859

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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: [email protected] (S. Khanmohammadi). http://dx.doi.org/10.1016/j.applthermaleng.2015.08.080 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

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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  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

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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  h2 Þ _ prod ðh5a  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  T2 Þ  ðT5  T3 Þ   2 ln TT65 T T3

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  ho Þ  To ðs  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)

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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 _  Ex _ Ex 1 C 2 WC

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

Heat exchanger

_

b¼

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

LHVðkJ=kgÞ ¼ HHV  hfg

9H M þ 100 100

jGT ¼

W_ GT _ 4 _ 3 Ex Ex

_ _ _ _ Ex D;CC ¼ Ex4 þ Exb1  Ex5

Combustion chamber

_

_

jGT ¼ Ex5_Ex4 Exb1

_ _ _ _ Ex D;gasif ¼ Exbiomass þ Exair  Exb1

Gasifier

(21)

_

_

jgasif ¼ Ex5_Ex4 Exb1

_ D;DHW ¼ Ex _  Ex _ 7 þ Ex _ _ Ex 6 W1  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 Ex2

_ _ _ _ Ex D;GT ¼ Ex3  W GT  Ex4

Gas turbine

(20)

_

6 jHE ¼ Ex_ 5a Ex _

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

_

_

Ex1 jcomp ¼ Ex2  _

(19)

Ex6 Ex7

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

Organic pump

W pump

_ D;eva ¼ Ex _ _ _ _ Ex 5b  Ex5c þ Ex2R  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 Ex2R jpump ¼ Ex _ _

Ex5b Ex5c

_ _ _ _ D;tur ¼ Ex Ex 3R  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_ Ex1R

Organic turbine



_

_

W1 jDHW ¼ Ex_W2 Ex _

W_ tur _ 4R _ 3R Ex Ex

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

Organic condenser

jtur ¼

_ 1R _ 4R Ex Ex _ C2 _ C1 Ex 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)

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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  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  iÞn  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  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

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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

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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.

817:7h3ex þ 1:464  104 h2ex þ 1722hex þ 132:9 C_ tot ðhex Þ ¼ 4 hex  56:98h3ex þ 898:6h2ex  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.

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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.

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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. 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.

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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  0:98

ð1 þ expðC32 Tcomb  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  C34 ÞÞ C32  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:

   C11 rp ln rp C12  hsc  .
C12 ¼ 0:9 ¼ 71:1 $ kgs1 

ZC ¼

ZAP ¼ C41

Air preheater :

 _ 5 ðh5  h6 Þ 0:6 m UDTLM

U ¼ 6; C41 ¼ 4122 Gasifier :

_ biomass Þ0:67 ZG ¼ 1600ð3600  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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