Comparative assessment of Organic Rankine Cycle integration for low temperature geothermal heat source applications

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Energy 102 (2016) 473e490

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Comparative assessment of Organic Rankine Cycle integration for low temperature geothermal heat source applications Muhammad Imran a, b, Muhammad Usman a, b, Byung-Sik Park a, b, *, Youngmin Yang a, b a b

Energy System Engineering, Korea University of Science and Technology (UST), 217 Gajeong-ro Yuseong-gu, Daejeon, Republic of Korea Energy Efﬁciency Research Division, Korea Institute of Energy Research (KIER), 152 Gajeong-ro, Yuseong-gu, Daejeon, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 July 2015 Received in revised form 11 January 2016 Accepted 21 February 2016 Available online xxx

Present study deals with the comparative assessment of three different conﬁgurations of ORC (Organic Rankine Cycle) system including basic ORC, recuperated ORC, and regenerative ORC system for low temperature geothermal heat source. The comparison of the performance of each cycle is carried out at their optimum operating condition using Non-dominated Sorting Genetic Algorithm-II for minimum speciﬁc investment cost and maximum exergy efﬁciency under logical bounds of evaporation temperature, pinch point temperature difference and superheat. Objective functions are conﬂicting, therefore, optimization results are presented in the form of a Pareto Front Solution. Thermal efﬁciency and the exergy efﬁciency for recuperated and regenerative are higher than basic ORC but with an additional average speciﬁc investment cost of 3% for basic and 7% for regenerative cycle. Working ﬂuids with critical temperature in the same range of heat source results in better thermal performance. R245fa has highest Exergy efﬁciency of 51.3% corresponding to minimum speciﬁc cost of 2423$/kW for basic cycle, 53.74% corresponding to 2475$/kW for recuperated, and 55.93% corresponding to 2567$/kW for regenerative cycle. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Recuperated Organic Rankine Cycle Regenerative Organic Rankine Cycle Thermo-economic optimization

1. Introduction The growing concern over the environmental impact and depletion of fossil fuels have accelerated the research in the ﬁeld of clean and efﬁcient energy technologies. Effective utilization of low-grade waste heat can signiﬁcantly reduce the environmental impact and energy cost. Simple construction, high reliability, mature technology and ease of maintenance makes the ORC (Organic Rankine Cycle) system an ideal choice for low grade geothermal heat sources [1,2]. Although the basic ORC has been successfully adopted by industry, the need for efﬁciency improvements and cost reduction persist. Therefore, different conﬁgurations of ORC systems have been developed including Recuperated, Regenerative, Organic Flash Cycle, Trilateral and Supercritical Cycle, Reheater, Vapor Injector and Cascade ORC systems [3]. The current study reports a comparative assessment and optimization of the BCORC (basic ORC), RCORC (recuperated ORC) and RGORC (regenerative ORC) based on exergy efﬁciency and speciﬁc investment cost. For the ORC system using a dry working ﬂuid, the working

* Corresponding author. E-mail address: [email protected] (B.-S. Park). http://dx.doi.org/10.1016/j.energy.2016.02.119 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

ﬂuid is always in superheated state after isentropic expansion [4e6], and as a result, the load on the condenser increases. This heat can be recovered by using a heat exchanger between the expander and the condenser, known as an internal heat exchanger or recuperator ORC system. If there is no limit of temperature to which the heat source can be cooled down, there will a be negligible effect on the increase in net power of the RCORC (Recuperated Organic Rankine Cycle) system [7,8]. Therefore, an RCORC system is beneﬁcial for heat sources where the higher outlet temperature limit of the heat source exists [9,10]. Aljundi I. H. [6] investigated the effect of dry working ﬂuids and critical point temperature for RCORC system performance. Results show that the use of an internal heat exchanger lowers the required input energy in the evaporator and improve the thermal efﬁciency of the system. W. Li et al. [10] analyzed the effect of evaporation temperature in an RCORC system and concluded that the addition of an internal heat exchanger results in an increase in thermal and exergy efﬁciency. However, the net power of the system slightly decreased compared to the BCORC system. Pei Gang et al. [11] analyzed solar thermal electric generation using RCORC on the basis of thermal efﬁciency. The results show that system efﬁciency has been improved by 3.7% compared to the BCORC conﬁguration.

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Nomenclature A b Bo D Dh f G L m_ Nc n h Nu P Pr q' Q Re T t W W x HPCD LMTD VPCD

Area of Heat Exchanger, (m2) Plate Spacing, (m) Boiling Number Port Diameter, (m) Hydraulic Diameter, (m) Friction Factor Mass Velocity, (kg m2 s1) Length of Plate, m Mass Flow Rate, (kgs1) No. of Channels No. of Thermal Plates Enthalpy, (kJ kg1) Nusselt Number Pressure, (Pa) Prandtl Number Average Heat Flux, (W m2) Heat Transfer Rate, (kW) Reynolds Number Temperature, ( C) Plate Thickness, (m) Width of Plate (m) Work, (kJ) Vapor Quality Horizontal Port Center Distance, (m) Log Mean Temperature Difference, (K) Vertical Port Center Distance, (m)

The RCORC system with a zeotropic working ﬂuid has been reported in a few studies as well [12e16], but the primary focus of these studies was the investigation of zeotropic working ﬂuid potential for ORC applications. However, in the cited articles of the RCORC system, the effect on increased pressure drop on thermal performance, and extra cost of recuperator are neglected. In RGORC (Regenerative Organic Rankine Cycle) system, a fraction of working ﬂuid is extracted between two stages of expansion and used in the direct contact feed heater to preheat the working ﬂuid. The mass fraction and bleeding pressure plays a key role in the performance of RGORC system. Pedro J. Mago [17] investigated the RGORC system using four different dry ﬂuids and concluded that the RGORC has higher exergy and energy efﬁciency than the BCORC for same power output. The working ﬂuid with higher boiling point shows better thermal performance than the low point boiling point working ﬂuid. Dominik Meinel et al. [18] presented Aspen Plus simulations of exergy analysis for the RCORC and RGORC system for a waste heat source of 490 C. For isentropic ﬂuids, the exergy efﬁciency of the RGORC was 1.22% and 2.25% higher than the RCORC and BCORC respectively. However for the dry ﬂuids the exergy efﬁciency of the RGORC was 2.68% and 3.5% higher than the RCORC and basic the BCORC respectively. Nishith B. Desai et al. [19] investigated the integration of the BCORC into coupled RC and RG cycle based on the thermodynamic performance. The efﬁciency of the new cycle conﬁguration was 16.5% higher than the BCORC. Yari M. et al. [20] analyzed thermodynamic performance of the waste heat recovery from a gas turbine-modular helium reactor with three different ORC conﬁgurations including BCORC, RCORC, and RGORC. The results show that the BCORC has the highest thermodynamic performance than RCORC and RGORC. Optimization of the thermal power system often involve complex, non-linear and conﬂicting objective function. Genetic algorithm can be used for optimization of such systems to ﬁnd solutions that balance the

