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Energy 32 (2007) 1698–1706 www.elsevier.com/locate/energy

Optimum design criteria for an Organic Rankine cycle using low-temperature geothermal heat sources H.D. Madhawa Hettiarachchia, Mihajlo Golubovica, William M. Woreka,, Yasuyuki Ikegamib a

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor Street, Chicago, IL 60607, USA b Institute of Ocean Energy, Saga University, Honjomachi 1, Saga 840-8502, Japan Received 17 April 2006

Abstract A cost-effective optimum design criterion for Organic Rankine power cycles utilizing low-temperature geothermal heat sources is presented. The ratio of the total heat exchanger area to net power output is used as the objective function and was optimized using the steepest descent method. Evaporation and condensation temperatures, geothermal and cooling water velocities are varied in the optimization method. The optimum cycle performance is evaluated and compared for working ﬂuids that include ammonia, HCFC123, n-Pentane and PF5050. The optimization method converges to a unique solution for speciﬁc values of evaporation and condensation temperatures and geothermal and cooling water velocities. The choice of working ﬂuid can be greatly affect the objective function which is a measure of power plant cost and in some instances the difference could be more than twice. Ammonia has minimum objective function and maximum geothermal water utilization, but not necessarily maximum cycle efﬁciency. Exergy analysis shows that efﬁciency of the ammonia cycle has been largely compromised in the optimization process than that of other working ﬂuids. The ﬂuids, HCFC 123 and n-Pentane, have better performance than PF 5050, although the latter has most preferable physical and chemical characteristics compared to other ﬂuids considered. r 2007 Published by Elsevier Ltd. Keywords: Organic Rankine cycle; Optimum design; Low-temperature; Power generation; Geothermal heat sources

1. Introduction Geothermal heat sources vary in temperature from 50 to 350 C, and can either be dry, mainly steam, a mixture of steam and water, or just liquid water. The temperature of the resource is a major determinant of the type of technologies required to extract the heat and the uses to which it can be applied [1,2]. Generally, the high-temperature reservoirs ð4220 CÞ are the ones most suitable for commercial production of electricity. Dry steam and ﬂash steam systems are widely used to produce electricity from high-temperature resources [1–3]. Dry steam systems use the steam from geothermal reservoirs as it comes from wells, and route it directly Corresponding author. Tel.: +1 312 996 5318; fax: +1 312 413 0447.

E-mail address: [email protected] (W.M. Worek). 0360-5442/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.energy.2007.01.005

through turbine/generator units to produce electricity. Flash steam plants are the most common type of geothermal power generation plants in operation today. In ﬂash steam plants, hot water under very high pressure is suddenly released to a much lower pressure, allowing some of the water to convert into steam, which is then used to drive a turbine. Medium-temperature geothermal resources, where temperatures are typically in the range of 100–220 C, are by far the most commonly available resource. Binary cycle power plants are the most common technology for utilizing such resources for electricity generation. There are many different technical variations of binary plants including those known as Organic Rankine cycles (ORC) and proprietary systems known as Kalina cycles [4–12]. Binary cycle geothermal power generation plants differ from dry steam and ﬂash steam systems in that the water or the steam from the geothermal reservoir never comes in

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706

Nomenclature A BO BO cP D d E F; F0 fP Gr g H h L l ‘ DT m M _ m N Nu W Pr PW P p Q q T t U V w X

heat transfer surface area ðm2 Þ Bond number (dimensionless) modiﬁed Bond number (dimensionless) heat capacity ðkJ kg1 K1 Þ diameter (m) depth of the ﬂute (m) exergy friction factor (dimensionless) pressure factor (dimensionless) Grashof number (dimensionless) gravitational acceleration ðm s2 Þ ratio of latent heat to sensible heat (dimensionless) enthalpy ðkJ kg1 Þ latent heat ðkJ kg1 Þ length (m) heat transfer length (m) logarithmic mean temperature difference ( C) molecular weight ðg mol1 Þ mass ﬂow rate ðkg s1 Þ number of plates Nusselt number (dimensionless) power (W) Prandlt number (dimensionless) pumping power (W) pressure (Pa) pitch of the ﬂutes on the plate (m) heat transfer (W) heat ﬂux ðW m2 Þ temperature ( C) thickness of the plate (m) overall heat transfer coefﬁcient ðW m2 K1 Þ velocity ðm s1 Þ width (m) non-dimensional number

