1 s2.0-s0960148117308571-main

A comparative profitability study of geothermal electricity production
in developed and developing countries: Exergoeconomic analysis and
optimization of different ORC configurations
Shahram Karimi a, *
, Sima Mansouri b
a
School of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Ave., Shiraz Iran
b
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 25 October 2016
Received in revised form
27 August 2017
Accepted 31 August 2017
Available online 1 September 2017
Keywords:
Geothermal
Exergoeconomic optimization
ORC
Economic indicators
Global warming
a b s t r a c t
By the growing usage of geothermal energy as an alternative approach to produce useful work such as
electricity, the emission of global greenhouse gases could be reduced because of its environmentally
friendly. In this paper, the thermodynamic and economic performances of three systems which contain a
basic Organic Rankine Cycle (ORC), a Regenerative Organic Rankine Cycle (RORC) and a Two-Stage
Evaporation Organic Rankine Cycle (TSEORC) are investigated in order to generate electrical power
from geothermal sources. For operating the considered cycles, three types of pure organic working fluids
including dry (R600a, R601a), wet (R152a and R134a) and isentropic (R11 and R123) ones are selected.
Firstly, according to thermodynamic aspect, Peng Robinson (PR) and Soave-Redlich-Kwong (SRK)
equations of state are used to determine thermodynamic properties of mentioned working fluids and
geothermal water, respectively. Furthermore, the operating parameters involving evaporator and
regenerative temperatures, degree of superheat and pinch point temperature difference in evaporator
are optimized with three optimization methods. Objective functions are exergy efficiency, Specific In-
vestment Cost (SIC) and a combination of exergy and SIC for thermodynamic, economic and exer-
goeconomic optimizations. The amount of boundary conditions constituting of heat source inlet
temperature, heat sink inlet temperature, heat source inlet pressure, heat sink inlet pressure temperature
of condenser, pinch point temperature in condenser and heat source mass flow rate are 423.14 (K), 293.15
(K), 5 (bar), 2 (bar), 308 (K), 5 (K) and 50 (kg/s) respectively. Optimizations results show that among all
considered operating parameters, degree of superheat ranged between 0 and 20 is the most effective
parameter which is almost obtained at lower, upper and in the middle range of optimization bounds in
the thermodynamic, economic and exergoeconomic investigations respectively. Secondly, from economic
view point, three economic indicators: Levelized Cost Of Electricity (LCOE), Return On Investment (ROI)
and Payback Period (PBP) are utilized so as to focus on the economic performance of three mentioned
ORC configurations based on exergoeconomic results for twenty countries with geothermal resources as
well as different cost of electricity production and tax rates. The results indicate that Australia has the
maximum amount of ROI making up a bit more than 100% and minimum amount of PBP accounting for
lower than four years when R123 is applied as the working fluid in TSEORC system. Also, the maximum
and minimum values of LCOE are obtained in basic ORC- R134a and RORC- R123 (0.1474 and 0.0493
respectively). In addition, the investigation of impact of operating parameters on economic indicators for
Iran illustrate that the ROI value dramatically rise by increasing the evaporator temperature and degree
of superheat. In contrast, pinch point temperature difference leads to a decline in the amount of ROI. This
note should be taken in to account that ROI and PBP show the reverse results.
© 2017 Elsevier Ltd. All rights reserved.
1. Introduction
Over the last decades, the consumption of fossil fuels leading to
enhance the emissions of Greenhouse Gases (GHGs) has increased* Corresponding author.
E-mail address: sh.karimmi@yahoo.com (S. Karimi).
Contents lists available at ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
http://dx.doi.org/10.1016/j.renene.2017.08.098
0960-1481/© 2017 Elsevier Ltd. All rights reserved.
Renewable Energy 115 (2018) 600e619

dramatically due to growing in the industrialization and the popu-
lation explosion throughout the world. Such issues have resulted in
taking place many environmental problems such as global warming,
air pollution, ozone layer depletion and so on [1]. For the purpose of
coping with the problems mentioned, different types of renewable
energy such as geothermal, solar and wind energy have been chiefly
investigated because of their low or zero GHGs emissions [2].
Geothermal energy is a kind of low grade heat source of renew-
able energy utilized in various applications such as heating build-
ings, agriculture sector and electricity production in power plants. In
terms of electricity production, an eligible technology is Organic
Rankine Cycle (ORC) come up with converting thermal energy into
sustainable power [3e6]. Consequently, many efforts have been
carried out to analyze the performance of ORCs, which they cover
different configurations based on basic ORC, selection of working
fluid, operating conditions, different optimization approaches, ORCs
economics and etc. Accordingly, in this paper, the literature review
section focuses on some recent works studied not only thermody-
namic and economic optimization but also economic evaluation
associated with several economic indicators including Levelized
Energy Efficiency Cost (LEEC), Levelized Cost Of Electricity (LCOE),
Return On Investment (ROI) and Pay-Back Period (PBP).
Wang and Dai [7] analyzed two different cycles performance by
using exergoeconomic optimization and also compared the results
of their considered cycles for different working fluids. The results
showed that the total product unit cost for the combination of
supercritical CO2 Brayton and ORC cycles is marginally lower than
the combination of supercritical CO2 Brayton and transcritical CO2
cycles. Two kinds of pure and zeotropic mixtures working fluids in
ORCs were studied by Kolahi et al. [8] and the results of thermo-
dynamic and economic analysis were compared. The results indi-
cated that at particular mass fractions of refrigerants, both the
energy and exergy efficiencies are maximized. Zare [9] compared
the performance of three structures of ORCs for binary geothermal
power plants through two different viewpoints: thermodynamic
and economic. The results revealed that in the first and second law
of thermodynamic viewpoint, ORC with internal heat exchanger
performed superiority, while the simple ORC is the best case among
cycles which were considered from the economic point of view. A
comparison between the results of various scales of ORCs from
economic viewpoint carried out by Meinel et al. [10]. They illus-
trated that economic evaluation was conducted due to outline the
economic merits of the turbine-bleeding cycle. Yang and Yeh [11]
investigated the thermo-economic optimization in order to
recover waste heat from large marine diesel engines by using ORC.
They also recognized that, R1234yf, R1234ze, R152a, and R600a had
the best performance in thermo-economic optimization, respec-
tively. Shokati et al. [12] studied three different ORCs (the basic,
dual-pressure and dual-fluid) and Kalina cycle for power genera-
tion from geothermal sources. Also, they compared these cycles
through different optimization which consist of energy, exergy and
exergoeconomic aspects. In comparison with other cycles, as re-
sults, they distinguished that dual-pressure ORC generated the
maximum value of electrical power and Kalina cycle produced the
minimum value of unit cost of power. In another study, Yang and
Yeh [13] investigated the optimization of ORC system by using
geothermal energy from economic viewpoint. The results indicated
that R600, R600a, R1233zd, R1234yf, R1234ze, and R290 had the
satisfactory performance, respectively in economic optimization.
The investigation of power plants was taken into consideration by
Yildirim and Ozgener [14] not only with thermodynamic (exergy)
aspects but also with economic point of view, simultaneously. They
analyzed the exergy efficiency with the focus on the effects of
thermal fluids which were used in power plants. Eyidogan et al.
[15] carried out technical and economic optimization to evaluate
the application of ORCs in Turkey. Also, renewable energy pro-
ductions and industrial waste heat recovery opportunities and the
investment payback period of ORC were investigated and revealed
by the government incentives. Toffolo et al. [16] showed a multi-
criteria approach in ORC for the optimal selection of working
fluids and design parameters in such systems. They indicated that
the maximum power output of isobutane for all considered tem-
peratures was lower than R134a. The combination of supercritical
CO2 (carbon dioxide) recompression for two cycles (Brayton/
organic Rankine cycle) by thermo-economic analysis and optimi-
zation point of view were studied by Akbari and Mahmoudi [17].
They concluded that the exergy efficiency of supercritical CO2
recompression Brayton cycle (SCRBC) obtained 11.7% lower than
SCRB/ORC. The results also showed the lowest cost of product unit
for the SCRB/ORC and the highest exergy efficiency are obtained
when Isobutane and RC318 are selected as the ORC working Fluids,
respectively. Chiaroni et al. [18] investigated an empirical analysis
in Italy in order to introduce a novel factor for the economic eval-
uation of industrial energy efficiency technologies. They proposed
an economic indicator called Levelized Energy Efficiency Cost
(LEEC) because it is an ordinary tool for evaluating of energy effi-
ciency. Zhang et al. [19] optimized operating parameters of R123,
R600, R245fa, R245ca and R600a with thermodynamic optimiza-
tion and evaluated their economics. Their results showed that the
considered working fluids had high level of thermal and exergy
efficiencies. However, R152a, R600, R600a, R134a, R143a, R125
observed low levelized cost value. Zhang et al. [20] illustrated the
significant parameters such as thermo-physical properties of the
working fluids and cycle type affected the performance of power
plant. El-Emam et al. [21] with the view point of thermodynamic
optimization and economic evaluation concluded that the cost rate
of the exergy destruction in the system was increased by the rise of
the dead state temperature. A same work has done by Astolfi et al.
[22] who indicated that the results of techno-economic optimiza-
tion were different from thermodynamic analysis since it
confirmed its significant role in the optimization of ORC plants.
Thermodynamic optimization, economic evaluation and thermo-
economic investigation were aspects of Ganjehsarabi et al. [23].
The results showed that the unit cost of geothermal fluid was 1.67
cents/kWh and the unit cost of electricity generation was 5.3 cents/
kWh. Heberle et al. [24] with thermo-economic investigation
proved that the lowest temperature difference of R600a in evapo-
rator and condenser were 3 K and 7 K respectively. An exer-
goeconomic modeling and optimization were carried out by Liu
et al. [25] in order to investigate the efficiency of various ORC
systems and working fluids related to geothermal energy. Garg
et al. [26], with exergoeconomic viewpoint, analyzed the perfor-
mance of ORCs to produce electricity from not only geothermal but
also waste heat recovery and solar thermal. Also, there are similar
exergoeconomic works studying ORC systems with different con-
figurations and a wide range of working fluids [27e30].
In this article, performance of three ORC configurations
including basic ORC, RORC and TSEORC are studied with selection of
R600a, R601a, R152a and R134a, R11 and R123 as six different pure
organic working fluids with two different viewpoints. On one hand,
from thermodynamic aspect, the operating parameters in the
mentioned cycles are optimized with three different objective
functions namely exergy, economic and exergoeconomic optimi-
zations. On the other hand, from economical point of view, profit-
ability estimation of the considered cycles is carried out with three
different economic indicators consisting of LCOE, ROI and PBP for
twenty countries that have geothermal water. The most attention of
this work is captured to evaluate and compare the economical
investigation of using geothermal water as an alternative method
for producing electricity for different developed and developing
S. Karimi, S. Mansouri / Renewable Energy 115 (2018) 600e619 601