DT ifg k U SIC PPTD

Terminal Temperature Difference, (K) Enthalpy of Vaporization, (kJ kg1) Thermal Conductivity, (W m1 K1) Overall Heat Transfer Coefﬁcient, (W m2 K1) Speciﬁc Investment Cost, ($/kW) Pinch Point Temperature Difference, ( C)

Greek letters b Chevron Angel, ( ) r Density, (kg m3) m Viscosity, (kg s1 m1) h Efﬁciency a Convective Heat transfer Coefﬁcient, (Wm2 K1) h Efﬁciency Subscripts c Cold Side h Hot Side eq Equivalent p Plate e Effective tu Turbine r Refrigerant w Water Side sp Single Phase f Fluid Phase g Vapor Phase pu Pump

trade-offs of each objective function in a timely and cost-effective manner by a stochastic search process based on the survival of the ﬁttest solution. Table 1 shows the application of multi-objective genetic algorithm for thermal systems and ORC system. Although, basic ORC system has been successfully adopted in industry but the need of cost reduction and efﬁciency improvement still persist. A careful literature review shows that although a number of studies have been conducted for comparison of different ORC architecture based on thermodynamic performance and for speciﬁc application. However, these studies do not include the effect of individual component design except few studies. Gang Li [43] performed thermodynamic evaluation of ORC system for various cycle conﬁguration under different heat sources. Results shows that recuperated ORC and regenerative ORC have high thermal efﬁciency than basic ORC system. Although this study provides the comprehensive results for exergy efﬁciency and thermal efﬁciency but lack in the component level modeling (evaporator/condenser) and economic aspects. Dominik Meinel et al. [44] investigated the regenerative and recuperated and regenerative conﬁgurations on the basis of exergo-economic analysis. An increase of sales between 16.98 and 73.28% has been observed based on the heat source scale and working ﬂuid compared to a standard ORC. However, they also did not included component level modeling of evaporator and condenser. For comparative assessment, best available practice is to model the system at component level and compare the performance of each cycle conﬁguration based on thermal performance and cost at their optimum operating condition. In open literature, the generalize approaches for comparative assessment of various ORC architecture are based on energy balance and generally ignore the pressure drop and heat transfer characteristics of evaporator and condenser. The efﬁciency of the ORC depends on the heat source

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Table 1 Review of application of Genetic Algorithm in thermal power systems. No.

Description

Objective function

Genetic algorithm Variable

[21] [22] [23] [24] [25] [26] [27]

Radial Turbine of ORC System Evaporator of Basic ORC System Condenser of ORC System Working Fluids for ORC Combined CHP System Flash-binary geothermal System Transcritical CO2 System

[28] [29]

Biomass-ﬁred Kalina cycle System Transcritical CO2 System

[30] [31] [32] [33]

Building CHP System Kalina Split-cycle System Air Bottoming Cycle System Large Ship Emission & Fuel Consumption optimization Integrated Multigeneration System Cogeneration Plant System Combined Cycle Power Plant Gas Turbine Power Plant Basic ORC System Basic ORC System Basic ORC System Basic ORC System Regenerative ORC System

[34] [35] [36] [37] [38] [39] [40] [41] [42]

Turbine Efﬁciency Total Cost & Pressure Drop Heat Transfer Area & Pressure Drop Net Power Output Power & Heat Transfer Area Exergy Efﬁciency Exergy Efﬁciency & Heat Exchange Area per net power output Net Power & System Efﬁciency Cost per net power & Ratio of heat exchangers cost to system's cost Net Efﬁciency Thermal Efﬁciency Net Power, Net present value & Total Volume Fuel Consumption & Emissions (NOx) Exergy Efﬁciency & Cost Rate Total Cost Rate Exergy Efﬁciency, Total Cost Rate & CO2 emission Exergy Efﬁciency & Total Cost Rate Ratio of output power to total heat transfer area Exergy Efﬁciency & Total Cost Thermal Efﬁciency Thermal Efﬁciency, Net present value & Total Volume Thermal Efﬁciency & Investment Cost

and heat sink conditions. Since these conditions are governed by the available heat source and environmental conditions. Therefore, the efﬁciency of power cycle depends on how effectively the heat is recovered in evaporator and how efﬁciently it is rejected into the condenser. Therefore, evaporator and condenser of an ORC system plays an important role in terms of system performance and cost of the system. In order to analyze the evaporator pressure drop and estimation of heat transfer area with reasonable accuracy, a detailed model of evaporator and condenser have been added in the study. In the present study a detailed design of evaporator and condenser is presented followed by the comparison of ORC architecture based on speciﬁc investment cost and exergy efﬁciency at their optimum operating condition. The concept of the speciﬁc investment cost (ratio of total cost to net power) and exergy efﬁciency can fairly provide the reasonable justiﬁcation for the comparison of the BCORC, RCORC and RGORC under same source and sink conditions. Comparative assessment for the current study is carried using multi objective genetic algorithm. The main objectives of the study are as. Development of the thermal and hydraulic design model of the plate heat exchanger, as they are widely used as evaporator and condenser due to the compact size and the efﬁcient heat transfer. Comparative assessment of BCORC, RCORC and RGORC under same source and sink conditions at the optimum operating condition based on individual component design. Analyze and investigate the effect of the evaporation temperature, superheat, and pinch point temperature difference on the exergy efﬁciency and speciﬁc investment cost of each ORC system conﬁgurations. The result of this study will be helpful for selection of suitable cycle conﬁguration based on trade-off between exergy efﬁciency and speciﬁc investment cost. The study include the detail design and of the evaporator and the condenser and thus will provide a

Type

9 3 3 6 4 5 3

Single Multi Multi Single Multi Single Multi

5 5

Multi Multi

3 9 10 9

Single Single Multi Multi

7 5 11 5 4 5 5 12 4

Multi Single Multi Multi Single Multi Single Multi Multi

better insight than conventional thermodynamic and parametric optimization studies.

