Performance comparison of three trigeneration systems using organic rankine cycles

Energy 36 (2011) 5741e5754

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Performance comparison of three trigeneration systems using organic rankine cycles Fahad A. Al-Sulaiman a, b, *, Feridun Hamdullahpur b, Ibrahim Dincer c a

Mechanical Engineering Department, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia Mechanical and Mechatronics Engineering Department, University of Waterloo, Waterloo, ON, Canada c Faculty of Engineering and Applied Science, University of Ontario Institute of Technology Oshawa, ON, Canada b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 November 2010 Received in revised form 21 May 2011 Accepted 4 June 2011

In this paper, energetic performance comparison of three trigeneration systems is presented. The systems considered are SOFC-trigeneration, biomass-trigeneration, and solar-trigeneration systems. This study compares the performance of the systems considered when there is only electrical power and the efficiency improvement of these systems when there is trigeneration. Different key output parameters are examined: energy efficiency, net electrical power, electrical to heating and cooling ratios, and (GHG) GHG (greenhouse gas) emissions. This study shows that the SOFC-trigeneration system has the highest electrical efficiency among the three systems. Alternatively, when trigeneration is used, the efficiencies of all three systems considered increase considerably. The maximum trigeneration efficiency of the SOFCtrigeneration system is around 76% while it is around 90% for the biomass-trigeneration system. On the other hand, the maximum trigeneration efficiencies of the solar-trigeneration system is around 90% for the solar mode, 45% for storage and storage mode, and 41% for the storage mode. In addition, this study shows that the emissions of CO2 in kg per MWh of electrical power are high for the biomasstrigeneration and SOFC-trigeneration systems. However, by considering the emissions per MWh of trigeneration, their values drop to less than one fourth. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Combined cooling heating and power Trigeneration Organic rankine cycle Solid oxide fuel cell Biomass Solar energy

1. Introduction Most of conventional power plants with single prime movers have an overall thermal efficiency less than 39% [1]. That is, more than 60% of the energy produced is lost as a waste heat, which is considered a huge amount of energy. On the other hand, most of the current power plants depend on fossil fuel as a source of energy. Therefore, finding a more efficient system is becoming more crucial than ever, especially with the depletion of fossil fuel and increment of the GHG emissions. One of the potential efficient power plant technologies is a trigeneration thermal system. A trigeneration system is defined as combined cooling, heating, and power production simultaneously from the same energy source [1]. In a trigeneration system, the waste heat from, for instance, an internal combustion engine is used for heating and cooling energy demands through a heat exchanger and single-effect absorption chiller, respectively.

* Corresponding author. Mechanical and Mechatronics Engineering Department, University of Waterloo, Waterloo, ON, Canada. Tel.: þ1 613 8843322; fax: þ1 613 5260583. E-mail addresses: [email protected] (F.A. Al-Sulaiman), fhamdullahpur@ uwaterloo.ca (F. Hamdullahpur), [email protected] (I. Dincer). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.06.003

One of the potential prime movers for trigeneration plants which has not received attention by researchers is (ORC) ORC (organic Rankine cycle) [1]. The ORC is characterized by its ability to utilize a low- or medium-temperature heat source through its evaporator to produce electrical power. The waste heat from the ORC is usually lost through its condenser. This heat can be utilized by replacing the condenser with a heat exchanger to obtain heating energy and with a single-effect absorption chiller to obtain cooling energy. With the utilization of the waste heat, as in this case described above, the system is called trigeneration system. As it can be noticed from this description and as discussed later, with the utilizing of the waste heat, the thermal efficiency of the system will increase considerably. Several studies have examined different prime mover for trigeneration plants. A comprehensive review based on trigeneration plants prime movers was conducted by Al-Sulaiman et al. [1]. In their study, it was observed that there are several studies that used internal combustion engines as prime movers; however, there are fewer studies on gas turbines and microturbines. Alternatively, there is less research on the other three prime movers: fuel cells, Rankine cycles, and Stirling engines. In terms of analysis type, most of the studies have been conducted using energy and economic analyses. In contrast, less attention has been given to

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environmental, exergy, and exergoeconomic analyses of trigeneration plants. Lai et al. [2] discussed different process modifications to enhance a trigeneration system feasibility and flexibility, and demonstrated some design considerations of a trigeneration system such that it can satisfy the periodical demand variations. In another study, Schicktanz et al. [3] conducted sensitivity analysis to examine the influence of some selected parameters on the primary energy savings and economics of combined heating and power and combined cooling and power system modes. The authors recommended some minimum operation hours for a trigeneration system to be economic. A few studies examined the feasibility of using trigeneration plants based on ORC, e.g [4e6]. Al-Sulaiman et al. [4] examined the feasibility of using trigeneration plant based on ORC and solid oxide fuel cells. It was found that the maximum net electrical efficiency is 46% and when trigeneration is used the trigeneration efficiency increases to 74%. In another study, Rentizelas et al. [5] studied the potential economic of using two trigeneration plants. The first trigeneration plant is based on an ORC and the second one is based on a gasification subsystem. In their study, it was shown that the gasification option is a better option since it has a higher electrical efficiency. In a different study, Al-Sulaiman et al. [6] studied a trigeneration system using biomass combustor and ORC. The authors found that the electrical energy efficiency is around 13%; alternatively, when trigeneration is used the efficiency increases to approximately 88%. In the current study, a comparison of three potential trigeneration systems, under thermoeconomic optimization conditions, is conducted through energy analysis. That is, in this study, the energy analysis is conducted after identifying thermoeconomic optimized conditions of some selected operating parameters. The potential

trigeneration systems considered are SOFC-trigeneration, biomasstrigeneration, and solar-trigeneration systems. These three systems are distinguished by their heat input source as described later. The systems considered are modeled to be able to produce 500 kW of electricity. The SFOC-trigeneration and biomass-trigeneration systems considered in this study are different from [4,6] by considering the energy analysis of these two systems under thermoeconomic optimization conditions. This study compares the performance of these three systems considering key output parameters: energy efficiency, net electrical power, electrical to heating ratio, electrical to cooling ratio, and GHG emissions. This study helps in identifying which system under specific operating conditions has a better energetic performance as compared to the other two systems all under thermoeconomic optimization conditions.

