Energy Conversion and Management 121 (2016) 391–401

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Energy Conversion and Management

journal homepage: www.elsevier .com/ locate /enconman

Thermodynamic, economic and thermo-economic optimization of a newproposed organic Rankine cycle for energy production from geothermalresources

http://dx.doi.org/10.1016/j.enconman.2016.05.0460196-8904/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: Department of Chemical Engineering, Faculty ofEngineering, Iran.

E-mail address: fereshteh.samadi1@gmail.com (F. Samadi).

Neda Kazemi, Fereshteh Samadi ⇑Department of Chemical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran

a r t i c l e i n f o

Article history:Received 14 March 2016Received in revised form 8 May 2016Accepted 17 May 2016Available online 26 May 2016

Keywords:Geothermal energyOrganic Rankine cycleOptimizationThermodynamic and economic analysis

a b s t r a c t

The main goal of this study is to propose and investigate a new organic Rankine cycle based on three con-sidered configurations: basic organic Rankine cycle, regenerative organic Rankine cycle and two-stageevaporator organic Rankine cycle in order to increase electricity generation from geothermal sources.To analyze the considered cycles’ performance, thermodynamic (energy and exergy based on the firstand second laws of thermodynamics) and economic (specific investment cost) models are investigated.Also, a comparison of cycles modeling results is carried out in optimum conditions according to differentoptimization which consist thermodynamic, economic and thermo-economic objective functions formaximizing exergy efficiency, minimizing specific investment cost and applying a multi-objective func-tion in order to maximize exergy efficiency and minimize specific investment cost, respectively.Optimized operating parameters of cycles include evaporators and regenerative temperatures, pinchpoint temperature difference of evaporators and degree of superheat. Furthermore, Peng Robinson equa-tion of state is used to obtain thermodynamic properties of isobutane and R123 which are selected as dryand isentropic working fluids, respectively. The results of optimization indicate that, thermal and exergyefficiencies increase and exergy destruction decrease especially in evaporators for both working fluids innew proposed organic Rankine cycle compared to the basic organic Rankine cycle. Moreover, the amountof specific investment cost in new organic Rankine cycle is obtained less than basic organic Rankine cycleduring thermodynamic and economic optimization for R123. Finally, a profitability evaluation of newproposed and basic systems is performed based on total production cost and return on investment forthree countries: Iran, France and America. Its results show that Iran has the maximum amount of returnon investment.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Geothermal energy, as a low-grade heat source, could be usedto produce and convert energy into useful work (i.e., electricity)by using organic Rankine cycle (ORC) technology [1]. This technol-ogy is based on principles of renewable energy, in which it couldreduce the emission of greenhouse gases (GHGs) caused by fossilfuels. In other words, an ORC is widely used in the geo-plant inorder to generate power in an environment friendly manner [2].

In such systems, at first water is injected into the ground, whichits injection wells were calculated geometrically and adsorbs thecertain amount of heat from the ground layers (geothermal

energy). Then, hot water is pumped from production wells to anevaporator. In the evaporator, heat is transferred from the hotwater to an organic fluid which is also known as ‘‘working fluid”.As a result, the working fluid in the evaporator is vaporized or evensuperheated according to the amount of heat it takes. In the nextstage, the saturated or superheated vapor expands through a tur-bine and produces electricity by an electrical generator which istransferred mechanical energy into electrical type. Afterwards,the expanded vapor is cooled by a condenser to liquefy and finally,to complete the cycle, working fluid is pumped to the evaporator[3].

Generally, the ORC system performance could be specified bythermodynamic efficiency which depends on several parameters,for instance the operating conditions, types of working fluids, thesystem components and also cycle configuration [4]. Accordingly,in recent decades, in order to improve the performance and

Nomenclature

A heat exchanger surface areaE _x exergy flow rate (kW)h specific enthalpy (kJ/kg)_I flow rate of destroyed exergy (or irreversibility) (kW)_m mass flow rate (kg/s)P pressure (bar)_Q heat transfer flow rate (kW)S specific entropy (kJ kg�1 K�1)T temperature (�C)U overall heat transfer coefficient (Wm�2 K�1)_W power output/input (kW)X vapor qualitySIC specific investment cost ($/kW)PPTD pinch point temperature difference (�C)ROI return on investment (%)ORC organic Rankine cycleRORC regenerative organic Rankine cycleTSORC two stage evaporator organic Rankine cycleNORC new proposed organic Rankine cycle

Greek lettersa coefficient of linear weighted evaluation functionb coefficient of linear weighted evaluation functiong efficiency (%)

Subscripts/superscriptscond condenser/condensationevap evaporator/evaporationt turbinep pumpin/out inlet/outleti/o inside/outsideis isentropichsi/hso heat source (or geothermal water) inlet/outletcsi/cso heat sink (or cooling water) inlet/outlettot totalh/c heat source/sink or hot/coldwf Working fluidelec electricalgen generatorreg/regen regenerative

392 N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401

increase the efficiency of ORC system, various studies have beenconsidered which include the investigation of different workingfluids effect, the optimization of operating parameters with anappropriate objective function such as thermodynamic, economicor thermo-economic and also variations in the cycle configuration.

In this respect, Yang and Yeh [5] analyzed an ORC system per-formance by using economic optimization. Their results showedthat R600 gave the best performance under economic optimizationamong working fluids which have the lower global warmingpotential (GWP) like R290, R600a, R1233zd, R1234yf andR1234ze. Also, the pinch point temperature differences in theevaporator altered more compared to the condenser.

Shokati et al. [6] carried out a comparative study in order toinvestigate an exergoeconomic analysis by optimization of basic,dual-pressure and dual-fluid ORCs and Kalina for geothermalapplications in power plants. They optimized parameters of men-tioned cycles in order to maximize the energy production and min-imize the cost of power generation. Their optimization resultsshowed that dual-pressure ORC generated the maximum value ofelectricity and also Kalina cycle had the minimum value of unitcost of power produced.

Yang and Yeh [7] used thermo-economic optimization in orderto evaluate the performance of R245fa, R1234yf, R1234ze, R152a,and R600a as working fluids in ORC systems. The results illustratedthat R1234yf gave the best performance in thermo-economicinvestigation among all considered working fluids.