2. System description ORC system consists of four major components, evaporator, expander, condenser, and pump. The low boiling point organic working ﬂuid recovers the low grade/waste heat in the evaporator. High pressure vapors from the evaporator expand through the turbine and generate power. The low pressure vapors from the expander condense to saturated liquid in the condenser and ﬁnally the working ﬂuid is pumped back to the evaporator and cycle repeats again. The basic schematic and Tes diagram of ORC system is shown in Fig. 1. Working ﬂuid selection is considered as an important part of the design and optimization of an ORC system since the properties of the working ﬂuid affect efﬁciency of system, design and size of the system components, system stability and safety, and environmental impact [45]. During last few years, extensive research had been conducted for selection methodologies and operating characteristics of working ﬂuids for various ORC applications [46e48]. However, only few working ﬂuids are used in commercial ORC applications. Table 2 shows the list of some of famous and well known ORC system manufacturers, their working ﬂuid, and heat source temperature. For low temperatures, R134a, for mid-range temperatures, R245fa, and temperature of heat source, OMTS, pentane, and toluene are preferred. We have selected R245fa, R600, R600a, SES36, R601a, and R601 as working ﬂuid on the basis of their commercial use in ORC units, heat source temperature (in our case 160 C), and safety/environmental impact. Properties of working ﬂuids are shown in Table 3 and the temperature-entropy diagram of these working ﬂuids is shown in Fig. 2. The heat source is a low temperature geothermal heat source with the temperature of 160 C and mass ﬂow rate of 5 kg s1 outlet temperature of the heat source is restricted to 70 C to avoid the

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Fig. 1. Schematic &Tes diagram of ORC system.

Table 2 ORC manufacturers and their system conﬁguration [49]. Manufacturer

Working ﬂuid

Heat source temperature

Atlas Copco Adoratec GmbH/Maxxtec AG Bosch KWK GmbH Calnetix Technologies LLC Conpower Cryostar SAS (Linde Group) Cryotec Anlagenbau GmbH Dürr Cyplan DeVeTec GmbH ElectraTherm Inc. Eneftech Innovation SA E-Rational Exergy (Maccaferri Industrial Group) Freepower GE Clean Cycle GMK (Germany) Inﬁnity Turbine LLC LTi Reenergy Opcon Orcan Energy GmbH Ormat Technologies Inc. PureCycle TAS Energy Tri-o-gen Turboden

Hydrocarbons OMTS R-245fa R-245fa SES36 R-245fa, R-134a OMTS, Hydrocarbons Hydrocarbons Ethanol R-245fa R-245fa R-245fa, SES36 Pentane, Isopentane, Hydrocarbons R-245fa GL160 (patented) R-134a, R-245fa N/A Ammonia N/A n-pentane R-245fa R-134a, R-234fa, R-245fa Toluene OMTS, Solkatherm

200e300 C 320 C >140 C >95 C >85 C N/A 120 C 90e1000 C 300e600 C 77e116 C 125e200 C 80e150 C 90e300 C N/A >155 C <300 C 80e140 C >160 55e250 C, >250 C N/A 150e300 91 Ce149 C 97e260 C >350 C 100e300 C

silica deposition [50]. Heat source and heat sink conditions of the ORC system are shown in Table 4. 3. System design For the complete ORC system modeling, an independent model of each component, evaporator, condenser, expander and the

working ﬂuid pump are developed in MATLAB. Their inputs and outputs are connected to develop the single ORC model, consisting of two parts, exergy efﬁciency model, and speciﬁc investment cost model. The ORC model is further optimized using the multi objective genetic algorithm in MATLAB optimization environment. The results of each conﬁguration of the ORC system are compared at the optimum operating point. The detailed layout of the complete model is presented in Fig. 3.

Table 3 Properties of working ﬂuids. Working ﬂuid

Molar mass

Critical pressure

Critical temperature

R-600a R-600 R-245fa SES-36 R-601a R-601

58.12 kg/Kmol 58.12 kg/Kmol 134.05 kg/Kmol 184.5 kg/Kmol 72.15 kg/Kmol 72.15 kg/Kmol

3.64 3.79 3.61 2.85 3.37 3.36

135 152 154 177 187 196

MPa MPa MPa MPa MPa MPa

3.1. Evaporator model

C C C C C C

The evaporator is divided into three sections, the single phase liquid section, two phase liquid þ vapor section, and the single phase vapor section. Each section is designed under the given operating conditions based on the LMTD (log mean temperature difference method). The total area of the evaporator is

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477

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u 2 3 u 8sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ9 bp u < t Pco 7 16 bp 2 = 7 1 þ 1 þ F¼ 6 þ 4 1 þ : 64 Pco ; 2 5 2

(6)

The mass velocity of each side of the heat exchanger

G¼

m_ =N c

Channel Mass Flow Rate ¼ Channel Cross Sectional Area ðb We Þ

(7)

Nc is number of channels, for the even number of thermal plates, no. of channels are as

ðNc Þcold ¼ ðNc Þhot ¼

n 2

(8)

For odd number of thermal plates, no. of channels are as

ðNc Þcold ¼ Fig. 2. Tes Diagram of working ﬂuids under investigation.

nþ1 n1 ; ðNc Þhot ¼ 2 2

(9)

The Reynolds number is given by

Table 4 Operating conditions of the orc system. Parameter

Value

Parameter

Value

Heat Source, Inlet Temperature Heat Source, Inlet Pressure Heat Source, Mass Flow Rate Isentropic Efﬁciency of Turbine

