A graphical criterion for working fluid selection and ...

Applied Thermal Engineering 89 (2015) 772e782

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Research paper

A graphical criterion for working fluid selection and thermodynamic system comparison in waste heat recovery Huan Xi, Ming-Jia Li, Ya-Ling He*, Wen-Quan Tao Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China

h i g h l i g h t s
A graphical method for ORC system comparison/working fluid selection was proposed.
Multi-objectives genetic algorithm (MOGA) was applied for optimizing ORC systems.
Application cases were performed to demonstrate the usage of the proposed method.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 December 2014 Accepted 14 June 2015 Available online 30 June 2015

In the present study, we proposed a graphical criterion called CE diagram by achieving the Pareto optimal solutions of the annual cash flow and exergy efficiency. This new graphical criterion enables both working fluid selection and thermodynamic system comparison for waste heat recovery. It's better than the existing criterion based on single objective optimization because it is graphical and intuitionistic in the form of diagram. The features of CE diagram were illustrated by studying 5 examples with different heat-source temperatures (ranging between 100  C to 260  C), 26 chlorine-free working fluids and two typical ORC systems including basic organic Rankine cycle(BORC) and recuperative organic Rankine cycle (RORC). It is found that the proposed graphical criterion is feasible and can be applied to any closed loop waste heat recovery thermodynamic systems and working fluids. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Waste heat recovery (WHR) Organic Rankine cycle (ORC) Graphical criterion Working fluid selection System comparison Multi-objectives genetic algorithm (MOGA)

1. Introduction With the rapid development of emerging economies, worldwide total energy usage is increasing rapidly. Low-temperature waste heat, which generally generates from industrial processes, has caused many serious environmental problems such as global warming, ozone layer destruction and atmospheric pollution [1]. For these reasons, new environmentally-friendly energy conversion and recovering technologies which can utilize lowtemperature energy resources need to be developed. To meet this need, organic Rankine cycles (ORCs) as one of the candidates for waste heat recovery has attracted increasing attention. Over the past decades, many efforts have been made to explore suitable thermodynamic systems, select working fluids, and optimize the operating parameters. To evaluate the system and working fluid, certain criteria or objective functions are needed. The past

* Corresponding author. Tel.: þ86 29 82665930; fax: þ86 29 82665445. E-mail address: [email protected] (Y.-L. He). http://dx.doi.org/10.1016/j.applthermaleng.2015.06.050 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

works mainly focused on the studies limiting one certain criterion, such as thermal efficiency, exergy efficiency, or net power output, etc. He C. et al. [2] proposed that R114, R245fa, R123, R601a, npentane, R141b and R113 were all optimal working fluids for subcritical organic Rankine cycle when the net power output was used as the objective function. Dai et al. [3] compared 10 working fluids by using exergy efficiency as the objective function, and R236ea was recommended as the suitable working fluid. The author used exergy efficiency as the objective function to compare the working fluids and systems using genetic algorithm as optimizer [4]. Guo et al. [5] reported that the optimal working fluid varied with the selected objective functions. Similar conclusion was drawn by Cayer et al. [6] and Zhang et al. [7]. Some researchers compared the working fluids by employing several criterias simultaneously. Drescher and Brüggemann [8] performed parametric optimization and working fluids selection by employing several objective functions such as thermodynamic properties, stability, safety, health and environmental aspects, availability and costs. They focused on thermodynamic properties while other

H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

criteria were discussed only in qualitative respects. Tchanche et al. [9] employed various criterias including efficiency, volume flow rate, mass flow rate, pressure ratio, toxicity, flammability, ODP (ozone depletion potential) and GWP (Global Warming Potential) for comparison, and R134a was recommended based on the above criterias. Amlaku AL and Olav B [10] operated a working fluids screen based on power production capability and component size requirements. 6 kinds of working fluids were compared under different heat source temperatures using the selected objective functions. The result showed that it is hard to recommend a working fluid with both minimum heat exchanger area and smallest turbine size. Thus the working fluids selection were still recommended and summarized according to their own strong points. Quoilin et al. [11] performed thermodynamic and economic optimization for ORC system respectively to select working fluids. They found that the point with maximum power did not correspond to minimum specific investment cost. Oguz A and Ozge Y [12] performed an ANN based optimization for power cycle, the weights of the most suitable ANN models integrated with the life cycle cost (LCC) concept were used to determine the most suitable design power plant. Athanasios IP et al. [13] presented systematic design and selection of optimal working fluids based on computer aided molecular design. It was based on group contribution methods and multi-objective optimization technology. Wang ZQ et al. [14] proposed working fluids selection based on multiobjective functions that use a simulated annealing algorithm. The criterias they considered include heat exchanger area per unit power output (m2/kW) and heat recovery efficiency. During the multiobjectives optimal calculation, they assumed weight coefficients of 0.6 and 0.4, respectively, thus simplifying the multi-objectives calculation to a single-objective calculation, essentially. The brief review presented above clearly shows that for working fluids selection and systems comparison, the past research works were compared comprehensively or with a certain calculated result of the objective function, therefore, a more intuitionistic criterion is needed to be addressed. To this end, by employing exergy efficiency and annual cash flow as objective functions, a new graphical criterion named CE diagram was proposed for working fluid selection and thermodynamic system comparison in waste heat recovery. To prove its feasibility, two typical ORC systems (i.e. BORC and RORC) and 26 chlorine-free working fluids were provided as the examples. Theoretical analysis towards thermodynamic systems and preselecting of the working fluids were both presented. Multiobjectives genetic algorithm (MOGA) based on Pareto optimal solution was then introduced as the optimizer. Detailed discussion of CE diagram was given to describe the graphing method. On these bases, the CE diagrams of two ORC systems and 26 chlorine-free working fluids under different heat source temperatures were then produced according to the calculating results. The meanings of endpoints were described and case studies were performed by segmenting the CE diagrams into different parts to discuss the usage of CE diagram. 2. Theoretical analysis of organic Rankine cycles 2.1. Preliminary selection of working fluids (1) Working fluids with poor environmental performance should not be recommended according to the Montreal protocol [15], for example, R21, R22, R123, R141b. (2) Condensing temperature and pressure are also the key factors in working fluids selection. In this study, condensing temperature has been set to 35  C [8]. (3) The working fluids with their critical temperature much higher than the heat source temperature should not be