countries. Therefore, the greatest novelty of this work is the eco-
nomic point of view. Also, other novelties are listed below:
Comparing equation of states (SRK and PR) to each other for the
sake of decreasing calculation errors associated with either
thermodynamic or economic aspects.
Optimization method being a linear function.
Investigating and expecting SIC for real plants.
Evaluating condenser and ambient conditions effects on the
performances of cycles studied in the current work.
2. Materials and methods
2.1. System description
Geo-plants could be applied to extract and exploit geothermal
energy sources as low-grade heat temperature fields. In such
plants, an organic working fluid within a closed Rankine cycles
known as ORCs is employed not only from technical viewpoints but
also by environmental aspects [31]. A basic ORC consists of four
major things namely an evaporator, a turbine, a condenser and a
pump. In this cycle, the organic working fluid by passing through a
pump enters into the evaporator in order to absorb thermal energy
from the geothermal water. The superheated working fluid is then
expanded in the turbine to generate electricity through a generator
and after that it cools down and condenses in the condenser before
being pumped again to the evaporator.
Although a basic ORC could be utilized to convert low-grade
heat sources in to useful work such as electricity, its efficiency is
low due to high system irreversibility [32].
Accordingly, in order to reduce irreversibility and enhance the
performance of ORC systems, numerous methods could be applied.
For instance, the configuration of basic ORC could be changed
which has been investigated by many researches. In this respect,
one of changes in restructuring of ORC is adding a regenerative to
the basic ORC components (RORC). Another method which has
been used is adding an extra evaporator in series to the main
evaporator of basic ORC known as TSEORC. The schematic diagrams
and temperature-entropy (T-S) graphs of three studied ORC con-
figurations consisting of the basic ORC, RORC and TSEORC pre-
sented in Ref. [33] and Ref. [34].
2.2. Assumptions
In the present study, the following assumptions are applied for
modeling of three mentioned cycles.
Steady-state condition is considered for each process in the
cycles.
Heat transfer parameters are calculated for the entirely devel-
oped flow.
In the heat exchangers, heat and friction losses are neglected.
Kinetic and potential energy are neglected for water as a heat
source and sink media.
Shell and tube types are selected for heat exchangers.
Peng Robinson (PR) and Soave-Redlich-Kwong (SRK) equations
of state are applied to calculate thermodynamic properties.
Six pure organic fluids, including R600a, R601a, R152a and
R134a, R11 and R123 were selected as working fluids.
2.3. Working fluid selection
In addition to cycle configuration, an appropriate choice of
working fluid in ORCs will play a significant role to change the cycle
efficiency. One of the most important characteristic that should be
taken into account during the working fluid selection is slope of the
saturation vapor line in the T-S diagram. Accordingly, Fig. 1 which is
designed in the present work by usage of Peng Robinson (PR)
equation of state indicates the T-S diagram for three working fluids
types. As can be seen in this graph, saturation vapor lines determine
working fluids categories as follow [35]:
R600a and R601a as a dry fluid with positive ds/dt slope.
R152a and R134a as a wet fluid with negative ds/dt slope.
R11 and R123 as an isentropic fluid with infinitely ds/dt slope.
Table 1 reveals thermodynamic properties of six kinds of
working fluids which are selected based on following characteris-
tics as well as previous works [36]:
Moderate critical temperature and pressure
Specific and high latent heat
Excellent heat transfer due to low viscosity and high thermal
conductivity
Environmentally friendly because of their ODP and GWP
Safety and chemical stability
From Table 1, u is the acentric factor. It can be seen that there are
two working fluids for each type (dry, wet and isentropic). With
this way, the effect of thermodynamic properties, especially critical
temperature on outcomes of a specific working fluid type could be
determined.
2.4. Exergoeconomic analysis
Exergoeconomic known as a branch of knowledge combines
two terms of exergy analysis and economic principles in order to
prepare some information which is not available through conven-
tional energy analysis and economic estimation. However, this in-
formation is so noticeable for the design of an operation in cost-
effective systems [37]. As regards, in the present study, exer-
goeconomic investigations are explained and discussed in details in
the following sections.
2.4.1. Exergy description
There are some losses when thermal energy converts into other
types of energy (e.g. electricity) by taking the primary heat system.
In other words, according to the second law of thermodynamics,
there are not any systems being 100% efficient. Therefore, the en-
ergy dissipation in a cycle or device cannot be investigated by the
first law of thermodynamics, because it does not distinguish the
quality and quantity of losses. Therefore, in recent decades, exergy
analysis is a useful method to evaluate, optimize and improve in
energy efficiency. Exergy is a thermodynamic expression that is
originated from the second law of thermodynamic and refers to the
maximum useful work in a thermodynamic equilibrium process
which can be obtained from cycles [38]. The exergy efficiency (hex)
in cycles is described as follow
hex ¼ Ex
·
useful
.
Ex
·
available (1)
where, Ex
·
useful and Ex
·
avialable are the output mechanical power of
cycle (W
·
net) and the variation of the exergy of the geothermal
water between the inlet and the outlet of the heat exchanger (Ex
·
h),
respectively. Therefore, this equation could be rewritten as follow:
S. Karimi, S. Mansouri / Renewable Energy 115 (2018) 600e619602

hex ¼ W
·
net
.
Ex
·
h (2)
With regard to the second law, governing equations of exergy
(useful and destroyed) efficiency has been modeled for each pro-
cess in ORCs [39]. Due to the basic equations mentioned in the
exergy of thermodynamic modeling; and in order to calculate the
thermodynamic efficiency of the cycles it needs to specify the pa-
rameters such as enthalpy, entropy and vapor pressure. In the
present work, Peng Robinson (PR) and Soave-Redlich-Kwong (SRK)
equations of state are employed to calculate enthalpy and entropy
[40] and modified Wagner equation is applied to calculate vapor
pressures of each working fluid [41]. Moreover, constant design
parameters for ORC systems are showed in Table 2.
2.4.2. Economic principles
In order to study economic term in the exergoeconomic analysis,
Specific Investment Cost (SIC) as a determining factor is considered
in this work. The SIC obtains from Equation (3) described as follow
[18]:
SIC ¼ FS Â
TCB
W
·
net
(3)
FS is a correction factor for overhead cost shown in Table 3.
Furthermore, TCB is the total cycle cost described in Equation (4).
TCB ¼
Xn
i¼1
Ci (4)
Ci is cost for each component, which it is illustrated in the following
s (kJ/kg.K)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
T(K)
250
300
350
400
450
500
R600a (Dry)
R152a (Wet)
R11 (Isentropic)
Fig. 1. TeS diagram obtained in this study from PR EOS for R600a, R152a and R11.
Table 1
Thermodynamic properties of considered working fluids and water [36].
Substance Type Tc (K) Pc (bar) u ODP GWP (100yr)
R600a Dry 407.85 36.40 0.19 0 20
R601a Dry 460.35 33.95 0.23 0 20
R152a Wet 386.41 45.17 0.28 0 124
R134a Wet 374.21 40.59 0.33 0 1430
R11 Isentropic 471.11 44.08 0.19 1 4750
R123 Isentropic 456.83 36.62 0.28 0.02 77
Water e 647.09 220.64 0.34 e e
Table 2
Constant design parameters for modeling of ORC systems.
Parameters Values
Isentropic efficiency of pump, hp
is
(%) [39] 80
Isentropic efficiency of turbine, ht
is(%) [39] 80
Electrical generator efficiency, ht
gen(%) [39] 95
Heat source and sink media water
Heat source inlet temperature,ThsiðKÞ 423.15
Heat sink inlet temperature,TcsiðKÞ 293.15
Heat source inlet pressure,PhsiðbarÞ 5
Heat sink inlet pressure,PcsiðbarÞ 2
temperature of condenser,TcðKÞ 308
Pinch point temperature in condenser,Tc
pinch
ðKÞ 5
Heat source mass flow rate,m
·
hðkg=sÞ 50
Table 3
Constants for the calculation of bare module cost of equipment (according to
equations (5)e(12)) [42].
Constants Equipment
Heat exchanger Pump Turbine
K1 4.3247 3.3892 2.2476
K2 À0.3030 0.0536 1.4965
K3 0.1634 0.1538 À0.1618
C1 0.0388 À0.3935 e
C2 À0.1127 0.3957 e
C3 0.0818 À0.0023 e
B1 1.6300 1.8900 e
B2 1.6600 1.3500 e
FM 1.0000 1.6000 3.5000
FS 1.7000 1.7000 1.7000

section.
2.4.2.1. Equipment cost. Selection of appropriate cost functions
would give rise to obtain valuable results that could be utilized both
in household and industrial scale. Consequently, in the present
work, bare module cost method is applied for calculating each
component cost in basic ORC, RORC and TSEORC as follow [42]:
Cost of pump (CP):
Cp ¼
527:7
397
Â C0;p Â
Â
B1;p þ
À
B2;p Â FM;p Â FP;p
ÁÃ
(5)
log C0;p ¼ K1;p þ K2;p

