Exergoeconomic Analysis of Ammonia–Water Based Power Cycles

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EXERGOECONOMIC ANALYSIS OF AMMONIA–WATER BASED POWER CYCLES
Mortaza Yari1, Farzad Mohammadkhani2, Faramarz Ranjbar2, S.Mohammad S.Mahmoudi2
1Department of Mechanical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
2Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
myari@uma.ac.ir, f.mohammadkhani@tabrizu.ac.ir, s.ranjbar@tabrizu.ac.ir, s_mahmoudi@tabrizu.ac.ir
ABSTRACT
An exergoeconomic analysis is reported for ammonia–water based Rankine (AWR) and ammonia–water
based regenerative Rankine (AWRR) power cycles. For this purpose, these cycles are first
thermodynamically analyzed through energy and exergy and temperature distributions of fluid streams in
the heat exchangers are closely examined. Then cost balances and auxiliary equations are applied to
subsystems, therefore, cost formation in the cycles is observed. The exergoeconomic analysis is performed
based on the specific exergy costing (SPECO) approach. Finally a parametric study is performed to reveal
the effect of ammonia concentration on important exergoeconomic parameters of the cycles. The results
show that, among all components, condenser and regenerator have the highest exergy destruction cost rate
in AWR and AWRR, respectively. The exergoeconomic factor is determined to be 36.35% and 46.31%, and
the unit cost of electricity produced by turbine is calculated as 11.87 and 13.85 cent/kWh for AWR and
AWRR systems, respectively. Also it is observed that increasing ammonia concentration increases the unit
cost of electricity produced by turbine as well as the total exergy destruction cost rate and decreases the
overall exergoeconomic factor for both AWR and AWRR.
Keywords: Energy, Exergy, Exergoeconomics, Rankine power cycle, Ammonia-water mixture, Ammonia
concentration, Heat exchanger
INTRODUCTION
Increasing concern regarding the depletion of fossil energy resources and the pollution of the environment
has led to the development of high efficiency energy systems. One of the more dependable methods for
increasing energy generation efficiency is utilizing every useful power and thermal energy that can be
extracted from a fuel source. Thus, great attention has been paid to the utilization of low grade waste heat to
generate power in recent years.
Development of Organic Rankine Cycle (ORC) technology has been attained in waste heat recovery of low
grade heat sources, such as geothermal sources, solar energy, bio-fuel electricity production plants and
vehicle exhaust gases during the last one hundred years (Shu et al., 2012). Since pure fluids have the
properties of boiling and condensing at constant temperature, large temperature differences occur in the
vapor generator and condenser and therefore, exergy destruction increases in these components. On the
other hand, the use of ammonia–water mixture, which is a zeotropic binary-mixture, as a working fluid in the
power generating system has been found to be a promising candidate for utilizing low temperature heat
source. In the power generation systems using ammonia-water as working fluid, heat can be supplied or
rejected at variable temperature but still at constant pressure. The variable-temperature heat transfer
process improves the temperature matching between hot and cold streams in heat exchangers and reduces
the exergy destruction in the power cycles (Kim et al., 2012).
Zamfirescu and Dincer evaluated the performance of an ammonia–water Rankine cycle that uses no boiler,
but rather the saturated liquid is flashed by a positive displacement expander for power generation. Their
results showed that the efficiency of the cycle running with ammonia–water is 0.30 in contrast to steam-only
case showing 0.23 exergy efficiency, which means an increment of 7.0%, is obtained for the same operating
conditions (Zamfirescu and Dincer, 2012). Wagar et al. performed a thermodynamic analysis of an
ammonia-water based Rankine cycle for renewable based power production as well as industrial waste heat.
They developed a model to optimize the cycle for maximum power output. They found that the cycle
efficiencies are drastically affected by the concentrations and temperatures and depending on the source
temperature, the cycle energy efficiency varies between 5% and 35% (Wagar et al., 2010). Kim et al.
comparatively analyzed ammonia–water based Rankine (AWR) regenerative Rankine (AWRR) power
generation cycles by investigating the effects of ammonia mass concentration in the working fluid on the
thermodynamic performances of systems. In this work, which will be discussed further in the present work,
the characteristics of temperature distributions of the fluid streams in the heat exchangers are illustrated and
effects of ammonia concentration on the thermodynamic performances of AWR and AWRR cycles are

