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Exergy and exergoeconomic analyses and optimization of geothermal organic Rankine cycle Rami Salah El-Emam a, b, *, Ibrahim Dincer a a b

Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario L1H 7K4, Canada Faculty of Engineering, Mansoura University, Mansoura, Egypt

h i g h l i g h t s Energy and exergy analyses are applied to a geothermal organic Rankine cycle. Economic and exergoeconomic analyses are investigated and studied. Parametric studies are performed on optimal design of geothermal source at 165 C. Flow rates, pinch temp and exergy destruction cost are studied at optimal design. Optimum performance for different hot source temperature values is investigated.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 December 2012 Accepted 6 June 2013 Available online 14 June 2013

This paper presents thermodynamic and economic analyses on a novel-type geothermal regenerative organic Rankine cycle based on both energy and exergy concepts. An optimization study is also performed based on the heat exchangers total surface area parameter. Parametric studies are performed to investigate the effect of operating parameters, and their effects on the system energetic and exergetic efﬁciencies and economic parameters are investigated. The energy and exergy efﬁciency values are found to be 16.37% and 48.8%, respectively, for optimum operating conditions at a reasonable rejection temperature range of the geothermal water from 78.49 C to 116.2 C. The mass ﬂow rates of the organic ﬂuid, cooling water and provided geothermal water are calculated for a net out power of 5 MWe. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Exergy Exergoeconomic Optimization Efﬁciency Organic Rankine cycle Geothermal energy

1. Introduction In the recent years, there has been a signiﬁcant increase in the low-grade heat recovery and renewable energy market. The geothermal energy is considered one of the most reliable and relatively least-expensive sources of renewable energy. To utilize this energy; organic Rankine cycle (ORC) is a promising technology for converting this energy into useful power. ORC also has the beneﬁt of being simple in construction, system components are available, and being of high ﬂexibility and safety [1e4]. Considerable research has been conducted to study the performance assessment of the organic Rankine cycle that is based on geothermal energy source. Researchers studied the choice of an appropriate working ﬂuid, optimal reinjection condition of the * Corresponding author. Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario L1H 7K4, Canada. E-mail addresses: [email protected], [email protected] (R.S. El-Emam). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.06.005

geothermal ﬂuid, the ability of cogeneration and the economic analysis of such a system. One of the main challenges in the study of ORC is the choice of the working ﬂuid and the cycle design to achieve the highest performance [5,6]. Hettiarachchi et al. [7] studied the performance of ORC using different pure working ﬂuids. Karellas and Schuster [8] simulated the processes of the ORC using normal and supercritical ﬂuids, and studied the variation of the system efﬁciency in various applications. Badr et al. [9] studied the characteristics of ideal working ﬂuid for an ORC operating between 120 C and 40 C. A comparative study and optimization analysis was conducted by Shengjun et al. [13] on subcritical and transcritical geothermal based ORC. They found that among sixteen different working ﬂuids that R125 led to an excellent economic and environmental performance for a transcritical cycle, and R123 gave the highest energy and exergy efﬁciencies for a supercritical cycle. Tchanche et al. [11] showed an increase of 7% in the energy efﬁciency of an ORC integrated with a reverse osmosis desalination system when a regenerator is used. The optimization analysis of ORC is performed based on the heat exchanger area and the exergy