contact with the turbine/generator units. In binary systems, the water from the geothermal reservoir is used to heat a secondary ﬂuid which is vaporized and used to turn the turbine/generator units. The geothermal water and the working ﬂuid are each conﬁned in separate circulating systems and never come in contact with each other. Although binary power plants are generally more expensive to build than steam-driven plants, they have several advantages. The working ﬂuid boils and ﬂashes to a vapor at a lower temperature than does water, so electricity can be generated from reservoirs with lower temperatures. This increases the number of geothermal reservoirs in the world with electricity-generating potential. Since the geothermal water and working ﬂuid travel through entirely closed systems, binary power plants have virtually no emissions to the atmosphere.

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Greek symbols dx dy a g Z m n r s

working ﬂuid side plate clearance (m) water side plate clearance (m) heat transfer coefﬁcient ðW m2 K1 Þ objective function ðm2 W1 Þ efﬁciency (dimensionless) viscosity (Pa s) kinematic viscosity ðm2 s1 Þ density ðkg m3 Þ surface tension ðN m1 Þ

Subscripts AP a C CWI CWO E eq G HWI HWO L N o P R V W WF WFS WFP WP WS T 1; 2; 3; 4

across plate atmospheric condenser cooling water inlet cooling water exit evaporator equivalent generator geothermal water inlet geothermal water exit liquid net reference or ambient state plate Rankine vapor water working ﬂuid working ﬂuid side working ﬂuid pump water pump water side total, turbine state points

Currently, the potential of electricity generation using low-temperature geothermal resources (especially in the range of 70–100 C) have been overlooked. Extension of binary power cycle technology to utilize low-temperature geothermal resources has received much attention [4–12]. Since the available temperature difference is less, the cycle efﬁciency (i.e., approximately 5–9%) is much lower than that of thermal power generation using medium temperature geothermal resources (i.e., approximately 10–15%) [2]. Further, in low-temperature systems, large heat exchanger areas are required to extract same amount of energy compared to medium-temperature systems. These factors impose limits on exploiting the low-temperature geothermal resources and emphasize the necessity of optimum, cost-effective design of binary power cycles.

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706

In this paper, a cost-effective design optimization method is presented for a binary Organic Rankine power cycle using low-temperature geothermal resources. It is desirable to use total electricity cost (ratio of total plant cost to total net power output) as the objective function in the optimum design of the Organic Rankine power plant. However, the total power plant cost depends on the place and the time that the power plant is constructed, the constructor and many other parameters. This makes it difﬁcult to use the total electricity cost in the optimum design of the power plant. It can be considered that the total cost of the heat exchanger area contributes largely to the total power plant cost in a low-temperature geothermal power plant. Therefore, the performance of the power plant is optimized using the optimization criterion given in Ref. [13], in which the ratio of total heat transfer area to total net power is considered to be the objective function. Evaporation and condensation temperatures, geothermal and cooling water velocities are varied in the optimization process. The optimum cycle performance is evaluated and compared for working ﬂuids which included ammonia, HCFC123, n-Pentane and PF5050. The optimization method converges to a unique solution for certain speciﬁc values of evaporation and condensation temperatures and, geothermal and cooling water velocities. The choice of working ﬂuid can be greatly affect the power plant cost, in some instances the difference could be twice. The working ﬂuid with minimum objective function also yields the maximum geothermal water utilization, but not necessarily maximum efﬁciency.

generated at the evaporator is used to drive a turbine. The working ﬂuid leaving the turbine is then condensed and pumped back to the evaporator. The working ﬂuid then passes through a series of devices that forms a closed loop. By modeling each device, a complete cycle simulation is achieved. The performance of power plant is optimized using the optimization criterion given by Ref. [13], in which the ratio of total heat transfer area to total net power is considered as the objective function: Objective function; g ¼