logW
·
p

þ K3;p

logW
·
p
2
!
(6)
log FP;p ¼
h
C1;p þ C2;p
À
log Pp
Á
þ C3;P
À
log Pp
Á2
i
(7)
where C0;p, FP;p and Pp are initial cost, pressure factor and the
output pressure of working from the pump (discharge pressure),
respectively.
Cost of turbine (Ct):
Ct ¼
527:7
397
Â C0;t Â FM;t (8)
log C0;t ¼ K1;t þ K2;t

logW
·
t

þ K3;t

logW
·
t
2
!
(9)
where C0;t and FM;t are the initial cost and the material factor of
turbine, respectively.
Cost of heat Exchangers (CHX):
CHX ¼
527:7
397
Â C0;HX Â
Â
B1;HX þ
À
B2;HX Â FM;HX Â FP;HX
ÁÃ
(10)
log C0;HX ¼
h
K1;HX þ K2;HXðlog AHXÞ þ K3;HXðlog AHXÞ2
i
(11)
log FP;HX ¼
h
C1;HX þ C2;HXðlog PHXÞ þ C3;HXðlog PHXÞ2
i
(12)
Where respectively, CHX, FM;HX, FP;HX, AHX and PHX are the cost,
the material factor, pressure factor, surface area and pressure for
heat exchangers which include evaporator, regenerative and
condenser. Equations (10)e(12) could also be used for initial heat
exchangers cost (secondary evaporator and regenerative). In
Equations (5)e(12), B1, B2, K1, K2, K3, C1, C2 and C3 are constants
related to the material in which their values are given in Table 3.
Moreover, 527.7 and 397 are chemical engineering plant cost in-
dexes for the year 2015 and 2001, respectively [43]. According to
bare module equipment cost equations, for the heat exchangers,
C0;HX is a function of heat transfer surface area (AHX) and also
material of construction. In this article, all the heat exchangers
include evaporators, condenser and regenerative are assumed to be
made of carbon steel due to a good compatibility with both organic
working fluids and geothermal water [44].
2.4.2.2. Calculation of heat exchanger surface area. One of the most
significant factor which affects heat exchanger cost is the type of
heat exchanger that should be specified. Generally, heat exchanger
type plays a crucial role as a function of heat transfer surface area,
operating conditions and also productive capacity ( _Wnet).
Although, plate heat exchangers are more suitable for _Wnet in the
range of lower than tens of kilowatts, shell and tube heat ex-
changers could be used for productive capacity of higher than
hundreds of kilowatts [45]. Consequently, a shell and tube heat
exchanger is chosen in this article, which its specifications are
depicted in Table 4.
Accordingly, in this study, Kern method is considered to calcu-
late the surface area of shell and tube heat exchangers [46]. The
equations of heat transfer process in heat exchangers are described
as follow:
Ahx ¼
Qhx
UFðDTLmÞ
(13)
where Qhx(kW) is the heat transfer interchanged in heat ex-
changers, U(w=m2k) is the overall heat transfer coefficient [47], F is
the LMTD (Logarithmic Mean Temperature Difference) correction
factor and DTLm (k) is the logarithmic mean temperature difference.
U ¼
do
hidi
þ
Rf;ido
di
þ
dolnðdo=diÞ
2k
þ Rf;o þ
1
ho
!À1
(14)
where hi and ho are heat transfer coefficient inside and outside
tubes, Rf;i and Rf;o are fouling factors inside and outside tubes,
respectively. Also, do and di are outer and inner diameters of tubes;
k is the fluid thermal conductivity. The LMTD correction factor F in
Equation (13) is calculated as below [48].
F ¼
1
RF À 1
log

1 À PF
1 À ðPF Â RFÞ

(15)
where RF and PF are:
RF ¼
À
Th;in À Th;out
Á
À
Tc;out À Tc;in
Á (16)
PF ¼
À
Tc;out À Tc;in
Á
À
Th;in À Tc;in
Á (17)
Also the logarithmic mean temperature difference (DTLm) is
determined as below:
DTLm ¼
ðTh;out À Tc;inÞ À ðTh;in À Tc;outÞ
ln
ÂÀ
Th;out À Tc;inÞ=ðTh;in À Tc;outÞ
Ã (18)
Where in Equations 16e18 Th;in and Th;out are the inlet and
outlet of hot fluid and also Tc;in and Tc;out are the inlet and outlet of
cold fluid respectively. In this work, the Gnielinski equation is used
to calculate the heat transfer coefficient inside of tube [49] and Kern
method is considered to evaluate the heat transfer coefficient
outside of tube [46]. According to the Gnielinski equation, the heat
transfer coefficient inside of tube (hi) is:
Table 4
Shell and tube heat exchanger data.
Inner tube diameter, di(mm) 10.92
Outer tube diameter, do(mm) 12.70
Tube pinch, PT (mm) 19.05
Fouling factor (m2 o
C/W) [61]
Hot water 0.0001761
Cold water 0.0001761
Refrigerant (vapor) 0.0001761
Refrigerant (liquid) 0.0003522
Total fouling resistance with two-phase 0.0006700

hi¼ Nu
ki
di
(19)
where Nu is the Nusselt number determined with Equation (20)
Nu ¼
ðf =8ÞðRe À 1000ÞPr
1 þ 12:7ðf =8Þ0:5À
Pr2=3À1
Á (20)
where f, Re, Pr are friction factor, Reynolds number and Prandtl
number of fluid inside of tube. According to the Gnielinski equation,
the mentioned parameters are calculated as below:
Friction factor for turbulent flow
f ¼ ½0:790lnðReÞ À 1:64ŠÀ2
(21)
Friction factor for laminar flow
f ¼ 64=Re (22a)
Reynolds number
Rei ¼
m
·
idi
miAi
(22b)
where m
·
i, di, mi and Ai are mass flow rate, the inside diameter of
tube, the dynamic viscosity of the fluid inside tube and the cross-
sectional area of tube respectively.
Prandtl number
Pri ¼
miCPi
ki
(23)
where Cpi and ki are the specific heat and the thermal conductivity
of the fluid inside tube. Also, according to the Kern method, the
heat transfer coefficient outside of tube (ho) is:
ho ¼
ko
do
Â0:36 Â
dom
·
o
Aomo
!0:55
Cpo
mo
ko
1=3
(24)
2.4.3. Optimization
The purpose of optimization is selection of correct operating
parameters, adoption and application of methods and policies
which lead to produce energy with the highest possible value and
the lowest possible cost [50]. Therefore, in this study, following
operating parameters are optimized for three mentioned cycles.
Basic ORC: evaporator temperature, degree of superheat (the
difference between the outlet temperature of geothermal water
and saturated vapor temperature in evaporator) and pinch point
temperature difference in evaporator.
RORC: in addition to the basic ORC parameters, in this cycle the
regenerative temperature is also optimized.
TSEORC: in this cycle in addition to the basic ORC parameters,
the temperature of secondary evaporator is optimized too.
These parameters are optimized through three different opti-
mization methods consisting of thermodynamic, economic and
exergoeconomic ones based on exergy efficiency, SIC and a
combination of exergy efficiency and SIC respectively.
Accordingly, the objective function for the thermodynamic
optimization is exergy efficiency which has to be maximized as
follow:
F1ðxÞ ¼ Maximize ðhexÞ ¼
W
·
t À W
$
p
m
·
h½Hhsi À Hhso À T0ðshsi À shsoÞŠ
(25)
Also, SIC is selected as economic objective function in the eco-
nomic optimization which has to be minimized as follow:
F2ðxÞ ¼ Minimize ðSICÞ ¼ FS Â
TCB
W
·
net
(26)
It should be noted that in this study, cost of working fluids in
three considered cycles were neglected. In addition, in evaluating
the ORCs performances, by the economic aspects more attention is
captured to specific investment cost as it provides more meaningful
assessment.
Moreover, a linear weighted evaluation function is selected for
exergoeconomic optimization (a multi objective function includes
exergy and economic objective functions simultaneously) [51]:
FðxÞ ¼ aF1ðxÞ þ bF2ðxÞ (27)
where a and b are weight coefficients of the mentioned objective
functions obtained from
a ¼

F1
2 À F2
2

h
F1
1 À F2
1

þ

F1
2 À F2
2
i (28)
b ¼ 1 À a (29)
Where according to Equations (27) and (28), F1
1 is the maximum
value of F1, F2
1 is the value of function F1 when F2 obtained a
minimum value, F2
2 is the minimum value of F2 and F1
2 is the value of
function F2 when F1 obtained a maximum value [51]. Therefore, for
the purpose of making the optimum parameters associated with
mentioned cycles, the F function in Equation (27) must be mini-
mized. Genetic algorithm is utilized for optimization of mentioned
objective functions [52] in which constraints and bounds of oper-
ating parameters are depicted in Table 5 [53]. The outlet temper-
ature of geothermal water from evaporator could be controlled
with degree of superheat reported in Table 5. Also, Table 6 contains
parameters associated with the genetic algorithm during
optimization.
2.5. Profitability estimation
In this study, although the performance of three mentioned
cycles has investigated by exergoeconomic view point, the evalu-
ation of profitability for these cycles is considered and investigated,
Table 5
Constraints 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)