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destruction in heat exchangers as the main parameter of study in different studies [7,12,13]. Some research is performed to analyze the geothermal ORC systems economically and exergoeconomically [1,14,15]. They studied the effect of different operating parameters of the ORC and the geothermal ﬂuid conditions on the cost rates associated with the energy and exergy streams through the system. In the present paper, an investigation of the energetic and exergetic performances of a regenerative ORC with a geothermal heat source is performed. Comprehensive economic and exergoeconomic analyses are also performed to study, along with an application, for an optimal design condition which is performed based on the surface area of the heat exchangers with respect to the useful power output from the system. 2. System description The organic Rankine cycle system analyzed in this work is represented by the schematic diagram shown in Fig. 1. It is mainly composed of a Rankine cycle components, namely, evaporator or vapor generator with a superheater section, an expander, a water cooling condenser and an organic ﬂuid pump. The system has a regenerative heat exchanger as part of the system. Geothermal ﬂuid and cooling water circulation pumps are integrated into the system analysis. The organic ﬂuid passes through the evaporator and extracts the heat from the geothermal ﬂuid. Superheating is provided to the organic ﬂuid and then it is directed to the expander where useful work is gained. The expander exist stream exchanges its heat with the cold feeding ﬂow after the system pump which facilitate better utilization of the provided energy and it is expected to increase the overall system performance [11]. However, it will increase the total capital cost of the system. The organic ﬂuid enters the condenser where it loses its heat to the cooling water and it is subcooled before entering the system pump. Table 1 shows the operating parameters and assumptions of the considered system. 3. Thermodynamic analysis The pre-described system is simulated by a code developed using Engineering Equation Solver (EES). The following assumptions are made in the analyses of the overall system and sub-systems: - All the processes and sub-systems are steady state. - The expander and all pumps are adiabatic devices.

Table 1 Speciﬁcations and operating parameters of the considered system. Parameter

Data

Organic ﬂuid Gross power Electric generator efﬁciency Expander isentropic efﬁciency Pump isentropic efﬁciency Geothermal water inlet temperature Cooling water inlet temperature Regenerator effectiveness

Isobutane 5 MWel 97% 89% 95% 160e175 C 15 C 85%

- Negligible pressure losses occur in any of the Organic Rankine Cycle devices and its piping system. - The dead state temperature is 288 K for the base case in all the exergy analysis calculations. - Condenser cooling water temperature is 288 K. The energy balance, based on the ﬁrst law of thermodynamics, is applied to each of the system components. The general steady state form of the energy balance equation for any components can be written as follows:

_ þ Q_ W

X

_ in hin m

X

_ out hout ¼ 0 m

(1)

_ represent the heat transfer and work energy where Q_ and W _ and h represent the crossing the component boundaries and m mass ﬂow rate and the speciﬁc enthalpy of the streams of the system working ﬂuid. Exergy analysis has become one of the most important tools for the design and analysis of thermal systems [16]. It is based on the second law of thermodynamics. Exergy is a measure of the system state departure from the environment state and is considered also as a measure of the quality of energy [17]. It can be thermodynamically deﬁned as the maximum theoretical useful work that can be obtained from the system when it interacts to equilibrium with the surrounding environment [5,16e18]. Applying the exergy balance on the system components at steady state, the exergy destruction in each component can be calculated as follows:

_ _ _ Ex di ¼ ExQ ExW þ

X

_ in exin m

X

_ out exout m

(2)

_ represents the exergy destruction rate that occurs at the where Ex d _ W and Ex _ represent the exergy rate due to work and heat device i, Ex Q _ transferacross thesystemboundaries, andthe term ðm$exÞ represents the exergy rate carried with the ﬂow in and out from the system. The exergy transfer due to heat and work can be expressed as follows:

_ Ex Q ¼

X To _ Q 1 T

_ _ W ¼ W Ex

(3)

(4)

where To is the dead state temperature that describes the state at which the system is in unrestricted equilibrium with the environment and it cannot undergo any state change through any kind of interaction with the environment [18,19] and T is the temperature on the boundary at which heat transfer occurs. The exergy destruction can be also calculated based on entropy generation in each component as:

_ ¼ To $S_ gen Ex d

Fig. 1. Schematic diagram of the geothermal regenerative organic Rankine cycle.

(5)

where S_ gen denotes the entropy generation rate in the component i and it is determined from applying the entropy balance equation

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for a steady state operation on each component of the system as follows:

S_ gen ¼

X

_ out sout m

X

_ in sin m

X Q_ =T

.X

_ Ex di

(7)

The overall system thermodynamics performance can be measured by the energy and exergy efﬁciencies. The energy efﬁciency can be calculated as follows:

hth

_ net W ¼ _ Q

Table 2 Heat exchanger speciﬁcations. Element

(6)

The exergy destruction ratio for each component of the system is deﬁned as the exergy destruction rate occurs in a certain component with respect to the total exergy destruction of the whole system:

_ yD ¼ Ex di

437

Heat transfer surface length, mm Width of the heat transfer plate, mm Clearance at organic ﬂuid side, mm Clearance at water side, mm Pitch of the ﬂute, mm Depth of the ﬂute, mm Plate material Plate thickness, mm Number of plates

1465 605 5 5 1 1 Titanium 0.9 200

Source: [6,23,24].

