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INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2008; 32:926–938 Published online 25 February 2008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/er.1406

An examination of exergy destruction in organic Rankine cycles P. J. Mago*,y, K. K. Srinivasan, L. M. Chamra and C. Somayaji Department of Mechanical Engineering, Mississippi State University, 210 Carpenter Engineering Building, P.O. Box ME, MS 39762-5925, U.S.A.

SUMMARY The exergy topological method is used to present a quantitative estimation of the exergy destroyed in an organic Rankine cycle (ORC) operating on R113. A detailed roadmap of exergy flow is presented using an exergy wheel, and this visual representation clearly depicts the exergy accounting associated with each thermodynamic process. The analysis indicates that the evaporator accounts for maximum exergy destroyed in the ORC and the process responsible for this is the heat transfer across a finite temperature difference. In addition, the results confirm the thermodynamic superiority of the regenerative ORC over the basic ORC since regenerative heating helps offset a significant amount of exergy destroyed in the evaporator, thereby resulting in a thermodynamically more efficient process. Parameters such as thermodynamic influence coefficient and degree of thermodynamic perfection are identified as useful design metrics to assist exergy-based design of devices. This paper also examines the impact of operating parameters such as evaporator pressure and inlet temperature of the hot gases entering the evaporator on ORC performance. It is shown that exergy destruction decreases with increasing evaporator pressure and decreasing turbine inlet temperatures. Finally, the analysis reveals the potential of the exergy topological methodology as a robust technique to identify the magnitude of irreversibilities associated with real thermodynamic processes in practical thermal systems. Copyright # 2008 John Wiley & Sons, Ltd. KEY WORDS:

exergy; exergy graph; organic Rankine cycles; second-law analysis; entropy generation

1. INTRODUCTION Traditional first-law-analysis-based energy accounting usually leads to correct conclusions. However, many times it is not possible to predict the reason for a particular system’s behavior just with first-law analysis. This is because the first-law embodies no distinction between work and heat and no provision for quantifying the quality of

energy. These limitations are not a serious drawback when dealing with familiar systems. For these, one can develop an intuitive understanding of the different parametric influences on system performance and a second-law qualitative appreciation of ‘grade of heat’ and effect of pressure loss. However, when analyzing novel and complex thermal systems, such an understanding should be complemented by a more rigorous quantitative

*Correspondence to: P. J. Mago, Department of Mechanical Engineering, Mississippi State University, 210 Carpenter Engineering Building, P.O. Box ME, MS 39762-5925, U.S.A. y E-mail: [email protected]

Copyright # 2008 John Wiley & Sons, Ltd.

Received 30 October 2007 Revised 10 January 2008 Accepted 10 January 2008

EXERGY DESTRUCTION IN ORGANIC RANKINE CYCLES

method. Second-law analysis, which encompasses availability or exergyz analysis, provides such a tool. Bejan [1] defines exergy or availability analysis involving the simultaneous employment of the first and second laws of thermodynamics for the purpose of analyzing the performance of thermodynamic processes in the reversible limit and for estimating the departure from this limit (irreversibility). Thermodynamics explains us that different kinds of energies are not equal. Mechanical and electrical energies are ultimately converted to one another less the dissipative energy of friction and electrical resistance. The less valuable kinds of energy such as heat cannot be converted to useful work completely at all times. Thus, the concept of available energy or exergy is introduced and described as a part of thermal energy that can be converted to shaft work completely. Open literature indicates several researches that have laid the framework for exergy analysis over the years [2–8]. The major discussion in these references includes the definition of exergy terms, the general exergy analysis methodology [2, 3], and some interesting insights into the subtle nuances, implications and limitations of exergy analysis [4–7]. Second-law and exergy analyses have been applied to the design and analysis of power generation systems [9–13], chemical refineries [14, 15], heat transfer enhancement devices [16, 17], and environmentally friendly industrial processes [18, 19]. The most important aspect of second-law analysis insofar as the practical design of thermal systems is concerned is thermoeconomics [20–22]. An important consequence of the second-law analysis is the principle of entropy generation minimization (EGM) introduced by Bejan [23–25]. This concept synthesizes the simple principles of heat transfer, fluid mechanics, and thermodynamics to optimize non-ideal and nontrivial thermodynamic systems, such as power plants, refrigeration plants, cryogenic systems, and storage systems that are subject to constraints of finite size and finite time processes. Another z

Exergy as defined by Bejan [1] is the maximum useful work delivered to an external user as the stream reaches the restricted dead state.