greatly. Profitability rate is one of the most important factors that
should be taken into account in order to confirm or reject a project
especially for industry (for instance ORC systems in geo-plants).
Calculation of profitability is usually carried out with the assist of
two different methods. Firstly, methods which are not considered
time value of money for example Return On Investment (ROI), Pay-
Back Period (PBP) and Net Return (NR). Secondly, methods
considered time value of money such as Net Present Worth (NPW)
and discounted cash flow rate of return [48]. In this respect, in this
article, economic indicators consist of simple Return On Investment
(ROI), Simple Payback Period (PBP) and Levelized Cost Of Electricity
(LCOE) are studied for considered cycles (basic ORC, RORC and
TSEORC) and working fluids which belong to twenty countries.
2.5.1. Return on investment (ROI)
ROI usually define as a ratio of net profit to total cost of in-
vestment as follow [54,55]:
ROI ¼
ð1 À tcorpÞðSannual À CTPCÞ
CTCI
(30)
where Sannual, CTPC, tcorp and CTCI are the annual sales revenue, the
total production cost through electricity generation, the corporate
tax rate and the cost of total capital investment, respectively. The
corporate taxes rate considered for twenty countries indicated in
Table 7 [56].
Furthermore, the equations related to the total production costs
are shown in Table 8. The annual sales revenue and the total capital
investment relations are listed as follow:
Annual sales revenue
Sannual ¼ MelCel (31)
Mel ¼ HannualW
· elec
net (32)
W
· elec
net ¼ W
· elec
t À W
$ elec
p (33)
Hannual¼ 0:9 Â 365 Â 24 (34)
In these equations, Mel reveals the annual electricity generation
according to the net electrical power output. Also, Cel which illus-
trates the electricity price for industry in year 2015, are considered
for twenty countries in Table 7 [57].
Total capital investment
CTCI ¼ CTPI þ CWC (35)
where CTPI, and CWC are total permanent investment and working
capital, which CWC is taken to be zero in the present economic
evaluation. Also, total permanent investment is obtained from
Equation (36).
CTPI ¼ CTDC þ Cland þ Croyal þ Cstartup (36)
where CTDC is total depreciable capital and also Cland,Croyal and
Cstartup are costs of land, royalties and plant startup, respectively. In
this article, Cland and Croyal are assumed to be zero and also cost of
plant startup covering geothermal energy exploitation and total
depreciable capital are calculated by Ref. [39]:
Cstartup¼ 0:1CTDC (37)
CTDC ¼ CDPI þ Ccont (38)
As it can be seen in Equation (38), total depreciable capital in-
cludes total direct permanent investment (CDPI) and cost of con-
tingencies and contractor's fee (Ccont), as [39]:
CDPI¼ TCB þ Csite þ Cserv þ Calloc (39)
Ccont¼ 0:18CDPI (40)
Sum of the total bare module cost (TCB, Equation (4)), cost of site
preparation (Csite), cost of service facilities (Cserv) and allocated
costs for utility plants and related facilities (Calloc) make up total
direct permanent investment. In addition, the following equations
can be used to evaluate these parameters [39].
Csite¼ 0:05TCB (41)
Csite¼ 0:05TCB (42)
Cserv¼ 0:05TCB (43)
Calloc¼ 792m
·
c (44)
m
·
c is the mass flow rate of cooling water that can be obtained from
Equation (45).
m
·
c ¼ m
·
wf

hcond
wf

at Dew Point
À hcond
wf;out
.
hcjat TL
À hcsi

(45)
2.5.2. Pay-Back Period (PBP)
Pay-Back Period (PBP) is one of the simplest capital budgeting
techniques. It calculates the number of years a project takes in
recovering the initial investment based on the future expected cash
inflows. PBP is widely used in economic evaluations to compare
alternatives [58].
PBP ¼
CTDC
cashflow
¼
CTDC
ð1 À tÞðSannual À CTPCÞ þ CD
(46)
The depreciation is a measure of reduction in value of equip-
ment over the time. Some factories utilize depreciation cost, CD, as
a means to set aside a fund in order to replace a plant when it does
not operate no longer [58]. In this article the depreciation cost for
geothermal sources to power plant is assumed to be zero.
Table 6
The main parameters of the genetic algorithm used in this work.
Parameters Type or value
Population type Double vector
Population size 20.0
Creation function Constraint dependent
Scaling function Rank
Selection function Stochastic uniform
Reproduction (Elite count) 2.0
Reproduction (crossover function) 0.8
Mutation function Constraint dependent
Crossover function scattered
Migration (fraction) 0.2
Migration (interval) 20.0

2.5.3. Levelized Cost Of Electricity (LCOE)
Levelized Cost Of Electricity (LCOE) is one of the economic in-
dicators which estimate the cost of electricity generated by a
generator in industries. This indicator will be able to calculate all
systems in which the lifetime costs are expected through power
output (kWh). LCOE as a financial tool is very precious for
comparing options of various generations that are considered
inflation and discounted to account for the time-value of money to
estimate benefit. The generation of electricity at a low cost which
probably leads to return more profitability in specific period of time
for the investor is a good definition of a relatively low LCOE [59].
LCOE of the project is calculated by Equation (47) as described in
Ref. [59].
LCOE ¼
CTCI þ
Pn
t¼1
CTPC
ð1þiÞ
t
Pn
t¼1
Mel
ð1þiÞ
t
(47)
where LCOE in $/kWh; Mel is electricity output in year t in kWh.
Also, i is annual interest rate (discount rate) and is assumed to be 7%
[13]; n is economical lifetime of plant and set to be 20 years; t is the
year of operation (1, 2, …, n).
3. Results and discussion
3.1. Verification
Energy and exergy efficiencies could be used to investigate the
performance of thermodynamic cycles. Therefore, some thermo-
dynamic parameters such as enthalpy and entropy should be
calculated by using appropriate methods such as thermodynamic
equations of state [40]. Accordingly, in the present study, both
Peng-Robinson (PR) and SoaveeRedlicheKwong (SRK) equations of
state (EoS) are used to calculate these thermodynamic parameters.
Then, the results obtained from the mentioned equations of state
are compared with NIST reference data bank (with ASHRAE Stan-
dard) [36] in order to check their validity and accuracy, as are
shown by Table 9.
This table contains the percentage of enthalpy and entropy er-
rors which are calculated from PR and SRK equations of state based
on NIST data in both liquid and vapor phases and for four fluids
considered in this study (R600a, R152a, R11 and water). As it is
obtained clearly from this table, the amount of PR error for all states
and fluids except water are less than SRK error. Moreover, the PR
errors in the calculations of enthalpy and entropy in the vapor
phase is less than liquid phase for all considered working fluids.
Accordingly, in this article, for the calculation of thermodynamic
parameters to investigation of cycle efficiency, combination of
these two equations of state is used. In other words, PR and SRK
equations of state are used to determine the thermodynamic pa-
rameters of working fluids and geothermal water, respectively. In
addition, thermodynamic efficiency of ORCs obtained from this
work are compared with the results of other papers (in the
modeling condition of these references) and presented in Table 10.
Although the second column of the table up to the seventh ones
relate to the modeling condition of reference articles, comparison
of exergy and energy efficiencies are carried out in the eighth and
ninth columns. Comparisons of these results clearly show that the
efficiencies obtained from the modeling in this work have a good
agreement with the other articles.
3.2. Optimization results
In this article, thermodynamic, economic and exergoeconomic
objective functions based on two accepts are considered to opti-
mize operating parameters. Firstly, it should be noted that oper-
ating parameters related to thermodynamic cycles could be
optimized through using different objective functions especially
exergy, economic and exergoeconomic ones in which the selection
of each method depends on the purpose of geo-plants. For instance,
the results of thermodynamic optimization can be used in a geo-
plant if more electricity production has intended even with a
higher cost, because the quality plays more important role than
price from its point of view. Secondly, the amount of exergy and SIC
are require independently to obtain optimal parameters from
exergoeconomic objective function, as is shown by equation (27).
Accordingly, in this article, three mentioned objective functions are
studied.
Table 11 indicates optimized parameters by using thermody-
namic and economic objective functions for six working fluids
R600a, R601a, R152a and R134a, R11 and R123. As illustrated by the
table, there is a moderate reduction in the amount of exergy, energy
and SIC from thermodynamic objective function to economic
objective function for three mentioned working fluid and cycles.
The reason of this decline relates to a downward trend of the
temperature of primary and secondary evaporators, Degree of Su-
perheat (DS) and also temperature of regenerative by changing the
thermodynamic to economic. The value of pinch point temperature
difference in evaporator (DTpp;evap) almost remains unchanged for
these two methods. Also, results of this table show that the amount
of exergy efficiency and SIC in thermodynamic optimization is more
than economic optimization. In addition, the a quantities needed
for exergoeconomic optimization for all considered fluids and
Table 7
Corporate tax rates and the average of electricity prices for twenty considered
countries [56].
Number country Corporate tax rates
in 2015 (% tcorp)
Average electricity prices in 2015
(Cel) [dollars per kilowatt hour]
1 Australia 30.00 0.49
2 Brazil 34.00 0.37
3 Jordan 20.00 0.35
4 Philippines 30.00 0.34
5 Germany 29.65 0.33
6 Italy 31.40 0.31
7 Japan 33.06 0.28
8 Chile 22.50 0.25
9 France 33.30 0.21
10 United Kingdom 20.00 0.21
11 Mexico 30.00 0.20
12 United States 40.00 0.18
13 South Africa 28.00 0.17
14 Iran 25.00 0.14
15 Canada 26.50 0.13
16 India 34.61 0.12
17 Spain 28.00 0.12
18 Thailand 20.00 0.11
19 China 25.00 0.11
20 Netherland 25.00 0.09
Table 8
Components of total production cost.
Cost of wages and benefits, CWB CWB¼ 0:035CTDC
Cost of salaries and benefits, CSB CSB¼ 0:25CWB
Cost of materials and services, CMS CMS ¼ CWB
Cost of maintenance overhead, CMO CMO¼ 0:05CWB
Direct manufacturing costs, CDMC CDMC ¼ CWB þ CSB þ CMS þ CMO
Cost of property taxes and liability
insurance, CPI
CPI¼ 0:02CTDC
Fixed manufacturing costs, CFIX CFIX ¼ CPI
Total annual cost of manufacture, CCOM CCOM ¼ CDMC þ CFIX
General expenses, CGE CGE ¼ 0
Total production cost, CTPC CTPC ¼ CCOM þ CGE

cycles are listed in this table.
After obtaining a and replacing it in Equation (27), operating
parameters can be optimized with the exergoeconomic objective
function. The values of these optimized operating parameters in
exergoeconomic optimization are indicated in Table 12. In this ta-
ble, in general, results show that the amount of optimal DS for dry
fluid reached a peak and followed by isentropic and wet working
fluids, respectively. Also, the amount of DTpp;evap, likewise ther-
modynamic and economic optimization, for all fluids and cycles are
approximately the same. In other words, it can be emphasized that
the degree of superheat is one of the most determining factors in
balancing efficiency and cost.
Table 9
Comparing the error of entropy and enthalpy in liquid and vapor phase for both PR and SRK equations of state in this study and NIST databank.
Substances T distance (K) P distance (bar) % SL_Errora
% SV_Errora
% HL_Errorb
% HV_Erro rb
PR SRK PR SRK PR SRK PR SRK
R600a 250.00e407.50 0.63e36.10 2.46 7.20 0.47 7.25 2.58 4.02 0.39 6.14
R152a 250.00e386.00 1.05e44.81 2.88 5.67 2.55 5.54 3.28 2.72 2.72 4.33
R11 270.68e471.11 0.36e44.08 3.75 10.64 1.84 8.91 3.55 6.88 1.37 6.99
Water 283.16e483.16 0.01e19.08 8.10 4.72 4.69 3.86 8.18 3.24 4.96 3.06
a
% Error ¼ 100
n
Pn
i
SL or V
This work SL or V
NIST
SL or V
NIST
!
.
b
% Error ¼ 100
n
Pn
i
HL or V
This work HL or V
NIST
HL or V
NIST
!
.
Table 10
The comparison of thermal efficiency values obtained through modeling in this study with other works.
Com. TGI (