2. Systems description ORC can be used as a prime mover for a trigeneration plant or it can be integrated with another prime mover. In this study, three systems are examined. These systems are combined SOFC with ORC, combined biomass combustor with ORC, and combined solar collectors with ORC. Schematic diagrams of these systems are shown in Figs. 1e3. SOFC has a potential application in the future since it has relatively high efficiency and low air pollution as compared with conventional fossil fuel systems. Therefore, a trigeneration system based on SOFC and ORC is selected. Biomass and solar energy are renewable energy sources that can be integrated with ORCs. Recent potential research that examines the feasibility of these two renewable energy sources is on ongoing. Therefore, trigeneration systems based on biomass and solar collectors are selected in this study.

Fig. 1. Schematic of the SOFC-trigeneration system.

F.A. Al-Sulaiman et al. / Energy 36 (2011) 5741e5754

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Fig. 2. Schematic of the biomass-trigeneration system.

The three systems examined consist of an ORC as a prime mover to produce the electrical power, a single-effect absorption chiller to supply the cooling load, and a heat exchanger to supply the heating load. It can be noticed that in these systems there are two cycles: ORC and cooling chilling cycles. The flow stream in the ORC is described first and then the flow stream in the chilling cycle. The flow in the ORC according to Fig. 1 is described as follows. The fluid exits the desorber (state 1) as saturated liquid. Next, the pump increases the pressure of the saturated liquid (state 2). Then, the working fluid enters the evaporator in a liquid state and exits as vapor (state 3). Next, the organic fluid expands through the turbine to produce the mechanical energy. The mechanical energy is used to rotate the electrical generator which is connected to the turbine shaft. Then, the working fluid exits the turbine (state 4) and supplies heat to the heating-process heat exchanger. The heatingprocess heat exchanger rejects heat to supply the heating load. After that, the organic fluid enters the desorber (state 5) as saturated vapor. The desorber absorbs heat to supply the cooling load for the single-effect absorption chiller. Then, the organic fluid exits from the desorber again as saturated liquid (state 1). The rejected heat to the desorber is the input energy to the single-effect absorption chiller. The flow streams transport between the components of this chilling cycle as either water or a mixture of lithium-bromide (LieBr) and water. As a result of the input heat into the desorber, water evaporates from the mixture of the LieBr and water, and enters the condenser (state 6). In the condenser, the heat is rejected. Therefore, the water cools down and exits the condenser as saturated liquid (state 7). After that, the

water is throttled and enters the evaporator (state 8) at low temperature. The evaporator supplies the cooling load. Next, water exits the evaporator and enters the absorber (state 9). The water mixes with the mixture of the LieBr and water. The mixture exits the absorber (state 10) and is pumped to the heat exchanger (state 11). Then, the mixture exits from the heat exchanger and enters the desorber (state 12). The mixture is heated in the desorber and part of the water into the mixture evaporates and exits the desorber (state 6). Next, as a result of the water evaporation, the mixture exits the desorber with a higher LieBr concentration into the mixture to enter the heat exchanger (state 13) to gain heat. After that, it exits the heat exchanger (state 14) and is throttled to the absorber (state 15). The input data for the ORC and single-effect absorption chiller is given in Table 1. Since there is a change in the solar radiation in 24 h of operation, the solar-trigeneration system considered in this study is assumed to operate in three modes. These three modes are selected based on the change in solar radiation densities, as presented in [7] for full tracking of the solar collectors for the sun. The first mode is from 6 am to 8 am and from 4 pm to 6 pm. In this mode, only the solar collectors are working and there is no energy storage. That is, all the solar energy collected is used to operate the solar-trigeneration system. This mode is called the solar mode. The second mode is from 8 am to 4 pm. In this mode, part of the solar energy is used to operate the solar-trigeneration system and the other part of the solar energy is stored in the hot storage tank. This mode is called the solar and storage mode. The third mode is from 6 pm to 6 am. In this mode, only the storage system is working. In this mode, the

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Fig. 3. Schematic of the solar-trigeneration system.

input energy into the solar-trigeneration system is from the energy stored in the hot tank storage. This mode is called the storage mode.

and, thus, high ORC efficiency is n-octane. Therefore, this fluid is selected for the ORC [8,9]. The properties of n-octane are shown in Table 2.

3. Fluid selection for the organic rankine cycle 4. Model development Many types of organic fluids can be used for ORC. However, only the organic fluids that operate with a high temperature are efficient for ORC. A typical working fluid that has a high critical temperature Table 1 Input data for the ORC and single-effect absorption chiller. ORC

Chilling cycle

Organic cycle turbine efficiency Organic cycle pump efficiency Effectiveness of the organic cycle evaporator Baseline turbine inlet pressure Organic pump inlet temperature Electrical generator efficiency Electrical motor efficiency ORC turbine inlet temperature (baseline) ORC pump inlet pressure (baseline) Overall heat transfer coefficient of the desorber Overall heat transfer coefficient of the condenser Overall heat transfer coefficient of the evaporator Overall heat transfer coefficient of the absorber Effectiveness of solution heat exchanger

80% 80% 85% 2000 kPa 365 K 95% 95% 549 K 36 kPa 70 kW/K 80 kW/K 95 kW/K 75 kW/K 70%

Several assumptions are made to carry out the analysis. It is assumed that the system is at steady state and pressure change is neglected except in the pumps, blowers, organic cycle turbine and valves. Other assumptions are discussed below. Table 2 Thermodynamic properties of n-octane. Substance name

n-octane

Mol. formula Mol. weight Freeze point (oC) Boiling point (oC) Crit. temp. (oC) Crit. pressure (bar) Crit. volume (cm3/mol) Crit. density (g/cm3) Crit. compressibility Accentric factor

C8H18 114.231 56.77 125.68 295.68 24.86 492.1 0.2322 0.259 0.396

Source: [23].