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selected. The fluid with critical temperature much higher than the evaporation temperature leads to higher expansion pressure ratio and thus bigger components [16]. Also, near the critical point, a small disturbance could lead to a dramatic property change of the working fluids, which may cause system instability [17]. Thus, in order to ensure the stability and reliability of the system, the working fluid whose critical temperature is much lower than the heat source temperature didn't take into account to avoid the system working at supercritical state, which is outside the scope of this article. The preselected 26 working fluids and their critical properties are shown in Table 1. All the data in Table 1 comes from REFPROP 8.0. 2.2. Thermodynamic model of organic Rankine cycles By employing the Second Law of Thermodynamics, the performance of two different ORC systems (i.e., BORC and RORC) was examined. The system layout and cycle T-s diagram of each ORC system are shown in Figs. 1e2, respectively. Before analyzing, several assumptions were employed: (a) the system was under steady state, (b) pipe pressure drop and heat losses from the evaporator, condenser, turbine and pump were all neglected, (c) the operating conditions were assumed as listed in Table 2. To cover the industry application as widely as possible, the heat source temperatures were assumed as 100  Ce260  C. The exergy analysis method was employed to evaluate the performance of each ORC system. The exergy destruction rate can be expressed as follows

2 _ 04 I_ ¼ T0 $ds_ ¼ mT

X

sout 

X

3 dssystem X qj 5  sin þ dt Tj

(1)

j

Table 1 The properties of selected working fluids.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 a b c d

Working fluid

M(kg/kmol)

Tca( C)

Pcb(MPa)

ODPc

GWPd

R227ea(C3HF7) R1234ze(C3F4H2) Perfluorobutane(C4F10) RC318(C4F8) R236fa(C3H2F6) Isobutane(C4H10) R236ea(C3H2F6) Isobutene(C4H8) Butene(C4H8) Perfluoropentane(C5F12) Butane(C4H10) R245fa(C3H3F5) Trans-butene(C4H8) Neopentane(C5H12) Cis-Butene(C4H8) R245ca(C3H3F5) R365mfc(C4H5F5) Isopentane(C5H12) Pentane(C5H12) Isohexane(C6H14) Hexane(C6H14) Acetone(C3H6O) Heptane(C7H16) Cyclohexane(C6H12) Benzene(C6H6) Toluene(C7H8)

170.03 114.04 238.03 200.03 152.04 58.122 152.04 56.106 56.106 288.03 58.122 134.05 56.106 72.149 56.106 134.05 148.07 72.149 72.149 86.175 86.175 58.079 100.2 84.161 78.108 92.138

101.75 109.37 113.18 115.23 124.92 134.66 139.29 144.94 146.14 147.41 151.98 154.01 155.46 160.59 162.6 174.42 186.85 187.2 196.55 224.55 234.67 234.95 266.98 280.49 562.05 318.6

2.925 3.6363 2.3234 2.7775 3.2 3.629 3.502 4.0098 4.0051 2.045 3.796 3.651 4.0273 3.196 4.2255 3.925 3.266 3.378 3.37 3.04 3.034 4.7 2.736 4.075 4.894 4.1263

0 0 0 0 0 0 0 e e e 0 0 0 0 0 0 e 0 0 0 0 0 0 0 0 0

3500 e 8830 10,000 9810 ~20 9810 e e e ~20 950 ~20 e ~20 693 e ~20 ~20 e e e e e e e

Pc: critical temperature. Tc: critical pressure. ODP: ozone depletion potential. GWP: global warming potential.

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H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

Fig. 1. System layout and cycle T-s chart of the BORC system.