(1)

The steepest descent method was used to optimize the objective function. During the optimization process, the objective function is minimized by varying evaporation and

geothermal water

THWI

QE 1

4

QC

3

2. Analysis The schematic of the Organic Rankine cycle and T-S diagram of the cycle are shown in Figs. 1 and 2, respectively. Geothermal water is passed through the evaporator heating a secondary ﬂuid, which is typically an Organic working ﬂuid with a low boiling point. Vapor Working fluid

AT . WN

Temperature

1700

TCWI

2

cooling water Specific Entropy

Fig. 2. Temperature-entropy diagram of the Rankine cycle.

1

Turbine Generator 2

Pump Evaporator Condenser

Cooling water

Geothermal water 4

Pump

3 Pump Fig. 1. Schematic diagram of the Rankine cycle.

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706

condensation temperatures, geothermal water velocity in the evaporator and the cooling water velocity in the condenser. Fig. 3 shows the ﬂow chart of the calculation procedure. Steady state operation of the cycle is considered in the analysis. Saturated vapor is considered at the turbine inlet and saturated liquid is assumed at the condenser exit. The Rankine cycle speciﬁcations considered in this analysis are listed in Table 1, where ﬂat plate type heat exchangers are used in the evaporator and condenser. Since we are considering low-temperature geothermal heat sources, obviously large heat exchanger area (per unit power output) will be expected at the evaporator and condenser, which would be a major design parameter in this type of a power plant. Plate type heat exchangers are preferred in this analysis due to their compactness and high heat transfer coefﬁcients which result less heat transfer area than would be needed for the same duty using shell and tube heat exchanger. Complete evaluation of evaporator and condenser is performed accounting for the total heat transfer area, the

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Table 1 Speciﬁcations of the Organic Rankine cycle considered Working ﬂuids

Ammonia, n-Pentane, HCFC-123, PF 5050

Gross power W Gross Condenser and evaporator

10 MWe Shell and plate type [14,15] Heat transfer plate material is titanium l ¼ 1460 mm, w ¼ 550 mm, t ¼ 0:6 mm, dx ¼ 5 mm, dy ¼ 5 mm 70–90 C

Geothermal water temperature T HWI Geothermal water and cooling water pump efﬁciency ZWP Working ﬂuid pump efﬁciency ZWFP Cooling water temperature T CWI Turbine efﬁciency ZT Generator efﬁciency ZG

0.80 0.75 30 C 0.85 0.96

overall heat transfer coefﬁcients and the pumping work. Numerical correlations are used to calculate heat transfer coefﬁcients and pressure drops in the heat exchangers [14–17]. The numerical calculations were carried out for a 10 MWe geothermal power plant considering a cold source temperature of 30 C and geothermal water temperatures varying from 70 to 90 C. Heat and mass balance across the devices and cycle efﬁciency are calculated as given below. Working ﬂuid mass ﬂow rate is calculated by

Plant conditions

Assume TE, TC, VCWI, VHWI

State points 1,2,3,4

_ WF ¼ m

. mWF, QE, QC, R

W Gross . ðh1 h2 ÞZT ZG

Heat supplied at the evaporator is evaluated as

Assume TP, TWF, TW

W,QW QAP

Condenser and Evaporator

|(QWF -QW)/QWF |> 10-3

|(n-n-1)/n |>10-3

_ WF ðh1 h4 Þ. QE ¼ m WF, QWF

QWF = QAP = QW

. U, NT, mW,VWF, ΔPW, ΔPWF, PWW, AT, WN

=

(2)

AT WN

Optimum conditions Fig. 3. Flow chart of the simulation procedure.

