Exergy analysis of micro-organic Rankine power cycles for a small scale solar driven reverse osmosis desalination system

Applied Energy 87 (2010) 1295–1306

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Exergy analysis of micro-organic Rankine power cycles for a small scale solar driven reverse osmosis desalination system B.F. Tchanche *, Gr. Lambrinos, A. Frangoudakis, G. Papadakis Department of Natural Resources and Agricultural Engineering, Agricultural University of Athens, 75 Iera Odos Street, 11855 Athens, Greece

a r t i c l e

i n f o

Article history: Received 5 December 2008 Received in revised form 9 June 2009 Accepted 15 July 2009 Available online 13 August 2009 Keywords: Organic Rankine engines Exergy analysis Desalination

a b s t r a c t Exergy analysis of micro-organic Rankine heat engines is performed to identify the most suitable engine for driving a small scale reverse osmosis desalination system. Three modified engines derived from simple Rankine engine using regeneration (incorporation of regenerator or feedliquid heaters) are analyzed through a novel approach, called exergy-topological method based on the combination of exergy flow graphs, exergy loss graphs, and thermoeconomic graphs. For the investigations, three working fluids are considered: R134a, R245fa and R600. The incorporated devices produce different results with different fluids. Exergy destruction throughout the systems operating with R134a was quantified and illustrated using exergy diagrams. The sites with greater exergy destruction include turbine, evaporator and feedliquid heaters. The most critical components include evaporator, turbine and mixing units. A regenerative heat exchanger has positive effects only when the engine operates with dry fluids; feedliquid heaters improve the degree of thermodynamic perfection of the system but lead to loss in exergetic efficiency. Although, different modifications produce better energy conversion and less exergy destroyed, the improvements are not significant enough and subsequent modifications of the simple Rankine engine cannot be considered as economically profitable for heat source temperature below 100 °C. As illustration, a regenerator increases the system’s energy efficiency by 7%, the degree of thermodynamic perfection by 3.5% while the exergetic efficiency is unchanged in comparison with the simple Rankine cycle, with R600 as working fluid. The impacts of heat source temperature and pinch point temperature difference on engine’s performance are also examined. Finally, results demonstrate that energy analysis combined with the mathematical graph theory is a powerful tool in performance assessments of Rankine based power systems and permits meaningful comparison of different regenerative effects based on their contribution to systems improvements. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Organic Rankine power cycle as energy conversion system is becoming widely recognized as a major technology in power engineering. An organic Rankine power plant is simply a steam power plant in which vapor steam is replaced by fluids such as siloxanes, refrigerants or hydrocarbons. An organic Rankine power system offers the advantage of being more suitable for low temperature heat recovery and small scale applications. The literature reviewed reveals that investigations on low temperature organic Rankine cycles (ORC) concern potential applications, working fluids as well as expansion devices. The applications include electricity generation, small cogeneration systems, water pumping, cooling and desalination. Quoilin et al. [1], Lemort [2], Nguyen et al. [3], Saitoh et al. [4], Kane et al. [5], Nguyen et al. [6], Riffat and Zhao [7], Oliveira et al. [8] and Yagoub et al. [9] are some of the authors * Corresponding author. Tel.: +30 (210) 529 4046; fax: +30 (210) 529 4032. E-mail addresses: [email protected], [email protected] (B.F. Tchanche). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.07.011

who reported studies on small ORCs designed for electricity generation. In view of harnessing the available solar radiation, solar thermal water pumping systems for freshwater and irrigation based on Rankine engine have been constructed and tested in different parts of the world including Africa and Asia [10]. The matching between the cooling demand and high solar radiation during the summer period, and the oil crisis of 1970s pushed towards investigations of solar cooling systems among which the so-called Duplex-Rankine driven cooling systems [11–13]. Another important application is the reverse osmosis (RO) desalination. The feature that makes the Rankine engine potentially suitable for reverse osmosis is the possibility of coupling between the turbine and the high pressure pump which forces the saline water to flow through the membrane modules. Owing to recent progress in membrane science, reverse osmosis has become the baseline technology for desalination and is being intensely discussed [14–18]. Bruno et al. [19] presented the feasibility study of solar Rankine driven osmosis desalination technology in two locations of Spain. As result, parabolic trough collectors were found

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Nomenclature c e E h g m P q Q s T V w W x z

molar concentration (–) specific exergy (kJ/kg) sum of exergy flow (kW) enthalpy (kJ/kg) gravitational constant (m/s2) mass flow rate (kg/s) pressure (MPa) specific heat (kJ/kg) heat rate (kW) entropy (kJ/kg K) temperature (°C) velocity (m/s) specific work (kJ/kg) work (kW) mole fraction (–) elevation (m)