Fig. 2. System layout and cycle T-s chart of the RORC system.

Table 2 Assumed working conditions. Temperatures of heat source(K) Mass flow rate of hot gas (kg$s1) Specific heat at constant pressure for hot gases(kJ$kg1$K1) Environment temperature (K) Environment pressure (kPa) Condensing temperature (K) Expander efficiency Pump efficiency Effectiveness of inner heat exchanger Pinch temperature difference in the evaporator (K) Pinch temperature difference in the condenser (K)

373.15/413.15/453.15/493.15/533.15 14.0 1.1 298.1 101.3 308.15 0.8 0.7 0.8 8.0 8.0

2 dS _ 04 I_ ¼ T0 ¼ mT dt

X

sout 

X

3 X qj 5 sin  Tj

(2)

j

For the ORC systems, the efficiency of expander and pump are assumed as 0.8 and 0.7, respectively. They can be expressed as:

hexp ¼ ðh1  h2a Þ=ðh1  h2 Þ

(3)

hpump ¼ ðh5  h4 Þ=ðh5a  h4 Þ

(4)

The net output power is defined as: where Tj is the heat source temperature, qj is the heat transferred from each heat source to working fluid, T0 is the ambient temperature. dsystem/dt is the time-variation of the entropy of the system, when the system reaches the steady-state, dsystem/dt ¼ 0, Eq. (1) could be expressed as:

_ exp  W _ pump  W _ _ net ¼ W W pump;cooling tower

(5)

where Wexp is turbine power which can be calculated as:

_ exp ¼ mðh _ 1  h2a Þ W The pump power can be expressed as:

(6)

H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

_ pump ¼ mðh _ 5a  h4 Þ W

(7)

_ W pump;cooling tower is pump power of cooling water side, which can be calculated as [18]:

_ _ water;cooling tower Mwater ðDPÞ W pump;cooling tower ¼ m

T2a  T2ai T2a  T5a

(9)

Based on the First Law of Thermodynamics, the thermal efficiency of ORC systems is defined as the ratio of the net power output to the heat addition:

. _ net Q_ hI ¼ W

(10)

T11 ¼ T3  DTC

Ex ¼ Q ð1  T0 =TH Þ

The economic analysis is based on the annual cash flow function, which is defined as [21]:

F ¼ INtot  Ctot



X . · · hII ¼ Ex  I_ Ex

INtot ¼ SWele h

S is the selling price of generated electricity (0.06$/(kW h) [22]), Wele is the annual output of the system (kW), h is system working hours per annual operation period (h/year), in this work it was assumed as 7500 h. Ctot in Eq. (18) is the total cost per year including the depreciation cost (Cd) and the operation and maintenance cost (COM). It can be expressed as [23]:

Ctot ¼ Cd þ COM

Cd ¼

X

   PECK $ ið1 þ iÞn ð1 þ iÞn  1

(21)

K

where i is interest rate, assumed to be moderate at 5%, n is the economic life, assumed at 20 years, PEC is purchased equipment costs for each system component.

m_ working fluid ¼ cp;heat source m_ heat source ðT7  T8 Þ=ðh1  h6 Þ

As for pump, evaporator, turbine (or expander) and condenser of the systems, they can be calculated using an empiric correlation based on a large number of manufacturing data [25]:

  m_ water;cooling water ¼ m_ working fluid ðh3  h4 Þ cp;cooling water ðT11  T10 Þ

T8 in Eq. (14) is determined based on pinch temperature, which can be expressed as:

(20)

Depreciation cost Cd can be calculated as [24]:

(13)

(14)

(19)

where

(12)

To calculate the net output power, the thermal efficiency and the exergy efficiency, the mass flow rate of working fluids and cooling water are indispensable. Based on the energy balance between the heat source fluid and the working fluid of ORC system, the mass flow rate of working fluid and cooling water can be calculated as [20]:

(18)

The INtot in Eq. (18) is the total income which is defined as [22]:

(11)

While the exergy efficiency can be calculated using the following equation [20]:

(8)

2.3. Economic methodology

TH was represented by logarithmic mean temperature, which can be calculated by:

TH ¼ ðT7  T9 Þ=lnðT7 =T9 Þ

(17)

In this work, the pinch points DTE and DTC are assumed as 8  C. The ondenser temperature (T3) is fixed to 35  C.