Dai et al. [8] investigated the performance of ORC for differentworking fluids using genetic algorithm. In their study, exergy effi-ciency was chosen as an objective function to optimize operatingparameters including inlet temperature and pressure of the tur-bine. They found, the working fluid R236EA has the highest exergyefficiency (35.43%) and thermal efficiency (12.37%).

A research was carried out by Xi et al. [9] in order to maximizethe exergy efficiency of ORC using single or double-stage regener-ative. They presented that an ORC with two-stage regenerative hadhigher exergy efficiency comparing to a basic ORC. Roy and Misra[10] optimized different parameters and analyzed the performanceof a regenerative organic Rankine cycle (RORC) for waste heatrecovery. They recognized, the performance of R123 as a workingfluid is better than R134a for this specified cycle within a

superheating at a constant pressure of 2.5 MPa. Thermo-economic optimization of RORC in order to recover the amountof heat losses were investigated by Imran et al. [11]. The resultsof optimization showed that R245fa is the best possible workingfluid under their cycle conditions and also, the thermal efficiencyof ORC was improved by adding a regenerative to the cycle.

Li et al. [12] optimized the operating parameters of a two-stageevaporator organic Rankine cycle (TSORC). Their studies showedthat the system performance would increase with geothermalwater inlet temperature and different range of evaporator temper-ature. Moreover, they figured out the irreversible losses woulddecline to a minimum value in the evaporator by using two-stage evaporator within two different temperature range. Li et al.[13] investigated the performance of the ORCs in order to usetwo stage evaporation strategies (parallel and series). In theirresearch, R245fa and geothermal water with a temperature rangeof 90–120�C were selected as working fluid and heat source,respectively. Although, they recognized both strategies couldreduce the system irreversibility, significant reduction was foundin series two-stage evaporator. Li et al. [14] proposed an ORC withdouble parallel evaporator which their research results stated adecrease in irreversible energy loss and an increase in productioncapacity from geothermal resources.

Zare [15] evaluated the performance of three different configu-rations (basic ORC, regenerative ORC and an ORC within an internalheat exchanger) through thermodynamic and exergoeconomicoptimization. The results illustrated that although the ORC withinan internal heat exchanger gave a premier performance in thermo-dynamic optimization, basic ORC showed the best behavior in eco-nomic optimization compared to the other considered cycles.

In this paper, three different points of view, including thechange in basic ORC configuration (a new arrangement of the cycleequipment), optimization of cycles operating parameters by usingthree different objective functions (thermodynamic, economic andthermo-economic) and survey of the effect of various working flu-ids are considered to improve and increase the efficiency of a basicORC. In other words, the restructuring of basic ORC equipment hasbeen investigated by adding an evaporator and a regenerative,simultaneously. Also, three selected objective functions have beenapplied to optimize heat exchangers temperatures (excluding

3

Evaporator

N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401 393

condenser), pinch point temperature difference of evaporator anddegree of superheat. Furthermore, two pure organic components,including isobutane (dry) and R123 (isentropic) were selected asworking fluids.

(a)

1

2

4

Pum

p Turbine

Condenser

T (k

)hso

hsi

PinchH

TH

2

3

2'4'

2. Materials and methods

Although, a basic ORC could be used to produce useable work byusing low-grade heat sources, its thermal efficiency is low due tosystem irreversibility [16]. Overall, irreversibility reduction is pos-sible by changing the basic ORC configuration which has beeninvestigated by previous works. One of the changes is adding aregenerative to ORC (RORC) in which, the amount of heat receivedby evaporator and the outlet work in the turbine would reduce,because a certain amount of superheated working fluid which istaken from the turbine is used to preheat the outlet subcooledworking fluid from the pump [11]. In contrast, another methodhas been applied by adding an extra evaporator either in seriesor parallel to the evaporator of basic ORC which is known as TSORC[13]. In TSORC system, the mass flow rate of vaporized workingfluid increases due to receive a large amount of heat from thegeothermal water compare to the basic ORC. Therefore, in the men-tioned cycle, the outlet work in the turbine raises. In other words,although use of this method would increase the electricity produc-tion, adding an extra evaporator would also increase the amount ofheat received from the heat resource. The method which has beenproposed in this article is use of both mentioned methods, simul-taneously. Description of the basic ORC and new proposed ORC(NORC) are explained in details as follow:

(b)

s (J.kg-1.k-1)

csocsi

PinchL

TL

1

4

Fig. 1. Basic ORC (a) schematic of the cycle and (b) T–S diagram.

2.1. Cycles description

2.1.1. Basic ORCThe main processes and temperature–entropy (T–S) diagram in

the basic ORC are illustrated in Fig. 1. According to Fig. 1(a), thecycle includes an evaporator, a pump, a condenser and a turbine.Geothermal water and cooling water are used in the evaporatorand condenser in order to heat and cool down the working fluidin the cycle, respectively. In addition, T–S diagram in Fig. 1(b)shows the trend of entropy variation for each process (in both isen-tropic and real states), geothermal and cooling water with theirtemperatures and also, the pinch point temperature differencesin the condenser and evaporator.

2.1.2. New organic Rankine cycleIn new proposed organic Rankine cycle (NORC), series two-

stage evaporator and also a regenerative are added to the basicORC equipment to improve the performance. The configurationof NORC and its T–S diagram are depicted in Fig. 2. According toFig. 2, compared to the basic ORC process, the outlet subcooledworking fluid from pump 1 enters a regenerative which is usedto heat the working fluid by an amount of superheated workingfluid taken from the turbine. Afterwards, the saturated workingfluid is pumped to the evaporator 2 (intermediate evaporator) toreceive heat from the geothermal water. In this stage, a portionof working fluid gets into the turbine and the rest moves to the firstevaporator. In the evaporator 1, at a constant pressure, the workingfluid is heated by absorbing the energy from geothermal water andthen is expanded through the turbine and produces electricity.

2.2. Assumptions

In this article, the following assumptions are applied for model-ing of the mentioned cycles.

� Steady-state condition is considered for each process in thecycles.

� Heat and friction losses are neglected in the heat exchangers.� Kinetic and potential energy are neglected for water as a heatsource and sink media.