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important and presently relevant problem that is being researched is the implications of second-law analysis applied to combustion processes [26, 27]. The Annual Energy Outlook [28] provided by the Energy Information Agency (EIA) reports that about 87% of the total energy consumption in the U.S. is due to fossil fuel (coal, natural gas, and liquid fuels) combustion. Increasingly ‘heated’ debates about global climate change, energy security, and sustainability are primary factors that are driving forces towards the adoption of biomass-based alternatives, such as biodiesel and ethanol, to conventional petroleum-based fossil fuels. To reap the long-term benefits of this paradigm shift in the energy policy of moving away from petroleum-based fuels, it is imperative to focus on novel strategies to improve existing energy utilization, conversion, and production technologies. According to Dunbar and Lior [26], exergy analysis of combustion processes, which are responsible for delivering most of our energy, reveals that approximately one-third of the fuel exergy is destroyed during combustion. Further, the analysis by Caton [29] reveals that ‘exhaust waste heat energy recovery’ technologies are of particular significance in recovering significant amounts of the fuel exergy that is destroyed during combustion. In this regard, it is relevant to examine the organic Rankine cycle (ORC), which can be used to recover some of the combusting fuel’s exergy that is otherwise lost to the exhaust. ORCs have been the subject of analysis of many researchers [30–37]. The subject of the aforementioned analyses in the open literature includes, but is not limited to, theoretical investigations of second-law efficiency considerations of ORCs [31–34] and practical implications involving the selection of appropriate organic fluids [34, 35]. Often, when analyzing complicated practical systems that involve many thermal reservoirs and thermodynamic processes, the issue of accounting for the various individual irreversibilities of subsystems and processes becomes a crucial issue. Therefore, it is convenient and less cumbersome to adopt graphical methods or exergy flow diagrams [38–45] to quantify the exergy loss associated with various components and thermodynamic processes in a practical thermal system. The objective of this Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er

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paper is to illustrate a ‘cradle-to-grave’ analysis of basic and regenerative ORCs using the application of the exergy topological method of Nikulshin et al. [43] and the exergy wheel diagram [1]. It will be shown that such a ‘visual’ analysis presents a clear picture of exergy flow and therefore simplifies the otherwise onerous task of identifying processes or sub-processes that can be optimized to improve the efficiency of ORCs.

2. ANALYSIS A schematic of basic and regenerative ORCs for converting waste heat into useful power is shown in Figure 1. As observed in Figure 1(a), there are four different processes: Process 1–2 (pumping process), Process 2–3 (constant pressure heat addition), Process 3–4 (expansion process), and Process 4–1 (constant pressure heat rejection). For the regenerative cycle, Figure 1(b), a feed-water heater is incorporated into the ORC. The vapor

extracted from the turbine mixes with the feedwater exiting the pump. Ideally the mixture leaves the heater as a saturated liquid at the heater pressure. The equations used to evaluate basic and regenerative ORCs are presented in Table I. The network topological methodology of Stegou-Sagia and Paignigiannis [41], Ozgener et al. [42], Nikulshin et al. [43] will be used to perform an exergy analysis of basic and regenerative ORCs. A flowchart with the different steps involved to apply the topological methodology is presented in Figure 2. In addition, an exergy map of the entire process is represented using the exergy wheel diagram. 2.1. Network topological method (or the exergy graph method) Network topology is the study of arrangement or mapping of elements (links and nodes) of a network, especially the physical and logical interconnections between the nodes. In this paper the topological methodology proposed by StegouSagia and Paignigiannis [41], Ozgener et al. [42], Nikulshin et al. [43] together with the exergy wheel representation is employed to perform an exergy analysis of ORCs. A complete description of the network topological methodology can be found in Stegou-Sagia and Paignigiannis [41], Ozgener et al. [42], Nikulshin et al. [43]. Some of the important parameters that can be determined using this methodology are as follows. 2.1.1. Degree of thermodynamic perfection. The degree of thermodynamic perfection of element i is the ratio of the exergy leaving the element, Eiout ; to the exergy flow into the element, Eiin : It can be expressed as [44] E out xi vi ¼ i in ¼ 1 in ð1Þ Ei Ei where xi is the exergy loss associated with element i: The exergy loss associated with element i can be determined as xi ¼ Eiin Eiout

Figure 1. Simple flow sheet diagram: (a) basic ORC and (b) regenerative ORC [Step 1]. Copyright # 2008 John Wiley & Sons, Ltd.