C) Tcool (

C) Tevap (

C) Tcond (

C) hexð%Þ (

C) hthð%Þ (

C) D.S (o
C) DTpp;ev DTpp;co Source Optimization method
R600 120.00 15.00 74.16 25.00 5.00 5.00 0.00 6.44 33.82 This work e
R600 120.00 15.00 74.16 25.00 5.00 5.00 0.00 e 34.38 Ref. [62] Thermodynamic
R152a 120.00 20.00 72.59 30.00 10.00 10.00 0.00 8.65 43.42 This work e
R152a 120.00 20.00 72.59 30.00 10.00 10.00 0.00 8.82 e Ref. [63] Without opt.
R11 150.00 40.00 150.00 40.00 20.00 20.00 10.00 14.91 44.24 This work e
R11 150.00 40.00 150.00 40.00 20.00 20.00 10.00 15.19 e Ref. [64] Thermodynamic
Water 150.00 288.15 85.18 30.00 0.50 3.00 60.00 10.73 43.72 This work e
Water 150.00 288.15 85.18 30.00 0.50 3.00 60.00 10.86 e Ref. [21] Techno-economic
Table 11
Thermodynamic and economic optimization results of working fluids in basic ORC, RORC and TSEORC.
Substance System Objective function Tevap1 (K) Tevap2 (K) Treg (K) D.S (K) DTpp;evap(K) hth hex SIC ($/W) a
R600a (Dry) ORC Thermo. 396.35 e e 1.20 5.00 0.1177 0.4824 4.3488 0.983
Econ. 392.97 e e 19.85 5.19 0.1164 0.4569 2.9016
RORC Thermo. 396.35 e 331.27 1.20 5.00 0.1291 0.5073 4.3808 0.974
Econ. 386.68 e 335.65 20.00 5.00 0.1221 0.4731 3.0824
TSEORC Thermo. 396.35 381.06 e 1.20 5.00 0.1151 0.4931 4.7320 0.990
Econ. 396.35 367.34 e 20.00 5.03 0.1102 0.4741 2.9330
R601a (Dry) ORC Thermo. 404.82 e e 0.07 5.00 0.1339 0.4725 3.3199 0.968
Econ. 387.91 e e 19.94 5.05 0.1184 0.4516 2.6861
RORC Thermo. 406.67 e 341.69 0.00 5.00 0.1489 0.5136 3.7374 0.957
Econ. 386.89 e 326.67 20.00 5.02 0.1250 0.4711 2.7862
TSEORC Thermo. 408.70 399.93 e 0.00 5.00 0.1336 0.4834 3.4543 0.970
Econ. 392.32 359.75 e 19.99 5.04 0.1076 0.4583 2.6382
R152a (Wet) ORC Thermo. 365.22 e e 19.55 5.00 0.0940 0.4249 7.1910 0.941
Econ. 357.94 e e 20.00 5.01 0.0862 0.3939 6.6934
RORC Thermo. 365.22 e 320.10 20.00 5.00 0.0991 0.4327 6.7833 0.867
Econ. 358.88 e 322.97 20.00 5.00 0.0925 0.4039 6.5950
TSEORC Thermo. 365.22 345.13 e 16.19 5.00 0.0911 0.4274 11.239 0.993
Econ. 358.22 341.82 e 20.00 5.00 0.0847 0.3988 7.1209
R134a (Wet) ORC Thermo. 359.37 e e 16.91 8.00 0.0829 0.4015 4.4010 0.996
Econ. 359.37 e e 20.00 8.00 0.0832 0.3994 3.8612
RORC Thermo. 359.37 e 325.29 7.70 8.00 0.0828 0.4052 11.650 0.999
Econ. 359.37 e 325.00 20.00 8.00 0.0818 0.4002 4.0101
R11 (Isen.) ORC Thermo. 413.06 e e 5.094 5.00 0.1538 0.5131 4.7330 0.991
Econ. 388.35 e e 19.99 5.00 0.1322 0.4926 2.5381
RORC Thermo. 417.17 e 344.77 0.83 5.00 0.1705 0.5569 12.047 0.993
Econ. 383.53 e 325.01 20.00 5.02 0.1332 0.5007 2.6385
TSEORC Thermo. 400.49 385.55 e 17.41 5.03 0.1379 0.5196 2.6186 0.872
Econ. 390.60 361.72 e 20.00 5.01 0.1198 0.4968 2.4632
R123(Isen.) ORC Thermo. 405.32 e e 0.02 5.00 0.1405 0.4916 3.0469 0.985
Econ. 393.08 e e 19.92 5.00 0.1299 0.4808 2.3376
RORC Thermo. 417.89 e 358.03 0.00 5.00 0.1664 0.5419 2.7104 0.866
Econ. 391.51 e 325.03 19.01 5.00 0.1359 0.5003 2.4401
TSEORC Thermo. 407.61 397.59 e 0.86 5.00 0.1386 0.5039 2.9938 0.977

SIC values and exergy efficiency obtained from exergoeconomic
optimization for three working fluids and also three considered
cycles are indicated in Fig. 2. From the graph it is clear that the
highest amount of exergy efficiency is related to R11 as working
fluid in the RORC, while R152a allocates the lowest efficiency in the
basic ORC. For all fluids, RORC is more efficiently than TSEORC
which has been much more efficient than basic ORC. Moreover, this
trend of changing is more significant for R11. Also, from the SIC
values indicating in Fig. 2, the amount of SIC for R152a has much
more than two other fluids in three cycles. In addition, this figure
clearly illustrates both the highest and the lowest amount of SIC
which are respectively related to R152a and R11 are appeared in
TSEORC.
In addition to the optimum parameters which are obtained by
optimization, there are some parameters in thermodynamic cycles
that determining their values can help in setting up and starting up
cycle in geo-plant. These parameters which are used in the
mentioned cycles and working fluids are listed in Tables 13 and 14.
From the tables, the role of regenerative and secondary evapo-
rator could be certainly clarified in the RORC and TSEORC,
respectively. To explain these points, firstly, there is a marked dip in
the amount of cooling water from basic ORC to RORC due to the
existence of a reduction in the amount of working fluid entrance to
the condenser. It should be noted that a portion of expanded
working fluid which is output the turbine entries the regenerative
in the RORC. Secondly, the rate of working fluid rises from basic ORC
to TSEORC because the amount of superheated working fluid
entered to the turbine goes up. It should be emphasized that the
secondary evaporator in the TSEORC makes a growth in the heat
flux transfer from geothermal water into working fluid compared
to basic ORC. As a result, flow rate of working fluid in TSEORC will
increase in comparison with basic ORC that this key point can be
distinguished clearly in Table 13. All mentioned factors cause that
RORC generates less electricity and has lower amount of heat flux in
condenser compared to basic ORC. On the other hand, TSEORC
system has more heat flux in evaporator and produces more elec-
tricity in comparison with basic ORC. As Fig. 3 indicates, it can be
concluded that the highest and lowest electricity production rates
relates to the TSEORC and RORC, respectively. Nevertheless, ac-
cording to Fig. 3, it is clear that the total cost for three mentioned
working fluids are increased in sequence of RORC, basic ORC and
TSEORC. In other words, the total cost for all considered working
fluids reaches a peak in TSEORC, stands at the second place in basic
ORC and reaches the lowest amount in RORC (see Fig. 4)
Another important parameter for the examination of cycle
performance is to determine the amount of exergy destruction in
cycles (cycle irreversibility). The exergy destruction of a cycle is the
sum of the exergy destruction of the processes that compose that
cycle [60]. Accordingly, Fig. 5 illustrates the amount of destroyed
exergy in total for three cycles include basic ORC, RORC and TSEORC
as well as all working fluids. This figure clearly shows that the
summation of destroyed exergy of three fluids R600a, R152a and
R11 are reduced for cycles RORC, TSEORC and basic ORC, respec-
tively. Moreover, most of the thermal dissipation is belonged to the
substance R152a in the RORC however this quantity is the same for
two other cycles (TSEORC and basic ORC).
3.3. Profitability results
The possibility of geothermal sources transforming into power
(electricity) can be authenticated after economic investigation. As
Table 12
Investigation of parameters and results of exergoeconomic optimization obtained
through linear weighting function.
Substance System Tevap1 (K) Tevap2 (K) Treg (K) D.S (K) DTpp;evap(K)
R600a (Dry) ORC 396.16 e e 8.32 5.07
RORC 396.35 e 334.17 10.75 5.00
TSEORC 395.62 366.73 e 5.32 5.08
R601a (Dry) ORC 395.64 e e 4.77 5.01
RORC 398.02 e 338.21 11.68 5.43
TSEORC 400.63 381.10 e 8.64 5.00
R152a (Wet) ORC 361.95 e e 20.00 5.00
RORC 362.47 e 323.51 20.00 5.00
TSEORC 365.10 341.81 e 20.00 5.00
R134a (Wet) ORC 359.36 e e 10.79 8.00
RORC 359.36 - 320.59 11.15 8.00
TSEORC 359.36 335.65 e 10.23 8.00
R11 (Isen.) ORC 403.77 e e 14.38 5.00
RORC 407.89 e 352.16 10.25 5.00
TSEORC 390.15 361.81 e 19.99 5.02
R123 (Isen.) ORC 394.41 e e 17.77 5.00
RORC 389.72 e 331.10 19.98 5.03
TSEORC 400.24 382.05 e 16.70 5.02
SIC($/W)
0
2
4
6
8
10
ExergyEfficiency(%)
0
20
40
60
R600a (Exergy)
R152a (Exergy)
R11 (Exergy)
R600a (SIC)
R152a (SIC)
R11 (SIC)
ORC TSEORCRORC
Fig. 2. Comparison of SIC and exergy efficiency obtained through exergoeconomic optimization for three considered working fluids in basic ORC, RORC and TSEORC.