160 C 3.5 bar 5 kg s1 75%

Condensing Temperature Pinch point Temperature, Evaporator Pinch point Temperature, Condenser Isentropic Efﬁciency of Pump

25 C 08 C 08 C 60%

A ¼ ðnÞ Ap

(1)

The total number of thermal plates are known, the plate length for each section is calculated by log mean temperature approach, the calculation process is an iterative and generalized layout of the design is presented in Fig. 4. Initially, the length of the plate is assumed and required plate length is recalculated based on the required amount of heat transfer, log mean temperature difference and overall heat transfer coefﬁcient. The iterative process continues until the assumed length is equal to the recalculated length. 3.1.1. Geometry The chevron plate proﬁle of plate heat exchanger provide a high degree of turbulence which results in a high heat transfer and makes plate heat exchanger an ideal choice as evaporator and condenser. The geometrical conﬁguration of the chevron type plate heat exchanger is presented in Table 5 and Fig. 5. The effective length and the width of the plate heat exchanger is given by

Le ¼ VPCD D

(2)

We ¼ HPCD þ D þ 0:015

(3)

Area of the single thermal plate is given by

AP ¼ We Le

(4)

The hydraulic diameter [51] of the plate heat exchanger

4 Channel flow area Wetted perimeter 4 ðb We Þ 2b whereas y ¼ 2 ðWe FÞ F

Re ¼

G Dh m

(10)

3.1.2. Single phase The heat transfer in the single phase section of the heat exchanger is given by

Q sp ¼ m_ h ðh5e h6 Þ

(11)

Log mean temperature difference for single phase is given by

LMTDsp ¼

ðT5e Tev Þ ðT6 T1 Þ

Tev Þ log ðTðT5e6 T 1Þ

(12)

The overall heat transfer of single phase section of the heat exchanger is calculated as

tp 1 1 1 ¼ þ þ Usp aw kp ar;sp

(13)

The single phase Nusselt No. correlation for water in the plate heat exchange is given by Ref. [52].

Nuw ¼ 0:724

6b 0:646 0:583 0:33 Re Pr p

(14)

The single phase heat transfer for R245fa in the plate heat exchanger [53].

Dh ¼

b < < We

The enlargement factor [51] is given by

(5)

kf mm 0:14 Re0:78 Pr 0:33 ar;sp ¼ 0:2092 Dh mwall

(15)

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Fig. 4. Layout of design procedure of plate heat exchangers.

Fig. 3. Detailed layout of the optimization approach.

Table 5 Geometry of plate heat exchanger.

For single phase section of the evaporator, the pressure drop for both cold and hot side consist of only frictional pressure drop. The pressure drop due to the elevation and port pressure loss are neglected.

DP ¼

4fNcG2 L 2rDh

(16)

The single phase frictional pressure drop factor for both the cold and the hot side is [54].

f¼

0:572 Re0:217

(17)

The length of the thermal plate for the single phase liquid section and the single phase vapor section

Parameter

Value

Effective Width (We) Corrugated Pitch (Pco) Plate Spacing (b) Plate Thickness (t) Chevron Angel (b)

0.650 m 0.0085 m 0.0025 m 0.0005 m 60 Degree

are assumed constant and the variation in temperature difference is linear. The discretized proﬁle of the two phase section of evaporator is shown in Fig. 6. The heat balance of the two phase region is given by

Q tp;i ¼ m_ r hf ;iþ1 hf ;i ¼ m_ w hw;iþ1 hw;i

(19)

The log mean temperature difference for each section is given by

Lsp;f ¼ Lsp;g ¼

Usp;f

Q sp;f ; LMTDsp;f We n

Usp;g

Q sp;g LMTDsp;g We n

(18)

LMTDtp;i ¼

Tw;iþ1 Tr;iþ1 Tw;i Tr;i # " ðT Tr;iþ1 Þ log w;iþ1 ðTw;i Tr;i Þ

(20)

The two phase overall heat transfer coefﬁcient for a single discretized section is given 3.1.3. Two phase The two phase section of the evaporator is discretized and divided into N parts. The thermodynamic properties in each part

tp 1 1 1 ¼ þ þ Ui aw;i kp ar;i

(21)

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The equivalent Reynolds number and the boiling number is given by

Reeq;i

2 !0:5 3 rf Geq Dh q” 5 ¼ ; Boeq;i ¼ ; Geq ¼ G41 x þ x mf Geq ifg rg (24)

While two phase frictional factor is given by Ref. [55]. G

fi ¼ Ge3;i Reeqe4;i

(25)

where as

5:27 3:03 Pco p b ; 2 Dh 0:62 0:47 Pco p b ¼ 1:314 2 Dh

Ge3;i ¼ 64710 Ge4;i

(26)

The heat transfer coefﬁcient of water side [54].

Nuw ¼ 0:724

The convective heat transfer coefﬁcient of the evaporation for R245fa in plate heat exchanger [55]. G

Ge1;i Ge2;i

DPf ¼

4fNcG2 Le 2rDh

(28)

The pressure drop due to the acceleration can be calculated by the relation

(22)

where as

0:041 2:83 Pco p b ¼ 2:81 ; 2 Dh 0:082 0:61 Pco p b ¼ 2:81 2 Dh

(27)

The pressure drop in the two phase region consists of four major components; pressure drop due to the acceleration of the refrigerant, due to the change in elevation, due to inlet/exit manifolds, and due to friction inside the corrugated plate heat exchanger. The frictional pressure drop inside the plate heat exchanger can be expressed as

Fig. 5. Geometrical proﬁle of plate heat exchanger.

0:4 Nui ¼ Ge1;i Reeqe2;i Bo0:3 eq Pr

6b 0:646 0:583 0:33 Re Pr p

DPac ¼ G2r x vg vf

(29)

Where as Gr is channel ﬂow area and can be calculated as

(23)

Gr ¼

mr b Nc We

Fig. 6. Temperature proﬁle of two phase section of evaporator.