Exergy flow can be calculated by: ·

(16)

Similarly, T11 in Eq. (15) can be expressed as:

 . rwater hpump;cooling tower

As shown in Fig. 2, in the RORC system, an internal heat exchanger was added. For the organic working fluids used in the organic Rankine cycle system, the heat capacity flow rate of vapor side is often lower than the liquid side, thus in the particular case, the effectiveness of the internal heat exchanger can be expressed as [19]:

s¼

T8 ¼ T6 þ DTE

775

logPEC ¼ K1 þ K2 $logX þ K3 ð logX Þ2

(15)

(22)

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H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

The parameters K1, K2 and K3 for the corresponding components are listed in Table 3 [26]. And X is the parameter value for each component which changes with different working conditions. The unit of X is also listed in Table 3. The heat exchanger surface for all the heat exchanger is calculated assuming an ideal counter current flow. To estimate the cost of the cooling tower, another correlation is recommended by Ref. [26]:

0:93  . PECcooling tower ¼ 154179 Q_ c 5193

In the past work, usually, Pareto optimal solutions were used in Computer Aided Molecular Design (CAMD) [30,31], working fluids selection [32] and parameter optimization [33]. As compared with the existing multi-objective optimization methodologies using Pareto optimal solutions, our work not only can select optimal working fluids and the operation parameters as a ‘optimizing tool’, it also proposes a kind of new graphical by fitting the Pareto optimal solutions into a fixed functional form. As a new method, the application has been described and demonstrated.

(23) 3.2. Multi-objectives genetic algorithm (MOGA)

To estimate the heat transfer area of the evaporator, condenser and internal heat exchanger, the LMTD method (Log Mean Temperature Difference) [27] is employed:

Genetic algorithm (GA), which is widely used as an optimizer, was first presented by Professor Holland in America [34]. Many

       Q ¼ UADTm ¼ UA TH;in  TC;out  TH;out  TC;in ln TH;in  TC;out TH;out  TC;in

where U is the overall heat transfer coefficient. Determining U often requires data not yet available in the preliminary stages of the design. Therefore, U is set at typical values of 0.4, 0.3 and 0.3 kW/ (m2
K) to estimate the size of the evaporator, condenser and internal heat exchanger [28]. The operation and maintenance cost (i.e. COM in Eq. (16)) is estimated by Ref. [28]:

COM ¼ 0:1Ctot

(25)

3. Optimized calculation

(24)

conventional optimization algorithms begin with a single given initial value, and thus they easily converge to sub-optimal solutions during the process of searching for the optimal values, especially in complicated problems such as discontinuous, nondifferentiable, or highly nonlinear problems. In the multi-objectives GA, there are three basic and indispensable operators: selection operator, crossover operator, and mutation operator. In this work, turbine inlet pressure and temperature (i.e. T1 and P1) are selected as variables. The twodimensional array [T1,P1] is chromosome. When generating the initial populations [T1n,p1n]n, the constraint conditions are:

n  o T1 2½333:15K; Tmax ; while Tmax ¼ min ðTcrit  10Þ; Tflue  8 ;

3.1. Multi-objective problem and the Pareto optimal solution

p1 2½200 kPa; psat ;T:

Many real world optimization problems in engineering have multiple objectives, which are often in conflict with each other. As a multi-objective problem (MOP), it can be described as follows:

Maximum : FðxÞ ¼ ð f1 ðxÞ; f2 ðxÞ… fn ðxÞ Þ Subject to : x2X (26) where x is the variable space, n is the amount of objective functions, X is a continuous definition domain space, fi ðxÞ (i ¼ 1,2 … n) are objective functions that are continuous on the continuous definition domain. Pareto optimal solutions are a set of solutions that satisfy the objectives at an acceptable level without being dominated by any other solution [29]. A solution is Pareto optimal solution if there exist no other feasible solution that improves at least one objective function without worsening another. Mathematically, Pareto optimal solution can be expressed as follows [29]: A solution x* 2X is Pareto optimal solution if there does not exist another solutionx2X, such that fi ðxÞ  fi ðx* Þ for all i and fi ðxÞ > fi ðx* Þ for at least one objective function. Table 3 Constants K1, K2 and K3 according to Eq. (18) for different system components. Component

Variable X (unit)

K1

K2

K3

Pump Evaporator Turbine Condenser

Power (kW) Area (m2) Power (kW) Area (m2)

3.3892 4.6656 2.6259 4.6656

0.0536 0.1557 1.4398 0.1557

0.1538 0.1547 0.1776 0.1547

The lower bound of T1 is 333.15 K, which is lower than all the optimal working conditions. The upper bound is given as the pinch point temperature and the critical temperature of the working fluid. The constraint (Tflue-8) is set according to the pinch point temperature, while the constraint (Tcrit-10) follows the rule that the highest temperature of the cycle should 10 K lower than critical temperature [35]. To enable the state of [T1,p1] to be overheated or saturated, the lower bound of p1 is 200 kPa, which is lower enough for all the working fluids and systems under the given conditions. The upper bound is generated by employing the saturation pressure psat,T associating with the generated T1. For the selected working fluids, the highest temperature of the critical (T1) should at least 8 K lower than the heat source temperature (the temperature of the heat source fluid at the inlet of the evaporator, T7) according to the assumed pinch point temperature. Within the limitation, different T1 generated as on of the elements of chromosome in GA to perform the optimized calculation. Same settings apply to P1. There are a certain number of chromosomes in the population. The selection operator is used for selecting the parents among existing chromosomes in the population with preference towards fitness to create the next generation. In this work, the “deterministic sampling” method is adopted as the selection operator [36]. The crossover operator is responsible for combining the selected two chromosomes to form new chromosomes. During this procedure, the simple arithmetic crossover is employed. The fundamental of arithmetic crossover is presented as follows [3]:

H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

(27)

where f1 and f2 are parents while c1 and c2 are offspring, and a is a random number between 0 and 1. Mutation operator is used to modify values of chromosomes randomly to avoid converging on local solutions. The “elite-preservation strategy” is used to protect the elites from crossover and mutation thus accelerating convergence [37]. Configurations of the GA in this work are listed at Table 4. The simulation program was written by the authors with Fortran language. To calculate the exergy efficiency and net output power, the thermodynamics properties of each state point for every chosen working fluid are indispensable. Therefore, the REFROP 8.0 was employed and the subroutines contained in REFROP 8.0 were called during the simulation process. 4. Characteristics of CE diagram 4.1. Drawing principles of CE diagram Multi-objectives genetic algorithm based on Pareto optimal solutions was employed as the optimizer. For a multi-objectives optimization problem such as in this work, the objectives (exergy efficiency and annual cash flow) are often in conflict with each other. It can be observed that the increase of exergy efficiency or annual cash flow is always at the expense of a decrease in the other. To achieve CE diagram, exergy efficiency (represented by the letter E), which is the characteristic parameter of energy utilization efficiency, was graphed as the horizontal axis, and the vertical axis was the annual cash flow (represented by the letter C), which is the characteristic parameter of economic performance. By observing the results, it can be concluded that all the data could be described using the following equation form under an acceptable error range:

C ¼ P1 þ P2 P3 =ðP3 þ EÞ

(28) 2

The parameters P1, P2 and P3 and R for each ORC system and each heat source temperature are listed in Appendix A. The corresponding CE diagrams are shown in Fig. 3(a) e (e), where the numbers 1 to 26 correspond with the different working fluids listed in Table 1. An apostrophe (') is used to distinguish the RORC system (with apostrophe) from the BORC system (without apostrophe). It should be noted that to describe the curve simply, Eq. (28) was achieved by fitting data, and the form of the equation was determined by the curve shape, therefore, the parameters of P1, P2 and P3 have no physical meanings. 4.2. The endpoints of CE diagram The results of single-objective optimized calculations always converge to a certain point, the value of which represents the

Table 4 Configurations of genetic algorithms. Population size Chromosome vector Crossover probability Mutation probability Elite count Stop generation

200 [T1,P1] 0.4 0.2 20 2000

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optimal value for this objective function. In contrast, Pareto optimal solutions, which were obtained by performing a multi-objectives optimization, are usually a group of points distributed in some certain sequence. When each objective of the multi-objectives was used to perform a single-objective optimized calculation, the resulted two certain points overlapped with the endpoints of curves on the CE diagram. This result means that the endpoints of curves on the CE diagram represent the maximum values of exergy efficiency and annual cash flow in all existing working conditions, respectively. For example, Fig. 4 is the CE diagram of isopentane under the 140  C heat source temperature with RORC system. From Fig. 4 we can clearly observe that for the RORC system, when performed under 140  C using isopentane as working fluid, the maximum exergy efficiency is 57% and the maximum annual cash flow is about $205 k for all the existed working conditions. 5. Results and discussion 5.1. Discussion Based upon above analyses, as a graphical method for working fluids selection, the CE diagrams are effective for recommending suitable working fluids. The following is an example that explains how to use CE diagrams to recommend suitable working fluids according to given working conditions. See Fig. 3(d). With a heat source temperature of 220  C, and exergy efficiency between 60.6% and 62.0%, only RORC system is available under these conditions as observed in the CE diagram. Pentane is recommended as the suitable working fluid, and the maximum annual cash flow is $1,140 k. By analogy, CE diagrams could also be used as an effective method to compare the thermodynamic systems under the same working fluid and operation parameters. We can also use CE diagram to determine the comprehensive dominant type for each thermodynamic system. For example, it can be observed from Fig. 3 that most curves of RORC systems were distributed at the bottom right area of the CE diagrams, which is most visible under relatively lower heat source temperatures conditions (see Fig. 3(a) and (b)). It can be inferred that RORC systems usually have higher energy utilization efficiency but weaker economic performance, even working with negative economic benefits in some particular cases. The further reason is stated as follows. For RORC systems, an internal heat exchanger is added to recover heat from the working fluid before reaching the condenser and to preheat the working fluid before reaching the evaporator. It is an effective way to increase energy utilization within systems. Acting as a preheater for the evaporator and a precooler for the condenser, the exergy efficiency would be improved and heat thermal load of evaporator and condenser would be reduced accordingly. Therefore, the heat exchanger areas of the evaporator and the condenser are reduced. However, with an internal heat exchanger added, the total heat exchanger area would increase again in most situations. As a key parameter of economic performance, the PEC of all the heat exchangers (i.e. internal heat exchanger, evaporator, and condenser) may be increased, thus decrease the economic performance of RORC. It is common in a multi-objectives optimization problem to have objectives that are in conflict with each other. The most direct manifestation is that there usually exists an obvious distance between the two endpoints in the CE diagrams. However, this conflict is not always obvious, especially under the relatively higher heat source temperatures conditions. As shown in Fig. 3(e), when operating under BORC system, the curves of heptane is focused into a quite small area. Therefore, based on the above analysis, the conflict between exergy efficiency and annual cash flow has been weakened. In that case, the optimum condition of systems with high exergy efficiency and annual cash flow could be achieved simultaneously.