F.A. Al-Sulaiman et al. / Energy 36 (2011) 5741e5754

4.1. Single-effect absorption chiller modeling

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The overall electrochemical equilibrium equation is

The performance analysis applied to the single-effect absorption chiller is similar to that used by Herold et al. [10]. The assumptions used in the single-effect absorption chiller are  Pure water is used as a refrigerant (states 6e9).  The liquid states at states 7, 10, and 13 are considered saturated liquid.  The water at state 9 is saturated vapor.  The pressures in the desorber and condenser are equivalent.  The pressures in the evaporator and the absorber are equivalent. The analysis of the single-effect absorption chiller is validated with Herold et al. [10], as shown in Fig. 4. The figure shows the coefficient of performance and evaporator heat transfer versus the desorber inlet temperature. The figure shows a very good agreement between the current single-effect absorption chiller model and the Herold et al. model. 4.2. SOFC modeling In this subsection the SOFC modeling is presented. The assumptions for this SOFC model are [11]  Both the air and fuel flows have the same temperature at the inlet of the SOFC.  Both the air and fuel flows have the same temperature at the exit of the SOFC.  The air that enters the SOFC consists of 79% N2 and 21% O2.  The gas mixture at the exit of the fuel channel is at chemical equilibrium.  The radiation heat transfer between gas channels and solid structure is negligible.  Contact resistances are negligible. The chemical equilibrium equations that occur within the anode and cathode of the fuel cell are

CH4 þ H2 O4CO þ 3H2

1 H2 þ O2 /H2 O 2

The cell voltage produced by the cell is the difference between the reversible cell voltage and the sum of the voltage loss. It is defined as

Vc ¼ VN  Vloss

(2)

0.8

16

(4)

where Vc, VN and Vloss are cell voltage, reversible cell voltage, and voltage loss, respectively. The equation of the reversible cell voltage is derived from Nernst equation and is defined as

DGf

VN ¼ 

2$F

 R$


TFC;exit xH2 O;27 $ln pffiffiffiffiffiffiffiffiffiffiffiffi 2$F xH2 ;27 $ xO2 ;19

(5)

where Gf is the Gibbs free energy, R is the universal gas constant (8.314 J/[mole-K]), and F is the Faraday constant (96,485 coulombs/ [g-mole]). The Vloss (voltage loss) is the sum of three voltage losses, which include the ohmic, activation polarization, and concentration losses. That is, the voltage loss is defined as

Vloss ¼ Vohm þ Vact þ Vcont

(6)

where Vohm is defined by Bossel [12] as follows:

Vohm ¼ ðRcontact þ ra $La þ rc $Lc þ re $Le þ rint $Lint Þ$j

(7)

where R is resistivity contact, j is current density, r is the electrical resistivity of cell components, and L is thickness of a cell component. The activation polarization losses are defined by Kim [13] as follows:

Vact ¼ Vact;a þ Vact;c

(8)

Vact;a ¼



R$TFC;exit j $ sin h1 2$joa F

(9)

Vact;c ¼



R$TFC;exit j $ sin h1 F 2$joc

(10)

(1)

CO þ H2 O4H2 þ CO2

(3)

The concentration voltage loss is defined by Chan et al. [14] as follows:

12

0.75

COP

10 0.7

8 6 COP, model (Herold et al.) .COP, current study Q . ev, model (Herold et al.) Q ev, current study

0.65

0.6 60

70

80

90

100

110

4

Evaporator heat transfer (kW)

14

2

Vcont ¼ Vcont;a þ Vcont;c

Vcont;a ¼ 


R$TFC;exit R$TFC;exit PH2 ;27 $j $lnð1  j=jas Þ þ $ln 1 þ PH2 O;27 $jas 2$F 2$F (12)


Vcont;c ¼ 

 R$TFC;exit $lnð1  j=jcs Þ 4$F

(13)

where jas is the exchange current density of anode and jcs is the exchange current density of cathode and defined as

0 120

o

Desorber inlet temperature ( C) Fig. 4. Validation of the single-effect absorption chiller model as compared to Herold et al. model; COP and evaporator heat rate versus desorber inlet temperature.

(11)

jas

2$F$PH2 ;27 $Daeff   R$TFC;exit $La   ¼ 1000000 cm3 =m3

(14)

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F.A. Al-Sulaiman et al. / Energy 36 (2011) 5741e5754 Table 3 Molar flow rates of the gases.

Table 4 Input data for the SOFC-trigeneration system.

n_ H2 O;26 ¼ 2:5$a n_ H2 O;26 ¼ 2:5$a n_ CH4 ;26 ¼ a n_ H2 ;27 ¼ 3$a þ b  c n_ CO;27 ¼ a  b n_ CO2 ;27 ¼ b n_ H2 O;27 ¼ 1:5$a  b þ c n_ O2 ;u ¼ c=2 n_ O2 ;18 ¼ n_ O2 ;19 þ n_ O2 ;u n_ O2 ;19 ¼ c=2$ð1=UO2  1Þ c n_ N2 ;19 ¼ 79=21$ 2$UO2 n_ N2 2;18 ¼ n_ N2 ;19 c ¼ ð3$a þ bÞ$Uf n_ anode;exit ¼ n_ H2 ;27 þ n_ CO;27 þ n_ CO2 ;27 þ n_ H2 O;27 n_ cathode;exit ¼ n_ O2 ;19 þ n_ N2 ;19 n_ anode;inlet ¼ n_ H2 O;26 þ n_ CH4 ;26 n_ cathode;inlet ¼ n_ O2 ;18 þ n_ N2 ;18

DCeAC converter efficiency Fuel utilization factor Active surface area Base current density Exchange current density of anode Exchange current density of cathode Effective gaseous diffusivity through the anode Effective gaseous diffusivity through the cathode Thickness of the anode Thickness of the cathode Thickness of the electrolyte Thickness of the interconnect Pressure of the cell Base inlet temperature to the SOFC Temperature difference between the inlet and the exit of the SOFC

95% 0.85 100 cm2 0.75 A/cm2 0.65 A/cm2 0.25 A/cm2 0.2 cm2/s 0.05 cm2/s 0.05 cm 0.005 cm 0.001 cm 0.3 cm 101. 3 kPa 1000 K 100 K

Source: [11].