Q_ ¼ U$A$LMTD

(12)

where A is the surface area of the heat exchanger and U is the overall heat transfer coefﬁcient which is calculated as follows:

(8)

Geo;in

U ¼

And the exergy efﬁciency is deﬁned as the useful exergy output of the system, which is the net-work gain, over the exergy of the utilized input to the system:

_ Ex

j ¼ _ useful output ExGeo hot source

(9)

It can also be expressed as a function of the exergy destruction rate in the system components as follows:

P _ Ex

d j ¼ 1 _ ExGeo hot source

(10)

Furthermore, we aim to assess the sustainability dimension of the system. It is known that sustainable development requires an efﬁcient use of the available resources besides using clean and affordable energy resources. Exergy analysis appears to be a signiﬁcant tool for energy systems which may contribute in improving the sustainable development. A simple assessment is possible through the sustainability index which is deﬁned as a function of exergy efﬁciency [20e22]:

SI ¼ 1=ð1 jÞ

(11)

The design of the evaporator and the condenser is discussed in this section. The regenerative heat exchanger overall heat transfer coefﬁcient is taken relative to the ones for the evaporator and condenser. The evaporator, condenser and regenerative heat exchanger in the proposed system are shell and plate type heat exchangers [7]. This type of heat exchangers matches well with the existing case because of its high heat transfer coefﬁcient that results in more compactness, especially with the relatively low temperatures of the heat sources in the proposed regenerative geothermal organic Rankine cycle [7,23]. The speciﬁcations and material properties of the shell and plate heat exchangers used in this analysis are given in Table 2. The logarithmic mean temperature difference (LMTD) method is used in the analysis of the heat exchangers and the calculation of the heat transfer area. The heat transfer rate is described as

þ

t 1 þ kp aw

(13)

where aOF is the convection heat transfer coefﬁcient of the organic ﬂuid, aW represents the convection heat transfer coefﬁcient for the hot source in the evaporator or the cooling water in the condenser. Also, t and k are the thickness and thermal conductivity of the heat exchanger plate material. The heat transfer coefﬁcients for hot and cold water side and the organic ﬂuid side are determined using empirical correlations from the literature [6,10,25e28] based on the calculation of Nusselt Number as

Nu ¼ a$Deq =k

(14)

where Deq denotes the approximate diameter which is approximated to equal twice the clearance of the heat exchanger plate [23]. For the water side heat transfer coefﬁcient at the system heat exchangers, the following correlation is used to calculate Nusselt Number [6]:

Nu ¼ 0:04Re0:8 Pr 0:33

(15)

where Re is Reynolds Number and Pr is Prandtl Number. The velocity of the water as for both geothermal source and cooling water is calculated as follows:

V ¼ 4. Heat exchanger surface area

1

aOF

V_ w$dx$N

(16)

where V_ is the water volumetric ﬂow rate, w and dx are the width of the plate and the clearance at the water side, respectively. N represents the number of the plates. The power required for geothermal water circulation pump is simply represented as a function of the pressure drop as follows:

_ _ ¼ V$DP W

h

(17)

where h is the pump efﬁciency and DP represents the pressure drop which is calculated using the following formula:

r$V 2 $l 4$w$dx

DP ¼ F$

(18)

Here, F is the friction factor and l is the heat exchanger plate length.