� Entirely developed flow is considered to calculate heat transferparameters.

� Heat exchangers are selected from shell and tube type.� Peng Robinson equation of state (PR EOS) is applied to calculatethermodynamic properties.

� Two pure organic fluids, including isobutane and R123 wereselected as working fluids.

2.3. Thermodynamic modeling

The first and second laws of thermodynamics could be consid-ered to investigate how the basic ORC performance would be mod-ified by changing its structure. In other words, the performance ofORC systems could be specified by thermal and exergy efficienciesanalysis based on the first and second laws of thermodynamics,respectively. In this respect, thermal efficiency is determinedaccording to Eq. (1):

(a)

(b)

1

23"

6

3

4

5

5"

7

8

Evaporator1

Pum

p 1

Pum

p 2

Regenerative

Turbine

Condenser

Pum

p 3

s (J.kg-1.k-1)

0.0 0.5 1.0 1.5 2.0

T (k

)

260

280

300

320

340

360

380

400

420

hso

hsi

cso

csi

Pinchh1

Pinchc

Th1

Tc

12

7

82'

8'3

4 4'

3'3"

Pinchh2

Th2

5

6 6'5"

5'

Evaporator2

Fig. 2. NORC (a) schematic of the cycle and (b) T–S diagram.

Table 1Constant design parameters for ORC systems modeling.

Parameters Values

Isentropic efficiency of pump, gpis (%) 80

Isentropic efficiency of turbine, gtis (%) 76

Electrical generator efficiency, gtgen (%) 95

Heat source and sink media WaterHeat source inlet temperature, Thsi (k) 423.15Heat sink inlet temperature, TcsiðkÞ 293.15Heat source inlet pressure, Phsi (bar) 5Heat sink inlet pressure, Pcsi (bar) 2Temperature of condenser, Tc (k) 308Pinch point temperature in condenser, Tc

pinch (k) 5

Heat source mass flow rate, _mh (kg/s) 50Temperature of the environment taken as standard-state value, T0

(k)298.15

394 N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401

gth ¼ _Wnet= _Qh ð1ÞIn addition, conversion of thermal energy into other types of

energy (e.g. electricity), by taking the primary heat system, bringssome energy losses. This dissipation in a cycle could not be inves-tigated by the first law of thermodynamics, since it cannot illus-trate the ability to convert low great heat into useful work [17].Therefore, exergy efficiency could be used to evaluate the maxi-mum useful work in a thermodynamic equilibrium process by fol-lowing equation [18]:

gex ¼ E _xuseful=E _xavialable ð2ÞAlso, total received exergy is equal to the ratio of useful exergy

to the amount of exergy received in evaporator by geothermalwater described as follow:

gex ¼ _Wnet=E _xh ð3ÞIn this regard to the first and second law, governing equations

of thermal and exergy (useful and destroyed) efficiencies havebeen modeled for each process in ORCs [19]. In addition, _mwf ; _mc

and X as a mass flow rate of working fluids, cooling water and also,a fraction of mass flow rate of working fluids into the regenerativeare described as follow (according to Figs. 1 and 2):

_mwf ¼ _mh hhsi � hhjat TH� �.

hevapwf ;out � hevap

wf

���at Bubble Point

� �ð4Þ

X ¼ ðh3 � h20 Þ=ðh30 � h20 Þ ð5Þ

_mc ¼ _mwf hcondwf

���at Dew Point

� hcondwf;out

� �.hcjat TL � hcsi

� �ð6Þ

Moreover, in order to calculate exergy and energy efficiencies,certain parameters such as enthalpy, entropy and vapor pressureshould be determined. Therefore, the value of enthalpy andentropy were obtained by using PR EOS and also, the vaporpressures of each working fluid were calculated using modifiedWagner equation, according to Refs. [20,21], respectively. Inaddition, constant design parameters for ORC systems areindicated in Table 1.

2.4. Economic modeling

In this article, not only thermodynamic modeling of each cyclewas considered but also their economic modeling investigated.Accordingly, specific investment cost (SIC) and return on invest-ment (ROI) were used for economic analysis. In order to computeSIC and ROI, costs of equipment have to be evaluated. Therefore,firstly, basic parameters for calculating SIC and ROI are describedas below:

2.4.1. Equipment costBare module method was selected to calculate each equipment

cost within the mentioned cycles [22]:

� Heat Exchangers cost

CHX ¼ 527:7397

� C0;HX � B1;HX þ ðB2;HX � FM;HX � FP;HXÞ½ � ð7Þ

logC0;HX ¼ K1;HX þ K2;HXðlogAHXÞ þ K3;HXðlogAHXÞ2h i

ð8Þ

log FP;HX ¼ C1;HX þ C2;HXðlog PHXÞ þ C3;HXðlog PHXÞ2h i

ð9Þ

where respectively, CHX; FM;HX; FP;HX; AHX and PHX are the cost, thematerial factor, pressure factor, surface area and pressure for heatexchangers which include evaporator, regenerative and condenser.Eq. (8) could also be used for initial heat exchangers cost.

N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401 395

� Cost of turbine

Ct ¼ 527:7397

� C0;t � FM;t ð10Þ

logC0;t ¼ K1;t þ K2;tðlog _W tÞ þ K3;tðlog _W tÞ2h i

ð11Þ

where C0;t and FM;t are the initial cost and the material factor of tur-bine, respectively.

� Cost of pump

Cp ¼ 527:7397

� C0;p � B1;p þ ðB2;p � FM;p � FP;pÞ� � ð12Þ

logC0;p ¼ K1;p þ K2;pðlog _WpÞ þ K3;pðlog _WpÞ2h i

ð13Þ

log FP;p ¼ C1;p þ C2;pðlog PpÞ þ C3;Pðlog PpÞ2h i

ð14Þ

where C0;p; FP;p and Pp are initial cost, pressure factor and pressureof pump, respectively. In Eqs. (7)–(14), B1; B2; K1; K2; K3; C1; C2

and C3 are constants related to the material which was used in eachequipment within the cycle and their values are given in Table 2.Moreover, 527.7 and 397 are chemical engineering plant costindexes for the year 2015 and 2001, respectively [23].