Greek letters a fraction of fluid extracted (–) b influence coefficient (%) c exergy factor (–) g efficiency (%) e effectiveness (–) I–VII components, nodes (–) l chemical potential (J/kg) m degree of thermodynamic perfection (%) P exergy loss (kW)

to be the most competitive option over other thermal collectors and equivalent PV-driven system. Manolakos et al. [20–23] designed and tested a small stand-alone system using a scroll expander; simulations of the latter were carried out by Schuster et al. [24] who put in evidence the influence of the collector slope on the system productivity. Till 1970s, the most commonly-used method for analysis of an energy conversion process was the energy analysis. Since this period, the depletion of fossil fuel reserves and the will to reduce harmful emissions from energy intensive systems pushed to the development of methods of analysis of thermodynamic processes. The new methodology is exergy analysis and its optimization component known as entropy generation minimization [25–27]. Exergy analysis provides the tool for a clear distinction between energy losses to the environment and internal irreversibilities in the process. Exergy analysis is a methodology for the evaluation of the performance of devices and processes, and involves examining the energy at different points in a series of energy conversion steps. Its results are often considered to provide a more meaningful and accurate representation of the efficiencies of the processes within a system; therefore, it is an important tool in the analysis of energy conversion processes. Numerous research works related to the exergy analysis of Rankine based power systems are available at the present in the scientific literature, such as those concerning Rankine driven vapor compression system [28], steam power plants [29,30], solar thermal power plants [31,32], geothermal power plants [33,34], cogeneration plants [35] and Rankine driven desalination plants [36]. However, only a few research works devoted to the comparison of different organic Rankine power cycles using simultaneous energy and exergy analyses are available [37,38]. In other works [39,40], we have established the criteria that should fulfill a good working fluid and proceeded to the selection

Subscript–superscript 1–16 points, flows a available ch chemical ex exergetic fl flow i, j, k flows, components kn kinetic in inlet o restricted dead state out outlet, exit p pump ph physical pp pinch point pt potential u useful R system Acronyms CFH closed feedliquid LHV lower heating value OFH open feedliquid ORC organic Rankine cycle RHE regenerative heat exchanger RO reverse osmosis SRE simple Rankine engine TTD terminal temperature difference

of most suitable ones for a low temperature organic Rankine cycle driven by a heat source temperature below 100 °C. The present work aims at comparing several organic Rankine cycle configurations in view of seeking an increase in system performance. The configurations considered are obtained from regenerative processes i.e. incorporation of a regenerator or a feedliquid heater. Limits in systems’ efficiency are further established for different configurations and analyzed for determining if it is worth modifying the simple Rankine system when designing a low temperature Rankine driven reverse osmosis desalination system. Moreover, the effects of the heat source temperature and pinch point temperature difference are also analyzed.

2. Background Desalination technologies can be classified in two groups according to their separation mechanism: thermal and membrane based technologies [14]. Thermal desalination separates salt from water by evaporation and condensation, whereas in membrane desalination water diffuses through a membrane, while the salts are almost completely retained. Major desalination techniques are given in Table 1. Reverse osmosis and multi-stage flash are the most widely used technologies. The cost of water produced depends upon energy source, plant size, technology, feed water

Table 1 Desalination technologies. Thermal desalination technologies

Membrane desalination technologies

Multi-stage flash distillation (MSF) Multi-effect distillation (MED) Vapor compression distillation (VCD)

Reverse osmosis (RO) Nanofiltration (NF) Electrodialysis (ED)

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salinity and required product quality [18]. Parameters influencing significantly the water cost are plant size and energy cost. In this regard, potable water from large capacity plants and conventional energy sources is cheaper compared with small size renewable energy powered desalination systems. Thus, research and development are needed for small scale renewable energy powered systems which are environmentally friendly and well adapted for remote areas.

flow while the concentrate brine is discharged through the energy recovery unit. 2.3. Exergy analysis

Reverse osmosis (RO) is a pressure driven separation technique based on a property of certain polymers called semi-permeability. While they are very permeable for water, their permeability for dissolved substances is low. By applying a pressure difference across the membrane the water contained in the feed is forced to permeate through the membrane. In order to overcome the feed side osmotic pressure, fairly high feed pressure is required. Pressures applied in reverse osmosis applications vary from 15 to 25 bars for brackish water and 60–80 bars for seawater [14]. The process includes the following steps: pre-treatment, pumping, membrane separation, brine energy recovery and post-treatment. Pumping process can be easily achieved through electricity or shaft power thus making RO the most suitable candidate for renewable energy powered desalination system [17].

The exergy analysis methodology is a combination of first and second laws of thermodynamics and takes into account the environmental conditions. Exergy analysis has been under a continuous development for many decades [25–27]. It is becoming the most appropriate tool for thermodynamic analysis and process optimization. As a powerful tool, it is being applied to a wide variety of processes [41–45]. Exergy is defined as the maximum work that may be achieved by bringing a system into equilibrium with its environment. Every substance not in equilibrium with its environment has some quantity of exergy, while an object or system that is in equilibrium with its environment has, by definition, zero exergy since it has no ability to produce work with respect to its environment. An exergy analysis is similar to an energy analysis, but takes into account the quality of the energy as well as the quantity. Since it includes a consideration of entropy, exergy analysis allows a system to be analyzed more comprehensively by determining where in the system the exergy is destroyed by internal irreversibilities, and causes of those irreversibilities. For an open system at steady state, the second law can be written as [46,47]:

2.2. Organic Rankine driven reverse osmosis desalination system

P¼

2.1. Reverse osmosis desalination technique

The Rankine driven RO system consists of three sub-systems: collector loop, Rankine heat engine and desalination sub-system. Fig. 1 shows the layout of the system. The collector loop is made of 82 m2 evacuated tube collectors (ETC.) in which water as heat transfer fluid is heated up to 85 °C and circulated by a circulation pump (P1). The heat gained by the heat transfer fluid is further transferred to the working fluid of the Rankine engine via the boiler/evaporator (EV). The working fluid in the boiler evaporates and undergoes an expansion process in the turbine/expander (EX), then, cooled in the condenser (CD) and pumped back to the boiler. The useful power delivered by the expander is used to power the high pressure pump (HPP). In the desalination sub-system, the feed pump (P3) driven by a hydraulic turbine (HT) raises the pressure of the saline water and pumps it through the condenser where its temperature is increased before it reaches the high pressure pump. The pressure generated across the membranes forces the water to

 X X X To 1 ðmj ej Þin  ðmk ek Þout Qi  W þ T i i j k

ð1Þ

where P represents the exergy destroyed in the system; T o is the ambient temperature of the system’s surroundings, and Q i is the ith heat transfer rate across the system boundary at a constant temperature T i . W is the work transfer rate across the system boundary. The mass flow rate of each material flows crossing the system boundary is represented by m and the specific exergy associated with each flow is represented by e. The specific exergy flow, e, is made up of physical exergy (eph), kinetic exergy (ekn), potential exergy (ept) and chemical exergy (ech). Summing the first three called flow exergy (efl), the expression below is obtained [46–47].

efl ¼ h  ho  T o ðs  so Þ þ 1=2ðV 2  V 2o Þ þ gðz  zo Þ

ð2Þ

The symbols h, s, V, z and g refer to the specific enthalpy, specific entropy, flow speed, the elevation above a reference position and the gravitational acceleration, respectively. o refers to the

RO

11 3

12

PE

4

BR EV

EX

HPP

13

5

ETC

10

CD 7 2

9

1

P1

P2

HT

P3

6

Solar Collector Loop Rankine Engine

SW, BW

14

8

Reverse Osmosis System Fig. 1. Schematic of a Rankine driven reverse osmosis desalination system. CD: condenser; HPP: high pressure pump; RO: reverse osmosis, EX: expander; EV: evaporator; P1, P2, P3: pump; ETC:evacuated tube collector; HT: hydro-turbine; BR: brine; PE: permeate; SW: seawater; BR: brackish water.

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environmental conditions. Effects of kinetic and potential specific exergies represented by third and fourth terms in the right hand of the Eq. (2) are usually neglected as their contribution is very small. The chemical energy derives from a composition imbalance between a substance and its environment, and accounts in part for a fuel’s ability to react chemically with its environment. On a molar basis, the chemical exergy of a material flow can be written as follows [27]:

ech ¼

X  X  xi loi  loio þ RTo xi ln ðci =cio Þ i

ð3Þ

i

where xi is the mole fraction of the substance i in the flow; loi and ci are the chemical potential and concentration of substance i in its present state; loio and cio are the chemical potential and concentration of substance i in its environmental state, and R = 8.31 kJ/ kmol K, the universal gas constant. 3. Systems analysis 3.1. Rankine engines The simple Rankine engine comprises four components: a heat supplier also called evaporator or boiler, an expansion de-

(a)

vice, a condenser for heat rejection and finally a pump to feed the boiler. Such engine is presented on Fig. 2 along with the corresponding T–s diagram. In this engine, heat in converted into work when the working fluid undergoes the following processes: 1–2: expansion of the saturated or superheated fluid, 2–3: heat rejection through a condenser, 3–4: pumping of the liquefied fluid and finally 4–1: heat addition in the evaporator. In Fig. 3, a heat exchanger is incorporated into the cycle in parallel with the evaporator and condenser. In case the expansion process ends in the superheated vapor area, the heat exchanger will help to transfer the heat contained in the vapor to the compressed liquid entering the evaporator. Fig. 4 represents the regenerative Rankine engine with an open feedliquid heater and the corresponding T–s diagram. An open feedliquid heater is basically a mixing chamber where fraction of fluid extracted from the turbine mixes with the feedwater exiting the pump. The last configuration shown in Fig. 5 along with its T–s diagram is a regenerative organic Rankine engine with a closed feedliquid heater. In a closed feedliquid heater, heat is transferred from the extracted fluid to the feedliquid without any mixing taking place. Both streams can be at different pressures since they do not mix.

(b)

Hot water in T

4

1

Evaporator

1 4

Water out Pump

Turbine

Water out

2

3

2

3

Condenser

2s

s Cold water in Fig. 2. Simple organic Rankine cycle: (a) flow sheet diagram and (b) T–s diagram.

(a)

Hot water in Evaporator

1

Water out T

Turbine

6

(b)

1

2 6 5 RHE 2 Pump

2s

5

4

3

Water out s 4

Condenser

3

Cold water in Fig. 3. Regenerative organic Rankine cycle with regenerative heat exchanger: (a) flow sheet diagram and (b) T–s diagram.

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Hot water in 5

Evaporator

4

(b)

T

Water out

5

Turbine

Pump 2

4 6(α)

2

6 3

2

Open FWH

3

7(1-α)

Conde nser

Water out

7

1

Cold water in

6s

7s

Pump 1

(a)

s

1

Fig. 4. Regenerative organic Rankine cycle with open feedliquid heater: (a) flow sheet diagram and (b) T–s diagram.