ð2Þ

Ideally the degree of thermodynamic perfection of any element should be 1. This ideal case will happen only when the exergy loss associated with Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er

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Table I. Thermodynamic Equations to Evaluate Basic and Regenerative ORCs. Component

Equation ’ ’ 1 h2s Þ ’ p ¼ W p;ideal ¼ mðh W Zp Zp ’ e ¼ mðh Q ’ 3 h2 Þ ’ t¼W ’ t;ideal Zt ¼ mðh W ’ 3 h4s ÞZt ’ c ¼ mðh Q ’ 1 h4 Þ ’p ’ tþW W Zcycle ¼ ’e Q

Basic ORC Pump (1–2) Evaporator (2–3) Turbine (3–4) Condenser (4–1) Cycle efficiency Regenerative ORC Feed-water heater (6–3–2)

h3 h2 h6 h2 " # ð1 X1 Þðh1 h2s Þ þ ðh3 h4s Þ ’ Wp ¼ m ’ Zp X1 ¼

Pump (1–2 and 3–4) Evaporator (2–3) Turbine (5–6 and 5–7)

’ e ¼ mðh Q ’ 5 h4 Þ ’ t;ideal Zt ¼ mZ ’ tþW W ’ t ½ðh5 h7s Þ þ X1 ðh7s h6s Þ

Condenser (7–1)

’ c þ mð1 Q ’ X1 Þðh1 h7 Þ ’p ’ tþW W Zcycle ¼ ’e Q

Cycle efficiency

’ heat rate; X; fraction of the flow rate that goes into the feed-water heater; m; ’ power; Q; h; enthalpy; W; ’ mass flow rate; Zp ; pump efficiency; and Zt ; turbine efficiency.

this element is zero. Therefore, from the thermodynamic point of view, the higher the degree of thermodynamic perfection of any element, the better the performance of this element. The overall exergy loss of the system is the sum of the exergy loss associated with all the elements of the system: n X xtotal ¼ xi ð3Þ i¼1

The degree of thermodynamic perfection of the system can be expressed as E out ð4Þ vtotal ¼ total in Etotal 2.1.2. Exergy efficiency. The exergy efficiency of element i is defined as the ratio of used exergy of element i; Eiu ; to the available exergy for the same element, Eia : It can be determined as defined by Bejan [1] Ziexergy

Eu ¼ ia Ei


ð5Þ

The available and used exergy can be determined using the equations presented in Table II. It is obvious that the higher the exergy efficiency for any element, the better the performance of this element. The overall system exergy efficiency is the ratio of the total system exergy used to the total available exergy of the system. It can be determined as Eu ð6Þ Zexergy;total ¼ total a Etotal 2.1.3. Influence coefficient. The influence coefficient of element i is defined as the ratio of the exergy available for element i to the total available a exergy of the system, Etotal : It is given by [44] bi ¼

Eia a Etotal

ð7Þ

This parameter gives the weight of any element on the total system performance. This parameter identifies the element(s) of the system that has to Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er

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be carefully designed and operated to increase the system efficiencies. One advantage of exergetic analysis is that this method makes the estimation of the flux and balance of energy and exergy for every element of

the system possible. One of the most effective methods of thermodynamic analysis and optimization is to merge the method of exergetic analysis with the mathematical method of graph theory commonly known as exergy topological method. 2.2. Exergy wheel diagram Exergy wheel diagram is an effective way of studying where the exergy is lost in a system. It allows one to easily observe the individual component contribution to the net exergy destroyed. The exergy wheel diagram presented in this paper is similar to the one proposed by Bejan et al. [1] with the difference that it uses flow availability instead of heat supply and rejected to a high- and lowtemperature reservoir, respectively. The results obtained from the topological methodology are used to create the exergy wheel diagram.

3. RESULTS AND ANALYSIS

Figure 2. Flowchart of the network topological method adapted from Nikulshin et al. [43–45].