2.4.2. Heat exchanger surface area calculationIn order to calculate cost of heat exchangers, the type of heat

exchanger should be known. Moreover, a heat exchanger shouldbe chosen according to the operating conditions as well as its heattransfer surface area. Generally, the amount of generating capacityin a geo-plant is one of the main crucial parameters for choosingthe best types of heat exchangers. In this basis, for productivecapacity ð _WnetÞ of lower than tens of kilowatts, the plate heatexchangers are most suitable, whereas shell and tube heatexchangers could be used for productive capacity of higher thanhundreds of kilowatts [12]. Hence, in this study, shell and tubeheat exchanger was chosen in which, flow in the tube and liquidin the shell [24] and its specifications are shown in Table 3.

Table 2Constants for the calculation of bare module cost of equipments (according to Eqs.(7)–(14)) [22].

Constants Equipment

Heat exchanger Pump Turbine

K1 4.3247 3.3892 2.2476K2 �0.3030 0.0536 1.4965K3 0.1634 0.1538 �0.1618C1 0.03881 �0.3935 –C2 �0.1127 0.3957 –C3 0.0818 �0.0023 –B1 1.6300 1.8900 –B2 1.6600 1.3500 –FM 1.0000 1.6000 3.5000FS 1.7000 1.7000 1.7000

Table 3Shell and tube heat exchanger data.

Inner tube diameter, di (mm) 10.92Outer tube diameter, do (mm) 12.7Tube pinch, PT (mm) 19.05

Fouling factor (m2 �C/W) [25]Hot water 0.0001761Cold water 0.0001761Refrigerant (vapor) 0.0001761Refrigerant (liquid) 0.0003522Total fouling resistance with two-phase 0.00067

Accordingly, kern’s method was used to determinate the heattransfer surface area of evaporator, regenerative and condenser[26]. And also, inner and outer heat transfer coefficients were cal-culated by using Gnielinski equation [27] and Kern’s method [26],respectively.

2.4.3. Specific investment cost (SIC)The value of SIC could be obtained from Eq. (15) described as

follow [28]:

SIC ¼ FS � TCB

_Wnet

ð15Þ

where FS is a correction factor for overhead cost and its values areillustrated in Table 2. Moreover, TCB is the total bare module costdescribed in equation (16) as follow:

TCB ¼Xn

i¼1

Ci ð16Þ

In this study, heat source cost (geothermal energy) and cost ofworking fluid in mentioned cycles were neglected.

2.4.4. Return on investment (ROI)Determination of this type of profitability is usually defined as a

ratio of net profit to total cost of investment [29]:

ROI ¼ ð1� tcorpÞðSannual � CTPCÞCTCI

ð17Þ

where Sannual; CTPC; tcorp and CTCI are the annual sales revenue, thetotal production cost (through electricity generation), the corporatetax rate and the cost of total capital investment, respectively.The corporate tax rate was considered to be 25.00% for Iran, 33.33for France and 35.00% for United States in year 2015 [30]. Theequations which related to the total capital investment and totalproduction costs are listed in Tables 4 and 5, respectively.

� Annual sales revenue

Sannual ¼ MelCel ð18Þ

Mel ¼ Hannual_Welec

net ð19Þ

_Welecnet ¼ _Welec

t � _Welecp ð20Þ

Hannual ¼ 0:9� 365� 24 ð21ÞIn these equations, Mel shows the annual electricity generation

according to the net electrical power output. Also, Cel which illus-trates the electricity price for industry in year 2015, was assumedto be 0.16, 0.11 and 0.07 $/kW h for Iran [31], France and UnitedStates [32], respectively.

Table 4Components of total capital investment.

Total bare module cost, TCB TCB ¼ PCHx þ Ct þ Cp

Cost of site preparation, Csite Csite = 0.05TCB

Cost of service facilities, Cserv Cserv = 0.05TCB

Allocated costs for utility plants andrelated facilities, Calloc

Calloc ¼ 792 _mc

Total direct permanent investment, CDPI CDPI = TCB + Csite + Cserv + CallocCost of contingencies and contractor’s fee,

Ccont

Ccont = 0.18CDPI

Total depreciable capital, CTDC CTDC = CDPI + CcontCost of land, Cland Cland = 0Cost of royalties, Croyal Croyal = 0Cost of plant startup, Cstartup Cstartup = 0.1CTDCTotal permanent investment, CTPI CTPI = CTDC + Cland + Croyal + CstartupWorking capital, CWC CWC = 0Total capital investment, CTCI CTCI = CTPI + CWC

Table 5Components of total production cost.

Cost of wages and benefits, CWB CWB = 0.035CTDCCost of salaries and benefits, CSB CSB = 0.25CWB

Cost of materials and services, CMS CMS = CWB

Cost of maintenance overhead, CMO CMO = 0.05CWB

Direct manufacturing costs, CDMC CDMC = CWB + CSB + CMS + CMO

Cost of property taxes and liability insurance,CPI

CPI = 0.02CTDC

Fixed manufacturing costs, CFIX CFIX = CPITotal annual cost of manufacture, CCOM CCOM = CDMC + CFIXGeneral expenses, CGE CGE = 0Total production cost, CTPC CTPC = CCOM + CGE

Table 7Thermodynamic properties of working fluids [34].

Substances Tc (K) Pc (bar) x

Isobutane 407.85 36.40 0.19R123 456.83 36.62 0.28Water 647.09 220.64 0.34

396 N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401

2.5. Optimization

The basic ORC operating parameters optimized in this paperinclude evaporation temperature, degree of superheat (D.S) andpinch point temperature difference in evaporator. In addition tobasic ORC parameters, regenerative temperature and temperatureof the second evaporator were also optimized for NORC. Further-more, selection of a suitable objective function plays a crucial rolefor optimization of these operating parameters. Therefore, threedifferent objective functions proposed in this paper contain: ther-modynamic, economic and thermo-economic. Accordingly, theobjective functions for thermodynamic and economic optimizationare described as below:

F1ðxÞ ¼ Maximize ðgexÞ ¼_W t � _Wp

_mh hhsi � hhso � T0ðshsi � shsoÞ½ � ð22Þ

F2ðxÞ ¼ Minimize ðSICÞ ¼ FS � TCB

_Wnet

ð23Þ

Moreover, linear weighted evaluation function was selected forthermo-economic optimization (a multi objective function) [33]:

FðxÞ ¼ aF1ðxÞ þ bF2ðxÞ ð24Þ

where a and b are weight coefficients of the mentioned objectivefunction:

a ¼ ðF12 � F2

2Þ½ðF2

1 � F11Þ þ ðF1

2 � F22Þ�

ð25Þ

b ¼ 1� a ð26Þ

where according to Eqs. (25) and (26), F11 is the maximum value of

F1; F21 is the value of function F1 when F2 obtained a minimum

value, F22 is the minimum value of F2 and F1

2 is the value of functionF2 when F1 obtained a maximum value [33].