(30)

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The change in the pressure due to the elevation can be estimated as

DPelev ¼ g rm Le

(31)

foff fd

(32)

Based on this equation, the inlet pressure under the off design condition is given by

The port pressure drop is given by

DPport ¼

1:5 G2r vm 2

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ " #2 u u . u1 P u out; off P u in; off ¼u " #2 u u

t1 P out; d P in; d

The plate length for the two phase section of evaporator is

Pn Ltp ¼ Pn i

Utp;i

Pn i

i

Qtp;i

LMTDtp;i We n

Pin; off ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m_ 2f ;of Tin; off Yd þ P2out;off

(41)

(33) whereas

Finally, the total length of the thermal plate of the heat exchanger is given by

Le ¼ Lsp;f þ Ltp þ Lsp;g

(40)

(34)

Yd ¼

P2in;d P2out;d

(42)

P2in;d f2d

The expander model is based on isentropic efﬁciency of 70%. 3.2. Condenser model 3.4. Pump model The condenser model is exactly similar to the evaporator model, except the heat transfer and pressure drop correlations. The single phase transfer and pressure drop correlations for the working ﬂuid are same as for evaporator while for R245fa condensation heat transfer coefﬁcient in plate heat exchanger is given by relation [56]. 0:3 0:4 6 Nu ¼ Ge5 ReGe eq Boeq Pr

(35)

(36)

(37)

whereas

7:75 Pco 4:17 p b ; 2 Dh 0:0925 1:3 Pco p b Ge8 ¼ 1:024 2 Dh

Ge7 ¼ 3521:1

(38)

By combining above equations

(44)

The pump model is based on the isentropic efﬁciency of 60%.

4.1. Basic Organic Rankine Cycle (BCORC) The schematic and Tes diagram of the basic ORC system is shown in Fig. 7. The system consists of an evaporator, turbine, condenser and pump. The working ﬂuid receives heat from the heat source at the constant pressure process from 1 to 2 and these high pressure vapors expand in the turbine during process 2 to 3 and power is produced. Working ﬂuid is condensed in the condenser and reject heat at constant pressure during process 3 to 4 and ﬁnally pumped back in the evaporator during process 4 to 1. Net power output of the basic ORC system is given by

Wn ¼ Wt Wp 3.3. Expander model

foff

And

(45)

The exergy efﬁciency of basic ORC is given by

"

Expander model is based on Stodola's ellipse approach [57], the inlet pressure depends on ﬂow characteristics and is given by

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Tin; off ¼ m_ f ;off Pin; off

(43)

4. Thermodynamic modeling

Two phase frictional factor for the condensation pressure drop is given by Ref. [56]. 8 f ¼ Ge7 ReGe eq

RPMoff Hoff RPMoff 2 m_ f ;off ¼ and ¼ RPMd Hd RPMd m_ f ;d

" #2 Hoff m_ f ;off ¼ Hd m_ f ;d

whereas

0:041 4:5 Pco p b Ge5 ¼ 11:22 ; 2 Dh 0:23 1:48 Pco p b Ge2 ¼ 0:35 2 Dh

The pump model is based on the system hydraulic characteristics and the pump afﬁnity law. According to pump afﬁnity law,

hex ¼ (39)

# ½h1 h6 hpu

½htu ½h2 h4 Wn ¼ ½ð25 26 Þ ð22 21 Þ εe

(46)

Where the 2 is the exergy destruction of component i of ORC system and is given by

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Fig. 7. Schematic & Tes diagram of basic ORC system [43].

εi ¼ εPhy ¼ ðh ho Þ To ðS So Þ

(47)

Where To is the reference temperature for exergy calculation. The reference temperature and pressure for the current study are taken as 20 C and 101.325 kPa respectively.

" ½htu ½h2 h4 hex ¼

# ½h1 h6 hpu

½ð27 28 Þ ð23 21 Þ þ ½ð25 26 Þ ð210 29 Þ (49)

4.3. Regenerative Organic Rankine Cycle (RGORC) 4.2. Recuperated Organic Rankine Cycle (RCORC) The dry and isentropic working ﬂuids have a considerable amount of exergy after expansion through the turbine which can be recovered with a recuperator and result in an increase of thermal efﬁciency of ORC system. The schematic and Tes diagram of recuperated cycle is shown in Fig. 8. Net power output of the recuperated ORC system is given by

Wn ¼ Wt Wp

In regenerative ORC system, the working ﬂuid is extracted between the two stages of expansion and used as a feed heater before the evaporator. The schematic and Tes diagram of working ﬂuid for single stage regenerative ORC system is shown in Fig. 9. Net power output of the regenerative ORC system is

Wn ¼ Wt Wp

(48)

(50)

The exergy efﬁciency of the regenerative ORC is given by

The exergy efﬁciency of recuperated ORC is given by

hex ¼

htu ½ðh4 h5 Þ þ ðð1 x1 Þðh5 h6 ÞÞ h1 ½ðh3 h2 Þ þ ð1 x1 Þðh1 h7 Þ pu

½ð28 29 Þ ð24 22 Þ þ ½ð26 27 Þ ð211 210 Þ

Fig. 8. Schematic & Tes diagram of recuperated ORC system [43].

(51)

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Fig. 9. Schematic & Tes diagram of regenerative ORC system [43].

5. Economics modeling The bare module cost method is one of the reasonable cost estimation approaches for power plant equipment [58] and has been used for cost estimation of ORC system as well [59,60]. The cost of the evaporator and the condenser is given by

CHX ¼

(52) where FS is an additional factor for the overhead cost, B1,HX and B2,HX are constants for the heat exchanger type and FM,HX is the additional material factor for heat exchanger, in this case stainless steel. The HX is the basic FP,HX is the pressure factor for heat exchanger and C cost of the heat exchanger made from stainless steel The basic cost of heat exchanger is given by in terms of heat transfer area 2 ¼ K logC HX 1;HX þ K2;HX ðlog AHX Þ þ K3;HX ðlog AHX Þ

o

(53)

where K1,HX, K2,HX, K3,HX are constants for the heat exchanger type. The pressure factor for the heat exchanger is given by

n

log FP;HX ¼ C1;HX þ C2;HX ðlog PHX Þ þ C3;HX ðlog PHX Þ2

o

(54)

where C1,HX, C2,HX, C3,HX are constant for the heat exchanger type. The total cost of the pump is given by the relation