The methodology described in the previous section as well as the exergy wheel diagram is applied to a basic and a regenerative ORC configuration. For the purpose of this study, R113, which has been proved to be a good candidate for ORC applications by Mago et al. [33, 35], was selected to apply the described exergy evaluation methodology. To apply the methodology, the following operating conditions were used.

Table II. Exergy rates associated with the different components of a Rankine cycle (also applicable to an ORC) adapted from Bejan et al. [46]. Component

Pump

Turbine

Heat exchanger

E2 E1 W

W E1 E2 E3

E2 E1 E3 E4

Schematic

Used exergy ðEiu Þ Available exergy ðEia Þ


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Operating conditions: Baseline evaporator pressure and condenser temperature were fixed at 2.5 MPa and 298 K, respectively. The isentropic efficiencies of the turbine and pump were 80 and 85%, respectively. The ORC receives heat from a heat source at a rate of 254 kW. The heat required in the evaporator is provided by a steady stream of hot gases initially at 1000 K and 0.1 MPa pressure. The hot gases exhaust at a temperature of 450 K to the ambient atmosphere, which is at 298 K and 0.1 MPa (reference state). The mean specific heat at constant pressure for the hot gases was assumed to be 1:1 kJ kg1 K1 ; which is the average value of the specific heat at constant pressure of nitrogen (one of the major components of exhaust gases). For the regenerative ORC calculations, an intermediate pressure of 1 MPa was assumed. Also, both pumps are assumed to run at the same efficiency despite operating at different flow conditions. The assumptions of the analysis presented in this paper are as follows: steady-state conditions, no heat losses and pressure drops in the evaporator and condenser, and isentropic efficiencies for the turbine and pump. 3.1. Application of the exergy graph methodology Step 1: The first step in the exergy graph methodology is to develop the flow sheet for the different systems under consideration. This is presented in Figure 1 for both configurations. It is important to observe how each element as well as each flow was identified with numbers. This is useful for Step 2 of this methodology. Step 2: In this step the exergy flow graph is created using the flow sheet generated in Step 1. Figure 3 shows the exergy flow graph for the two ORC configurations presented in Figure 1. The different circles represent elements and the arrows entering and leaving these elements represent the exergy flow. Once the exergy flow graph has been created, the corresponding matrix of incidence can be constructed. Step 3: This step involves generating the matrix of incidence for the evaluated system. Table III presents the matrix of incidence for the basic ORC corresponding to the exergy flow graph shown in Figure 3(a), whereas Table IV presents the matrix of incidence for the regenerative ORC corresponding to the exergy flow graph shown in Figure 3(b). Copyright # 2008 John Wiley & Sons, Ltd.

Figure 3. Exergy flow graph for the ORCs presented in Figure 1: (a) basic and (b) regenerative [Step 2]. Table III. Matrix of incidence corresponding to the exergy flow graph for basic cycle (Step 3). Element Flow 1 2 3 4 5 6 7 8 9 10

I

II

III

IV

þ1 1 0 0 0 0 0 0 0 þ1

0 þ1 1 0 þ1 1 0 0 0 0

0 0 þ1 1 0 0 1 0 0 0

1 0 0 þ1 0 0 0 þ1 1 0

In the matrix of incidence, the different components that are connected can be clearly seen. The exergy flow coming into a component is marked Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er

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with a ‘þ1’ and the exergy flow going out is marked with a ‘1’. When a flow and an element are not tied it is marked with a ‘0.’ Step 4: In this step the flow parameter data for the cycle have to be determined. Tables V and VI present the flow parameter data for basic ORC and regenerative ORC, respectively. Both tables include pressure, temperature, specific enthalpy, specific entropy, specific exergy, and exergy rate associated with each of these components. The values for the flow parameter table were obtained using a software called REFPROP (NIST) [47]. It is important to note that at Point 1 in Tables V and VI, although the saturation pressure of the

Table IV. Matrix of incidence corresponding to the exergy flow graph for regenerative cycle (Step 3). Element Flow 1 2 3 4 5 6 7 8 9 10 11 12 13 14