The mentioned objective functions were optimized by geneticalgorithm [9] in which constraints and bounds of operating param-eters are illustrated in Table 6. And also, thermodynamic proper-ties of working fluids are shown in Table 7 [34].

Table 6Constraints and bounds for optimization.

Parameters (constraints) Lower bound Upper bound

Temperature of evaporator 1 335 (K) 485 (K)Temperature of evaporator 2 335 (K) 485 (K)Temperature of regenerative 335 (K) 485 (K)Degree of superheat 0 (K) 20 (K)PPTD in evaporator 1 5 (K) 20 (K)Pressure of evaporator 1 5 (bar) 30 (bar)

3. Results and discussion

3.1. Verification

Table 8 shows a comparison of thermodynamic parameters cal-culated by PR EOS with NIST Reference Database (ASHRAE Stan-dard) [34]. According to this table, the results of present studyindicate a good agreement with NIST data bank.

Also, Table 9 illustrates comparison results between basic ORCof this study and previous researches. Pressure and thermal effi-ciency in this table show that the modeling results have a goodagreement between the present work and pervious ones. Further-more, exergy efficiency values versus evaporator temperature,obtained from present model are compared with study carriedout by Shengjun et al. [38] for R123 fluid in Fig. 3. According to thisfigure, it is obvious that exergy efficiency obtained in this articlehas a low error as well as a similar pattern in Ref. [38].

3.2. Optimization results and cycles performance investigation

In order to make a valuable comparison between the perfor-mance of both basic ORC and NORC, it could better to use optimiza-tion results of cycles with the same objective function. Accordingly,Table 10 shows the optimization results of basic ORC and NORCwith both thermodynamic and economic objective functions andtwo different working fluids. According to the table, the resultsof thermal and exergy efficiencies show that the NORC gives a bet-ter performance than the basic ORC. In addition, by comparing theresults of optimized parameters, it can be concluded that in boththermodynamic and economic optimization, the evaporating tem-peratures are between the boundaries and also, the pinch pointgets the minimum value of its optimization bands. However, thedegree of superheat for two objective functions behaves oppo-sitely, so that degree of superheat tends to be the minimum inthermodynamic objective function and the maximum in economicobjective function.

According to Section 2.1, the NORC was designed based onRORC and TSORC reviewed by previous researchers. In this basis,in order to investigate the deviation performance of NORC in thepresent work in respect to RORC and TSORC performances, Eq.(27) was employed:

% Deviation ¼ 100ðPai � PaORCÞPaORC

ð27Þ

where PaORC and Pai denote the parameters of ORC and other cycles.Table 11 shows the results of NORC, RORC and TSORC in respect ofthe basic ORC. According to this table, the new cycle has moreexergy efficiency than the other cycles for both working fluids.

According to the results of thermodynamic and economic objec-tive functions (see Table 10), it was found that these two objectivefunctions have the contrary behaviors during the optimization ofdegree of superheat. For this purpose, in order to investigate thesetwo functions simultaneously, thermo-economic objective func-tion was used. Table 12 indicates the results which obtainedthrough thermo-economic optimization of basic ORC and NORCfor isobutene and R123. The value of a shown in the table was usedas the weight coefficient of thermo-economic objective function.

Table 8Comparing the error of entropy and enthalpy in this study and NIST databank.

Substances T distance (K) P distance (bar) % SL_Errora % SV_Errora % HL_Errorb % HV_Errorb

Isobutane 269.73–407.81 1.39–36.29 1.99 0.49 2.08 0.43R123 272.00–456.83 0.31–36.62 2.95 1.23 3.59 1.06

a % Error ¼ 100n

Pni

SL or VThis work�SL or V

NIST

SL or VNIST

� �:

b % Error ¼ 100n

Pni

HL or VThis work�HL or V

NIST

HL or VNIST

� �:

Table 9comparison of thermal efficiency obtained through modeling in this study with other papers.

Com. TGI (�C) Tcool (�C) Tevap (�C) Tcond (�C) DTpp;co (�C) DTpp;eV (�C) D.S (�C) Pevap (bar) Pcond (bar) gth (%) Ref.

Pentane 150.00 20.00 107.00 38.10 6.30 2.60 0.00 6.93 1.09 11.69 This workPentane 150.00 20.00 107.00 38.10 6.30 2.60 0.00 – – 11.70 Ref. [35]R134a 120.00 25.00 67.75 30.00 10.00 10.00 0.00 20.11 7.71 7.29 This workR134a 120.00 25.00 67.75 30.00 10.00 10.00 0.00 20.00 7.72 7.48 Ref. [14]R134a 120.00 25.00 67.75 30.00 10.00 10.00 0.00 20.00 7.72 7.74 Ref. [36]Water 150.00 15.00 85.18 30.00 0.50 3.00 60.00 0.53 0.03 10.73 This workWater 150.00 15.00 85.18 30.00 0.50 3.00 60.00 0.57 0.04 10.86 Ref. [37]

Evaporating Temperature (oC)

50 55 60 65 70 75 80 85 90

Exc

ergy

Eff

icie

ny (%

)

36

38

40

42

44

46

48

50

52

54

56

R123 (REF. [38])R123 (This Work)

Fig. 3. Comparison of exergy efficiency obtained through modeling in this studywith Ref. [38].

Table 11Comparing the results of thermodynamic optimization in RORC, TSORC and NORCbased on basic ORC for Isobutane and R123.