CPP ¼

527:7 B FS C PP 1;PP þ B2;PP FM;PP FP;PP 397 (55)

where B1,PP and B2,PP are constants for the pump type and FM,PP is the additional material factor, FP,HX is the pressure factor for pump HX is the basic cost of the pump. The basic cost of pump is and C given by in terms of pump power

o n 2 ¼ K logC PP 1;PP þ K2;PP ðlog WPP Þ þ K3;PP ðlog WPP Þ

(56)

where K1,PP, K2,PP, K3,PP are constants for pump type. The pressure factor for the pump is given by

o n log FP;PP ¼ C1;PP þ C2;PP ðlog PPP Þ þ C3;PP ðlog PPP Þ2

527:7 F FS C TR M;TR 397

(58)

HX is where FM,TR is pressure & material factor for the turbine and C the basic cost of the turbine, given by

o n 2 ¼ K logC TR 1;TR þ K2;TR ðlog WTR Þ þ K3;TR ðlog WTR Þ

527:7 B FS C HX 1;HX þ B2;HX FM;HX FP;HX 397

n

CTR ¼

(57)

where C1,PP, C2,PP, C3,PP are constant for pump type. The cost of the turbine is given by the relation

(59)

where K1,TR, K2,TR, K3,TR are constants for turbine type. The cost of the feed heater is given by the relation

CFH ¼

527:7 B FS C FH 1;FH þ B2;FH FM;FH FP;FH 397 (60)

where B1,FH and B2,FH are constants for the feed heater type and FM,PP is the additional material factor, FP,HX is the pressure factor for HX is the basic cost of the feed feed U-tube type feed heater and C heater. The basic cost of the feed heater is given in terms of its heat transfer area

o n 2 ¼ K logC FH 1;FH þ K2;FH ðlog AFH Þ þ K3;PP ðlog AFH Þ

(61)

where K1,FH, K2,FH, K3,FH are constants for feed heater type. The pressure factor for the feed heater is given by the relation

o n log FP;FH ¼ C1;FH þ C2;FH ðlog PFH Þ þ C3;FH ðlog PFH Þ2

(62)

where C1,FH, C2,FH, C3,FH are constant for feed heater type. The value of constants for economic analysis is shown in Table 6. The speciﬁc investment cost of each conﬁguration is calculated as Table 6 Constants for cost estimation of individual component of ORC system. Constant

Value

Constant

Value

Constant

Value

FS B1,HX B2,HX FM,HX K1,HX FM,TR K1,TR K2,TR K3,TR K2,FH C2,FH

1.70000 1.63000 1.66000 2.40000 4.66560 3.70000 2.24760 1.49650 0.1618 0.3030 0.0263

K2,HX K3,HX C1,HX C2,HX C3,HX B1,FH B2,FH FM,FH K1,FH K3,PP C3,FH

0.1618 0.1517 0.1250 0.15361 0.0286 1.74000 1.55000 1.70000 4.32470 0.16340 0.01230

B1,PP B2,PP FM,PP K1,PP K2,PP K3,PP C1,PP C2,PP C3,PP C1,FH

1.89000 1.35000 2.05000 3.38920 0.05360 0.15380 0.39350 0.39570 0.00226 0.40161

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Table 8 Genetic algorithm parameters.

Total Cost of ORC System Specific Investment Cost ¼ SIC ¼ Net Psower of ORC Sysetm TC ¼ Wn (63)

NSGA-II Parameters

Values

Objective Function Tolerance Cross Over Fraction Mutation Fraction Selection Method

0.00001 0.70 0.06 Tournament

The total cost of components is sum of individuals cost of components

TC ¼ CHX;EV þ CTR þ CHX;CO þ CPP þ CFH

(64)

These values of the constants for cost estimation are valid for the speciﬁc size, operating condition and material as presented in Table 7.

6. Exergo-economic optimization Each ORC conﬁguration is optimized for the maximum exergy efﬁciency and the minimum speciﬁc investment cost under the logical bound of the pinch point temperature difference, evaporation temperature and superheat. The heat source inlet condition is ﬁxed, so the mass ﬂow rate of working ﬂuid is controlled by evaporation pressure and superheat.

6.1. Multi objective optimization Evolutionary algorithms are ideal optimization approach for non-linear and complex objective functions of thermal power systems. Evolutionary algorithms are stochastic search methods based on the natural biological evaluation. There are ﬁve major evolutionary algorithm including PSO (particle swarm optimization), BBO (biogeography based optimization), GA (genetic algorithm), ICA (imperialist competitive algorithm), and FFA (ﬁreﬂy optimization algorithm). PSO is based on bird ﬂocking or ﬁsh schooling, BBO based on biogeography, GA based on survival of ﬁttest, ICA based on socio-political behaviors, and FFA based on ﬁreﬂies. Lower computational time, avoid local mini/max, and provide better quality results compared to PSO, BBO, ICA and FFA. Therefore, in the present study optimization is performed using NSGA-II (Non-dominated Sorting Genetic Algorithm-II) in MATLAB optimization environment. The parameters of the multi objective genetic algorithm are shown in Table 8. The genetic algorithm is based on the principal of survival of the ﬁttest. From given range of operating conditions, the objective functions are evaluated for the ﬁrst iteration. For the next iteration, decision variables that have higher values of objective function are chosen. The process evolves towards the optimum solution while the decision variables are improved by using the crossover and the mutation operators of the genetic algorithm. The iterative process continues until there is no further change in the objective functions. The detailed layout of the multi objective genetic algorithm is presented in Fig. 10. The mathematical expression of the objective functions and corresponding

Fig. 10. Layout of multi objective genetic algorithm.

limits and bounds for the each ORC system are presented below. For basic ORC system

"

Maximizeðhex Þ¼

½h1 h6 ½htu ½h2 h4 hpu

#

½ð25 26 Þð22 21 Þþ½ð23 24 Þð28 7Þ CHX;EV þCTR þCHX;CO þCPP # MinimizeðSICÞ¼ " fh1 h4 g _ mr htu fh2 h3 g hpu (65) Subjected to