The net overall electrical power is defined as



jcs ¼

_ net ¼ W _ _ _ _ W FC;stack;ac þ hmotor W ot  W op =hmotor  W sp =hmotor _ =h _ =h _ wp =h W W W ð22Þ

4$F$PO2;19 $Dceff   P00  PO2;19 $R$TFC;exit $Lc P00   1000000 cm3 =m3

b1

(15)

where the subscripts ohm, act. cont, a, c, e, and int indicate ohmic, activation, concentration, anode, cathode, electrolyte, and interconnect, respectively. The symbol Dceff is the effective gaseous diffusivity through the cathode and Daeff is the effective gaseous diffusivity through the anode. The electrical sensitivities are defined as [12]





re ¼ C1e $exp C2e =TFC;exit 

1



(16)

ra ¼ C1a =TFC;exit $exp C2a =TFC;exit 



rc ¼ C1c =TFC;exit $exp C2c =TFC;exit 

1

1



rint ¼ C1int =TFC;exit $exp C2int =TFC;exit

1

(17) (18) (19)

where C1e  C2int are constants defined in [12]. The model used to carry out the equilibrium equations of the SOFC is based on a validated model developed by Colpan et al. [11], assuming the methane is fully converted as presented later in this subsection. The molar conversion rates of Equation (1e3) are a, b, and c, respectively. The molar flow rates of the gases are derived next. The molar flow rates _ of the reactions Equation (1e3) are given in Table 3. In this table, n, U_ f , and U_ O2 are molar flow rate, fuel utilization ratio, and oxygen utilization ratio, respectively. 4.2.1. Energy modeling of the SOFC-trigeneration system In this subsection the energy modeling of the SOFCtrigeneration system is presented. The input data for the SOFC subsystem is given in Table 4. The total inlet heat energy of the SOFC-trigeneration system is defined as

Q_ in ¼ NFC $n_ CH4 ;26 $LHVCH4 þ Q_ boiler

(20)

where NFC is the total number of the fuel cells, n_ CH4 ;26 is the methane molar flow rate, LHVCH4 lower heating value of the methane, and Q_ boiler is heat input from the auxiliary boiler. The stack AC power of the fuel cell is defined as

_ _ W FC;stack;ac ¼ hinverter $W FC;stack

(21)

motor

b2

motor

motor

_ is the power and the subscripts g, ot, op, wp, b1, b2, and sp where W indicate generator, ORC turbine, ORC pump, water pump, air blower, methane blower, and solution pump, respectively. 4.2.2. Validation of the SOFC model The experimental data with methane as fuel as presented by Tao et al. [15] are used for validating the current model. The validation is shown in Table 5. This table shows the variation of both the cell voltage and power density with the current density. It can be noticed that the model has a good agreement with the experimental work with an error less than 7%. 4.3. Energy modeling of the biomass-trigeneration system In this subsection energy modeling of the biomass-trigeneration system is presented. The characteristic of the biomass fuel used is given in Table 6. The total inlet heat rate energy of the biomasstrigeneration system is defined as

_ biomass $LHVbiomass Q_ i ¼ m

(23)

_ biomass is the mass flow rate of the biomass fuel and where m LHVbiomass is the lower heating value of the biomass and defined as [16]

LHVbiomass ¼ HHVbiomass  226:04$WH  25:82$Mw

(24)

where Mw is the moisture content in the biomass fuel and HHVbiomass is the higher heating value of the biomass and defined, using Dulong’s formula [17], as

HHVbiomass ¼ 338:3$WC þ 1443$ðWH  WO =8Þ þ 94:2$WS

(25)

Table 5 Validation of the current SOFC model with the experimental data by Tao et al. [15]. Current density (A/cm2)

Cell voltage (V) (model)

Cell voltage (V) (Exp [15])

Power density (W/m2) (model)

Power density (W/m2) (Exp. [15])

0.2 0.3 0.4 0.5 0.6

0.788 0.714 0.642 0.57 0.50

0.76 0.68 0.62 0.57 0.52

0.158 0.214 0.257 0.285 0.299

0.15 0.21 0.26 0.295 0.315

F.A. Al-Sulaiman et al. / Energy 36 (2011) 5741e5754

where hc,ca is the convection heat coefficient between the cover and the ambient and defined as

Table 6 Biomass fuel characteristics. Type of biomass fuel Moisture content in biomass (%wt) Ultimate analysis WC WH WO WS

Pine sawdust 10% (%wt dry basis) 50.54% 7.08% 41.11% 0.57%

Source: [24].

where WC, WH, WO and WS are the dry-biomass weight percentages of carbon, hydrogen, oxygen and sulfur, respectively and their values are listed in Table 6. The net electrical power of the biomasstrigeneration system is defined as

_ net ¼ h $W _ ot  W _ op =h _ W g motor  W sp =hmotor

(26)

4.3.1. Solar collectors In this subsection, the energy analysis of the parabolic trough solar collectors (PTSC) is presented. The energy analysis of the PTSC in this section is based on the equations presented in [7,18]. This energy analysis is validated with these two references and with the experimental study by Dudley et al. [19]. The validation with [19] is presented at the end of this section. The useful power from the collector is defined as

_ r $ Cpr;o $Tr;o  Cpr;i $Tr;i Q_ u ¼ m



   Q_ u ¼ Aap $FR $ S  Ar =Aap $UL $ Tr;i  T0

(28)

where Aap is the collector aperture area, FR is the heat removal factor, S is the absorbed radiation by the receiver, Ar is the receiver area, and UL is solar collector overall heat loss coefficient. The aperture area is defined as

  ¼ w  Dc;o $L

(29)

where w is the collector width, Dc,o is the cover outer diameter, and L is the collector length. The absorbed radiation by the receiver is defined as

S ¼ Gb $hr

(30)

where Gb is the solar radiation in W=m2 and hr is the receiver efficiency. The heat removal factor is defined as



 _ r $Cpr m Ar $UL $F1 FR ¼ $ 1  exp  _ r $Cpr m Ar $UL

(31)

where Cpr is the specific heat of the oil in the receiver and F1 is the collector efficiency factor and defined as

F1 ¼ Uo =UL

(32)

The solar collector heat loss coefficient between the ambient and receiver is defined as


UL ¼

Ar   þ 1=hr;cr hc;ca þ hr;ca $Ac

(34)

where Nus, Kair, and Dc,o are Nusselt number, thermal conductivity of the air, and outer diameter of the cover, respectively. The radiation heat coefficient is defined as





3cv $s$ðTc þ Ta Þ$ Tc2 þ Ta2



(35)

The subscripts c and a indicate the cover and ambient, respectively. The symbol T,3cv, and s are the temperature, emittance, and StefaneBoltzmann constant, respectively. The radiation heat coefficient between the cover and receiver is





hr;cr ¼

!