Substance i % Wni % Qei % EHxi % gexi % Ctbm % SICi

Isobutane RORC �6.65 �14.68 �11.25 5.16 �5.95 0.71TSORC 11.62 14.47 9.16 2.22 21.46 8.78NORC 2.73 �4.52 �3.48 6.40 12.64 9.60

R123 RORC �97.88 �98.21 �98.08 10.22 �81.14 789.40TSORC 44.18 46.19 40.68 2.49 41.67 �1.74NORC 25.93 15.56 14.12 10.35 43.77 14.16

N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401 397

According to Eq. (25), in order to calculate a, thermodynamic andeconomic objective function values reported in Table 10, couldbe used. Therefore, by calculating a for each cycle and fluid individ-ually, thermo-economic weighting function and the correspondingparameters were optimized. By comparing the results of Table 12,it could be concluded that the thermodynamic efficiency of pro-posed cycle is higher than the basic ORC. Also, the degree of super-heat which was obtained for this objective function was in therange of 0–20 �C, due to an adverse effect of thermodynamic andeconomic objective functions.

In Fig. 4, thermal and exergy efficiencies for two consideredcycles in this paper (new and basic ORC) were compared with basic

Table 10Thermodynamic and economic optimization results of Isobutane and R123 in basic ORC a

Substance System Objective function Tevap1 (K) Tevap2 (K)

Isobutane ORC Thermo. 396.35 –Econ. 392.97 –

NORC Thermo. 396.30 376.76Econ. 396.35 357.06

R123 ORC Thermo. 405.32 –Econ. 393.08 –

NORC Thermo. 407.44 398.60Econ. 392.93 363.81

ORC result carried out by Heberle and Brüggemann [39] for isobu-tane. These results have analyzed in thermo-economic optimiza-tion with the inlet temperature of geothermal water 423.15 K.According to this figure, it is observed that not only exergy effi-ciency of new cycle is more than two other basic cycles but also,the performance of basic ORC investigated in this work is betterthan the work carried out by Heberle and Brüggemann, due to dif-ferent assumptions and methods of optimization.

According to Table 13, thermal efficiency and specific invest-ment cost for new and basic ORCs in this paper are compared withconsidered cycles (basic ORC, regenerative ORC and double stageregenerative ORC) in Ref. [11] for R123. Due to Table 13, it canbe concluded that new and basic cycles in this paper have morethermal efficiency and less SIC than each cycle studied in Ref.[11]. These differences can be seen in assumptions and optimiza-tion conditions.

Fig. 5 illustrates the irreversibility of each equipment in fourmentioned cycles including, basic ORC, RORC, TSORC and NORC.According to this figure, it can be concluded that the destroyedexergy in the basic ORC was reduced by changing cycle configura-tion, especially in the new proposed cycle. It should be noted that

nd NORC.

Treg (K) D.S (K) DTpp;evap (K) gth gex SIC ($/W)

– 1.20 5.00 0.1177 0.4824 4.3488– 19.85 5.19 0.1164 0.4569 2.9016

337.33 1.20 5.05 0.1270 0.5133 4.7678325.00 20.00 5.03 0.1120 0.4779 3.0419

– 0.02 5.00 0.1405 0.4916 3.0469– 19.92 5.00 0.1299 0.4803 2.3262

346.05 0.07 5.03 0.1531 0.5425 3.4783325.01 19.99 5.00 0.1229 0.5003 2.2705

Table 12Investigation of parameters and results of thermo-economic optimization obtained through linear weighting function.

Substance System Tevap1 (K) Tevap2 (K) Treg (K) D.S (K) DTpp;eV (K) gth gex SIC ($/W) a

Isobutane ORC 396.159 – – 8.319 5.064 0.1183 0.4709 3.405 0.983NORC 396.315 373.988 329.926 9.516 5.085 0.1235 0.5047 3.543 0.980

R123 ORC 394.416 – – 17.774 5.002 0.1312 0.4822 2.378 0.985NORC 399.347 383.103 335.908 18.556 5.108 0.1397 0.5253 2.459 0.966

Eff

icie

ncy

(%)

0

10

20

30

40

50

60ThermalExergy

ORC [Ref. 39] ORC [This Work] NORC [This Work]

Fig. 4. Comparison of thermodynamic efficiencies (thermal and exergy) for twoconsidered cycles obtained through thermo-economic optimization in this studywith Ref. [39] for isobutane.

Table 13A Comparison of thermal efficiency for two considered cycles obtained throughthermo- economic optimization in this study with Ref. [11] for R123.

Parameters Cycles

ORC [ThisWork]

NORC [ThisWork]

ORC[11]

RORC[11]

DoubleRORC [11]

gth 0.1312 0.1397 0.7264 0.8724 0.9204SIC ($/W) 2.3780 2.4590 3.5560 3.7490 4.0570

% I

0

20

40

60

80Cond.PumpEvap.Turb.Regen.

ORC RORC TORC NORC

Fig. 5. Comparison of exergy destruction in each cycles equipment.

Table 14The investigation of thermodynamic parameters obtained through thermo-economic optimization for Isobutane and R123 in studied cycles.

Substance System Pevap1. (bar) Pevap2. (bar) Preg (bar) Pcond (bar) _mw1 (kg/s) _mw2 (kg/s) X1 _mc (kg/s)

Isobutane ORC 29.906 – – 4.628 33.805 – – 240.766NORC 29.985 20.191 8.062 4.628 32.932 9.782 0.143 260.819

R123 ORC 12.290 – – 1.303 41.230 – – 153.090NORC 13.541 9.746 3.095 1.303 33.327 20.983 0.134 174.732

Fig. 6. The effects of primary evaporator temperature and degree of superheated onexergy efficiency in NORC.

Fig. 7. The effects of secondary evaporator temperature and degree of superheatedon exergy efficiency in NORC.

398 N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401

Fig. 8. The effects of regenerating temperature and degree of superheated onexergy efficiency in NORC.

Fig. 9. The effects of primary evaporator temperature and degree of superheated onspecific investment cost (SIC) in NORC.

Fig. 10. The effects of pinch point temperature difference and degree of super-heated on exergy efficiency in NORC.