(3)

Heat rejection at the condenser is calculated by _ WF ðh2 h3 Þ. QC ¼ m

(4)

The Rankine cycle efﬁciency is deﬁned as QE QC . QE

ZR ¼

(5)

Exergy efﬁciency for the binary geothermal power plants is deﬁned as the rate of exergy output to the exergy input. In binary geothermal cycles, the geothermal ﬂuid leaving the evaporator is reinjected in to the ground and its exergy is lost. Therefore efﬁciency is based on the initial heat source exergy as given by Eq. (6): Zex ¼

E out E heat

,

(6)

source

where E heat

source

¼ ðhHWI h0 Þ T 0 ðsHWI s0 Þ

(7)

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706

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and

by [14–17]

_ HW m 273:15cP exp mCW sHWO Þ sCWI hCWI .

E out ¼ ðhHWI hHWO Þ

_ HW m _ CW m

1=3

NuW ¼ 0:047 Re0:8 W PrW , where ð8Þ

NuW ¼ aW ðDeq ÞW =kW ,

Eq. (8) is derived using energy and entropy balances for the entire cycle. Heat transfer coefﬁcients, pressures drops, total heat exchanger area, geothermal and cooling water pumping power and net-power for the cycle are evaluated using the followings. The overall heat transfer coefﬁcient (at the condenser or evaporator), U is deﬁned by 1 1 t 1 ¼ þ þ . (9) U aWFS k aWS

ReW ¼ V W ðDeq ÞW =nW ,

ðsHWI

The total evaporator and condenser heat exchanger area is given by AT ¼ AE þ AC ¼

QE QC þ . U E ðDT m ÞE U C ðDT m ÞC

(10)

PrW ¼ ðcP ÞW mW =kW . The condensation heat transfer coefﬁcient, aWF for all working ﬂuids is evaluated using [14] NuWF ¼ 1:77BOð0:1Þ ðGr Pr=HÞ1=4 , NuWF ¼ aWF ðDeq ÞWF =kWF , BO ¼ BOðp=‘Þðp=dÞ, BO ¼ grL p2 =s,

ðT HWI T 1 Þ ðT HWO T 4 Þ ðDT m ÞE ¼ lnfðT HWI T 1 Þ=ðT HWO T 4 Þg

Pr ¼ ðcP ÞL mL =kL .

(12)

rW V 2W l 2ðDeq ÞW

(13)

PW W

_ WF m . wðdxÞrWF N

(14)

(15)

2rWF V 2WF l gDeq

(16)

and the working ﬂuid pump work is calculated by PW WF ¼

_ WF fðP1 P2 Þ þ ðDPWF ÞC þ ðDPWF ÞE g m . rWF ZWFP

NuWF ¼ aWF ðDeq ÞWF =kWF , f P ¼ P=Pa ,

P0 ¼ 1:976 W and M ¼ 900 m1 .

(17)

Numerical correlations are used to calculate the heat transfer coefﬁcients and pressure drops in the condenser and evaporator as listed below. The water side heat transfer coefﬁcient in the condenser and evaporator aW is obtained

(23)

For the working ﬂuids HCFC 123, PF 5050 and n-Pentane: C ¼ 1:180 for f P X p62 and C ¼ 6:646 for f P X 462. For the working ﬂuid ammonia: C ¼ 0:716 for f P X p14:9 and C ¼ 2:218 for f P X 441:9. The net power of the binary Rankine cycle is obtained by W N ¼ W Gross ðPW WF þ ðPW W ÞE þ ðPW W ÞC Þ.

The working ﬂuid pressure drop is determined using DPWF ¼ F 0

(22)

3=2

The working ﬂuid velocity is calculated using V WF ¼

NuWF ¼ Cðf P X Þ0:919 H 0:834 ðrL =rV Þ0:448 ,

X ¼ ððcp ÞL r2L g=P0 M 2 kL sLrV Þ0:5 ðDeq ÞE qE ,

and the water pumping power is determined by _ W ðDPW Þ m ¼ . rW ZWP

and

where

The water side pressure drop is calculated using the equation DPW ¼ F

(21)

The boiling heat transfer coefﬁcient, aWF is calculated using the correlation [15]

and ðT 2 T CWI Þ ðT 3 T CWO Þ . lnfðT 2 T CWI Þ=ðT 3 T CWO Þg

(20)

where

Gr ¼ ðg‘3 =n2 ÞðrL rV Þ=rL

(11)