40 C Tev 145 C; 0 Superheat 15 C 3 C PPTDev 15 C; 3 C PPTDco 15 C

(66)

For recuperated ORC system,

Table 7 Operating Conditions range for estimation of plant equipment. Equipment

Type

Size range

Pressure ranger

Material

Feed Pump Expander Evaporator Condenser Feed Heater

Centrifugal Radial Gas Turbine Plate Heat Exchanger Plate Heat Exchanger U tube type

1e300 kW 100e1500 kW 10e1000 m2 10e1000 m2 10e1000 m2

10 < P < 100 bar e 10 < P < 40 bar 5 < P < 40 bar 10 < P < 40 bar

SS CS SS316 SS316 CS

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½htu ½h2 h4 Maximize ðhex Þ ¼

" # ½h1 h6 hpu

½ð27 28 Þ ð23 21 Þ þ ½ð25 26 Þ ð210 29 Þ CHX;EV þ CTR þ CHX;CO þ CPP þ CFH " # Minimize ðSICÞ ¼ fh h6 g m_ r htu fh2 h4 g 1 hpu

Subjected to

(67)

7. Results and discussion

40 C Tev 145 C; 0 Superheat 15 C 3 C PPTDev 15 C; 3 C PPTDco 15 C

(68)

For regenerative ORC system,

The objective functions are conﬂicting and a single value of the decision variables cannot satisfy both the objective functions simultaneously. Therefore, optimization result of basic, recuperated, and regenerative ORC system are presented in the form of

1 ½ðh h2 Þ þ ð1 x1 Þðh1 h7 Þ hpu 3 ½ð28 29 Þ ð24 22 Þ þ ½ð26 27 Þ ð211 210 Þ CHX;EV þ CTR þ CHX;CO þ CPP þ CFH

htu ½ðh4 h5 Þ þ ðð1 x1 Þðh5 h6 ÞÞ Maximize ðhex Þ ¼ Minimize ðSICÞ ¼

"

m_ r htu ½ðh4 h5 Þ þ ðð1 x1 Þðh5 h6 ÞÞ

1 ½ðh h2 Þ þ ð1 x1 Þðh1 h7 Þ hpu 3

Subjected to

40 C Tev 145 C; 0 Superheat 15 C 3 C PPTDev 15 C; 3 C PPTDco 15 C

(70)

(69) #

Pareto Front solution, as shown in Fig. 11. For exergy efﬁciency lower than 45%, at the same value of exergy efﬁciency, the regenerative ORC system has the highest speciﬁc investment cost and basic ORC system has lowest speciﬁc investment cost. While for exergy efﬁciency higher than 45%, at same value of speciﬁc investment cost, regenerative ORC system has highest value of the exergy efﬁciency and basic ORC has lowest value. For current study, empirical correlation of speciﬁc investment cost of basic, recuperated and regenerative ORC system have

Fig. 11. Pareto Front solution of basic, recuperated and regenerative orc system.

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Table 9 Optimization results for basic Organic Rankine Cycle. Optimum Value of operating Parameters

Turbine Inlet Pressure (bar) Exergy Efﬁciency (%) Thermal Efﬁciency (%) Net Power Output (kW) Evaporator Design Parameter UAe(W/K) Condenser Design Parameter UAc(W/K) Speciﬁc Investment Cost ($/kW) PPTD Evaporator ( C) PPTD Condenser ( C)

Working ﬂuids R600a

R600

R245fa

SES36

R601a

R601

18.56 46.23 9.87 70.25 10887 22487 2702 16.45 10.25

17.48 49.17 10.62 72.58 9845 21054 2616 15.24 11.25

16.96 51.23 11.62 79.77 9452 19357 2423 13.38 9.64

10.17 47.25 10.42 74.52 8078 21758 2558 14.83 9.89

9.82 45.84 9.72 68.45 7415 19847 2583 14.05 12.42

7.54 44.39 9.02 67.36 7381 18347 2707 13.92 12.58

Table 10 Optimization results for recuperated Organic Rankine Cycle. Optimum Value of operating Parameters

Turbine Inlet Pressure (bar) Exergy Efﬁciency (%) Thermal Efﬁciency (%) Net Power Output (kW) Evaporator Design Parameter UAe(W/K) Condenser Design Parameter UAc(W/K) Recuperator Design Parameter UArec(W/K) Speciﬁc Investment Cost ($/kW) PPTD Evaporator ( C) PPTD Condenser ( C)

Working ﬂuids R600a

R600

R245fa

SES36

R601a

R601

19.74 48.33 10.64 68.69 9745 18697 5842 2791 15.24 9.87

18.89 51.86 11.71 68.34 8419 18974 4874 2687 14.83 10.63

17.98 53.74 12.42 75.22 8764 17684 3759 2475 12.47 9.24

11.58 49.80 11.53 69.98 8645 17245 4268 2614 13.67 8.97

10.27 47.81 10.64 66.58 7808 17672 4710 2667 13.57 11.63

8.53 46.10 9.93 65.87 7693 16874 4337 2798 13.08 11.41

Table 11 Optimization results for single stage regenerative Organic Rankine Cycle. Optimum Value of operating Parameters

Turbine Inlet Pressure (bar) Exergy Efﬁciency (%) Thermal Efﬁciency (%) Net Power Output (kW) Evaporator Design Parameter UAe(W/K) Condenser Design Parameter UAc(W/K) Speciﬁc Investment Cost ($/kW) PPTD Evaporator ( C) PPTD Condenser ( C) Mass Fraction Ratio

Working ﬂuids R600a

R600

R245fa

SES36

R601a

R601

20.51 50.15 11.36 61.89 8746 19426 2911 13.25 9.57 0.21

19.45 54.22 13.81 63.71 7691 18746 2804 12.68 9.75 0.28

18.74 55.93 14.02 69.42 7349 17983 2567 10.74 9.05 0.25

12.69 52.04 12.07 64.17 6475 17468 2718 11.36 8.85 0.21

11.01 49.52 11.16 60.38 6169 16879 2778 12.63 10.55 0.18

9.24 47.58 10.57 60.74 5987 16548 2744 12.91 10.19 0.23

been developed based on the value of exergy efﬁciency. For basic ORC System

SIC

$ kW

¼ 0:0372h5ex 7:0184h4ex þ 526:68h3ex 19659h2ex

(71) For recuperated ORC system,

$ kW

$ kW

¼ 0:0191h5ex 3:78h4ex þ 298:03h3ex 11668h2ex þ 226868hex 2 106

þ 364943hex 3 106

SIC

SIC

¼ 0:029h5ex 5:63h4ex þ 434:23h3ex 16646h2ex þ 316964hex 2 106 (72)