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comparatively studied. Results of the work showed that thermal and exergy efficiencies of AWRR system
are generally better than those of AWR system (Kim et al., 2012).
In the analysis of energy systems, the methods which combine scientific principles with economic disciplines
to attain optimum design are growing. Combining the second law of thermodynamics with economics
provides a very powerful tool for the systematic study and optimization of energy systems and forms the
basis of the relatively new field of thermoeconomics or exergoeconomics. Exergoeconomics combines the
exergy analysis with the economic principles and incorporates the associated costs of the thermodynamic
inefficiencies in the total product cost of an energy system. These costs help designers understand the cost
formation process and can be used in optimizing thermodynamic systems, where minimizing the unit cost of
the system product is the main task (Ahmadi and Dincer, 2010).
In the literature, there exist a number of papers concerning exergoeconomic analysis and optimization of
energy systems. Baghernejad and Yaghoubi performed exergoeconomic analysis and optimization of an
Integrated Solar Combined Cycle System (ISCCS) using genetic algorithm. Their analysis showed that
objective function for the optimum operation is about 11% lower than that for a base case. Also cost of
electricity produced by steam turbine and gas turbine in the optimum design of the ISCCS are about 7.1%
and 1.17% lower in comparison with the base case. These objectives are achieved with 13.3% increase in
capital investment (Baghernejad and Yaghoubi, 2011). Mohammadkhani et al. applied the exergoeconomic
concept to a Gas Turbine-Modular Helium Reactor (GT-MHR) combined with two Organic Rankine Cycles
(ORCs). They also performed a parametric study to reveal the effects of significant parameters on the
exergoeconomic performance of the combined system (Mohammadkhani et al., 2014).
As pointed out above, Kim et al. investigated the thermodynamic performances of ammonia–water based
power cycles. In the present work, exergoeconomic formulations and procedure are developed for
ammonia–water based Rankine (AWR) and ammonia–water based regenerative Rankine (AWRR) power
cycles. For this purpose, these cycles are first thermodynamically analyzed through energy and exergy.
Then cost balances and auxiliary equations (based on the SPECO approach) are applied to subsystems and
exergoeconomic parameters are calculated for the components and entire cycles. Finally a parametric study
is done to reveal the effect of ammonia concentration in the working fluid on important exergoeconomic
parameters of the cycles.
SYSTEM DESCRIPTION
Schematics of ammonia–water based Rankine (AWR) and ammonia–water based regenerative Rankine
(AWRR) power cycles are shown in Fig. 1 and Fig. 2, respectively.
Fig. 1. Schematic of ammonia–water based Rankine (AWR) power cycle

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Fig. 2. Schematic of ammonia–water based regenerative Rankine (AWRR) power cycle
The working fluid of the cycles is ammonia and water mixture. Energy of the cycles is supplied using the
source with temperature of Ts and the ammonia-water mixture is cooled in the condenser with the cooling
water in Tcw. The sequence of processes in the AWR follows: compression in the pump, heating in the
evaporator, expansion in the turbine and condensation in the condenser, and in the AWRR: compression in
the pump, preheating in the regenerator, heating in the evaporator, expansion in the turbine, cooling in the
regenerator and condensation in the condenser.
The following assumptions are made in this work (Kim et al., 2012):
 The mixture at the exit of heat exchanger is pure vapor at Ts-∆Ts.
 The mixture at the condenser outlet is saturated liquid at Tcw+∆Tcw.
 The minimum temperature difference between hot and cold streams in the evaporator, regenerator
and condenser should be maintained to be greater than a prescribed pinch point, ∆Tpp.
 The turbine and pump have isentropic efficiencies.
 The vapor fraction at the exit of turbine should be greater than a prescribed limit.
 The mixture at the inlet of turbine is supposed to be pure vapor.
EXERGOECONOMIC ANALYSIS
Exergoeconomics is the branch of engineering that combines thermodynamic evaluations based on an
exergy analysis with economic principles, at the level of system components, in order to present information
that is useful to the design and operation of a cost effective system, but not attainable by energy or exergy
analysis and economic analysis, separately. Exergoeconomics based on the concept that exergy is the only
rational basis for assigning monetary costs to the interactions that a system experiments with its
surroundings and to the sources of thermodynamic inefficiencies within it (Tsatsaronis, 2007).
There are different exergoeconomic approaches in the literature (Abusoglu and Kanoglu, 2009). The
SPECO (specific exergy costing) approach is used in the present work. This method is based on specific
exergies and costs per exergy unit, exergetic efficiencies, and the auxiliary costing equations for
components of thermal systems and consists of three main steps: (i) quantifying the energy and exergy for
streams, (ii) definition of fuel and product for each component of system and (iii) allocation of cost equations
(Lazzaretto and Tsatsaronis, 2006).
Quantifying the energy and exergy for streams
Mass and energy conservation expressions for any steady state system can be written as (Cengel and
Boles, 2006):
 ei mm 
(1)
 