(19)

and

The log mean temperature difference for the evaporator and the condenser is deﬁned as

ðDT m ÞC ¼

(18)

(24)

3. Choice of working ﬂuids There are several general criteria that the working ﬂuid should ideally satisfy. Stability, non-fouling, non-corrosiveness, non-toxicity and non-ﬂammability are a few preferable physical and chemical characteristics. Also, the working ﬂuid should have relatively low boiling point to be used in a binary power cycle, since we deal with lowtemperature geothermal waters. However, in a cycle design, not all the desired general requirements can be satisﬁed.

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706 Table 2 List of working ﬂuids considered

0.24

T CRIT ðKÞ

pCRIT (MPa)

PF 5050 HCFC 123 Ammonia n-Pentane

421.1 456.86 405.40 469.5

2.01 3.675 11.33 3.36

0.20

Efficinecy

Working ﬂuid M (g/mol) 288 288 17.03 72.15

1703

0.16 Present simulation [4]

0.12

0.08

tane n-Pe n

HCFC123

0.04 300

400

320

340 360 380 400 420 Turbine Inlet Temperature (K)

440

460

Fig. 5. Validation of the numerical model with the previously published data [4] for the ideal Rankine cycle assuming working ﬂuid as HCFC 123 and T 3 ¼ 293 K.

PF5050

ia

on

m

Am

350

300

1

Ammonia THWI = 90°C TCWI = 30°C

2

2

3 4 Specific entropy, s (kJ/kgK)

5

6

Fig. 4. T-S diagram for the working ﬂuids considered.

Four working ﬂuids that are suitable for a binary geothermal power cycle are considered in this analysis. Ammonia is toxic with exposures of more than 500 ppm posing an immediate danger to life and health. N-Pentane is highly ﬂammable. HCFC has ozone depletion properties. PF5050 is non-toxic, non-ﬂammable and it has zero ozone depletion potential. Table 2 lists some properties of the ﬂuids considered and their T-S is shown in Fig. 4.

Objective function, γ (m2/kW)

Temperature, T (K)

450

1.6

1.2

0.8

0.4

0

500 1000 Number of simulation steps, n

1500

Fig. 6. Objective function, g, with number of simulation steps for three different initial guesses.

4. Accuracy and validation Throughout this investigation, the accuracy of the results was maintained at least to the third digit. This accuracy is believed to be sufﬁcient for most engineering applications. Numerical solution is validated with the results of Liu et al. [4] for the ideal Rankine cycle using HCFC 123 as the working ﬂuid and for the same operating conditions. The comparison shows very good agreement between present solution and the results of Liu et al. [4] as shown in Fig. 5. 5. Results and discussion A cost effective design optimization method was presented for Organic Rankine power cycle using low-

temperature geothermal heat resources. The ratio of total heat exchanger area to net power output is used as the objective function. Optimum cycle performance is evaluated and compared for working ﬂuids ammonia, HCFC123, n-Pentane and PF5050. The optimization method converges to a unique solution irrespective of the initial conditions assumed at the beginning of the simulation as shown in Fig. 6. The objective function reaches a minimum for speciﬁc values of evaporation and condensation temperatures and, geothermal and cooling water velocities. This tells us that there exits a set of optimum design parameters which gives minimum heat exchanger area per unit power output.

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706

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30 Ammonia n-Pentane HCFC 123 PF 5050

Ammonia n-Pentane HCFC 123 PF 5050

25 Efficiency / Objective function (kW/m2)

Objective function, γ(m2/kW)

3

2

1

20

15

10

5

0 40

45 50 55 Temperature difference (THWI-TCWI ) °C

60

Fig. 7. Minimum objective function, g for different working ﬂuids with operating temperature difference (T HWI T CWI ).

10

Efficiency %

9

8

7

6

45 50 55 Temperature difference (THWI-TCWI ) °C

60

Fig. 9. Ratio of Rankine cycle efﬁciency to objective function for different working ﬂuids at optimum design.