Table 13
The investigation of thermodynamic parameters obtained through exergoeconomic optimization for different working ﬂuids in studied cycles.
Substance System Pevap1. (bar) Pevap2.(bar) Preg (bar) Pcond (bar) m

c(kg/s) m

w2(kg/s) X1 m

w1 (kg/s)
R600a (Dry) ORC 29.91 e e 4.63 33.81 e e 240.78
RORC 30.00 e 8.89 4.63 32.30 e 0.17 191.18
TSEORC 29.63 17.61 e 4.63 36.15 11.33 e 338.16
R601a (Dry) ORC 11.47 e e 1.28 20.54 e e 154.82
RORC 11.99 e 3.14 1.28 17.25 e 0.15 109.90
TSEORC 12.60 8.58 e 1.28 15.98 11.85 e 209.83
R152a (Wet) ORC 28.17 e e 7.95 65.82 e e 402.06
RORC 28.46 e 11.94 7.95 65.71 e 0.10 360.01
TSEORC 29.99 18.38 e 7.95 65.15 5.80 e 433.35
R134a (Wet) ORC 30.00 e e 8.83 113.71 e e 435.20
RORC 30.00 e 14.35 8.83 122.42 e 0.16 395.76
R11 (Isen.) ORC 15.07 e e 1.49 24.71 e e 96.96
RORC 16.24 5.12 1.49 18.47 e 0.19 58.87
TSEORC 11.66 6.42 e 1.49 43.63 31.31 e 293.98
R123 (Isen.) ORC 12.29 e e 1.30 41.23 e e 153.09
RORC 11.18 e 2.69 1.30 47.38 e e 156.33
TSEORC 13.77 9.53 e 1.30 32.45 23.68 e 208.48
Table 14
The areas of different heat exchangers used in this work through exergoeconomic optimization.
Substances Area (m2
)
System Evaporator 1 Evaporator 2 Regenerative Condenser
R600a (Dry) ORC 414.71 e e 8.04 Eþ3
RORC 453.86 e 232.21 5.89 Eþ3
TSORC 778.59 465.81 e 12.79 Eþ3
R601a (Dry) ORC 293.52 e e 3.87 Eþ3
RORC 284.46 e 86.29 2.43 Eþ3
TSORC 492.22 293.44 e 4.72 Eþ3
R152a (Wet) ORC 789.84 e e 23.78 Eþ3
RORC 899.39 e 370.45 21.52 Eþ3
TSORC 1058.00 436.42 e 27.29 Eþ3
R134a (Wet) ORC 1103.61 e e 25.85 Eþ3
RORC 1244.92 e 759.44 22.05 Eþ3
TSORC 1599.81 434.09 e 27.14 Eþ3
R11 (Isen.) ORC 139.39 e e 1.83 Eþ3
RORC 143.86 e 116.27 1.28 Eþ3
TSORC 439.59 368.84 e 4.88 Eþ3
R123 (Isen.) ORC 248.15 e e 1.84 Eþ3
RORC 338.79 e 76.74 1.85 Eþ3
TSORC 388.79 257.36 e 2.47 Eþ3
Netelectricalpoweroutput(kW)
0
500
1000
1500
2000
2500
3000
R600a (Dry)
R152a (Wet)
R11 (Isentropic)
ORC TSEORCRORC
Fig. 3. Comparison of net electricity production results obtained through exergoeconomic optimization for three considered working ﬂuids in basic ORC, RORC and TSEORC.

mentioned in the previous section, the ORCs performances were
studied in three considered cycles through maximizing the exergy
efficiency and minimizing SIC with three different objective func-
tions and usage of R600a, R601a, R152a and R134a, R11 and R123 as
pure working fluids. In addition, in this article, more attention is
paid to the results of profitability indicators such as LCOE, ROI and
PBP with two various points of view which consist of profitability
estimation for twenty countries among five continents and the
effects of operating parameters on profitability indicators as follow:
3.3.1. Profitability estimation for different countries
Table 15 provides some information about LCOE indicator for
three different considered ORCs and working fluids. As can be seen,
the maximum value of LCOE for a basic ORC obtained by R152a as a
wet working fluid, while two other cycles (RORC and TSEORC)
showed nearly the same value of LCOE for R11 and R600a. However,
in RORC system R600a (isentropic) consists of the least quantity of
LCOE among two other fluids. The table also illustrates the amount
of 0.0538, 0.0766 and 0.1426 for R11, R600a and R152a, respectively
in TSEORC cycle. According to Equation (47), LCOE indicator has the
same amount for different countries but it varies with different
working fluids in various ORC configurations. Consequently, in the
present work, in order to investigate the profitability in different
countries, ROI and PBP are selected as economic indicators due to
corporate tax rates and electricity price for industrial consumers
which alter according to different countries in Equation (21) and
Table 6.
In this respect, Table 16a and b highlights the ROI results for
three considered cycles for twenty countries among five continents.
The results also are explained according to two categories: devel-
oped and developing countries. Developed countries listed as num.
1, 5, 6, 7, 8, 9, 10, 12, 15, 17, 20 and developing countries contain
num. 2, 3, 4, 11, 13, 14, 16, 18 and 19. The initial impression from this
table is Australia (num.1) which has the maximum amount of ROI
for all working fluids in three cycles due to low corporate tax rate
and high electricity price for industrial consumers. FromTable 16a,
the maximum and minimum amount of ROI among all value is
allocated to TSEORC configurations for R11 and R152a in Australia
and Netherland with 112.11 and 1.94, respectively. It is important to
note that although it is expected that the developed countries
should have behaved better than developing ones, they have a
Fig. 4. Comparison of total cost obtained through exergoeconomic optimization for
three considered working fluids in basic ORC, RORC and TSEORC.
Totalftowrateofexergydestruction(kW)
0
2000
4000
6000
8000
R600a (Dry)
R152a (Wet)
R11 (Isentropic)
ORC TSEORCRORC
Fig. 5. Comparison of total flow rate of exergy destruction obtained through exergoeconomic optimization for three considered working fluids in basic ORC, RORC and TSEORC.
Table 15
LCOE results for three considered working fluids in basic ORC, RORC and TSEORC.
Substance System LCOE ($/kWh)
R600a (Dry) ORC 0.0672
RORC 0.0658
TSEORC 0.0766
R601a (Dry) ORC 0.0631
RORC 0.0638
TSEORC 0.0621
R152a (Wet) ORC 0.1322
RORC 0.1287
TSEORC 0.1426
R134a (Wet) ORC 0.1337
RORC 0.1259
TSEORC 0.1474
R11 (Isen.) ORC 0.0653
RORC 0.0835
TSEORC 0.0538
R123 (Isen.) ORC 0.0510
RORC 0.0522
TSEORC 0.0493