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For the organic ﬂuid heat transfer coefﬁcient at the evaporator, considering isobutane as the working ﬂuid in the organic Rankine cycle, the following correlations are used [6,7]

8 0:919 > < 1:18 fp X $H0:834 $ðrl =rv Þ0:448 ; fp X 62 Nu ¼ 0:919 > : 6:646 fp X $H 0:834 $ðrl =rv Þ0:448 ; fp X > 62

(19)

where H represents the ratio between sensible heat and latent heat. fp is the pressure factor and is presented as a function of the critical pressure and the atmospheric pressure as follows:

P Pcr

fp ¼

3

þ1

P Pa

0:7 (20)

Here, X in the Nusselt correlation is a dimensionless parameter that is calculated as follows:

X ¼ D1:5 eq;ev $qE

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ M$cp;l $r2l =kl $s$hfg $rv

(21)

where M is a constant value equals 6.129 m2/N s, Deq is the equivalent diameter at the organic ﬂuid side of the evaporator and is equal to double the clearance of the plate at the organic ﬂuid side. For the convection heat transfer coefﬁcient of the organic ﬂuid at the condenser, the following correlation is used [24,26]:

Nu ¼ 2:018$ðBo$LÞ0:1 $ðGrl $Prl =HÞ1=4

(22)

where Bo is Bond number, L is a dimensionless value that is function of the heat exchanger plate parameters and is calculated as follows:

L ¼

p2 l$dh

(23)

where p, l and dh are the pitch of the ﬂutes on the heat exchanger plate, the heat transfer length and the depth of the ﬂutes, respectively. The Bond Number (Bo) and Grashof Number (Gr) are dimensionless numbers and are deﬁned as

Bo ¼ g$rl $p2 =s Gr ¼

g$l3

n2

(24)

rl rv rl

(25)

_ out C_ out ¼ cout Ex

(27)

_ C_ in ¼ cin Ex in

(28)

_ C_ W ¼ cW W

(29)

_ C_ Q ¼ cQ Ex Q

(30)

Here, c denotes the average cost per exergy unit and is expressed in $/GJ. The exergy rate values in these equations are determined based on the exergy analysis of the system. The total cost rate associated with the products of the proposed system is expressed in the following equation as a function of the total fuel cost rate, C_ fuel and the annual investment cost rate of the system components, Z_ total , as follows:

C_ P;total ¼ C_ fuel þ Z_ total

(31)

_ is calcuThe annual investment cost rate of any component Z, lated for the proposed system. It is the summation of the annual capital investment cost rate and the annual O&M cost rate. The total capital investment (TCI) is considered in two parts; direct capital cost (DCC) and indirect capital cost (ICC). The direct capital cost for this study is the purchase equipment cost (PEC). The components and equipment are expressed as function of some design parameters. The indirect capital cost can be expressed as a function of the purchase cost of equipment or as a function of design parameters and operating conditions [29]. In the following analysis, the equipment purchasing cost is calculated as function of the components design parameters. The correlations used in this analysis are stated in the form of turbine work output, pumps power and heat exchangers surface area. These correlations are formed based on manufacturing data and give the costs in US Dollars [8,14,30]. For the organic ﬂuid expander, the following correlation is utilized to calculate the purchase cost:

_ exp log10 PECexp ¼ 2:6259 þ 1:4398log10 W i2 h _ exp 0:1776 log10 W

(32)

_ exp , is provided in kW. where the expander work, W The purchase cost for the heat exchangers, i.e; evaporator, condenser and regenerative heat exchanger, is calculated using the following correlation as a function of the heat transfer surface area:

log10 ðPECHE Þ ¼ 4:6656 0:1557log10 ðAÞ þ 0:1547½log10 ðAÞ2

5. Economic and exergoeconomic analyses

(33) The system economic analysis is performed taking into account the purchased components and equipment cost, operation and maintenance (O&M) cost and the cost of the energy input. The exergoeconomic (thermoeconomic) analysis is the study of the economic principles considering the exergy analysis of the system under study. The thermoeconomic analysis is performed by applying the cost balance equation on the system components where the steams crossing the components boundaries are expressed in the form of exergy cost rates of these streams. This equation can be formulated in a general form as follows:

X

C_ out þ C_ W ¼

X

C_ in þ C_ Q þ Z_

(26)

where C_ denotes the total cost rates of the exergy streams across a speciﬁc component in the system, and its values are expressed in $/h. They are deﬁned as follows:

where A is surface area of the heat exchanger in m2. The purchase prices of the organic Rankine cycle pump and geothermal ﬂuid circulation pump are determined by applying the following formula which is a function of the pump power:

_ pump log10 PECpump ¼ 3:3892 þ 0:0536log10 W i2 h _ pump þ 0:1538 log10 W

(34)

The total capital investment (TCI) is calculated for each component as 6.32 times the purchase equipment cost as given by Bejan et al. [16]. The O&M cost of each speciﬁc equipment is taken as 20e25% of the purchase equipment cost [16]. The fuel cost and O&M costs are exposed to cost escalation over the years of operation. The levelized

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439

Table 3 Assumed economic data for the economic and exergoeconomic modeling. Economic constant Effective annual cost of money, ieff Nominal escalation rate, rn Economic life, n Annual operating hours, s

12% 5% 20 year 7000 h

values of these expenditures are obtained by using the constantescalation levelization factor (CELF). This factor links the calculations of expenditures at the ﬁrst year to an equivalent annuity [16].

CELF ¼ CRF$

kð1 kn Þ 1k

(35)

where k is function of the effective annual cost of money rate, ieff and the nominal escalation rate, rn, and CRF is the capital recovery factor. These factors are applied to the fuel cost and O&M costs and they are deﬁned as follows [16]:

k ¼

1 þ rn 1 þ ieff

(36)

n 1 þ ieff CRF ¼ ieff $ n 1 þ ieff 1

(37)

Table 4 Optimization results for the system operation at different geothermal source temperatures.

Thf,out, C Tcf,out, C Tcd, C dTsubcool, C dTsuperheat, C Texp,,in, C Tpinch,cd, C Tpinch,ev, C Acd, m2 Aev, m2 ARHE, m2 Atot, m2 cp, $/GJ C_ P , $/h J, % h, % Opt _ CW , kg/s m _ HF , kg/s m _ OF , kg/s m

respectively. It can also be represented as function of the expander produced work. For this study, the drilling cost is taken as 250$/kW of produced useful power [31e33]. The cost rate of exergy destruction in each component is calculated with respect to the unit cost of the product of this component as follows:

_ C_ D ¼ cP Ex d

where n is the number of years, the values of ieff and rn are given in Table 3. The annual investment cost rate of the components which is used in the thermoeconomic balance equation is calculated based on the operational time of the component expressed in hours. The cost rate of the fuel is expressed in this study as the summation of the total cost rate of the electric power for the geothermal pump and the levelized values of the annual investment cost rate of drilling and the geothermal circulation pump [14,15]. The drilling cost can be calculated as a percentage of the total capital investment. It ranges from 25% to 40% and around 70% of the TCI for high temperature plants and low temperature plants,

Operating & design parameters

Fig. 2. Tes diagram of the organic Rankine cycle.

(38)

where the unit cost of the component product is calculated though the unit costs of the exergy associated with the products from this component. The values of the unit cost of exergy streams are calculated from the thermoeconomic cost balance equation and the exergy destruction rates are provided from the thermodynamics analysis of the system. The exergoeconomic factor, f, and the relative cost difference, r, are determined for each of the system components as follows [16]:

r ¼ ðcP cF Þ=cF f ¼ Z_

. _ Z_ þ cF Ex d

(39)

(40)

Geothermal source temperature 160 C

165 C

170 C

175 C

116.2 28.51 34.26 4.631 17.23 146.1 6.107 12.09 740.6 415.1 149.2 1305 99.64 5379 28.27 17.48 0.2558 422.6 154.5 70.56

78.49 29.33 35.05 3.88 7.197 136.1 5.957 5.347 810.1 390.6 124.8 1326 86.39 4723 48.8 16.37 0.2598 432.7 84.36 78.06

84.34 27.83 35.13 1.874 12.51 141.4 7.736 6.701 639.6 415.5 152.4 1208 83.68 4554 47.49 17.04 0.2367 460.4 81.59 74.15

88.72 28.23 34.98 2.704 15.47 144.3 7.196 9.661 703.6 398.6 168 1270 87.16 4738 46 17.33 0.249 437.8 79.53 72.24

Fig. 3. Temperatureeenthalpy diagram for the evaporator at optimal design for geothermal ﬂuid temperature at 165 C.