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Fig. 3. CE diagram of BORC and RORC systems under different heat source temperature of ranges from 100 to 260  C.

5.2. Case study 5.2.1. Case Ⅰ: comparison between different working fluids without intersecting point on CE diagram Fig. 5 shows the CE diagram of cis-butene and R245fa under the 140  C heat source temperature with RORC system. As a common case of working fluid comparison, it can be seen from Fig. 5 that there is no intersection point between the two curves of each working fluids. In order to give a further detailed discussion of this case, the CE diagram could be divided into three sections by using endpoints as cutoff points. They are: Section Ⅰ: The section which covers the area between the leftmost endpoints of the two curves. In this part, it can be seen from Fig. 5 that R245fa had the most remarkable economic performance (maximum

annual cash flow) but poor energy utilization efficiency (quite low exergy efficiency lead more energy released to environment, which cause thermal pollution). In this section, the energy utilization efficiency was sacrificed to increase the economic performance. For this reason, this section could be properly named as economy-dominated section. The unique working fluid in this section (i.e. R245fa) should be recommended when the economic performance is at the highest desired value for special industry situations. Section Ⅱ: See Fig. 5. In this section, when fixed at a certain value of annual cash flow, R245fa has a higher exergy efficiency (a2 ¼ b2 while b1> a1) than cis-butene. Meanwhile, R245fa obtained a higher annual cash flow when fixed at the same value of exergy efficiency (c1 ¼ d1 while d2>c2). Thus R245fa is recommended as a superior working fluid for its superiority in both aspects.

H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

Fig. 4. CE diagram of isopentane under the 140  C heat source temperature with RORC system.

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Fig. 6. Case Ⅱ: CE diagram of neopentane and hexane under the 140  C heat source Temperature with RORC system.

point. Section Ⅰ(economy dominant section) and section Ⅲ (energy utilizing-dominated) are both similar to that of case Ⅰ. The other sections are discussed as follows: Section Ⅱ1: See Fig. 6. In this area, when fixed at a certain value of annual cash flow, neopentane has a higher exergy efficiency (c2 ¼ d2 while d1 > c1) compared to hexane. Meanwhile, neopentane obtain a higher annual cash flow when fixed at same value of exergy efficiency (a1 ¼ b1 while a2 > b2). Thus neopentane is recommended as superior working fluid in this section. Section Ⅱ2: Similar to the analysis method in section Ⅱ1, in this section, when fixed at a certain value of annual cash flow, hexane has a higher exergy efficiency (e2 ¼ f2 while f1 > e1) compared to neopentane. Meanwhile, hexane obtained a higher annual cash flow when fixed at same value of exergy efficiency (g1 ¼ h1 while h2 > g2). Thus hexane is recommended as superior working fluid in this section which is contrary to the results of section Ⅱ1. Fig. 5. Case I: CE diagram of cis-butene and R245fa under the 140  C heat source temperature with RORC system.

Section Ⅲ: This section, which covers the area between the two rightmost endpoints of the two working fluids, could be named the energy utilizing-dominated section for its unassailable exergy efficiency. In this section, economic performance was sacrificed to maximize energy utilization efficiency. The unique working fluid in this section (i.e. R245fa) should be selected when the energy utilization efficiency is at the greatest desired value for special industry situations. It should be noted that in this section, increasing exergy efficiency leads decreasing annual cash flow, it is meaningless in the aspect of economics. However, in the environment aspect, higher exergy efficiency should reduced the energy direct released to the environment, thus avoid the thermal pollution in this sense. From this view, this section is still has reference value, especially for some particular process or some situation with strict environmental requirements.

5.2.2. Case Ⅱ: comparison between different working fluids with intersection points on CE diagrams Fig. 6 shows the CE diagram of neopentane and hexane under the 140  C heat source temperature with RORC system. This is another common case of working fluid comparison. Compared with CaseⅠ, there is an intersection point between the two curves of each working fluid. For this case the CE diagram was divided into four sections according to the value of endpoints and the intersection

6. Conclusions In the present work, we proposed a CE diagram by achieving the Pareto optimal solutions of the Cash flow and Exergy efficiency. This new graphical criterion enables both working fluid selection and thermodynamic system comparison for waste heat recovery. The graphing method, the meaning of endpoints and the feasibility of CE diagram were proved by providing several examples of 5 different heat-source temperatures (ranging between 100 and 260  C), 26 chlorine-free working fluids and two typical ORC systems (i.e. BORC and RORC). The “predictive power” of CE diagram haven't been fully explored. The specific and unified mathematical relation between P1, P2, P3 and the thermodynamics parameters have not been found. However, under the current conditions, we could according to the certain working condition, make CE diagram using the method proposed in this work to operate working fluids or system comparison. The proposed graphical method is feasible and would be applicable to any closed loop waste heat recovery thermodynamic systems and working fluids. Acknowledgements This work is supported by the National Key Basic Research Program of China (973 Program) (2013CB228304) and the Key Project of National Natural Science Foundation of China (No. 51436007).