3.2. Modeling

ei ¼ hi  ho  T o ðsi  so Þ

The analysis of the Rankine engines will be carried out based on combination of exergy analysis and mathematical graphs theory known as exergy topological method. The components are considered as nodes or elements of a network where they are linked by pipes and valves. More details on this approach can be found in [48–51]. For components and systems performance evaluation, energy efficiency model and other models developed by Nikulshin et al. [51]: exergy loss model (EXL) and exergy efficiency model (EEF) will be used. The global model is executed in three main steps or blocks:

where hi and si are the specific enthalpy and specific entropy of the point considered, respectively. Specific exergy associated to i-heat flow is expressed as

ð5Þ

  To q ei ¼ 1  Ti i

ð6Þ

Ti is the temperature at which the heat flow qi is transferred (added or removed from the body). Specific exergy of work of i-flow is equal to the specific work of the flow. Thus,

ei ¼ wi

ð7Þ

 First block: Construction of the exergy flow graph and its matrix of incidence corresponding to the flow sheet diagram.  Second block: Determination of exergy flows associated with each connection represented on the energy flow graph.

Specific exergy of fuel is approximated by the following equation:

For thermal power systems, there are four types of exergy flows: mass flow, work, heat and fuel. Specific mass exergies related to these types can be calculated by the following equations: Specific exergy associated to i-flow of mass is the sum

where c stands for the exergy factor and denotes LHV the lower heating value of the fuel material. The exergy flow rate is

ei ¼ c  LHV

ð8Þ

Ei ¼ mi ei

pt kn ch ei ¼ eph i þ ei þ ei þ ei

ð4Þ

In absence of chemical reaction (chemical equilibrium with the surroundings), and neglecting the potential and kinetic exergies, only the physical part of exergy is considered. Eq. (4) then becomes

(a)

ð9Þ

For the full determination of the exergy flows, a reference state also called ‘‘restricted dead state” should be defined and the mass and energy balance equations applied to all components in view of determining the works output or input and the heat added or

Hot water in 6

Evaporator

T Water out

6

Turbine

5

2

4

Cond Water enser Cold out water in 1

3

7

5 9

9

Pump 2

4

8(1-α)

7(α)

Closed FWH

Mixing Chamber

(b)

2

3

7s 8

1

8s s

Pump 1

Fig. 5. Regenerative organic Rankine cycle with closed feedliquid heater: (a) flow sheet diagram and (b) T–s diagram.

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rejected. Mass and energy balances for any control volume at steady state with negligible potential and kinetic energy changes can be given, respectively, by [46]

The energy efficiency of component i (giex ), is defined as the ratio between its used and available exergy flow rates. This is expressed by

X X ðmj Þout ¼ ðmk Þin

ð10Þ

giex ¼ Eui =Eai

ð11Þ

The coefficient of influence of component i (bi), defined as the ratio of the available energy of the component to the total available exergy of the system indicates to which extend the component influences the system performance and is expressed as

j

k

Q W ¼

X

mj hj

 out



j

X

ðmk hk Þin

k

 bi ¼ Eai EaR

In organic Rankine cycles, dry fluids offer several advantages over wet fluids; wet fluids are less efficient and present a risk of droplets in the turbine which could damage the blades. In case a dry fluid is chosen as working fluid, a regenerator can be used to transfer the heat contained in the vapor after expansion to the compressed stream entering the boiler. The effectiveness of this regenerative heat exchanger is defined as the ratio of the actual temperature change of the liquid stream to the maximum possible temperature change. From Fig. 2, the regenerator effectiveness (e) can be expressed as [52]:

e ¼ ðT 6  T 5 Þ=ðT 2  T 5 Þ

PR ¼

.

ð19Þ

The system exergetic efficiency (gRex ), is the ratio of system total exergy used to the system total available exergy and is expressed as



gRex ¼ EuR EaR

ð20Þ

The system thermal or energy efficiency as parameter which shows how the energy is converted in the engine is the ratio of the net power output to the heat input to the engine. It is written as

 Third block: Determination of exergy losses, degree of thermodynamic perfection, exergy efficiency and coefficient of influence.

gRth ¼ W net =Q in ¼ ðW t  RW p Þ=Q in

ð21Þ

where Wnet is the net power produced by the system and Qin the total heat input.

Once the exergy flows are determined, energy input, exergy output, used energy, available exergy, and exergy losses can be calculated using the definitions given in Table 2 [47]. Then, the components and systems performance can be evaluated using the parameters defined below. Exergy losses associated with component i (Pi), defined as the difference between the inlet and outlet energy flow rates is expressed as:

3.3. Operating conditions The solar desalination system described in Section 2.2 is designed to operate at low temperature below 100 °C. In this range of temperature, water as heat carrier is suitable and will not turn into steam and most medium temperature collectors (flat plate, evacuated tube or compound parabolic collectors) can be used. These collectors offer the advantage of low initial and low maintenance costs over parabolic trough collectors. The following operating conditions were set for the organic Rankine engine sub-system:  Heat source: hot water is supplied at 85 °C and the pinch point is DTpp = 3 °C.  Condenser cooling fluid: water supplied at 25 °C.

ð14Þ

The degree of thermodynamic perfection of component i (mi), is the ratio of the exergy leaving to the energy flowing into the component and is given by

.

ð18Þ

mR ¼ Eout Ein R R

TTD is the terminal temperature difference.

.