reverse trend in special cases. For instance, although Brazil, Jordan
and Philippines have three maximum ROI amount, they belong to
developing countries. On the other hand, Germany, Italy, Japan,
Chile, United Kingdom and France which are listed as developed
ones indicate less numerical value of ROI compared to three
mentioned countries (num. 2, 3 and 4). Another obvious point re-
lates to Iran with num. 14 which is one of the developing countries
that illustrates average ROI results among developing country in
Asia continent. In addition, the ROI results of nine remained
countries (num. 12, 15, 17, 20 as developed countries and num. 11,
13, 16, 18 and 19 as developing ones) are obtained in the range of
the highest and lowest value.
Referring to Fig. 6, PBP of twenty countries which their names
are listed in Table 16a and b considered according to R600a as dry
working fluid in three cycles: basic ORC, RORC and TSEORC. As can
be seen in this figure, the best numerical value of PBP (year) shows
less than one year for num. 1 (Australia) in all cycles. However, the
PBP for num. 20 (Netherland) has a reverse result that the
investment expected to return in more than 7 years for TSEORC. It is
noticeable that countries with num. 2 to 13 to be quite the same
PBP which is started in 1 to approximately 2.5 years. Furthermore,
other countries (num. 14 to 20) have nearly the similar upward PBP
and leveled off in closely 6 years for basic ORC and RORC.
The value of PBP as an economic indicator for R152a (wet fluid)
in three ORCs configurations for twenty countries are indicated in
Fig. 7. In comparison with Fig. 6, it is clear that the period of pay-
back for R152a as a wet fluid seems longer remarkably than
R600a as dry working fluid. According to the performances of three
ORC systems for wet fluid, the trend of considered ORCs resemble
closely, though the PBP obtained in TSEORC has longer period
rather than two other cycles especially for the last seven countries
(num.14 to 20). It should be noted that the start of PBP is at one
point with 2 years for Australia (in three cycles), while the lines
reach a plateau in different points for Netherland with 23, 26 and
37 years in RORC, basic ORC and TSEORC, respectively.
As can be seen in Fig. 8, the PBP for R11 (isentropic fluid) depicts
Table 16a
ROI results for three considered working fluids in basic ORC, RORC and TSEORC for twenty countries.
Number Country R600a (Dry) R152a (Wet) R11 (Isn.)
ORC RORC TSEORC ORC RORC TSEORC ORC RORC TSEORC
1 Australia 88.35 90.37 76.82 41.80 43.12 38.27 91.22 69.94 112.11
2 Brazil 61.43 62.86 53.21 28.28 29.22 25.77 63.47 48.31 78.34
3 Jordan 70.04 71.68 60.62 32.03 33.11 29.15 72.38 55.00 89.43
4 Philippines 59.35 60.75 51.35 27.05 27.96 24.59 61.34 46.57 75.83
5 Germany 57.70 59.07 49.89 26.19 27.08 23.81 59.64 45.24 73.78
6 Italy 52.48 53.73 45.33 23.61 24.43 21.43 54.25 41.06 67.20
7 Japan 45.66 46.76 39.36 20.22 20.94 18.29 47.22 35.59 58.64
8 Chile 46.44 47.58 39.92 20.14 20.89 18.15 48.06 36.04 59.86
9 France 32.60 33.42 27.89 13.59 14.13 12.15 33.77 25.08 42.29
10 United Kingdom 39.10 40.09 33.45 16.29 16.94 14.57 40.50 30.08 50.73
11 Mexico 32.28 33.10 27.57 13.28 13.81 11.84 33.45 24.76 41.97
12 United States 24.35 24.99 20.72 9.69 10.11 8.58 25.25 18.55 31.83
13 South Africa 27.23 27.95 23.12 10.62 11.09 9.36 28.26 20.66 35.71
14 Iran 22.15 22.77a 18.62 7.90 8.30 6.82 23.03 16.51 29.42
15 Canada 19.68 20.24 16.47 6.71 7.08 5.73 20.48 14.55 26.29
16 India 15.70 16.16 13.06 5.05 5.35 4.24 16.36 11.49 21.14
17 Spain 17.29 17.79 14.38 5.56 5.89 4.67 18.01 12.65 23.27
18 Thailand 16.99 17.52 14.04 5.06 5.39 4.15 17.74 12.27 23.09
19 China 15.94 16.42 13.16 4.74 5.06 3.89 16.63 11.51 21.65
20 Netherland 11.79 12.19 9.52 2.63 2.89 1.94 12.36 8.17 16.47
Table 16b
ROI results for three considered working fluids in basic ORC, RORC and TSEORC for twenty countries.
Number Country R601a (Dry) R134a (Wet) R123 (Isn.)
ORC RORC TSEORC ORC RORC TSEORC ORC RORC TSEORC
1 Australia 94.65 93.42 96.17 41.25 44.21 36.84 118.59 115.66 122.81
2 Brazil 65.91 65.03 66.99 27.89 29.99 24.75 82.96 80.87 85.96
3 Jordan 75.18 74.17 76.42 31.59 34.00 27.98 94.73 92.33 98.16
4 Philippines 63.72 62.86 64.78 26.66 28.71 23.60 80.33 78.29 83.26
5 Germany 61.97 61.13 62.99 25.82 27.82 22.83 78.17 76.18 81.02
6 Italy 56.38 55.62 57.33 23.27 25.10 20.54 71.23 69.41 73.84
7 Japan 49.10 48.43 49.93 19.92 21.53 17.51 62.19 60.58 64.49
8 Chile 49.99 49.29 50.86 19.83 21.50 17.34 63.52 61.86 65.90
9 France 35.17 34.67 35.79 13.36 14.57 11.56 44.95 43.75 46.67
10 United Kingdom 42.18 41.58 42.93 16.02 17.47 13.86 53.91 52.47 55.98
11 Mexico 34.85 34.34 35.47 13.05 14.26 11.25 44.62 43.42 46.34
12 United States 26.34 25.95 26.81 9.52 10.45 8.13 33.88 32.95 35.20
13 South Africa 29.48 29.04 30.02 10.42 11.48 8.85 38.03 36.98 39.53
14 Iran 24.08 23.70 24.55 7.73 8.63 6.38 31.41 30.51 32.70
15 Canada 21.43 21.09 21.86 6.55 7.38 5.33 28.10 27.29 29.28
16 India 17.14 16.86 17.49 4.92 5.60 3.91 22.62 21.95 23.58
17 Spain 18.88 18.56 19.26 5.42 6.16 4.31 24.91 24.17 25.97
18 Thailand 18.62 18.29 19.01 4.91 5.67 3.78 24.76 24.01 25.84
19 China 17.45 17.16 17.82 4.60 5.31 3.54 23.21 22.51 24.23
20 Netherland 13.03 12.79 13.33 2.52 3.10 1.65 17.75 17.17 18.57

the changing patterns for three cycles and 20 countries which are
mentioned in Table 16a and b. It should be underlined that, unlike
two previous figures (6 and 7) TSEORC operates the greatest trend
for returning the investment and making profits, while RORC has
the longer PBP which is leveled out the graph at maximum point of
PBP (almost 8.5 years). Furthermore, the PBP obtained for Australia
is not exactly the same value in three ORCs so that 0.5 year in
TSEORC, 0.7 year in basic ORC and 1 year in RORC. As illustrated in
this figure, the PBP for the first eight countries (listed in Table 16a
and b) in all cycles has more compressed whereas country num.9 to
the end of the list (num.20) vary tremendously in PBP value. In
other words, the period (year) obtained for each 12 mentioned
countries differ widely in all cycles.
In the present work, one of the most distinguishing features is
that Iran with num.14 (Table 16a and b) is selected for investigation
of effects of operating parameters on profitability indicators since it
has a great average of PBP and ROI according to the performances of
basic ORC, RORC and TSEORC for all six working fluids (R600a,
R601a, R152a and R134a, R11 and R123) as described in previous
figures and Table 16a and b.
Number of Countries
0 2 4 6 8 10 12 14 16 18 20 22
PBP(year)
0
1
2
3
4
5
6
7
8
ORC
RORC
TSEORC
Fig. 6. PBP results for R600a as a dry fluid in three ORC configurations based on exergoeconomic optimziation for twenty countries.
Number of Countries
0 2 4 6 8 10 12 14 16 18 20 22
PBP(year)
0
10
20
30
40
ORC
RORC
TSEORC
Fig. 7. PBP results for R152a as a wet fluid in three ORC configurations based on exergoeconomic optimziation for twenty countries.

3.3.2. Effects of operating parameters on profitability indicators
a) ROI
Fig. 9 illustrates the variation of ROI indicator as a function of
degree of superheat and primary evaporator temperature by using
R11 as a working fluid in TSEORC system for Iran. As shown in this
figure, at a constant degree of superheat, by increasing the evap-
orator temperature, ROI indicator increases. Also, by increasing the
degree of superheat at a constant evaporating temperature, the
amount of ROI will improve more. Referring to this figure, it can be
concluded that degree of superheat has more significant effect on
ROI variation. Furthermore, ROI variation in respect to the changes
in the degree of superheat and the secondary evaporator tem-
perature demonstrates in Fig. 10. According to this figure,
increasing in degree of superheat at a constant value of secondary
evaporating temperature and also, increasing in evaporating
temperature at a constant degree of superheat leads to an increase
of ROI amounts in TSEORC system for Iran when R11 selected as a
working fluid.
In addition to the degree of superheat and evaporator temper-
atures, pinch point temperature difference is another operating
parameter which its effect is investigated on profitability results.
Consequently, Fig. 11 depicts the variation of pinch point temper-
ature difference and degree of superheat which affect the ROI in-
dicator when R11 operates as fluid in TSEORC for Iran. According to
Number of Countries
0 2 4 6 8 10 12 14 16 18 20 22
PBP(year)
0
2
4
6
8
10
ORC
RORC
TSEORC
Fig. 8. PBP results for R11 as an isentropic fluid in three ORC configurations based on exergoeconomic optimziation for twenty countries.
Fig. 9. The effects of primary evaporator temperature and degree of superheat on ROI
indicator for R11 in TSEORC system with Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.
Fig. 10. The effects of secondary evaporator temperature and degree of superheat on
ROI indicator for R11 in TSEORC system with Tevap1 ¼ 390.15 K and DTpp;evap ¼ 5.02 K.

the figure, through an increase in pinch point temperature differ-
ence at a constant degree of superheat, the amount of ROI reduces.
In contrast, at a constant value of pinch point temperature differ-
ence, by increasing the degree of superheat, ROI indicator increases.
b) PBP
According to Fig. 12 which depicts the impact of degree of su-
perheat and primary evaporator temperature on PBP for R11 in
TSEORC, it can be deduced that PBP and ROI behave conversely. By
which it is meant that with the improvement of temperature of
evaporator at constant degree of superheat, the PBP value plummet
noticeably, while ROI increases. On the other hand, by going down
of degree of superheat the amount of PBP raises significantly and
ROI indicator slumps.
The PBP variation (for TSEORC by using R11) as a function of two
operating parameters which consist of the secondary evaporating
temperature and degree of superheat are shown in Fig. 13. With
respect to the color bar which is allocated beside the graph, simi-
larly with the results in Fig. 12, the maximum amount of PBP is
obtained when the temperature of secondary evaporator decreases
also the lowest value of degree of superheat leads to obtain the PBP
at the highest level.
In Fig. 14, the variation of PBP in respect with degree of super-
heat and pinch point temperature difference in the TSEORC system
through using R11 as working fluid are represented. Regarding to
this figure, by increasing the pinch point temperature difference at
low constant degree of superheat, PBP value grows massively in
comparison with the high constant amount of degree of superheat.
However, by improving the degree of superheat at constant pinch
point temperature difference, PBP value declines. Consequently,
degree of superheat and pinch point temperature difference have a
vise versa effects on PBP variation.
Fig. 11. The effects of pinch point temperature difference and degree of superheat on
ROI indicator for R11 in TSEORC system with Tevap1 ¼ 390.15 K and Tevap2 ¼ 361.81 K.
Fig. 12. The impacts of primary evaporator temperature and degree of superheat on
PBP indicator for R11 in TSEORC system with Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.
Fig. 13. The impacts of secondary evaporator temperature and degree of superheat on
PBP indicator for R11 in TSEORC system with Tevap1 ¼ 390.15 K and DTpp;evap ¼ 5.02 K.
Fig. 14. The impacts of pinch point temperature difference and degree of superheat on
PBP indicator for R11 in TSEORC system with Tevap1 ¼ 390.15 K and Tevap2 ¼ 361.81 K.