2 s$ Tc þ Tr;av $ Tc2 þ Tr;av 1=3r þ Ar =Ac $ð1=3cv  1Þ

(36)

The overall heat coefficient is defined as

!1
  Dr;o Dr;o 1=UL þ þ $ln Dr;o =Dr;i hc;r;in $Dr;i 2$kr

Uo ¼

(37)

where hc,r,in is defined as

hc;r;in ¼

Nusr $kr Dr;i

(38)

(27)

where the subscripts r, i, and o indicate receiver, inlet, and outlet, _ r is the mass respectively. The symbol Q_ u is the useful power and; m flow rate of the oil in the receiver (pipe). In addition, this power can be calculated from

Aap

  hc;ca ¼ Nus$kair =Dc;o

hr;ca ¼



5747

where the subscripts r indicates the receiver. The cover average temperature can be calculated using this equation

Tc ¼

  hr;cr $Tr;av þ Ac =Ar $ hc;ca þ hr;ca $T0   hr;cr þ Ac =Ar $ hc;ca þ hr;ca

The amount of the solar radiation that falls on the collector is calculated using this equation

Q_ solar ¼ Aap $FR $S$Colr

4.3.2. Energy modeling of the solar-trigeneration system The overall performance assessment equations of the solartrigeneration system considered are presented in this section. The input data for the solar subsystem is given in Table 7. The input total heat energy of this system is defined as

Q_ in ¼ Q_ u

Table 7 Input data for the solar-trigeneration plant. w L

hr

Gba Gbb

3r

Colnc Colrc _ rc m Dr,ic

5.76 m [25] 12.27 m [25] 0.765 [25] 0.5 kW/m2 [7] 0.85 kW/m2 [7] 0.92 [26] 50 7 8 kg/s 0.045 m

During low sun radiation. During high sun radiation. Based on the thermoeconomic optimization results. b

(33)

(40)

where Colr is the total number of the solar collectors rows.

a

1

(39)

c

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F.A. Al-Sulaiman et al. / Energy 36 (2011) 5741e5754

The net electrical power is defined as

_ net ¼ h $W _ ot  W _ op =h _ _ W g motor  W sp =hmotor  W sol;p =hmotor _ _ W ð41Þ st1;p =hmotor  W st2;p =hmotor where the subscripts sol, p, st1, p, and st2, p indicate solar pump, thermal storage pump 1, and thermal storage pump 2, respectively. 4.3.3. Validation of the solar collectors model In this subsection the validation of the solar collectors model is presented as shown in Table 8. The model is validated with Dudley et al. [19]. The table shows the variation of the heat loss for both the model and the experiment data under different absorber fluid temperature. The baseline simulation of the solar-trigeneration system in this study has an absorber fluid temperature of less than 200 oC above ambient temperature. Thus, the model has a good agreement with the experimental results by [19], as demonstrated in this table.

_ net =Q_ hel ¼ W i

(42)

The efficiency of the heating cogeneration is defined as

_ net þ Q_ W h ¼ Q_

where CO2, el indicates the emissions when there is only electrical power production in the system considered. That is, the emissions of CO2 in kg per MWh of the net electrical power produced. In contrast, the subscript CO2, tri indicates the emissions when there is trigeneration production in the system considered. That is, the emissions of CO2 in kg per MWh of the total trigeneration power (cooling, heating and electrical). The efficiency of trigeneration is defined as

htri ¼

_ net þ Q_ þ Q_ W ev h Q_

(43)

where Q_ h is the heating power and the subscript cog, h indicates the heating cogeneration. The heating power is defined as

(44)

_ hp is the mass flow rate of the heating process, and hhp,1 where m and hhp,2 are the specific enthalpy of the water at the inlet and exit of the heating-process heat exchanger, respectively. The efficiency of the cooling cogeneration is defined as

_ net þ Q_ W ev Q_

(45)

i

where the subscripts cog, c and ev indicate the cooling cogeneration and cooling energy produced by the system through the evaporator, respectively. The cooling power of the evaporator is defined as

  _ 8 $ðh9  h8 Þ ¼ m _ ev $ hev;1  hev;2 Q_ ev ¼ m

(46)

where hev,1 and hev,1 are the specific enthalpy of the water at the inlet and exit of the cooling evaporator, respectively. The CO2 emissions when there is only electrical power is defined as

_ net $3600 _ CO2 =W EmiðCO2 ; elÞ ¼ m

(49)

i

The electrical to heating ratio is defined as

(50)

_ net =Q_ rel;c ¼ W ev

(51)

5. Results and discussion

i

_ hp $ hhp;2  hhp;1 Q_ h ¼ m

(48)

The electrical to cooling ratio is defined as

The net electrical efficiency of the system is defined as

hcog;c ¼

  _ net þ Q_ þ Q_ $3600 _ CO2 = W EmiðCO2 ; triÞ ¼ m ev h

_ net =Q_ rel;h ¼ W h

4.4. Overall system equations

hcog;h

On the other hand, the emissions when there is trigeneration is defined as

(47)

Table 8 Validation of the current model as compared with Dudley et al. [19]: heat losses change with the average temperature above the ambient of the fluid inside the absorber. Taam (K)

Heat loss (Model)

Heat loss (Exp. [19])

100.6 149.1 196.7 245.8 293.3

8.7 19.3 34.2 53.0 75.5

10.6 19.3 30.6 45.4 62.9

This section discusses the results of the energy modeling of the three systems considered under thermoeconomic optimization conditions. That is, the thermoeconomic optimization was conducted first, where the thermoeconomic optimized values of some selected parameters are identified. Then the energy analysis, as presented in this study, is conducted considering these optimized values. The objective of the optimization was to minimize the exergetic cost of the final product (combined cooling, heating and power). 5.1. Effect of the ORC pump inlet temperature The effects of the ORC pump inlet temperature variation on the efficiency, electrical power, electrical to cooling ratio, electrical to heating ratio, and GHG emissions are illustrated in Figs. 5e10. The subscripts of the parameters used in these figures are explained next. The subscript SOFC indicates the trigeneration system based on the solid oxide fuel cells. The subscript BM refers to the trigeneration system based on the biomass combustor. The subscript So indicates the trigeneration system based on the solar subsystem. The subscripts so, so-st, and st refer to the solar, solar and storage, and storage modes for the solar-trigeneration system, respectively. The subscripts el and tri indicate electrical and trigeneration, respectively. Fig. 5 presents the electrical efficiencies of the three systems considered. This figure demonstrates that as the ORC pump inlet temperature increases, the electrical efficiency decreases. This decrement is owing to the decrease in the temperature difference between the maximum and minimum temperatures in the ORC. This figure illustrates that the electrical efficiency of the SOFCtrigeneration system is the highest because it has another subsystem that has high efficiency, e.g. the SOFC subsystem. The efficiency of this system drops from almost 19% at 345 K to 17% at 380 K. In contrast, the electrical efficiency of the biomasstrigeneration system drops from almost 15% at 345 K to around 11% at 380 K. On the other hand, the electrical efficiency of the solar-trigeneration system for the solar mode is close to the

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Fig. 5. Effect of the ORC pump inlet temperature on the electrical efficiency.