Pi

The degree of thermodynamic perfection of the system (mR), is the ratio of the sum of exergy flowing out of the system to sum of exergy flowing into the system; and is being given by

ð13Þ

in mi ¼ Eout Ein i i ¼ 1  Pi Ei

n X i¼1

Similarly to steam power plants, the efficiency of organic power cycles could be increased by the incorporation of feedliquid heaters. In case a feedliquid heater is included to the engine as in Fig. 5, the temperature of the feedliquid after heating can be given as

out Pi ¼ Ein i  Ei

ð17Þ

The engine or system total exergy loss (PR), is the sum of exergy lost in all components.

ð12Þ

T 9 ¼ T 3  TTD

ð16Þ

ð15Þ

Table 2 Exergy rates associated with different components [47]. Components

Heat exchanger

Schematic

Hot stream, E3

Mixing unit

Cold stream, E1

E2

Pump

Hot stream E2 Cold stream

E3 + E1 E2 + E4 E2  E1 E3  E4

E1

E2 E3 (Wp)

E4 (Wt)

E3

E1 E4

Energy, in (Ein) Energy, out (Eout) Used energy (Eu) Available energy (Ea)

Turbine

E1 E2 + E1 E3 E3 E2 + E1

E3 + E1 E2 E2  E1 E3

E2

E3

E1 E2 + E3 + E4 E4 E1  E2  E3

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ers and the mixing units are well insulated. A simulation package EES (Engineering Equation Solver) [53] that contains the thermodynamic properties of a certain number of fluids is used for calculations and evaluation of flow parameters.

 Working fluid: R134a.  Turbine: pressure ratio, PR = 3; power output, Wt = 2 kW; isentropic efficiency, gst = 70%; mechanical efficiency, gmt = 60%.  Pumps: isentropic efficiency, gp = 80%.  Feedliquid heater pressure is chosen through the following relation:

Pflh ¼ P in

exp

 1=2ðP in

exp

 Pout

4. Results and discussion

exp Þ

From the flow sheet diagrams corresponding to different configurations, the exergy flow graphs with all interconnections were built and displayed on Fig. 6. Since these flow graphs sufficiently show the interactions between components and directions of flows, there is no interest for drawing the matrixes of incidence. After execution of equations built in EES, Tables 4a–4d of flow parameters which show different operating points of the systems and energy rates were produced. Using definitions in Table 2 and Eqs. (14)–(21), performance parameters of components and systems are calculated. Performances of several fluids are also investigated and compared. R245fa and R600 are dry fluids with

where Pin_exp and Pout_exp are inlet and outlet pressures of the turbine.  Terminal temperature difference, TTD = 3 °C.  Effectiveness of the regenerator, e = 0.80.  Restricted dead state (ambient conditions): Po = 0.1 MPa and To = 25 °C. Along with the operating conditions above set, the following assumptions are made: steady-state conditions, no heat losses and pressure drops in the heat exchangers, and the feedliquid heat-

(b)

(a)

E8 E1

E6

E5 II

E7 Π3

Π2

E6 II Π3

E7

III

Π2

E3

E5 I

Π5

E2 E3 Π1

IV

E10 E8

E4

I

E10

V

E9 Π4

E12

(c)

(d)

E11

Ε12

Π4

Ε11

Ε6

III

E10

Ε13

IV

Π3 Π3

E5

III

II

E9

E9

Π4

E2

E1

E4

Π1

IV

III

E11

Π2 E6 VI

E4

Ε8

Ε7

Ε5

Π5

Ε15 II

Π2

Π6

E7

Ε9

V

Π7 VII

E3 E2

Ε1

Ε4 Π1

I

Π5

V

Ε3

E12

IV E1

E8

Ε14

Π4 I

E14

Ε2

E13

Π1

VI Π6

Ε10 Ε16 Fig. 6. Exergy flow graphs: (a) simple Rankine engine, (b) Rankine engine with regenerative heat exchanger, (c) Rankine engine with open feedliquid heater and (d) Rankine engine with closed feedliquid heater.

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Table 3 Characteristics of the working fluids. Fluids R134a R245fa R600

1,1,1,2- Tetrafluoroethane 1,1,1,3,3-Pentafluoropropane N-Butane

Table 4a Flow parameters for configuration 1(simple organic Rankine cycle). MW (kg/kmol)

Tcrit (°C)

Pcrit (MPa)

ODP

102 134 58.12

101.3 154.1 152

4.059 3.639 3.796

0 0 0

higher critical temperature in comparison to R134a which is isentropic (see Table 3).

State

Fluid

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg K)

e (kJ/kg)

E(kW)