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Appendix A

Table.A.1 Original data for CE diagram of BORC and RORC systems under the heat source temperature of 100  C Cycles

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

BORC

RORC 2

Paramaters

P1

P2

P3

R

R227ea R1234ze C4F10 RC318 R236fa Isobutane R236ea Isobutene Butene C5F12 Butane R245fa Trans-butene Neopentane Cis-butene R245ca R365mfc Isopentane Pentane

33572.23517 35699.54996 33,499.81652 34854.06885 37996.09374 43225.50012 38623.75931 44841.61403 45746.57394 38967.77968 47653.21626 44190.35823 48890.03324 39512.71958 47898.63518 45524.65028 41561.89712 44735.6179 40539.40061

157.6907742 354.1485834 30.10611201 160.7718653 445.5571301 1160.374724 474.6122418 1490.694442 1661.558544 217.1771597 1845.539999 1222.17836 2181.693165 536.5332903 2128.305689 1420.057005 642.3636085 1277.013771 560.0566531

0.464931504 0.492586884 0.44299498 0.466260856 0.495657782 0.519655948 0.504291725 0.535919159 0.540876521 0.456771175 0.539974509 0.531967643 0.552446245 0.510131943 0.557508929 0.540992341 0.519606945 0.538834828 0.523365567

0.999434564 0.997585314 0.950305699 0.99105486 0.996806082 0.997193441 0.993202 0.997443456 0.997528863 0.997784763 0.995869189 0.996621003 0.997307554 0.992846033 0.995176599 0.991243137 0.984095064 0.986749721 0.99566278

P1

P2

P3

R2

9810.164288 11612.37339 11769.28286 12090.57744 16283.27787 18800.03898 16607.80785 16331.86807 16861.69179 19199.01482 19507.26017 17990.54332 18971.77291 15867.21531 18414.99829 22393.64437 21912.46221 21682.05336 23721.29724

12.03563642 13.72528896 169.7708182 45.45042976 202.1224368 438.334135 175.1495556 160.5766883 191.1580637 580.6906116 420.8117089 222.3295581 339.1128074 95.15631887 279.5049472 628.6505843 624.9498893 617.3595017 880.491222

0.506122625 0.507755665 0.527233422 0.514249029 0.53261286 0.544684042 0.539696081 0.537087461 0.539640426 0.552415346 0.553161789 0.546106038 0.548559144 0.539798078 0.548836951 0.563566073 0.573399644 0.571920575 0.581386677

0.963839746 0.99013366 0.992747414 0.938059899 0.990688052 0.959532787 0.98946593 0.993984392 0.982412799 0.995948207 0.983964241 0.983104932 0.995683974 0.994564609 0.985502101 0.975156109 0.994003174 0.989034899 0.976954772

Table.A.2 Original data for CE diagram of BORC and RORC systems under the heat source temperature of 140  C

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Cycles

BORC

Parameters

P1

P2

P3

R2

RORC P1

P2

P3

R2

Isobutene Butene C5F12 Butane R245fa Trans-butene Neopentane Cis-butene R245ca R365mfc Isopentane Pentane Isohexane Hexane Acetone

249459.5257 253088.6991 256596.4942 248111.9641 249439.1487 256058.9803 248578.8014 266848.8576 254078.2402 252701.8809 256639.9966 256649.8439 255820.5786 258583.5403 269533.0611

781.0819474 1167.547048 3.65288339 604.1877683 570.0716679 1691.320411 185.063699 2850.242483 1062.689919 746.3924905 1170.032743 1352.33043 1300.262599 1796.10493 6315.50248

0.527434952 0.533041629 0.465894643 0.524967199 0.525893048 0.541024724 0.507293864 0.551748097 0.533621625 0.523447035 0.530144453 0.535682824 0.53156004 0.540512209 0.599407169

0.995104359 0.993804237 0.999660961 0.996792548 0.996740929 0.998770894 0.987589511 0.968390545 0.996961976 0.995398937 0.996967987 0.987371994 0.978279216 0.987156749 0.999123381

212841.5253 206848.549 246218.839 213965.2115 212362.518 204921.3397 268953.3666 217211.6187 216300.9177 247535.2499 218329.4831 234654.5077 234737.1309 232515.4356 213251.2659

767.3973124 239.4668297 1372.606569 979.1339893 567.3629353 252.6827713 9118.502068 1214.47107 1168.317292 5534.259164 1525.784757 4021.916413 4280.607198 4108.690203 1459.296559