Net work / Geothermal water mass flow rate (kJ/kg)

Ammonia n-Pentane HCFC 123 PF 5050

40

Ammonia n-Pentane HCFC 123 PF 5050

2

1.5

1

0.5 40

45 50 55 Temperature difference (THWI-TCWI) °C

60

40

45 50 55 Temperature difference (THWI-TCWI) °C

60

Fig. 8. Rankine cycle efﬁciency for different working ﬂuids at optimum design.

Fig. 10. Geothermal water utilization for different working ﬂuids at optimum design.

Fig. 7 shows the inﬂuence of different working ﬂuids on the value of the optimum objective function, where the objective function is a measure of cost per unit power output. The choice of working ﬂuid can greatly affect the power plant cost; in some instances the difference could be more than twice as shown in Fig. 7. The objective function decreases with the increase of geothermal water temperature for all working ﬂuids as expected. Ammonia has less

objective function value compared to other working ﬂuids while PF5050 being the highest. The small heat exchanger area due to large heat transfer coefﬁcients in the ammonia cycle results low objective function value. Fig. 8 presents the efﬁciency of the power cycle for different working ﬂuids at the optimum design that corresponding to the minimum objective function. In general, cycle efﬁciency is low and obviously increases

ARTICLE IN PRESS H.D. Madhawa Hettiarachchi et al. / Energy 32 (2007) 1698–1706

with the increase of geothermal water temperature. Both Ammonia and PF 5050 has slightly less efﬁciency than both n-Pentane and HCFC123. The enthalpy change in the evaporator and condenser are the most important factors affecting the system efﬁciency and, the evaporation and condensation temperatures are decided by the simulation procedure. Thus the difference in thermal efﬁciency is closely related to the ﬁnal evaporation and condensation

28 26 Exergy Efficiency %

24 22 Ammonia n-Pentane HCFC 123 PF 5050

20 18 16 14 12 10 35

40

45 50 55 60 Temperature difference (THWI-TCWI) °C

65

Fig. 11. Exergy efﬁciency for different working ﬂuids at optimum design.

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temperatures and the slope of the T-S curve. Also it is interesting to note that different working ﬂuids give opposite results and trends for objective function and efﬁciency as shown in Figs. 7 and 8. In order to have a better insight about the quality of the working ﬂuid and its selection, the ratio between efﬁciency and objective function was plotted as shown in Fig. 9. According to the plot, ammonia is the most preferred selection followed by HCFC 123, n-Pentane and PF5050, respectively. Geothermal water utilization for different working ﬂuids at the optimal design is shown in Fig. 10. It increases with the increase of geothermal water temperature. Ammonia has much larger geothermal water utilization compared to other working ﬂuids. This may well due to the high overall heat transfer coefﬁcient at the evaporator that enables to extract large portion of heat from the geothermal water. Fig. 11 shows the exergy efﬁciency for different working ﬂuids at optimum design. The exergy efﬁciency decreases with the geothermal water temperature. This may due to the increase of irreversibility with increase of temperature differences across evaporator and condenser. Exergy analysis reveals the irriversibilities and shows the possibilities where improvements in efﬁciency could be made. According to Fig. 11, ammonia has much larger exergy efﬁciency than other working ﬂuids despite its low thermal efﬁciency. This tells us that the efﬁciency of the ammonia

Table 3 Numerical results for an optimized 10 MWe power plant considering geothermal water temperature of 90 C and cooling water temperature of 30 C Working ﬂuid

PF5050

HCFC 123

Ammonia

n-Pentane

Gross power W Gross (MWe) Geothermal water inlet temperature T HWI ( C) Cooling water temperature T CWI ( C) Evaporation temperature ( C) Evaporation pressure (MPa) Condensation temperature ( C) Condensation pressure (MPa) Geothermal water outlet temperature ( C) Geothermal water velocity (m/s) Cold water outlet temperature ( C) Cold water velocity (m/s) Geothermal water ﬂow rate (kg/s) Cooling water ﬂow rate (kg/s) Working ﬂuid ﬂow rate (kg/s) Net power produced (kW) Geothermal water pumping power (kW) Cooling water pumping power (kW) Working ﬂuid pumping power (kW) ðaW ÞC ðkW=m2 KÞ ðaWF ÞC ðkW=m2 KÞ U C ðkW=m2 KÞ ðaW ÞE ðkW=m2 KÞ ðaWF ÞE ðkW=m2 KÞ U E ðkW=m2 KÞ Evaporator area AE ðm2 Þ Condenser area AC ðm2 Þ Objective function g Rankine cycle efﬁciency ZR