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Fig. 4. Temperatureeenthalpy diagram for the condenser at optimal design for cooling water inlet temperature at 15 C.

where cP and cF are the unit cost of the exergy associated with the component products and fuel, respectively, and they are calculated for each component of the system as follows:

C_ cP ¼ P _ P Ex

(41)

C_ F _ F Ex

(42)

cF ¼

where C_ P and C_ F refers to the cost rate of the product and fuel _ P and streams through a certain component, respectively, and Ex _ F are the exergy rate of the product and fuel streams of that Ex component, respectively.

Fig. 6. Exergy destruction at the system components and the total exergy destruction at the whole system at different evaporator pressure values.

Obj ¼

At _ W

where At is the total heat transfer surface area of the heat ex_ is the net power in kW. changers of the system in m2, and W In the optimization process, the objective function is minimized considering the variable metric method with varying the pressure of the condenser and the temperature values at the expander inlet and condenser outlet as the decision variables. Superheating and subcooling are considered. The temperature of the rejected geothermal ﬂuid is arranged to be not less than 80 C [12]. 7. Results and discussion

The performance of the proposed organic Rankine cycle is optimized using a heat exchanger surface area based objective function [7,10,13]. The objective function used in this study is deﬁned as the ratio of the total surface area of the heat exchangers to the useful output power as follows:

A complete thermodynamic analysis based on the ﬁrst and second law is performed on the system shown in Fig. 1. The mass, energy, entropy and exergy balance equations are applied on each of the system components at steady state operation. The optimal designs of the ORC at four different values of the geothermal water inlet temperature are presented in Table 4. The calculations of the mass ﬂow rate of the organic ﬂuid, the corresponding geothermal ﬂuid and cooling water are calculated. The temperature values at

Fig. 5. Exergy destruction at the system components and the total exergy destruction at the whole system at different expander inlet temperature values.

Fig. 7. Overall energy and exergy efﬁciency at different expander inlet temperature values.

6. Thermodynamics optimization

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441

Fig. 8. Performance parameters vs. expander inlet temperature.

Fig. 10. Performance parameters vs. evaporator pressure.

the turbine inlet and the amount of subcooling of the condenser outlet are also calculated and presented in Table 4. The results in Table 4 show that the exergy efﬁciency decreases gradually after increasing the temperature of the geothermal source over 165 C, based on the tested temperature values and the values of the optimal operating parameters. The corresponding Tes diagram of the organic Rankine cycle with the geothermal and cooling water is presented in Fig. 2. This diagram is for the case when geothermal temperature is at 165 C. Figs. 3 and 4 show the temperature proﬁle with the total enthalpy change of the organic ﬂuid for the evaporator and the condenser, respectively. The pinch temperature is shown to be taken at the inlet of the two phase ﬂow section of the organic ﬂuid at the evaporator at the saturated liquid condition, and at the inlet section of the two phase ﬂow at the condenser at the saturated vapor condition of the organic ﬂuid. The results shown in Figs. 5e13 represent the optimum performance condition at evaporator pressure of 33 bar and inlet temperature of 165 C for the geothermal water. The effect of the expander inlet temperature on the exergy destruction of the ORC components is demonstrated at Fig. 5. The exergy destruction occurs at the condenser, which represents about 38% of the total exergy destruction in the system, decreases with the increase of the expander inlet temperature. The evaporator exergy destruction increases with the increase of expander inlet temperature till it reach a maximum at about 10 C over the saturation temperature of

the evaporator operating pressure and then starts to decrease. The regenerative heat exchanger has a considerable percentage of the total exergy destructions in the system and it increases in a linear form with the increase of the expander inlet temperature. The total exergy destruction in the ORC is also shown. Fig. 6 shows the effect of the evaporator pressure on the exergy destruction that occurs at the ORC system components. The superheating temperature is kept constant at the value determined from the optimization analysis, shown in Table 4. Figs. 7 and 8 show the energy and exergy efﬁciencies and the sustainability index for the performance of the organic Rankine cycle at different expander inlet temperature values. From Fig. 7, the energy efﬁciency increases by 5% with the superheating of 30 C over the saturation temperature of the evaporator pressure, while the exergy efﬁciency decreases for the same range of superheating. Fig. 8 shows that the trend of sustainability index is the same for the exergy efﬁciency of the overall performance. The effect of increasing the evaporator pressure on the overall system performance for the