0.583463702 0.568650831 0.568501177 0.586073351 0.577846989 0.573586373 0.630919996 0.586972051 0.589645126 0.619988583 0.592919895 0.616882263 0.621482131 0.622747544 0.594788608

0.991206513 0.998787893 0.982882405 0.998258786 0.991335628 0.994776914 0.996502274 0.979881085 0.995231694 0.987417981 0.984327369 0.995169759 0.998277283 0.982073608 0.992902416

Table.A.3 Original data for CE diagram of BORC and RORC systems under the heat source temperature of 180  C Cycles

17 18 19 20 21 22 23 24 25 26

BORC

RORC 2

Parameters

P1

P2

P3

R

P1

P2

P3

R2

R365mfc Isopentane Pentane Isohexane Hexane Acetone Heptane Cyclohexane Benzene Toluene

628498.5482 631244.7371 617561.9928 623951.7044 596081.8408 609448.4431 607370.891 605990.1752 623380.9231 599731.7791

108.5551185 182.7398129 236.6046689 542.8802087 182.509345 6488.093215 631.1073672 2038.862553 7465.073536 4928.331352

0.531614849 0.534822793 0.537622563 0.531136453 0.532485557 0.59639213 0.533332932 0.565003668 0.597709891 0.589514214

0.998320086 0.959558024 0.993866146 0.970639927 0.958971035 0.997162027 0.989606217 0.995695251 0.995638293 0.993215556

712314.9265 735502.3366 758548.395 693907.8445 605164.6983 553705.0799 626009.8528 593262.0219 559197.2921 530220.6179

16060.70836 22348.61747 30348.27108 16099.41139 6204.965425 3236.191234 11351.11575 8970.604158 5051.735433 2399.521124

0.642899732 0.658316569 0.673441572 0.649207814 0.633266186 0.62308122 0.648646257 0.650870502 0.640734129 0.63572885

0.976327863 0.960589862 0.992274897 0.964318586 0.974729605 0.971053053 0.981061212 0.963308598 0.985828417 0.944033804

H. Xi et al. / Applied Thermal Engineering 89 (2015) 772e782

781

Table.A.4 Original data for CE diagram of BORC and I RORC systems under the heat source temperature of 220  C

20 21 22 23 24 25 26

Cycles

BORC

Parameters

P1

P2

P3

R2

RORC P1

P2

P3

R2

Isohexane Hexane Acetone Heptane Cyclohexane Benzene Toluene

1169459.437 1149327.539 1043409.67 1126525.354 1106123.074 1057038.266 1080393.31

18.64944121 46.91108617 2040.232302 103.0814509 708.7818428 2534.573934 2815.91159

0.549118961 0.548908467 0.587100773 0.541654004 0.566323442 0.58749475 0.584063591

0.998481018 0.997412521 0.993250641 0.998964338 0.998135497 0.993615479 0.998566526

1877407.715 1527363.322 1049493.293 1425430.882 1306821.808 1034895.438 1111643.816

83709.76 38658.14675 7077.501721 35711.65785 41891.34891 8520.044171 21797.57606

0.683857867 0.667250165 0.64512117 0.670003641 0.693765872 0.65603021 0.686580753

0.964441309 0.953504101 0.994313235 0.978574107 0.992540945 0.98856078 0.991747579

Table.A.5 Original data for CE diagram of BORC and RORC systems under the heat source temperature of 260  C.

23 24 25 26

Cycles

BORC

Parameters

P1

P2

P3

R2

P1

RORC P2

P3

R2

Heptane Cyclohexane Benzene Toluene

27807737.72 1791181.463 1693945.589 1702526.138

24059093.2 58.91562641 1030.079737 865.89156

7.772758874 0.58141125 0.59318791 0.586983933

0.988579043 0.998472931 0.989994138 0.997881858

1755833.914 1793866.822 1792268.941 1765844.746

382.3889037 23688.47155 23658.61184 20168.90085

0.65079435 0.677082205 0.67752407 0.678193134

0.988618003 0.985869426 0.979895997 0.950549145

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Nomenclature Ex: exergy content (kJ/kg) h: enthalpy (kJ/kg) I: exergy loss (kJ/kg) m: mass flow rate (kg/s) P: pressure (MPa) Q: heat addition of working fluid (kg/s) s: entropy (kJ/(kg K)) T: temperature (K) cp: specific heat capacity (kJ/(kg K)) W: power (kW) M: molecular weight

DT: pinch temperature PEC: purchased equipment costs i: bank rate n: economic life Greek symbols

h: efficiency s: effectiveness of internal heat exchanger Subscripts 0: environmental state 1e12: state point of ideal condition i: each state point a: state point of actual condition b: boiling point exp: expander pump: pump cooling tower: cooling tower heat source: heat source fluid working fluid: working fluid in: inlet of heat exchanger out: outlet of heat exchanger net: net m: mean I: first law of thermodynamics II: second law of thermodynamics