Fig. 7. Effect of the ORC pump inlet temperature on the net electrical power.

electrical efficiency of the biomass-trigeneration system. However, the electrical efficiencies of the solar and storage, and storage modes of the solar-trigeneration system are noticeably lower. This drop is owing to the decrease in the amount of the heat input to the ORC during these two modes. During the solar and storage mode a major portion of the collected energy from the solar collectors is stored in the storage tank. Therefore, during this mode the efficiency is lower as compared to the solar mode. The electrical efficiency of the solar and storage mode drops from 7% at 345 K to 6% at 380 K. The efficiency of the storage mode drops from 6% at 345 K to 5% at 380 K. The electrical-trigeneration efficiency is presented in Fig. 6. This figure demonstrates that the efficiency improves significantly when trigeneration is used. This figure also shows that the

biomass-trigeneration and solar mode of the solar-trigeneration system have the highest trigeneration efficiency, which is around 90%, whereas the SOFC-trigeneration system has a lower trigeneration efficiency, 76%. The SOFC-trigeneration system has two devices that produce electrical power, the SOFC and the electrical generator, where most of the electricity is produced by the SOFC; because of this, less energy is needed for the ORC to produce the remaining portion of the electricity as compared to the other two systems. Thus, the amount of the heat that enters the ORC is lower. As a result of the lower heat, lower waste heat is available for heating and cooling. Thus, the trigeneration efficiency for the SOFC is lower than the other two systems. The trigeneration efficiencies of the solar and storage, and storage modes of the solartrigeneration system are less than that of the solar mode, since

Fig. 6. Effect of the ORC pump inlet temperature on the trigeneration efficiency.

Fig. 8. Effect of the ORC pump inlet temperature on the electrical to cooling ratio.

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Fig. 9. Effect of the ORC pump inlet temperature on the electrical to heating ratio.

less energy is available for these two modes, as discussed above. The trigeneration efficiency of the solar and storage mode is around 45% and for the storage mode is around 41%. Fig. 7 illustrates the variation of the net electrical power as the ORC inlet temperature changes. The electrical power decreases as this temperature increases because the operating temperature range in the ORC is reduced and, thus, less power can be obtained from the turbine. It can be observed that the electrical power during the solar mode for the solar-trigeneration system is the highest. This power can be reduced by storing part of the collected energy during the operation of this mode. The electrical power in this mode changes from 830 kW at 345 K to 600 kW at 380 K. The electrical power during the solar and storage mode is 645 kW at 345 K and decreases to 510 kW at 380 K. The electrical power of the storage mode decreases from 575 kW at 345 K to 420 kW at 380 K.

Alternatively, the electrical power of the biomass-trigeneration system decreases from 640 kW at 345 K to 440 kW at 380 K. It can be noticed that the electrical power of the SOFC-trigeneration system is less sensitive to the change in this temperature as compared to the other two systems. The reason of this reduced sensitivity is because major part of the electrical power is produced from the SOFC subsystem. Hence, less power is produced by the ORC where the change in this temperature has a direct effect on the electrical power produced. Fig. 8 presents the electrical to cooling ratio of the three systems considered. This figure shows that the electrical to cooling ratio is sensitive to the change in the ORC pump inlet temperature for the three systems. The degree of sensitivity is related mainly to the sensitivity of the electrical power produced by these three systems as this temperature varies. The electrical to cooling ratio of the solar mode of the solar-trigeneration system is the highest while the electrical to cooling ratio of the SOFC-trigeneration system is the lowest. For the SOFC-trigeneration system, this ratio varies from 6.3 at 345 K to 2.7 at 380 K. However, for the biomass-trigeneration system, this ratio varies from 6.7 at 345 K to 2.2 at 380 K. Alternatively, for the solar-trigeneration system, this ratio varies from 8.7 at 345 k to 3.1 at 380 K for the solar mode, from 6.7 at 345 K to 2.6 at 380 K for the solar and storage mode, and from 6 at 345 K to 2.1 at 380 K for the storage mode. Fig. 9 shows the electrical to heating ratio of the three systems considered. This figure illustrates that as the ORC pump inlet temperature increases, this ratio decreases. This decrement is attributed to the decrease in electrical power as this temperature decreases. This figure shows that this ratio is the highest for the SOFC-trigeneration system. This high ratio is obtained since most of the electrical power is produced from the SOFC subsystem for this trigeneration system. Thus, less electrical power is produced by the ORC and, hence, less heating energy is available from this system. This ratio varies from 0.34 at 345 K to 0.33 at 380 K for the SOFCtrigeneration system. On the other hand, for the other cases this ratio varies from around 0.19 at 345 K to 0.16 at 380 K. Fig. 10 demonstrates the emissions of CO2 in kg per MWh of electrical and trigeneration powers. This figure presents the emissions for the SOFC and biomass-trigeneration system. This figure shows that the emissions per MWh of electrical power are significantly high. Alternatively, when trigeneration is used, the emissions per MWh of trigeneration drop significantly. This figure reveals that the emissions of CO2 per MWh of electrical power for both systems increase as the ORC pump inlet temperature increases. This increase is attributed to the drop in the electrical efficiencies of these two systems as this temperature increases. The CO2 emissions per MWh of electrical power from the biomasstrigeneration system increases from 2500 kg/MWh at 345 K to 3200 kg/MWh at 380 K. In contrast, the emissions for the SOFCtrigeneration system increase from 1750 kg/MWh at 345 K to 1900 kg/MWh at 380 K for the electrical power production. Alternatively, when trigeneration is used, the emissions drop significantly to around 400 kg/MWh for these two systems. 5.2. Effect of the turbine inlet pressure

Fig. 10. Effect of the ORC pump inlet temperature on the CO2 emissions.