I

II

III

IV

V

VI

0 0 þ1 1 0 0 0 þ1 0 0 0 0 0 0

0 0 0 þ1 1 0 0 0 þ1 1 0 0 0 0

0 0 0 0 þ1 1 1 0 0 0 1 0 0 0

1 0 0 0 0 0 þ1 0 0 0 0 þ1 1 0

þ1 1 0 0 0 0 0 0 0 0 0 0 0 þ1

0 þ1 1 0 0 þ1 0 0 0 0 0 0 0 0

refrigerant is lower than the reference state pressure, the exergy contribution is very small that it is neglected in the analysis. Using the information provided in Tables IV and V, the boiler heat rate, the condenser heat removal rate, the organic fluid mass flow rate, the pump power, and the turbine power can be determined. All these values are tabulated in Tables VII and VIII for basic and regenerative ORCs, respectively. Step 5: In this step all the calculations to determine the thermodynamic characteristic of the evaluated system are performed. Tables IX and X present the thermodynamic characteristics of the analyzed basic and regenerative ORCs, respectively. These tables include parameters such as exergy leaving and entering each component, the exergy loss associated with each component, used and available exergy of each component, exergy efficiency, degree of thermodynamic perfection, and coefficient of influence for each component. The exergy loss, degree of thermodynamic perfection, and exergy efficiency for the entire system are also presented. Step 6: This step includes the analysis of the results obtained in Step 5. From Table IX it can be seen that the evaporator is the component that has the highest exergy losses (40 kW). Also, it is the component with the lowest second-law efficiency (62%). The exergy loss in the evaporator is mainly due to the irreversibility associated with heat transfer over a finite temperature difference. The high exergy loss also causes a decrease in the degree of thermodynamic perfection that shows its lowest value in the evaporator (76.1%). On the

Table V. Flow parameters of the evaluated basic ORC (Step 4). Point

T ð8CÞ

P (MPa)

h ðkJ kg1 Þ

s ðkJ kg1 K1 Þ

e ðkJ kg1 Þ

E (kW)

1 2 3 4 5 6 7 8 9 10

25 25.75 193.52 67.68 300 177 } 25 35 }

0.044831 2.5 2.5 0.044831 0.1 0.1 } 0.1 0.1 }

222.67 224.39 464.23 415.21 } } } } } }

1.0793 1.0799 1.6776 1.7121 } } } } } }

0 1.533 63.156 3.673 88.186 32.095 49.024 0 0.684 1.72

0.00 1.62 66.89 3.89 165.55 60.25 51.92 0.00 3.34 1.83



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Table VI. Flow parameters of the evaluated regenerative ORC (Step 4). Point

T ð8CÞ

P (MPa)

h ðkJ kg1 Þ

s ðkJ kg1 K1 Þ

e ðkJ kg1 Þ

E (kW)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

25 25.29 139.26 140.63 193.52 152.87 85.09 } 300 177 } 25 35 }

0.044831 1 1 2.5 2.5 1 0.044831 } } } } 0.1 0.1 }

222.67 223.27 335.5 336.72 464.23 454.09 415.21 } } } } } } }

1.0793 1.0793 1.3965 1.3965 1.6776 1.6836 1.7127 } } } } } } }

0 0.575 18.243 19.450 63.156 51.237 3.6731 1.220 88.187 32.096 30.116 0 0.684 0.308

0.00 0.59 36.34 38.74 125.81 49.63 3.76 2.43 165.55 60.25 59.99 0 3.226 0.614

Table VII. Performance parameters of the evaluated basic ORC (Step 4). Boiler heat rate (kW) Condenser heat rejection (kW) Turbine power (kW) Pump power (kW) Net power (kW) Thermal efficiency (%) Mass flow rate (organic fluid) ðkg s1 Þ Mass flow rate (water) ðkg s1 Þ Mass flow rate (gas) ðkg s1 Þ

254 203.91 51.92 1.83 50.09 19.72 1.06 4.88 1.88

other hand, the evaporator is the component with the highest influence coefficient, which reflects the fact that the evaporator is the critical component of the evaluated basic ORC. The second component that has more influence on the ORC performance is the turbine. It shows the second highest coefficient of influence (38%). However, the degree of thermodynamic perfection and exergy efficiency are higher compared with the evaporator. The total system exergy loss is 51.9 kW; the degree of thermodynamic perfection is 69%; and the thermal and exergy efficiencies are 19.72% and 31.4%, respectively. Table X demonstrates that for regenerative ORC the highest exergy loss still occurs in the evaporator (18.2 kW). However, it is reduced by 55% compared with the basic ORC (40 kW). This Copyright # 2008 John Wiley & Sons, Ltd.