10 90 30 80.0 0.48 41.0 0.14 85.7 0.73 35.2 0.98 8496 6598 1243 8718 395 522 365 9.9 9.9 4.4 11.7 4.21 2.87 7059 3961 1.26 7.8

10 90 30 79.9 0.49 41.6 0.16 85.0 0.96 35.5 1.21 5972 4864 669 8766 454 567 212 11.8 14.9 5.50 14.6 7.74 4.46 3766 2773 0.70 9.8

10 90 30 76.9 3.83 43.0 1.70 81.45 1.63 37.41 1.662 3693 3898 494 7766 767 842 624 15.5 131.1 9.9 21.9 90.64 11.91 1364 1377 0.35 8.9

10 90 30 80.2 0.37 40.7 0.12 86 0.77 35.7 1.2 7236 4640 294 8940 374 518 169 11.6 22.7 6.3 12.3 4.06 2.82 5660 2317 0.89 9.9

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cycle has been largely compromised in the optimization process to reach the minimum objective function than that of other working ﬂuids. Simulation results for a 10 MWe power plant operating between geothermal water temperature of 90 C and a cooling water temperature of 30 C has been given in Table 3. Optimum power cycle performance parameters at the minimum objective function are listed for the working ﬂuids considered. For PF 5050, minimum objective function yields at the evaporation and condensation temperatures of 80.0 and 41:0 C and, geothermal and cooling water velocities of 0.73 and 0:98 ms1 , respectively. Low overall heat transfer coefﬁcients at the condenser and evaporator result large heat exchanger areas which leads to larger objective function value. All cycles have similar operating pressures and temperatures except for ammonia that has much higher operating pressure which may result additional expenses in the plant design. According to Fig. 4, the slope of the saturated ammonia vapor line is negative and this implies that the ﬂuid needs to be superheated to avoid excessive moisture at the end of the expansion process in the turbine. In the case of n-Pentane and PF 5050 the saturated vapor line is regressive and in the case of HCFC the saturation vapor line almost vertical. This implies that without initial superheat, end points lie in the dry vapor region with irreversible expansion and initial super heat is not required for the working ﬂuids, Pentane, HCFC 123 and PF 5050. Further, in the case of HCFC 123, the end point superheat is less than that of the pentane and PF 5050 and less vapor stage heat rejection occurs in the condenser. Although ammonia has relatively better performance, the wet vapor at the end of the expansion and the very high evaporation pressure limits its usage in low-temperature geothermal applications. HCFC 123 and n-Pentane have better performance than PF 5050 although latter has most preferable physical and chemical characteristics compared to the other ﬂuids considered in this work. 6. Conclusions The performance of four working ﬂuids that are suitable for low-temperature geothermal binary power cycles are investigated using an optimization criterion, ratio of heat transfer area to net power produced, which is a good measure of the total power plant cost. It was shown that the simulation converges to a minimum objective function at a particular set of operating conditions. Results shows that the choice of working ﬂuid can greatly affect the power plant cost, in some instances the difference could be more than twice. Ammonia has minimum objective

function and maximum geothermal water utilization, but not necessarily maximum cycle efﬁciency. An exergy analysis reveals that the ammonia cycle efﬁciency has been largely compromised for the minimum plant cost. Ammonia is the preferred selection followed by HCFC 123, n-Pentane and PF5050, respectively, although the latter has most preferable physical and chemical characteristics. But the presence of wet vapor at the end of the expansion and very high evaporation pressure limits the use of ammonia in low-temperature geothermal applications.

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