The effect of the turbine inlet pressure variation on the performance of the three systems is shown in Figs. 11e16. The range of turbine inlet pressure [20e22] considered here are taken from the literature. The upper values of the pressure selected are relatively higher than the values available in the literature because of the potential improvements in the ORC design. Fig. 11 presents the effect of the pressure variation on the electrical efficiency. It can be noticed that the electrical efficiency of the SOFC-trigeneration system is more sensitive to the pressure variation as compared to

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Fig. 11. Effect of the turbine inlet pressure on the electrical efficiency.

Fig. 13. Effect of the turbine inlet pressure on the net electrical power.

the other two systems. The SOFC-trigeneration system is sensitive to the pressure variation since the size of the ORC where the power produced by the turbine and mass flow rate of the working fluid is smaller than the other two systems. The electrical efficiency of the SOFC-trigeneration system increases from 18% at 345 K to 19.5% at 380 K. Alternatively, the electrical efficiency of the biomasstrigeneration system is around 12.5%. On the other hand, the electrical efficiency of the solar-trigeneration system is around 13% for the solar mode, 6.5% for the solar and storage mode, and 5.5% for the storage mode. Fig. 12 presents the effect of the turbine inlet pressure on the trigeneration efficiency of the systems considered. It can be noticed that the effect of varying this pressure is negligible on the trigeneration efficiencies of all three systems. Therefore, these systems could be operated at low pressure, since this will result in cost

savings. It is observed that the trigeneration efficiency of the SOFCtrigeneration system is lower than the biomass and solar (solar mode) systems; unlike the electrical efficiency of the SOFC which was the highest. The reason for that was discussed above. The trigeneration efficiency of the biomass-trigeneration system is approximately 90% while this efficiency is around 76% for the SOFCtrigeneration system. The trigeneration efficiencies of the solartrigeneration system are around 90% for the solar mode, 46% for the solar and storage mode, and 41% for the storage mode. Fig. 13 illustrates the effect of the turbine inlet pressure variation on the net electrical power. This figure shows that as the pressure increases, the electrical power of the SOFC-trigeneration system increases. It increases from 560 kW at 2000 kPa to 610 kW at 7000 kPa. Nevertheless, the electrical power of the biomasstrigeneration system decreases from 530 kW at 2000 kPa k to

Fig. 12. Effect of the turbine inlet pressure on the trigeneration efficiency.

Fig. 14. Effect of the turbine inlet pressure on the electrical to cooling ratio.

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increase is attributed to the relative small size of the ORC and the mass flow rate of the working fluid in the ORC, as mentioned above. This ratio increases from 0.33 at 2000 kPa to 0.38 at 7000 kPa. The electrical to heating ratio for the other two systems is around 0.18. Fig. 16 illustrates the effect of pressure variation on the emissions of CO2 in kg/MWh. This figure reveals that the emission of CO2 is insignificant to the pressure change. This figure also shows that the emissions, when there is only electrical power production, are significantly high. However, when trigeneration is used, the emissions drop significantly. The emissions of the biomass-trigeneration system increase from 2900 kg/MWh at 2000 kPa to 3050 kg/MWh at 7000 kPa for the electrical power production. Conversely, when trigeneration is used, the emissions drop considerably to around 400 kg per MWh of trigeneration power. In contrast, the emissions for the SOFC-trigeneration system are around 1700 kg/MWh while, when trigeneration is used, the emissions drop significantly to around 400 kg/MWh. Note that the emissions of the SOFCtrigeneration system are relatively high since it has an auxiliary biomass boiler to heat up the inlet fluids of the SOFC subsystem. 6. Conclusion Fig. 15. Effect of the turbine inlet pressure on the electrical to heating ratio.

480 kW at 7000 kPa. Alternatively, the electrical power of the solartrigeneration system increases from 700 kW at 2000 kPa to 730 kW at 7000 kPa for the solar mode. The electrical power of the solar and storage mode is around 520 kW, whereas it is around 470 kW for the storage mode. Fig. 14 illustrates the electrical to cooling ratio variation as the pressure varies. This figure reveals that the effect of the pressure variation on this ratio is insignificant. This electrical to cooling ratio is around 3.7 for the SOFC-trigeneration system and 3.1 for the biomass-trigeneration system. Regarding the solar-trigeneration system, this ratio is around 4.5 for the solar mode, 3.5 for the solar and storage mode, and 3 for the storage mode. Fig. 15 presents the effect of pressure on the electrical to heating ratio. This figure shows that as the pressure increases this ratio increases noticeably only for the SOFC-trigeneration system. This

Fig. 16. Effect of the turbine inlet pressure on the CO2 emissions.

In this study, energetic performance comparisons of the three trigeneration systems considered are conducted. The three systems are SOFC, biomass, and solar-trigeneration systems. The main findings from this comparative study are summarized below.  The SOFC-trigeneration system has the highest electrical efficiency among the three systems. However, the trigeneration efficiencies of the biomass-trigeneration system and solar mode of the solar-trigeneration system are higher than the trigeneration efficiency of the SOFC-trigeneration system.  The maximum electrical efficiency for the SOFC-trigeneration system is 19% while it is 15% for the biomass-trigeneration system. On the other hand, the maximum electrical efficiency for the solar-trigeneration system is around 15% for the solar mode, 7% for the storage and solar mode, and 6% for the storage mode.  The efficiency increases considerably when trigeneration is used. The maximum trigeneration efficiency of the SOFCtrigeneration system is around 76% and it is around 90% for the biomass-trigeneration system. The maximum trigeneration efficiencies of the solar-trigeneration system is around 90% for the solar mode, 45% for storage and storage mode, and 41% for the storage mode.  The electrical to cooling ratio is sensitive to the variation of the ORC pump inlet temperature. Therefore, when it is needed to increase or decrease the cooling power, it can be controlled through the variation of this temperature. This ratio is the highest and most sensitive for the solar mode, where it could vary from 8.8 to 3.1. For the other two modes and the other two trigeneration systems, this ratio varies from approximately 6.5 to 2.5 as this temperature increases.  The solar-trigeneration system has zero CO2 emissions. Alternatively, the other two systems have significant CO2 emissions per MWh of electrical power. When trigeneration is used, the emissions per MWh of these two systems drop significantly. The emissions per MWh of trigeneration for these two systems are reasonable, around 400 kg/MWh of trigeneration power. However, the biomass-trigeneration system is not recommended for electrical production only. Regarding the SOFCtrigeneration system, the emissions are high per MWh of electricity since the hot streams at the exit of SOFC subsystem are partially used to heat the ORC. Therefore, more heat (biomass fuel) is needed from the auxiliary biomass boiler to

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heat the stream inlets of the SOFC and, thus, there are considerable emissions per MWh of electricity for the SOFCtrigeneration system.