Table VIII. Performance parameters of the evaluated regenerative ORC (Step 4). Boiler heat rate (kW) 254 Condenser heat rejection (kW) 197.05 Turbine power (kW) 59.99 Pump power (kW) 3.04 Net power (kW) 56.95 Thermal efficiency (%) 22.42 Mass flow rate (organic fluid) ðkg s1 Þ 1.99 Mass flow rate fraction that goes into the feed- 0.486 water heater 4.71 Mass flow rate (water) ðkg s1 Þ Mass flow rate (gas) ðkg s1 Þ 1.88

reduction in the exergy loss entails an improvement on the evaporator exergy efficiency from 62% (for a basic ORC) to 82.7% (for a regenerative ORC). This is due to the fact that the exergy used in the evaporator increases for the regenerative case compared with the basic case. The reduction in the exergy loss also causes an increase in the degree of thermodynamic perfection from 76.1% (basic) to 91.1% (regenerative). Similar to the basic ORC, the evaporator is the component with the highest coefficient of influence (63.6%) followed by the turbine (43.7%). The total system exergy loss is reduced by 13% (45.1 kW) compared with basic ORC. For this case the degree of thermodynamic perfection is 73.2%, whereas the thermal and exergy efficiencies are 22.4 and 36.2%, Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er

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Table IX. Thermodynamic characteristics of the evaluated basic ORC (Step 5). Element Pump (I) Evaporator (II) Turbine (III) Condenser (IV) Total system

Eiin (kW)

Eiout (kW)

xi (kW)

Eiu (kW)

Eia (kW)

ni (%)

bi (%)

Ziexergy (%)

1.8 167.2 66.9 3.9 167.4

1.6 127.1 55.8 3.3 115.5

0.2 40.0 11.1 0.6 51.9

1.6 65.3 51.9 3.3 51.9

1.8 105.3 63.0 3.9 165.6

88.6 76.1 83.4 85.8 69.0

1.1 63.6 38.1 2.3 }

88.6 62.0 82.4 85.8 31.4

Table X. Thermodynamic characteristics of the evaluated regenerative ORC (Step 5). Element Pump (I) Evaporator (II) Turbine (III) Condenser (IV) Pump (V) Feed-water heater (VI) Total system

Eiin (kW)

Eiout (kW)

xi (kW)

Eiu (kW)

Eia (kW)

ni (%)

bi (%)

Ziexergy (%)

38.77 204.3 125.8 3.8 0.61 50.2 168.6

38.74 186.1 113.4 3.2 0.59 36.3 123.5

0.03 18.2 12.4 0.5 0.03 13.9 45.1

2.40 87.1 60.0 3.2 0.59 36.3 60.0

2.43 105.3 72.4 3.8 0.61 50.2 165.6

99.9 91.1 90.1 85.8 95.8 72.4 73.2

1.5 63.6 43.7 2.3 0.4 30.3 }

98.9 82.7 82.8 85.8 95.8 72.4 36.2

respectively. Both efficiencies are higher compared with the efficiencies obtained for basic ORC. From the results presented in Tables IX and X, it can be concluded that, for the same heat rate available for the evaporator from a hot gas stream, regenerative ORC shows higher thermal and exergy efficiencies than basic ORC, thereby, reducing the total system exergy losses and improving the degree of thermodynamic performance. Figure 4 illustrates the percentage of the exergy destroyed in each component with respect to the total system exergy loss for both configurations. Figure 4 demonstrates that for the basic ORC the evaporator is the component with the highest exergy loss contribution (77%) followed by the turbine with 21.4%. For the regenerative ORC, the evaporator is still the highest contributor to the total exergy loss of the system. However, it is reduced from 77 to 40.4% compared with the basic ORC. This exergy reduction is mainly due to the presence of the feed-water heater that accounts for 30.8% of exergy losses. 3.2. Application of the exergy wheel diagram The results obtained from the topological methodology can be easily represented using an exergy Copyright # 2008 John Wiley & Sons, Ltd.