Fig. 9. Overall energy and exergy efﬁciency at different evaporator pressure values.

Table 5 Exergy and exergoeconomic parameters at different geothermal temperature values. _ D [kW] Ex

yD [%]

C_ D [$/h]

r [e]

f [%]

Condenser Evaporator Expander Pump RHE

930.3 1419 504.9 16.78 160.7

30.68 46.8 16.65 0.55 5.3

32.27 65.14 78.05 1.198 47.6

0.2934 0.388 0.4454 4.657 1.017

59.27 66.33 72.51 94.5 59.56

Tgeo ¼ 165 C Condenser Evaporator Expander Pump RHE

1033 1009 530.6 18.31 73.35

38.78 37.88 19.92 0.69 2.75

34.8 34.58 74.86 1.291 25.7

0.2804 0.404 0.494 4.483 1.549

59.47 79.18 73.35 94.51 71.36

Tgeo ¼ 170 C Condenser Evaporator Expander Pump RHE

1054 1024 515 17.09 103.7

38.84 37.73 18.98 0.63 3.82

33.07 36.47 70.76 1.214 31.5

0.1878 0.4151 0.5075 4.596 1.347

58.06 78.8 74.43 94.56 69.22

Tgeo ¼ 175 C Condenser Evaporator Expander Pump RHE

1008 1153 508.1 16.79 132.5

35.76 40.9 18.02 0.6 4.7

33.5 41.19 71.45 1.196 38.94

0.2327 0.4232 0.4936 4.637 1.255

58.52 76.03 74.24 94.54 65.7

Component

Tgeo ¼ 160 C

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R.S. El-Emam, I. Dincer / Applied Thermal Engineering 59 (2013) 435e444

Fig. 11. Effect of dead state temperature on the exergoeconomic factor for ORC components.

same expander superheating temperature difference is shown in Figs. 9 and 10. The performance is shown in terms of energy and exergy efﬁciencies and the sustainability index. Both energy and exergy efﬁciencies increase with the pressure increase. From the exergoeconomic analysis, the cost rate of the exergy destruction in different components is shown in Table 5. The results are expressed for four different geothermal water inlet temperature values. Also the values of the exergoeconomic factor and the relative cost difference are calculated for the different cases. From Table 5, it can be concluded that the highest exergy destruction cost rate is the one associated with expander exergy destruction, however, the exergy destruction ratio is higher at the evaporator and the condenser, 37e40% and 30e38%, respectively. Figs. 11e13 show the effects of the dead state temperature on the exergoeconomic analysis of the system. The dead state temperature is assumed to change in a reasonable range of values. Fig. 11 shows the effect of dead state temperature on the values of the exergoeconomic factor for the ORC system components. Changing the dead state temperature from 0 to 30 C causes a general decrease in the value of the exergoeconomic analysis, but in different ratios. The value of the exergoeconomic factor for the condenser decreases from 70.3% to 26.07%. Also for the regenerative heat exchanger, the values for the exergoeconomic factor changes in a relatively big range from 63.2% to 41.2%. For the expander, evaporator and the

Fig. 13. Effect of dead state temperature on the product cost and the total cost rate of exergy destruction.