UA UL Uo

Acknowledgment The authors acknowledge the support of King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, and the Natural Sciences and Engineering Research Council of Canada (NSERC). List of Symbols

a A Aap Ac Ar b c C Cp Coln Colr D COP Daeff Dceff Emi E_ F FR F1 G Gb hc hr I j jas jcs joa joc k K L HHV LHV m Mw n_ NFC Nus P Q Q_ R rel,h rel,c S T Uf UO2

Extent of steam reforming reaction for methane, mole/s Active surface area, cm2 Aperture area, m2 Area of the receiver cover, m2 Area of the receiver, m2 Extent of water gas shift reaction, mole/s Extent of electrochemical reaction, mole/s, cell, or cost per unit of exergy, $/GJ Constant or heat capacity, kW/K Specific heat, kJ/kg-K Total number of collectors per single row Total number of solar collectors rows Diameter, m Coefficient of performance Effective gaseous diffusivity through the anode, cm2/s Effective gaseous diffusivity through the cathode, cm2/s Emission Energy rate, kW Faraday constant, C Heat removal factor Collector efficiency factor Change in specific molar Gibbs free energy, J/mole Solar radiation, W/m2 Convection heat coefficient, kW/m2-K Radiation heat coefficient, kW/m2-K Current, A Current density, A/cm2 Anode-limiting current density, A/cm2 Cathode-limiting current density, A/cm2 Exchange current density of anode, A/cm2 Exchange current density of cathode, A/cm2 Thermal conductivity, W/m Equilibrium constant Thickness of an SOFC layer, cm Higher heating value, kJ/kg Lower heating value, kJ/kg Mass, kg Moisture content in the biomass fuel, % wt, dry basis Molar flow rate Total number of fuel cells Nusselt number Pressure, kPa Heat, kJ Heat rate, kW Universal gas constant, J/mol-K, or resistivity contact Electrical to heating energy ratio Electrical to cooling energy ratio Absorbed radiation by the receiver, W/m2 Temperature, Co or K Fuel utilization ratio Air (oxidant) utilization ratio

V w _ W _ W FC x

5753

Overall heat coefficient and area, kW/K Overall heat loss coefficient of the solar collector, kW/m2-K Heat loss coefficient between the ambient and receiver of the solar collector, kW/m2-K Voltage, V Collector width, m Power, kW Power of the fuel cell (W) Molar concentration

Greek letters 3cv Emittance of the receiver cover h Energy efficiency u Moisture content factor s StefaneBoltzmann constant, kW/m2-K4 r Density, kg/m3 or electrical resistivity of fuel cell components, ohm-cm Subscripts 0 Atmospheric conditions a Anode, absorber, or ambient ac AC current, actual act Activation aam Above ambient BM Biomass-trigeneration system b1 Blower 1 b2 Blower 2 c Cathode or receiver cover conc Concentration cog, c Cooling cogeneration cog, h Heating cogeneration e Electrolyte, exit eq Equilibrium ev Evaporator f Fuel FC Fuel cell g Generator h Heating HEx Heat exchanger hp Heating process i Inlet int Interconnect inverter DC to AC inverter m Motor oe Organic cycle evaporator ohm Ohmic op Organic cycle pump ot Organic cycle turbine N Nernst p Product r Reactant or receiver So Solar-trigeneration system so Solar mode of the solar-trigeneration system SOFC SOFC-trigeneration system sol, p Pump of the solar system soest Solar and storage mode of the solar-trigeneration system sp Solution pump st Storage mode of the solar-trigeneration system st1, p First pump in the thermal storage system st2, p Second pump in the thermal storage system wgs Water gas shift reaction tri Trigeneration u Useful

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Superscripts e Molar base . Rate of a component 0 At standard pressure CH Chemical exergy PH Physical exergy Acronyms GHG Greenhouse gas LieB Lithium-bromide ORC Organic Rankine cycle SEAC Singe-effect absorption chiller SOFC Solid oxide fuel cell References [1] Al-Sulaiman FA, Hamdullahpur F, Dincer I. Trigeneration: a comprehensive review based on prime movers. International Journal of Energy Research 2011;35(3):233e58. [2] Lai SM, Hui CW. Feasibility and flexibility for a trigeneration system. Energy 2009;34(10):1693e704. [3] Schicktanz MD, Wapler J, Henning HM. Primary energy and economic analysis of combined heating, cooling and power systems. Energy 2011;36(1):575e85. [4] Al-Sulaiman FA, Dincer I, Hamdullahpur F. Energy analysis of a trigeneration plant based on solid oxide fuel cell and organic rankine cycle. International Journal of Hydrogen Energy 2010;35(10):5104e13. [5] Rentizelas A, Karellas S, Kakaras E, Tatsiopoulos I. Comparative technoeconomic analysis of orc and gasification for bioenergy applications. Energy Conversion and Management 2009;50(3):674e81. [6] Al-Sulaiman FA, Hamdullahpur F, Dincer I. Energy and exergy assessments of a new trigeneration system based on organic rankine cycle and biomass combustor. In: Proceedings of ASME 2010 4th International Conference on energy Sustainability; 2010, ES2010e90258. [7] Kalogirou S. Solar energy engineering: processes and systems. Elsevier; 2009. [8] Bruno JC, Lopez-Villada J, Letelier D, Romera S, Coronas A. Modelling and optimisation of solar organic rankine cycle engines for reverse osmosis desalination. Applied Thermal Engineering 2008;28(17e18):2212e26.

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