3.4. Condenser effects
Figs. 15e19 provide information about the effects of condenser
temperature on the thermodynamic and economic performances of
considered cycles, when R11 is used as the working fluid. From
Fig. 15, there is a decline in the exergy efficiency of each cycle by
growing the condenser temperature. The amount of net electrical
power output follows a similar pattern showing in Fig. 16. On the
other hand, economic indicators namely SIC, ROI and PBP have a
different pattern. In fact, the amount of SIC and PBP illustrated in
Figs. 17 and 18 fall with a plateau at around the condenser tem-
perature of 315 K and then go up for each cycles. In contrast, from
Fig. 19, ROI values first reach a peak at about the condenser tem-
perature of 315 K and then go down for each cycle.
Another parameter which could be important is the ambient
conditions of studied countries. The ambient conditions affect the
heat sink inlet temperature, which it changes the condenser pres-
sure. Therefore, these effects are provided in Fig. 20 indicating the
information about the ROI of studied cycles versus the heat sink
inlet temperature (Tcsi) for R11, Iran and exergoeconomic optimi-
zation data. It is clear that the overall trend of ROI for each cycles
falls by rising Tcsi.
3.5. Real plants
There is a possibility that a SIC expected by the bare module cost
method might be different with its real one. Equation (48) has been
introduced by Refs. [65,66] to tackle such problems.
ca
cb
¼

Aa
Ab
n
(48)
where c and A are cost and capacity of both real systems (a) and
expected ones (b) respectively. n for chemical industries is usually
near to 0.6. Therefore, Equation (48) can be replaced by Equation
(49) for ORCs plants.
Fig. 16. The impacts of condenser temperature on net electrical power output for R11
in TSEORC system with Tevap1 ¼ 390.15 K, Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.
Fig. 15. The impacts of condenser temperature on exergy efficiency for R11 in TSEORC
system with Tevap1 ¼ 390.15 K, Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.
Fig. 17. The impacts of condenser temperature on net electrical power output for R11
in TSEORC system with Tevap1 ¼ 390.15 K, Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.
Fig. 18. The impacts of condenser temperature on PBP for R11 in TSEORC system with
Tevap1 ¼ 390.15 K, Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.

ca¼ BðAaÞ0:6
(49)
where B is
B ¼
cb
ðAbÞ0:6
(50)
The parameters containing in Equation (49) are provided in
Table 17. From the table, the values of B for different cycles of a
specified working fluid type are almost same. Therefore, an average
numbers of B are calculated for each working fluid type making up
6.15 Eþ4, 1.41 Eþ5 and 4.67 Eþ4 (dry, wet and isentropic respec-
tively). These values are used to plot a graph shown in Fig. 21. The
figure illustrates the cost trends of real ORCs versus real capacity for
each working fluid types. It can be inferred from the figure that the
amount of real cost related to each working fluid type climbs within
the real capacity.
4. Conclusions
In the present study, the application of geothermal energy as a
kind of renewable one was studied for producing electricity
based on two general aspects. Firstly, three ORC configurations
contained basic ORC, RORC and TSEORC were designed as heat
conversion technologies to convert geothermal heat into elec-
tricity. In this stage, after thermodynamic and economic
modeling, some crucial operating parameters related to these
thermodynamic cycles were optimized by using thermodynamic,
economic and exergoeconomic optimization methods for three
different working fluids, namely R600a and R601a (dry), R152a
and R134a (wet) as well as R11 and R123 (isentropic). Secondly, a
profitability approach was carried out with economic indicators
included LCOE, ROI and PBP through considered cycles and
working fluids based on exergoeconomic results and twenty
countries among five contents. Also, in this part, the impacts of
operating parameters on economic indicators for Iran were
investigated. According to the foregoing results the main con-
clusions could be drawn as follow:
Fig. 19. The impacts of condenser temperature on ROI for R11 in TSEORC system with
Tevap1 ¼ 390.15 K, Tevap2 ¼ 361.81 K and DTpp;evap ¼ 5.02 K.
Fig. 20. The impacts of the heat sink inlet temperature (Tcsi) on ROI for R11 in TSEORC
system with Tevap1 ¼ 390.15 K, Tevap2 ¼ 361.81 K, Tcond. ¼ 308 K andDTpp;evap ¼ 5.02 K.
Table 17
Parameters related to equation (50) to analyze real SIC.
Substance System Ab (W) cb ($) B ($/W0.6
)
R600a (Dry) ORC 1.80 Eþ3 5.84 Eþ6 6.50 Eþ4
RORC 1.64 Eþ3 5.24 Eþ6 6.16 Eþ4
TSEORC 2.33 Eþ3 8.60 Eþ6 8.21 Eþ4
R601a (Dry) ORC 1.24 Eþ3 3.76 Eþ6 5.24 Eþ4
RORC 1.02 Eþ3 3.23 Eþ6 5.07 Eþ4
TSEORC 1.50 Eþ3 4.60 Eþ6 5.70 Eþ4
R152a (Wet) ORC 2.01 Eþ3 1.29 Eþ7 1.35 Eþ5
RORC 1.95 Eþ3 1.22 Eþ7 1.30 Eþ5
TSEORC 2.19 Eþ3 1.52 Eþ7 1.51 Eþ5
R134a (Wet) ORC 2.19 Eþ3 1.42 Eþ7 1.41 Eþ5
RORC 2.12 Eþ3 1.30 Eþ7 1.31 Eþ5
TSEORC 2.15 Eþ3 1.54 Eþ7 1.55 Eþ5
R11 (Isen.) ORC 8.12 Eþ2 2.56 Eþ6 4.60 Eþ4
RORC 5.59 Eþ2 2.28 Eþ6 5.13 Eþ4
TSEORC 1.95 Eþ3 4.94 Eþ6 5.25 Eþ4
R123 (Isen.) ORC 1.22 Eþ3 2.96 Eþ6 4.16 Eþ4
RORC 1.30 Eþ3 3.24 Eþ6 4.39 Eþ4
TSEORC 1.63 Eþ3 3.82 Eþ6 4.51 Eþ4
Fig. 21. Real cost variation of ORC plants versus capcity for the studied working fluid
according to the exregoeconomic optimization.

The thermodynamic properties of three considered pure organic
working fluids and geothermal water obtained respectively
from PR and SRK equations of state had a good agreement with
NIST standard reference databank.
In thermodynamic optimization, the amount of exergy effi-
ciency and SIC were more than economic optimization results.
The Degree of Superheat (DS) was considerably more influential
in the optimization trend of mentioned cycles than the other
operating parameters.
The optimal amount of DS reached a peak for dry fluid and
followed by isentropic and wet working fluids, respectively.
The results of exergoeconomic optimization for three working
fluids illustrated that the maximum amount of exergy efficiency
obtained for R11 in the RORC, while R152a allocates the mini-
mum efficiency in the basic ORC.
The highest and the lowest amount of SIC were appeared to
R152a and R11, respectively in TSEORC system. Also, the
maximum and minimum electricity production rates related to
the TSEORC and RORC, respectively.
According to the results of profitability indicators, Australia and
Netherland have the most and the least PBP value, respectively
when R11 was selected in TSEORC. Also, R152a in basic ORC and
R600a in RORC gave rise to obtain the highest and lowest
amount of LCOE.
Although both evaporator temperature and degree of superheat
were directly proportional to ROI, The pinch point temperature
difference varied inversely with this economic indicator for Iran.
Nomenclature
A heat exchanger surface area (m2
)
C cost ($)
d diameters of tubes (m)
Ex
·
exergy flow rate (kW)
F LMTD correction factor
FS correction factor for overhead cost
f friction factor
H specific enthalpy (kJ/kg)
h heat transfer coefficient (W/(m2
K))
I
·
flow rate of destroyed exergy (or irreversibility) (kW)
k thermal conductivity (W/(m K))
m
·
mass flow rate (kg/s)
Mel annual electricity generation
Nu Nusselt number
P pressure (bar)
Pr Prandtl number
PPTD pinch point temperature difference (0
C)
Q
·
heat transfer flow rate (kW)
Re Reynolds number
S specific entropy (kJ kgÀ1
KÀ1
)
S annual annual sales revenue
t corp corporate tax rate
TCB total cycle cost
T temperature (0
C)
U overall heat transfer coefficient (W mÀ2
KÀ1
)
W
·
power output/input (kW)
Subscripts and abbreviations
ORC Organic Rankine Cycle
RORC Regenerative Organic Rankine Cycle
TSEORC Two-Stage Evaporation Organic Rankine Cycle
LCOE Levelized Cost Of Electricity
PBP Pay-Back Period
ROI Return On Investment (%)
SIC Specific Investment Cost ($/Kw)
cond condenser/condensation
evap evaporator/evaporation
t turbine
p pump
HX heat Exchangers
in/out inlet/outlet
i/o inside/outside
is isentropic
hsi/hso heat source (or geothermal water) inlet/outlet
csi/cso heat sink (or cooling water) inlet/outlet
tot total
h/c heat source/sink or hot/cold
wf Working fluid
elec electrical
gen generator
reg/regen regenerative
Greek symbols
a coefficient of linear weighted evaluation function
b coefficient of linear weighted evaluation function
h efficiency (%)
m dynamic viscosity (Pa s)
References
[1] A. Desideri, S. Gusev, M. Broek, V. Lemort, S. Quoilin, Experimental comparison
of organic fluids for low temperature ORC (organic Rankine cycle) systems for
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