 eeii hmWhmQ 



(2)

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When power is produced from a low temperature energy source, generating maximum possible power from
the given energy source is the main priority. In order to achieve this, mass flow rate of the working fluid
should be maximum. The mass flow is expected to have the maximum value when the minimum
temperature difference between the hot and cold fluids in the evaporator reaches the pinch point of ∆Tpp.
Thus, temperature difference between hot and cold fluids in the evaporator, ∆T, can be expressed as (Kim
et al., 2012):
)(
),,(
),( ,
12
1
,, outssoutsoutsTT
hh
hxPTh
TTTTT 



(3)
Where, T and h are temperature and enthalpy of the mixture in the evaporator, respectively, and the
subscripts 1 and 2 indicate the inlet and outlet of the evaporator, respectively. x is the ammonia
concentration in the working fluid. The condition of maximum produced power is satisfied by the following
equation:
0),(min , ppoutsTTTT
(4)
Similarly in the condenser:
)(
),,(
),( ,
12
1
,, cwoutcwoutcwoutcw TT
hh
hxPTh
TTTTT 



(5)
0),(min , ppoutcw TTTT
(6)
Where, h1 and h2 are enthalpies of the mixture at the outlet and inlet of condenser, respectively.
And, in the regenerator of the AWRR:
6523 hhhh 
(7)
0),,(min 63  pp
ThhTT
(8)
The energy efficiency is generally defined as:
)( inputenergytotal
productsinenergy


(9)
The exergy balance is applied to any component of the system as follows:
   DeeWiiQ EemEemE 




(10)
Here, subscripts i and e denote the control volume inlet and outlet, ĖD is the exergy destruction rate and, ĖQ
and ĖW are the exergy rate associated with heat transfer and mechanical power, respectively.
The exergy efficiency is generally defined as:
)( inputexergytotal
productsinexergy


(11)
Definition of fuel and product for each component of system
In the SPECO method, fuel and product are defined for each component of system. The fuel represents the
resources required to generate the product and the product represents the desirable result produced by the
system. Both the fuel and the product are represented in terms of exergy (Baghernejad and Yaghoubi,
2011). Table 1 represents definitions of the exergies of fuels, ĖF, and products, ĖP, for each component of
the AWR and AWRR systems.

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Table 1. Fuel-product definitions for the components of AWR and AWRR systems
Component
ĖF
ĖP
AWR
Evaporator
Ės,in – Ės,out
Ė3 – Ė2
Turbine
Ė3 – Ė4
ẆT
Condenser
Ė4 – Ė1
Ėcw,out – Ėcw,in
Pump
ẆP
Ė2 – Ė1
AWRR
Evaporator
Ės,in – Ės,out
Ė4 – Ė3
Turbine
Ė4 – Ė5
ẆT
Regenerator
Ė5 – Ė6
Ė3 – Ė2
Condenser
Ė6 – Ė1
Ėcw,out – Ėcw,in
Pump
ẆP
Ė2 – Ė1
Cost balances
In exergy costing, for each flow line in the system, a parameter called flow cost rate Ċ ($/s) is defined and
the cost balance equation for a component receiving heat and generating power is written as
(Mohammadkhani et al., 2013):
  
e i kkikqkwke ZCCCC 
 ,,,,
(12)
jjj EcC 

(13)
In Eq. (12), i and e indicate the entering and exiting streams for component k, and Żk is the cost rate
because of capital investment and operating and maintenance costs. The corresponding equations for
calculating capital investment of the components of AWR and AWRR are presented below.
For the evaporator and the condenser (Rodriguez et al., 2012):
8.0
,588AZ ce 
(14)
For the regenerator (Cheddie and Murray, 2010):
78.0
093.0
130 