1 2 3 4 5 6 7 8 9 10

R134a R134a R134a R134a Water Water – Water Water –

75 30.8 30.8 31.98 85 73.85 – 25 35 –

2366 788.6 788.6 2366 100 100 – 100 100 –

280.8 266.2 94.74 96.41 355.9 309.2 – 104.8 146.7 –

0.895 0.916 0.352 0.353 1.134 1.002 – 0.367 0.505 –

67.33 46.56 43.28 44.61 22.33 15.11 8.773 0 0.686 1.665

15.35 10.61 9.86 10.17 20.08 13.59 2 0 0.64 0.38

4.1. Rankine engines with R134a as working fluid 4.1.1. Configuration 1: simple Rankine engine In the simple Rankine engine, only four components are considered: expander, evaporator, pump and condenser. As can be seen in Table 5, the highest exergy loss occurs in the expander: 2.74 kW which represents 65% of the total exergy destroyed in the system as shown by the exergy loss distribution (Fig. 7a). The direct consequence is the low exergy efficiency, 42.24% and low degree of thermodynamic perfection, 82.18%. The poor performance of the expander is due to the irreversibilities during the expansion process: radial and flank leakages and thermal losses. The evaporator is the most critical component with a degree of influence of 32.31%, followed by the expander 23.58%. This simple engine consumes 4.23 kW exergy and, exergy efficiency and degree of thermodynamic perfection are 8% and 79.34%, respectively. 4.1.2. Configuration 2: Rankine engine with regenerative heat exchanger The role assigned to the regenerator is to increase the average evaporator temperature. From Table 4b (flow parameters) it can be seen that the temperature at the evaporator inlet (point 6, 31.04 °C) is lower than temperature at the pump outlet (point 5, 31.98 °C) which means that the heat exchanger cools instead of heats. From the results displayed in Table 5, it can be seen that the regenerator has a very small coefficient of influence (0.05%) which means very little effect on the system. And of course, the exergy efficiency of the system in comparison with the simple Rankine engine is unchanged and the degree of thermodynamic perfection is slightly decreased, by 8%. Unnecessary use of regenerator can be drawn as conclusion confirming the uselessness of this device when the working fluid is an isentropic one such as R134a. No exergy is destroyed in the regenerator and the energy loss distribution is similar to that of the basic engine (see Fig. 7b). The evaporator is still the most important component with a coefficient of influence of 32.53% followed by the turbine. 4.1.3. Configuration 3: Rankine engine with open feedliquid In this configuration, a feedliquid or mixing unit is incorporated in the simple Rankine engine. The pump (first pump) exit exergy is mixed to exergy extracted from the expander in order to reduce the exergy destruction in the evaporator. In comparison to the basic engine, this configuration will be more expensive as it requires two more devices: an additional pump and a mixing unit. From Table 5, it is observed that the feedliquid plays a significant role; the total amount of energy destroyed is reduced from 4.2 kW in first two configurations to 3.9 kW. The degree of thermodynamic perfection is also increased from 79.34% in the first configuration and 79.16% in the second configuration to 83.7%. In contrast, the exergy efficiency is reduced by 15.38% compared with first two configurations; this is due to pumps’ works. The evaporator performs better in this config-

Table 4b Flow parameters for configuration 2 (regenerative Rankine engine with internal heat exchanger). State

Fluid

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg.K)

e (kJ/kg)

E (kW)

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

R134a R134a R134a R134a R134a R134a Water Water – Water Water –

75 30.8 31.28 30.8 31.98 31.04 85 73.77 – 25 35 –

2366 788.6 788.6 788.6 2366 2366 100 100 – 100 100 –

280.8 266.2 267.6 94.74 96.41 95.06 355.9 308.9 – 104.8 146.7 –

0.8951 0.9157 0.9202 0.3517 0.3528 0.3483 1.134 1.001 – 0.3669 0.5049 0.8951

67.33 46.56 46.59 43.28 44.61 44.58 22.33 15.07 8.773 0 0.6862 1.665

15.35 10.61 10.62 9.866 10.17 10.16 20.08 13.55 2 0 0.6463 0.3795

Table 4c Flow parameters for configuration 3 (Rankine engine with open feedliquid heater). State

Fluid

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg.K)

e (kJ/kg)

E (kW)

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

R134a R134a R134a R134a R134a R134a R134a – Water Water – Water Water –

30.8 31.4 57.29 58.17 75 57.29 30.8 – 85 76.24 – 25 35 –

788.6 1577 1577 2366 2366 1577 788.6 – 100 100 – 100 100 –

94.74 95.57 135 135.9 280.8 275.6 266.2 – 355.9 319.2 – 104.8 146.7 –

0.3517 0.3522 0.4763 0.4768 0.8951 0.9019 0.9157 – 1.134 1.03 – 0.3669 0.5049 –

43.28 43.94 46.35 47.11 67.33 60.1 46.56 0.924 22.33 16.55 11.9 0 0.6862 0.8324

8.97 9.109 12.3 12.5 17.87 3.49 9.651 0.2452 23.37 17.33 2 0 0.583 0.1725

Table 4d Flow parameters for configuration 4 (Rankine engine with closed feedliquid heater). State

Fluid

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg.K)

e (kJ/kg)

E (kW)

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

R134a R134a R134a R134a R134a R134a R134a R134a R134a – Water Water – Water Water –

30.8 31.98 57.29 58.17 55.04 75 57.29 30.8 54.29 – 85 75.94

788.6 2366 1577 2366 2366 2366 1577 788.6 2366 – 100 100 – 100 100 –

94.74 96.41 135 135.9 130.9 280.8 275.6 266.2 129.7 – 355.9 317.9 – 104.8 146.7 –

0.3517 0.3528 0.4763 0.4768 0.4617 0.8951 0.9019 0.9157 0.4581 – 1.134 1.027 – 0.3669 0.5049 –

43.28 44.61 46.35 47.11 46.63 67.33 60.1 46.56 46.53 0.924 22.33 16.37 7.691 0 0.6862 1.665

9.098 9.378 2.309 2.347 12.13 17.51 2.994 9.788 9.781 0.04602 22.9 16.79 2 0 0.5913 0.35