Evaporator (II) 77% Pump (I) 0.4%

Condenser (IV) 1.2%

Turbine (III) 21.4%

(a) Evaporator (II) 40.4%

Pumps (I) and (V) 0.2%

Turbine (III) 21.4%

(b)

Condenser (IV) 1.1%

Feed water heater (VI) 30.8%

Figure 4. Percentage of the exergy loss in each component: (a) basic ORC and (b) regenerative ORC. Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er


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Figure 6. Exergy wheel diagram for a regenerative ORC. Figure 5. Exergy wheel diagram for a basic ORC.

wheel diagram. Using the exergy rate values presented in Tables V and VI together with the exergy flow graph presented in Figure 3, the exergy wheel was assembled for both configurations. The exergy wheel graph for the basic ORC is presented in Figure 5, whereas the exergy wheel diagram for the regenerative ORC is presented in Figure 6. This diagram presents a visual representation of the fate of exergy associated with various components of the ORC. 3.3. Effect of different parameters on the ORC performance Figure 7 illustrates the variation of the thermal and exergy efficiencies and the total system exergy loss with the evaporator pressure while maintaining the turbine inlet temperature at saturated conditions for both configurations. The evaporator pressure was changed from 2 to 3 MPa while maintaining the same operating conditions as before. From Figure 7 it can be seen that the thermal efficiency increases with the incremental increase in the evaporator pressure for both configurations and that regenerative ORC presents higher Copyright # 2008 John Wiley & Sons, Ltd.

efficiency than basic ORC. Regenerative ORC shows an increase in the thermal efficiency of 8.4–15.4% for the lowest and highest turbine inlet pressures, respectively. Higher evaporator pressure increases both the specific net work and the specific evaporator heat. However, the percentage of increase in the net work is higher than the increase in the evaporator heat rate, which leads to improvement in the first-law efficiency. Figure 7 also illustrates that the exergy efficiency increases and the system total exergy loss decreases with the increment in the evaporator pressure for both configurations. Both results are consistent since a decrease in the total system exergy loss entails an increase in the system exergy efficiency. This is due to the fact that when the evaporator pressure is increased, the difference between the evaporator temperature and the temperature of the hot gas stream entering the evaporator is reduced. This reduction in the temperature difference leads to an improvement in the exergy efficiency or a reduction in the system exergy loss. For low inlet turbine pressures, the second-law efficiencies for regenerative ORC are approximately 12.8% higher than those obtained for basic ORC, whereas for high inlet turbine pressures the second-law efficiencies for regenerative ORC are Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er

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Basic ORC - Thermal Efficiency Regenerative ORC - Thermal Efficiency Basic ORC - Exergy Efficiency Regenerative ORC - Exergy Efficiency Basic ORC - Exergy Loss Regenerative ORC - Exergy Loss

80

60

P = 2.5M Pa T = 298 K Q = 254 kW m = 1.88 kg/s

50

η = 80% η = 85%

60

60

50

40

40

20

30

Efficiency (%)

η = 80% η = 85%

Exergy Loss (kW)

Thermal Efficiency Exergy Efficiency Total Exergy Loss

70

60

40

50

30

40

20

30

10

20 500

520

540

(a) 0 1.8

560

580

600

620

640

660

680

700

Hot Gas Inlet Te mperature (K)

20 2.0

2.2

2.4

2.6

2.8

3.0

3.2

70

80

Evaporator Pressure (MPa)

approximately 17.4% higher than those obtained for basic ORC. Figure 8 shows the effect of the hot gas inlet temperature on the thermal and exergy efficiencies and the total system exergy loss for both configurations. To generate this figure, the evaporator pressure was maintained constant at 2.5 MPa, whereas the condenser temperature was maintained constant at 298 K. The ORC receives heat from a heat source at a rate of 254 kW at a constant mass flow rate of 1:88 kg s1 : The hot gas inlet temperature was changed from 523 to 673 K. As expected, the ORC thermal efficiency remains constant for both configurations with the increase in the hot gas stream temperature. However, once again, it is demonstrated that regenerative ORC produces better thermal efficiencies than basic ORC. Additionally, the exergy efficiency decreases, whereas the system exergy loss increases with the increase in the hot gas temperature. Similar to the results presented in Figure 7, an increase in the inlet hot gas temperature leads to a decrease in the exergy efficiency. Figure 8 basically shows how the difference between the evaporator temperature and the hot gas temperature entering the evaporator affects the system performance. The smaller this temperature difference, the better the exergy efficiency and less exergy loss will be present in the system. Copyright # 2008 John Wiley & Sons, Ltd.