A
Zr
(15)
For the turbine (Rodriguez et al., 2012):
7.0
4405 tt WZ 

(16)
And, for the pump (Rodriguez et al., 2012):
8.0
1120 pp WZ 

(17)
In the above equations, Zk is the purchase cost of kth component in dollar. To convert the capital investment
into the cost per time unit, one can write (Mohammadkhani et al., 2013):
)3600/(..  NCRFZZ kk


(18)
Where φ is the maintenance factor (1.06), N is the number of system operating hours in a year (7446 h) and
CRF is the Capital Recovery Factor, which can be written as:
1)1(
)1(


n
n
i
ii
CRF
(19)
Here, i is the interest rate (assumed to be 10%) and n is the system life (assumed to be 20 years).

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For calculating the cost rate of exergy destruction in the components, first we should solve the cost balance
equations. Generally, if there are N exergy streams exiting the component, we have N unknowns and only
one equation, the cost balance. Therefore, we need to formulate N–1 auxiliary equations. This is performed
with the aid of the F and P principles in the SPECO approach (Lazzaretto and Tsatsaronis, 2006).
Developing cost balance equation for each component of the AWR and AWRR systems and auxiliary
equations (according to F and P rules) leads to the system of equations presented in Table 2.
Table 2. Cost balances and corresponding auxiliary equations for the components of AWR and AWRR systems
Component
Cost balance equation
Auxiliary Equations
AWR
Evaporator
outsevapinsCCZCC ,3.,2 

 
outs
outs
ins
ins
E
C
E
C
,
,
,
,





Turbine
turbwturb CCZC ,4.3 


4
4
3
3
E
C
E
C




Condenser
outcwcondincw CCZCC ,1.,4 

 
1
1
4
4
E
C
E
C




, Ċcw,in=0
Pump
2,1 CZCC pumppumpw 

 
.
,
,
turb
turbw
pump
pumpw
W
C
W
C





AWRR
Evaporator
outsevapinsCCZCC ,4.,3 

 
outs
outs
ins
ins
E
C
E
C
,
,
,
,





Turbine
turbwturb CCZC ,5.4 


5
5
4
4
E
C
E
C




Regenerator
63.52 CCZCC reg 

 
6
6
5
5
E
C
E
C




Condenser
outcwcondincw CCZCC ,1.,6 

 
1
1
6
6
E
C
E
C




, Ċcw,in=0
Pump
2,1 CZCC pumppumpw 

 
.
,
,
turb
turbw
pump
pumpw
W
C
W
C





By solving the system equations presented in Table 2, the costs of unknown streams are obtained. In
exergoeconomic assessment of thermal systems certain quantities, known as exergoeconomic variables,
play a significant role. These variables include the average cost per exergy unit of fuel (cF,k), the average
cost per exergy unit of product (cP,k), the exergoeconomic factor (fk), and the cost flow rate associated with
the exergy destruction (ĊD). Mathematically, these variables are expressed as (Bejan et al., 1996):
kF
kF
kF E
C
c,
,
,


(20)
kP
kP
kP E
C
c,
,
,


(21)
kDkFkD EcC ,,, 

(22)
kLkDk
k
kCCZ
Z
f,, 




(23)
The exergoeconomic factor, fk, is an important exergoeconomic parameter that shows the relative
importance of a component cost to the associated cost of exergy destruction and loss in that component
(Mohammadkhani et al., 2013).