Fig. 11. The effects of pinch point temperature difference and degree of super-heated on SIC in NORC.

N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401 399

the highest amount of exergy destruction in the basic ORC isrelated to evaporator due to this figure and Ref. [40] which couldbe reduced to the lowest possible value in NORC.

According to optimized parameters obtained from thermo-economic objective function and also, the modeling equationsdescribed in the Section 2, important operating parameters suchas heat exchangers pressure, mass flow rate of working fluid, massflow rate of cooling water and thermal efficiency were calculatedand tabulated in Table 14. These results could be used in designand simulation of various processes in the ORC systems.

3.3. Parameters investigation of NORC

According to the sections 2–5 and 3–2, temperatures of heatexchangers (the primary and secondary evaporators and regenera-tive), degree of superheat and pinch point temperature differencein the primary evaporator were optimized for the NORC usingthree different objective functions. Changes in any of these param-eters could affect the cycle performance and its costs. Conse-quently, in this section, the effects of crucial parameters variationon thermodynamic efficiency and also SIC of NORC are studied.

Fig. 6 demonstrates the variation of NORC exergy efficiency ver-sus degree of superheat and primary evaporator temperature forisobutene fluid. The value of parameters include pinch point tem-perature, temperature condenser, the second evaporator tempera-ture and the temperature of regenerative were taken fromTable 12. According to the figure, at a constant degree of superheat,by increasing the evaporator temperature, the exergy efficiencyincreases. In contrast, at a constant evaporating temperature, byincreasing the degree of superheat, the exergy efficiency reduces.Furthermore, the variation of regenerative and secondary evapora-tor temperatures are affected the NORC exergy efficiency whichdepicted in Figs. 7 and 8.

Fig. 9 shows SIC variation in respect to the changes in the pri-mary evaporator temperature and the degree of superheat. Accord-ing to the figure, increasing the degree of superheat at a constantvalue of evaporating temperature and also, increasing the evapora-tion temperature at a constant degree of superheat give rise to areduction in the SIC of proposed cycle.

Figs. 10 and 11 respectively represent the variations of exergyefficiency and SIC of NORC in respect with degree of superheat

Fig. 12. The effects of condenser temperature and degree of superheated on exergyefficiency in NORC.

Table 15ROI results for basic ORC and NORC in Iran, France and America.

Substance System %ROIIRAN %ROIFRANCE %ROIUSA

Isobutane ORC 27.3310 14.2367 6.3066NORC 26.6125 13.8088 6.0492

R123 ORC 38.2263 20.7254 10.2095NORC 37.0504 20.0251 9.7883

400 N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401

and pinch point. According to this figure, it can be concluded thatfor a given value of pinch point, by increasing the degree of super-heat, the exergy efficiency decreases while the SIC reduces, andalso, at a constant degree of superheat, with increasing the pinchpoint, the exergy efficiency decreases and SIC increases.

The effect of changes in the condenser temperature and thedegree of superheat on the variation of exergy efficiency is shownin Fig. 12. According to the figure, reducing the temperature of con-denser and the degree of superheat in the optimum thermo-economic condition leads to an increase in the exergy efficiency.

3.4. ROI results

In this section, ROI is investigated using the thermo-economicparameters of optimization results for three countries, Iran, Franceand America. Table 15 shows the amount of ROI for basic ORC andNORC in these three countries. The results of comparative studyshow that, the amount of ROI in Iran for both working fluids ismore than two other countries. The high value of electricity priceand low corporate tax rate in Iran can give rise to this result.

4. Conclusions

In this study, geothermal energy was investigated with the aimof producing more electricity and also reducing the emission ofgreenhouse gases which is one of the main causes of global warm-ing. Thereby, a new ORC was designed and its performance wasevaluated by comparing with basic ORC results in optimum condi-tions for two different types of working fluids (isobutane as dryand R123 as isentropic). The optimization of cycles’ operatingparameters was carried out using three methods: thermodynamic,economic and thermo-economic objective functions. Optimizedoperating parameters contain the temperature of evaporators and

regenerative, degree of superheat and pinch point temperature dif-ference. Furthermore, an economic investigation based on ROI wasperformed in order to evaluate practical applications of consideredORCs for Iran, France and USA. The following results wereconcluded:

� Thermodynamic properties obtained from PR EOS had a goodagreement with NIST standard reference database andliteratures.

� In mentioned optimization procedure, evaporator temperatureand pinch point temperature difference tended to be maximumand minimum in their optimization bands, respectively. How-ever, degree of superheat illustrated a different pattern in eco-nomic (SIC) and thermodynamic (exergy) optimization.

� According to NORC results compared to the basic ORC, RORCand TSORC performances, it was observed that NORC had higherefficiency (exergy and energy) than other cycles for both work-ing fluids and three objective functions.

� Destroyed exergy in the basic ORC was reduced by designing anovel ORC configuration studied in this paper (NORC).

� The amount of ROI calculated for Iran, France and USA haddecreasing trends, respectively.

Acknowledgment

The authors are grateful to the Islamic Azad University of Shirazfor supporting this research.

References

[1] Hung T-C. Waste heat recovery of organic Rankine cycle using dry fluids.Energy Convers Manage 2001;42:539–53.

[2] Cammarata G, Cammarata L, Petrone G. Thermodynamic analysis of ORC forenergy production from geothermal resources. Energy Proc 2014;45:1337–43.

[3] Tchanche BF, Lambrinos G, Frangoudakis A, Papadakis G. Low-grade heatconversion into power using organic Rankine cycles – a review of variousapplications. Renew Sustain Energy Rev 2011;15:3963–79.

[4] Wang X, Dai Y. Exergoeconomic analysis of utilizing the transcritical CO2 cycleand the ORC for a recompression supercritical CO2 cycle waste heat recovery: acomparative study. Appl Energy 2016;170:193–207.

[5] Yang M, Yeh R. Economic performances optimization of an organic Rankinecycle system with lower global warming potential working fluids ingeothermal application. Renew Energy 2016;85:1201–13.

[6] Shokati N, Ranjbar F, Yari M. Exergoeconomic analysis and optimization ofbasic, dual-pressure and dual-fluid ORCs and Kalina geothermal power plants:a comparative study. Renew Energy 2015;83:527–42.