60

Efficiency (%)

Figure 7. Effect of the variation of the evaporator pressure on the thermal efficiency, exergy efficiency, and system total exergy loss for both ORC configurations.

Thermal Efficiency Exergy Efficiency Total Exergy Loss

70

50

60

P = 2.5M Pa T = 298 K P = 1 MPa Q = 254 kW = 1.88 kg/s m

40

50

η = 80% η = 85%

30

40

20

30

10

20 500

(b)

Total System Exergy Loss (kW)

Efficiency (%)

80

70

70 T = 573 K T = 298 K Q = 254 kW

Total System Exergy Loss (kW)

100

520

540

560

580

600

620

640

660

680

700

Hot Gas Inlet Te mperature (K)

Figure 8. Variation of the system thermal and exergy efficiencies and the mass total system exergy loss with the hot gas inlet temperature: (a) basic ORC and (b) regenerative ORC.

4. CONCLUSIONS The exergy topological method developed by Nikulshin et al. [43–45] was used to present a quantitative estimation of the exergy destroyed in an organic Rankine cycle (ORC) operating on R113. A detailed roadmap of exergy flow is presented using an exergy wheel diagram [1] and parameters such as degree of thermodynamic perfection, exergy efficiency, and influence coefficient were evaluated and compared for both ORC configurations. The analysis presented in the paper leads to the following salient conclusions: 1. It was shown that the regenerative ORC not only produces higher thermal and exergy efficiencies and a higher degree of Int. J. Energy Res. 2008; 32:926–938 DOI: 10.1002/er


2.

3.

4.

5.

6.

7.

thermodynamic perfection than the basic ORC but also has lower total system exergy loss. For both ORC configurations, the evaporator is the component with the highest influence coefficient and highest exergy loss with respect to the overall system exergy loss. For basic ORC the evaporator exergy loss contribution is around 77%, whereas for regenerative ORC the evaporator exergy loss contribution is around 40.4%. This reduction in exergy loss is mainly due to the presence of the feed-water heater, which increases the temperature of the working fluid before it enters the evaporator, thereby minimizing the heat transfer across a finite temperature difference. Results showed that for both configurations the thermal and exergy efficiencies increase and the system total exergy loss decreases with the increase in the evaporator pressure for the analyzed case. These results are consistent since a decrease in the total system exergy loss entails an increase in the system exergy efficiency. The reason for this behavior is attributed to the fact that with increasing evaporator pressure the temperature of the organic fluid is closer to the temperature of the hot gas entering the evaporator, thereby facilitating heat addition across a lower temperature difference. Results showed that for both configurations the thermal and exergy efficiencies increase and the system total exergy loss decreases with the increase in the evaporator pressure for the analyzed case. The effect of the hot gas inlet temperature on the system performance was examined. It was found that the smaller the difference between the evaporator temperature and the hot gas temperature, the better the exergy efficiency and the smaller the exergy loss. The results obtained for both configurations were represented using the exergy wheel diagram. It was shown how this visual analysis or representation presents a clear picture of the exergy flow and exergy destroyed associated with different ORC components. Finally, it can be concluded that the methodology proposed by Nikulshin et al. [43–45] was successfully adapted to analyze the


937

performance of ORC and it could be adapted to evaluate even more complex, energyintensive system configurations.

NOMENCLATURE e out Etotal in Etotal

Eiout Eiin Eiu u Etotal Eia a Etotal

¼ specific exergy ¼ total exergy flow leaving the system ¼ total exergy flow entering the system ¼ exergy flow leaving element i ¼ exergy flow entering element i ¼ used exergy of element i ¼ total system exergy used ¼ available exergy of element i ¼ total system available exergy

Greek letters bi Zexergy;total Ziexergy xi xtotal ni ntotal

¼ influence coefficient of element i ¼ overall system exergy efficiency ¼ exergy efficiency of element i ¼ the exergy loss associated with element i ¼ total system exergy loss ¼ degree of thermodynamic perfection ¼ degree of thermodynamic perfection of the system

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