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RESULTS AND DISCUSSION
The basic assumptions and input parameters used in the simulation are listed in Table 3 (Kim et al., 2012).
Table 3. Parameter values used in the simulation
Parameter
Value
Unit
Source temperature, Ts
180
°C
Cooling water temperature, Tcw
15
°C
Temperature difference at source inlet, ∆Ts
20
°C
Temperature difference at cooling water inlet, ∆Tcw
10
°C
Pinch point temperature difference, ∆Tpp
5
°C
Turbine inlet pressure, PH
18
bar
Ammonia mass concentration, x
80
%
Isentropic efficiency of pump, ηp, and turbine, ηt
85, 90
%
Table 4 shows the thermodynamic data of the AWR and AWRR systems. These data are obtained from
developed EES (Engineering Equation Solver) thermodynamic model for the systems.
Table 4. Thermodynamic properties of fluids of AWR and AWRR systems
State no.
Temperature
(°C)
Pressure
(bar)
Vapor
fraction
(-)
Specific
volume
(m3/kg)
Specific
enthalpy
(kJ/kg)
Specific
entropy
(kJ/kg K)
Specific
exergy
(kJ/kg)
AWR
1
25
8.09
0
0.0014
-23.56
0.32
141
2
25.2
18
0
0.0014
-21.89
0.32
142.4
3
160
18
1
0.1083
1830
5.44
493.8
4
116.3
8.09
0.97
0.2161
1698
5.48
351.4
AWRR
1
25
8.09
0
0.0014
-23.56
0.32
141
2
25.2
18
0
0.0014
-21.89
0.32
142.4
3
86.1
18
0.61
0.0535
930.6
3.17
261.6
4
160
18
1
0.1083
1830
5.44
493.8
5
116.3
8.09
0.97
0.2161
1698
5.48
351.4
6
47.4
8.09
0.55
0.1001
745.6
2.83
175.4
Temperature distributions of fluid streams in the heat exchanging components could play a significant role in
designing the power cycles using ammonia–water mixture. Therefore, in the present work, this is studied for
heat exchangers. As previously stated in Table 3, the present analysis is performed by considering the
prescribed limit of pinch point, 5 °C.
Fig. 3 shows the temperature distributions of fluid streams in the evaporator and condenser of AWR system
as a function of relative heat transfer, Q. Here, Q is defined as the ratio of heat transfer at an arbitrary
position to the total heat transfer in heat exchanging device.
Fig. 3. Temperature distributions of fluid streams (a) in the evaporator, and (b) in the condenser of AWR system

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Also, Fig. 4 shows the temperature distributions of fluid streams in the evaporator, regenerator and
condenser of AWRR system.
Fig. 4. Temperature distributions of fluid streams (a) in the evaporator, (b) in the regenerator, and (c) in the condenser of AWRR system
As stated previously, by solving the system of cost balance and auxiliary equations, the cost of unknown
streams of the system are obtained. The unit cost of heat source (unit steam cost) is an important parameter
in determining the cost of products. In this work, it is assumed to be 15.24 $/GJ (A.S. Mehr et al., 2013).
Table 5 outlines the major exergy and exergoeconomic parameters for different components of the AWR
and AWRR systems.
Table 5. Exergy and exergoeconomic parameters for the components of AWR and AWRR systems
Component
ĖF
(kW)
ĖP
(kW)
ĖD
(kW)
Ɛ
(%)
ĊD,k
($/h)
Żk
($/h)
Żk+ĊD,k
($/h)
f
(%)
AWR
Evaporator
31.55
25.28
6.27
80.13
0.344
0.153
0.497
30.79
Turbine
10.24
9.46
0.79
92.32
0.058
0.355
0.413
85.76
Condenser
15.14
6.95
8.19
45.91
0.614
0.070
0.684
10.28
Pump
0.12
0.10
0.02
84.29
0.002
0.003
0.005
60.55
AWRR
Evaporator
25.36
23.30
2.06
91.87
0.113
0.195
0.308
63.24
Turbine
14.28
13.18
1.10
92.32
0.106
0.448
0.554
80.88
Regenerator
17.66
11.96
5.70
67.72
0.550
0.098
0.648
15.10
Condenser
3.45
1.34
2.11
38.81
0.204
0.098
0.302
32.47
Pump
0.17
0.14
0.03
84.29
0.004
0.004
0.008
55.17
The components having the highest value of the sum of Żk+ĊD,k are the most important components from
the exergoeconomic viewpoint. Table 5 shows that, this value is highest for the condenser in the AWR
system. Also, the regenerator has the highest value of Żk+ĊD,k in the AWRR system. Also these components
have the highest values of exergy destruction cost rate and the lowest values of exergoeconomic factor
among the other components of the cycles. This means that the exergy destruction cost in this component
dominates the owning and operating cost. The relatively higher values of exergy destruction in these
components are mainly due to the temperature differences between the streams. The low value of f for
these components suggests that an increase in capital cost is merited, through increasing the heat transfer
area.
In both the AWR and AWRR systems, the turbine has the highest exergy efficiency and relatively lower
value of the exergy destruction. This means that exergetic performance of this component is satisfactory.
Moreover, the turbine has the highest exergoeconomic factor among the other components showing that the
capital cost of this component dominates the exergy destruction cost rate.
Changes in the exergoeconomic parameters of the pump do not affect notably the exergoeconomic
performance of the system, as the value of Żk+ĊD,k associated with this component is the lowest in both the
AWR and AWRR systems.