25 35 –

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B.F. Tchanche et al. / Applied Energy 87 (2010) 1295–1306 Table 5 Thermodynamic characteristics for different configurations. Element

Ein i (kW)

(kW) Eout i

Eai (kW)

Eui (kW)

Pi (kW)

giex (%)

mi (%)

bi (%)

1-Simple rankine engine Pump (I) Evaporator (II) Turbine (III) Condenser (IV) System

10.25 30.25 15.35 10.61 20.46

10.17 28.94 12.61 10.51 16.23

0.38 6.487 4.735 0.749 20.08

0.305 5.179 2 0.641 1.62

0.075 1.308 2.735 0.108 4.226

80.23 79.83 42.24 85.61 8.07

99.27 95.68 82.18 98.98 79.34

1.89 32.31 23.58 3.731 –

2-Regenerative heat exchanger Pump (I) 10.25 RHE (II) 20.78 Evaporator (III) 30.24 Turbine (IV) 15.35 Condenser (V) 10.62 System 20.46

10.17 20.78 28.9 12.61 10.51 16.19

0.3795 0.01 6.531 4.735 0.755 20.08

0.305 0.01 5.186 2 0.646 1.62

0.075 0.00 1.345 2.735 0.109 4.264

80.23 100 79.41 42.24 85.60 8.07

99.27 100 95.55 82.18 98.98 79.16

1.89 0.05 32.53 23.58 3.76 –

3-Open feedliquid Pump 2 (I) Evaporator (II) Turbine (III) Condenser (IV) Pump 1 (V) Feedliquid (VI) System

12.55 35.87 17.87 9.651 9.143 12.6 23.79

12.5 35.19 15.14 9.553 9.109 12.3 19.91

0.245 6.045 4.724 0.681 0.173 12.6 23.37

0.200 5.365 2 0.583 0.139 12.3 1.538

0.045 0.68 2.724 0.098 0.034 0.299 3.88

81.79 88.76 42.33 85.61 80.30 97.63 6.77

99.64 98.11 84.75 98.98 99.63 97.63 83.69

1.05 25.87 20.22 2.91 0.74 53.91 –

4-Closed feedliquid Pump 2 (I) Mixing Unit (II) Evaporator (III) Turbine (IV) Condenser (V) Pump 1 (VI) Feedliquid (VII) System

2.355 12.13 35.03 17.51 9.788 9.448 12.37 23.3

2.347 12.13 34.3 14.78 9.689 9.378 12.09 19.38

0.046 12.13 6.113 4.726 0.69 0.35 0.685 22.9

0.038 12.13 5.382 2 0.591 0.281 0.402 1.604

0.008 0.001 0.731 2.726 0.099 0.07 0.283 3.92

81.79 100 88.04 42.32 85.61 80.23 58.75 7.00

99.64 100 97.91 84.43 98.98 99.27 97.72 83.18

0.20 52.95 26.69 20.63 3.02 1.53 2.99 –

Fig. 7. Exergy loss distribution: (a) simple Rankine engine, (b) Rankine engine with regenerative heat exchanger, (c) Rankine engine with open feedliquid heater and (d) Rankine engine with closed feedliquid heater.

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R134a

R245fa

(b)

R600

5 4.8 4.6 4.4 4.2 4 3.8 3.6 3.4 3.2 3

R134a

R245fa

R600

8.6

Exergertic efficiency (%)

Energy efficiency (%)

(a)

8.2 7.8 7.4 7 6.6 6.2 5.8 5.4 5

SRE

RHE

OFH

CFH

SRE

RHE

(c) Degree of therm. perfection (%)

OFH

CFH

Engines

Engines R134a

R245fa

R600

86 85 84 83 82 81 80 79 78 77 76

SRE

RHE

OFH

CFH

Engines Fig. 8. Performance parameters: (a) Energy efficiency, (b) Exergetic efficiency and (c) degree of thermodynamic perfection. (SRE: simple rankine engine, RHE: regenerative heat exchanger, OFH: open feedliquid heater, CFH: closed feedliquid heater.)

4.2. Rankine engines and working fluids In this section, different Rankine engine configurations are compared using different parameters: thermal efficiency, exergetic efficiency and degree of thermodynamic perfection. The thermal efficiency indicates how the energy conversion takes place in the system. The exergetic efficiency is the ratio between the exergy

20 18

Energy and Exergy efficiencies (%)

4.1.4. Configuration 4: Rankine engine with closed feedliquid heater A Rankine engine with a closed feedliquid heater is more complex than the previous configurations. Three components are added to the simple engine: an additional pump, a mixing unit and the feedliquid heater making it the most expensive engine. Compared to the Rankine engine with open feedliquid, results are similar. There is a slight increase in exergy efficiency and a slight decrease in degree of thermodynamic perfection (see Table 5). The exergy loss distribution (see Fig. 7d) is almost the same with no exergy destroyed in the mixing unit which is also the most critical component with a coefficient of influence of 52.95%. Concluding this section, the simplest the cycle the best it will be from an exergetic efficiency viewpoint. The regenerative heat exchanger is regarded as useless using R134a. The incorporation of feedliquid improves the thermodynamic operation of the engine by reducing the exergy losses but the cost for that is a decrease in exergetic efficiency. The mixing unit, evaporator and expander appear as the key components. However, different modifications did not affect the expander for which the performances remained poor.