pump, the reductions in the factor values were very limited compared with the other components. It changed from 52.3% to 51.4% for the expander, 88.9% to 84.3% for the evaporator and ﬁnally, for the pump, it changed from 94.8% to 94.2%. Low value of the exergoeconomic factor indicates that there is a potential to increase the cost savings by improving the component performance and reducing the exergy destruction occurs through it, this may come on the expenses of the capital investment cost of the component [16]. From the exergy and thermoeconomic analyses, the increase in the dead state temperature value generally caused an increase in the cost rate of the exergy destruction in different system components, however, the cost rates of the exergy destruction expressed as percentage of the total cost rate of exergy destruction have different trends with the change in the dead state temperature as shown in Fig. 12. The cost rates of the exergy destruction in the condenser increase from 29.94 to 33.23$/h with the dead state temperature increase from 0 to 30 C. But as a percent of the total exergy destruction cost rate, it deceased from 6.9 to 5.72%. For the expander, it increased from 187.7 to 194.7$/h while its percentage decreased from 43.6 to 33.5%. The cost rate and its share in the total exergy destruction cost rate increased for the evaporator from 173.9 to 261.4$/h and from 40.4 to 45.05%, respectively. The RHE shows an increase of the exergy destruction cost rate from 37.62 to 89.68$/h and an increase in its representation in the total amount from 8.7 to 15.4%. The exergy destruction cost rate at the pump increased slightly from 1.22 to 1.36$/h, however, the cost percentage decreased from 0.28 to 0.23%. In Fig. 13, it shows a decrease in the total product cost rate with the increase of the dead state temperature. The change in the total product cost has a linear form. The total cost rate associated with the system exergy destruction increase with around 140$/h for the same temperature change. 8. Conclusions An organic Rankine cycle with a geothermal heat source and isobutane as working ﬂuid is studied thermodynamically, based on energy and exergy concepts. Exergoeconomic analysis is performed on the system, and different economic factors are calculated at different operating parameters. The following remarks can be extracted from this study:

Fig. 12. Effect of dead state temperature on the cost rate associated with exergy destruction for ORC components.

Different geothermal water temperatures are considered in the present analysis and an optimal performance is achieved at 165 C which was considered as a base case for the analysis.

R.S. El-Emam, I. Dincer / Applied Thermal Engineering 59 (2013) 435e444

Both energy and exergy efﬁciencies are calculated as 16.37% and 48.8%, respectively, at a hot source temperature of 165 C. The evaporator and the condenser have the highest exergy destruction rates, accounting for about 75% of the total exergy destruction rate of the overall system. The exergoeconomic factor values show relatively high values for the pump and expander and moderate values for the heat exchanger devices in the system. The effects of changing the dead state temperature, evaporator pressure and inlet temperature of the expander on the system thermodynamics and thermoeconomic parameters are also studied. The increase of the dead state temperature value causes an increase in the cost rate of the exergy destruction in the system. Nomenclature

a dh dx dy h r s s j

area, m2 Bond number cost per exergy unit, $/GJ cost rate, $/h speciﬁc exergy, kJ/kg exergy rate, kW exergy destruction, kW exergoeconomic factor, % Grashof Number speciﬁc enthalpy, kJ/kg thermal conductivity, W/m K length of heat transfer surface, mm mass ﬂow rate, kg/s number of operating years number of heat exchanger plate Nusselt Number pitch of the plate ﬂute, mm pressure, kPa, bar Prandtl Number Heat rate, kW relative cost difference Reynolds Number speciﬁc entropy, kJ/kg K entropy generation, kW/K temperature, C, K overall heat transfer coefﬁcient, W/m2 K velocity, m/s volumetric ﬂow rate, m3/s work, kW annual investment cost rate, $/h convection heat transfer coefﬁcient, W/m2 K clearance of the heat exchanger plate, mm clearance of the plate at water side, mm clearance of the plate at the organic ﬂuid side, mm energy efﬁciency, % density, kg/m3 surface tension, N/m annual operating hours, h exergy efﬁciency, %

Subscript cd cf cr Cw ev Exp F HE

condenser cooling ﬂuid critical cooling water evaporator expander fuel heat exchanger

A Bo c C_ ex _ Ex _ Ex

d

F Gr H K l _ m N N Nu P P Pr Q_ R Re s S_ gen T U V V_ _ W Z_

hf in L OF out P V W

443

hot ﬂuid steam in liquid organic ﬂuid steam out product vapor water

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