9
The energy and exergy efficiencies of the AWR system are calculated as 7% and 28.55%, respectively.
These values are 14.43% and 39.7% for the AWRR system. Also the value of total exergy destruction is
15.26 and 11 kW for the AWR and AWRR systems. These mean that using regenerator in the Rankine
power cycle leads to better performance from the energy and exergy viewpoints.
The unit cost of electricity produced by the turbine is an important parameter of the exergoeconomic
analysis. This value is determined to be 11.87 and 13.85 cent/kWh for the AWR and AWRR, respectively
and means that the power production in the AWRR turbine has the higher cost in comparison with the AWR
turbine. Total exergy destruction cost rate is calculated as 1.019 and 0.98 $/h for the AWR and AWRR,
respectively.
Also value of the exergoeconomic factor, f, is 36.35% and 46.31% for the AWR and AWRR, respectively.
The ammonia mass concentration in the working fluid is an important parameter of the ammonia-water
based power cycles. In the following, effects of change in the ammonia mass concentration in the working
fluid on exergoeconomic performance of the AWR and AWRR systems are investigated.
Fig. 5 shows the effects of change in ammonia mass concentration on the unit cost of electricity produced
by turbine, total exergy destruction cost rate and overall exergoeconomic factor for the AWR and AWRR
systems.
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
10
12
14
16
18
20
Ammonia mass concentration
Unit cost of the electricity pr oduced by turbine [cent/kWh]
AWRAWR
AWRRAWRR
(a)
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Ammonia mass concentra tion
Total exergy destruction cost rate [$/h]
AWRAWR
AWRRAWRR
(b)
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
25
30
35
40
45
50
55
60
65
Ammonia mass concentra tion
Overall exergoeconomic factor [%]
AWR
AWRRAWRR
(c)
Fig. 5. Effects of change in ammonia mass concentration on the (a) unit cost of electricity produced by turbine, (b) total exergy destruction cost
rate, and (c) overall exergoeconomic value for the AWR and AWRR systems
Fig. 5 shows that increasing the ammonia mass concentration in the working fluid increases the unit cost of
electricity produced by turbine and total exergy destruction cost rate. The unit cost of electricity produced by
turbine for the AWRR is higher than that for the AWR system in all ammonia concentrations. Exergy
destruction cost rate is higher for AWR system in relatively lower ammonia concentrations while this trend is
changed with increasing the ammonia concentration. The overall exergoeconomic factor decreases with
increasing the ammonia mass concentration and this value is higher for AWRR system in all ammonia
concentrations.

10
CONCLUSIONS
In this work, an exergoeconomic analysis is performed for ammonia–water based Rankine (AWR) and
ammonia–water based regenerative Rankine (AWRR) power cycles. First energy and exergy relations and
then cost balances and auxiliary equations (based on the SPECO approach) are developed for the
components of AWR and AWRR systems. The results show that the condenser (in the AWR system) and
regenerator (in the AWRR system) are the most important components from the exergoeconomic viewpoint.
In both the AWR and AWRR systems, the turbine has the highest exergy efficiency and relatively lower
value of the exergy destruction. Also, it is concluded that the power production in the AWRR turbine has the
higher cost than the AWR turbine, while, the energy and exergy analysis results recommend the using of the
regenerator in Rankine power cycle. Moreover, the results of parametric study show that increasing
ammonia mass concentration in the working fluid increases the unit cost of electricity produced by turbine
as well as total exergy destruction cost rate and decreases the overall exergoeconomic factor for both the
AWR and AWRR systems.
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