86 R600

Exergy eff. eff. (%) T hermal eff. Thermal eff. (%) Degree of therm. perf. perf. (%) (%)

16 14

85

84

12 10

83

8 82

6 4

81

2 0 60

65

70

75

80

85

90

95

Degree of thermodynamic perfection (%)

uration: exergy efficiency increased from 79.83% (configuration 1) and 79.41% (configuration 2) to 88.76%. The degree of thermodynamic perfection does the same as can be seen in Table 5. The feedliquid heater is the most critical component; it has the highest coefficient of influence (53.91%) and contributes to the reduction of energy losses in the evaporator significantly. This reduction reaches 50% (see Table 5) while the expander remains the site of highest energy losses with 2.72 kW and contributes for 70% of total energy destroyed (Fig. 7c).

80 100

Heat source temperature (ºC) Fig. 9. Variation of the performance parameters with the temperature of the heat source.

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B.F. Tchanche et al. / Applied Energy 87 (2010) 1295–1306

4.3. Heat source temperature and pinch point temperature difference Fig. 9 shows the influence of the heat source temperature on the system performance. The pinch point and the temperature difference between the heat reservoir and the turbine inlet are kept at 3 °C and 10 °C, respectively, and the turbine inlet point is maintained on the saturation curve while the temperature of the water is increased. The increase in heat source temperature is followed by a decrease in exergetic efficiency while the energy efficiency remains almost constant. The degree of thermodynamic perfection decreases and passes through a minimum.

20 R600 =5°°C C ΔΤpp=5

Exergetic efficiency (%)

18

°C ΔΤpp=4 °C

16

°C ΔΤpp=3 °C

14 12 10 8 6

90

Degree of thermodynamic perfection (%)

gained (useful energy) and the exergy input (contained in the hot water supplied at the evaporator inlet). The degree of thermodynamic perfection shows how the energy input is transformed by the system i.e. exergy destruction level; thus it is a suitable indicator for entropy generation minimization. In Fig. 8, performances of different fluids in different configurations are displayed. From an energy point of view, the regenerative heat exchanger allows better energy conversion for dry fluids (R245fa, R600) while the closed feedliquid is suitable for the isentropic one: R134a (see Fig. 8a). The exergetic efficiency is highest for all three fluids in the simple Rankine engine as can be seen in Fig. 8b. Fig. 8c shows the engine with the open feedliquid heater as the configuration with the highest degree of thermodynamic perfection. Seeking for best fluid in the best configuration, the energy efficiency is higher for R600 in configuration 2 and the degree of thermodynamic perfection is higher for R600 in configuration 3; while the exergetic efficiency is higher for R134a in configuration 1. The incorporation of the heat exchanger for R600 leads to an increase of 7% in the energy efficiency in comparison to the simple Rankine; what is not significant. For the same fluid the incorporation of the feedliquid heater and second pump lead to an increase in the degree of thermodynamic perfection of 3.5%, comparison made with the simple Rankine engine. Although, different modifications give better energy conversion and less exergy destroyed, the improvements are not significant enough and could not probably be economically feasible. Therefore, for heat source temperature below 100 °C, the simple Rankine cycle is the best configuration from manufacturing and cost viewpoints.

89

R600

°C ΔΤpp=5 °C °C ΔΤpp=4 °C

88

°C ΔΤpp=3 °C

87 86 85 84 83 82 81 60

65

70

75

80

85

90

95

100

Temperature of the heat source (°C) Fig. 11. Influence of the pinch point temperature difference on the degree of thermodynamic perfection.

On Figs. 10 and 11, the influence of the pinch point temperature difference can be appreciated. The increase of the pinch point reduces the exergetic efficiency but at the same time improves the thermodynamic behavior of the system. These graphs reveal an opposition between both exergetic efficiency and degree of thermodynamic efficiency; what was observed earlier on Fig. 8b and c. 5. Conclusions Performances of organic Rankine heat engines operating with several fluids were evaluated using an innovative exergy study approach called exergy topological method based on combination of exergy analysis and mathematical graph theory. Using parameters such as exergy loss, exergy efficiency, degree of thermodynamic perfection and coefficient of influence, components and systems performance were compared. Various devices incorporated in the simple Rankine cycle, gave different results: the regenerative heat exchanger has positive effects only on dry fluids; the incorporation of feedliquid heaters improve the degree of thermodynamic perfection of the system but leads to loss in exergetic efficiency. Mixing units, open feedliquid heater, evaporator and turbine are the most important elements in regard to the coefficients of influence in different configurations. For different engines and fluids considered, the energy conversion is poor, less than 5% and energy efficiency does not exceed 10%. The integration of different devices is not significantly rewarded in terms of gain; therefore, it is preferable to keep the simple Rankine engine when designing a system such as the small scale RO desalination system with an integrated Rankine engine operating on low temperature heat below 100 °C. It was also shown how the pinch point temperature difference should be lowered so as to produce high energy efficiency. The present study proved the capability of structural energy analysis approach to serve not only as evaluation tool, but also as decision support tool.

4

References

2 60

65

70

75

80

85

90

95

100

Temperature of the heat source (°C) Fig. 10. Influence of the pinch point temperature difference on the exergetic efficiency.

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