[7] Yang M, Yeh R. Thermo-economic optimization of an organic Rankine cyclesystem for large marine diesel engine waste heat recovery. Energy 2015:1–13.

[8] Dai Y, Wang J, Gao L. Parametric optimization and comparative study oforganic Rankine cycle (ORC) for low grade waste heat recovery. EnergyConvers Manage 2009;50:576–82.

[9] Xi H, Li M-J, Xu C, He Y-L. Parametric optimization of regenerative organicRankine cycle (ORC) for low grade waste heat recovery using geneticalgorithm. Energy 2013;58:473–82.

[10] Roy J, Misra A. Parametric optimization and performance analysis of aregenerative organic Rankine cycle using R-123 for waste heat recovery.Energy 2012;39:227–35.

[11] Imran M, Park BS, Kim HJ, Lee DH, Usman M, Heo M. Thermo-economicoptimization of regenerative organic Rankine cycle for waste heat recoveryapplications. Energy Convers Manage 2014;87:107–18.

[12] Li T, Wang Q, Zhu J, Hu K, Fu W. Thermodynamic optimization of organicRankine cycle using two-stage evaporation. Renew Energy 2015;75:654–64.

[13] Li T, Zhang Z, Lu J, Yang J, Hu Y. Two-stage evaporation strategy to improvesystem performance for organic Rankine cycle. Appl Energy 2015;150:323–34.

[14] Li T, Zhu J, Hu K, Kang Z, Zhang W. Implementation of PDORC (parallel double-evaporator organic Rankine cycle) to enhance power output in oilfield. Energy2014;68:680–7.

[15] Zare V. A comparative exergoeconomic analysis of different ORCconfigurations for binary geothermal power plants. Energy Convers Manage2015;105:127–38.

[16] DiPippo R. Second law assessment of binary plants generating power fromlow-temperature geothermal fluids. Geothermics 2004;33:565–86.

[17] Goswami DY. The CRC handbook of mechanical engineering. CRC Press; 2004.[18] Moran MJ, Shapiro HN, Boettner DD, Bailey MB. Fundamentals of engineering

thermodynamics. John Wiley & Sons; 2010.

N. Kazemi, F. Samadi / Energy Conversion and Management 121 (2016) 391–401 401

[19] Le VL, Kheiri A, Feidt M, Pelloux-Prayer S. Thermodynamic and economicoptimizations of a waste heat to power plant driven by a subcritical ORC(Organic Rankine Cycle) using pure or zeotropic working fluid. Energy2014;78:1–17.

[20] Peng D-Y, Robinson DB. A new two-constant equation of state. Ind Eng ChemFundam 1976;15:59–64.

[21] Perry Robert H, Green Don W, Maloney James O. Perry’s chemical engineers’handbook. New York: Mc Graw-Hills; 1997. p. 56–64.

[22] Turton R, Bailie RC, Whiting WB, Shaeiwitz JA. Analysis, synthesis and designof chemical processes. Pearson Education; 2008.

[23] Peters MS, Timmerhaus KD, West RE, Timmerhaus K, West R. Plant design andeconomics for chemical engineers. New York: McGraw-Hill; 1968.

[24] Lecompte S, Huisseune H, van den Broek M, De Schampheleire S, De Paepe M.Part load based thermo-economic optimization of the Organic Rankine Cycle(ORC) applied to a combined heat and power (CHP) system. Appl Energy2013;111:871–81.

[25] Jim H. Standards of the Tubular Exchanger Manufacturers Association. 8th ed.Tubular Exchanger Manufacturers Association, Inc.; 1999.

[26] Kern DQ. Process heat transfer: international. Student ed. InternationalAuckland Bogota: McGraw-Hill; 1986.

[27] Gnielinski V. New equations for heat and mass-transfer in turbulent pipe andchannel flow. Int Chem Eng 1976;16:359–68.

[28] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization ofwaste heat recovery organic Rankine cycles. Appl Therm Eng2011;31:2885–93.

[29] Seider W, Seader J, Lewin D. Product and process design principles, synthesis,analysis and evaluation. New York: John Willey & Sons, Inc.; 2003.

[30] KPMG, Corporate tax rates table, 2015.[31] Ministry of Energy. Renewable Energy Organization of Iran (SUNA), 2015.

<http://www.suna.org.ir/>. [in Persian].

[32] EIA US. Electric power monthly, 2015.[33] Xiao L, Wu S-Y, Yi T-T, Liu C, Li Y-R. Multi-objective optimization of

evaporation and condensation temperatures for subcritical organic Rankinecycle. Energy 2015;83:723–33.

[34] Lemmon E, McLinden M, Friend D. Thermophysical properties of fluid systemsin NIST chemistry WebBook. In: Linstrom PJ, Mallard WG, editors. NISTstandard reference database number 69. Gaithersburg (MD): National Instituteof Standards and Technology; 2011. p. 20899. Webbook.nist.gov/chemistry/fluids [accessed April, 2015].

[35] Kheiri A, Feidt M, Pelloux-Prayer S. Thermodynamic and economicoptimizations of a waste heat to power plant driven by a subcritical ORC(Organic Rankine Cycle) using pure or zeotropic working fluid. Energy2014;78:622–38.

[36] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for low-temperature organic Rankine cycles. Energy 2007;32:1210–21.

[37] Astolfi M, Romano MC, Bombarda P, Macchi E. Binary ORC (Organic RankineCycles) power plants for the exploitation of medium–low temperaturegeothermal sources – Part B: Techno-economic optimization. Energy2014;66:435–46.

[38] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametricoptimization of subcritical Organic Rankine Cycle (ORC) and transcriticalpower cycle system for low-temperature geothermal power generation. ApplEnergy 2011;88:2740–54.

[39] Heberle F, Brüggemann D. Exergy based fluid selection for a geothermalorganic Rankine cycle for combined heat and power generation. Appl ThermEng 2010;30:1326–32.

[40] Mago P, Srinivasan K, Chamra L, Somayaji C. An examination of exergydestruction in organic Rankine cycles. Int J Energy Res 2008;32:926–38.