For regenerative ORC system,

(73) The optimum values of the exergy efﬁciency and the speciﬁc investment cost were chosen from pareto front solution based on restriction of exergy efﬁciency higher than 40% and speciﬁc investment cost lower than 3000 $/kW. The selected optimization results for the basic ORC system, recuperated ORC system and regenerated ORC system for the four different working ﬂuids are shown in Tables 9e11 respectively. The use of the recuperator in the basic ORC system results in an increase in the thermal efﬁciency and exergy efﬁciency, but the net power is decreased by 7e10%. The decrease in net power is associated with decrease in low mass ﬂow rate for high pressure in working ﬂuid due to restriction in exit temperature of heat source. However, the proﬁle matching between heat source and working ﬂuid in the evaporator results in the increase in exergy efﬁciency.

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Table 12 Comparison of the optimization results under present conditions. Cycle Parameters

Basic ORC system

Difference (%)

Present study

Ref. [61]

Exergy Efﬁciency (%) Thermal Efﬁciency (%) Net Power Output (kW) Evaporator Design Parameter UAe(W/K) Condenser Design Parameter UAc(W/K) Speciﬁc Investment Cost ($/kW)

47.18 10.88 79.77 9452 19357 2360

45.36 10.42 76.84 8909 20714 2473

Cycle Parameters

Recuperated ORC System Present Study

Ref. [61]

44.66 11.53 75.22 8764 17684 3759 2565

42.09 11.65 73.26 8367 16574 4041 2608

Exergy Efﬁciency (%) Thermal Efﬁciency (%) Net Power Output (kW) Evaporator Design Parameter UAe(W/K) Condenser Design Parameter UAc(W/K) Recuperator Design Parameter UAr(W/K) Speciﬁc Investment Cost ($/kW)

3.86% 4.23% 3.67% 5.74% 7.01% 4.79% Difference (%) 5.75% 1.04% 2.61% 4.53% 6.28% 7.50% 5.75%

Table 13 Pareto Front Solution: maximum exergy efﬁciency and maximum net power. Cycle

BCORC

Objective function

Case 1

Case 2

RCORC

Case 1

Case 2

RGORC

Case 1

Case 2

Optimum Value of Operating Parameters

Working ﬂuids R600a

R600

R245fa

SES36

R601a

R601

Exergy Efﬁciency (%) Net Power Output (kW) Speciﬁc Investment Cost Exergy Efﬁciency (%) Net Power Output (kW) Speciﬁc Investment Cost Exergy Efﬁciency (%) Net Power Output (kW) Speciﬁc Investment Cost Exergy Efﬁciency (%) Net Power Output (kW) Speciﬁc Investment Cost Exergy Efﬁciency (%) Net Power Output (kW) Speciﬁc Investment Cost Exergy Efﬁciency (%) Net Power Output (kW) Speciﬁc Investment Cost

46.23 70.25 2702 40.04 72.51 2641 48.33 68.69 2791 42.44 70.70 2733 50.15 61.89 2911 44.60 63.46 2856

49.17 72.58 2616 48.62 75.55 2541 51.86 68.34 2687 51.33 70.88 2617 54.22 63.71 2804 53.72 65.77 2737

51.23 79.77 2423 45.65 83.69 2340 53.74 75.22 2475 48.42 78.58 2399 55.93 69.42 2567 50.90 72.11 2494

47.25 74.52 2558 41.96 77.77 2480 49.80 69.98 2614 44.73 72.76 2542 52.04 64.17 2718 47.23 66.38 2649

45.84 68.45 2583 45.24 71.00 2516 47.81 66.58 2667 47.25 68.84 2604 49.52 60.38 2778 48.99 62.16 2718

44.39 67.36 2707 43.75 69.72 2641 46.10 65.87 2798 45.50 67.97 2641 47.58 60.74 2744 47.01 62.42 2688

($/kW)

($/kW)

($/kW)

($/kW)

($/kW)

($/kW)

The integration of BCORC into RCORC results in an increase in thermal efﬁciency of 6e9%, exergy efﬁciency 3e5% with an additional cost of 2e3% depending on the working ﬂuid. The integration of BCORC into RGORC results in an increase in thermal efﬁciency by 6e9% and exergy efﬁciency by 13e17% with an additional cost of 5e13%. Selection of the working ﬂuid also plays an important role on the thermal and economic performance of the ORC system. For each conﬁguration, R-245fa, corresponds to the lowest speciﬁc investment cost due to the lower area of the heat exchangers and high net power. R601 shows the lowest thermal performance and the highest speciﬁc investment cost due to the lower net power and the high heat transfer area. The critical temperature of working ﬂuid inﬂuence thermal performance of ORC system. Working ﬂuids which have critical temperature close to the heat source temperature have better match between working ﬂuid and heat source and thus results in higher thermal efﬁciency and exergy efﬁciency [43]. The optimization results of the present study are compared with one of the advance optimization algorithm which uses direct search optimization algorithm based on the standard Lipschitzian approach. The comparison is performed under the present operating conditions and using the R245fa as working ﬂuid. The result of the compassion are shown in Table 12.

The error within ±5%, except the heat exchanger design factor, UA. This can be explained by the difference is effective heat transfer area estimated by Ref. [61] and present stud. In the reference study [61] heat exchanger design factor is estimated based on energy balance while in present study it is estimated by proper thermal and hydraulic modeling of heat exchanger. In order to provide a better insight to thermal performance of each cycle, two optimization cases are considered. In the case 1, exergy efﬁciency is maximized and SIC (speciﬁc investment cost) is minimized under considered operating conditions and corresponding net power is calculated. In the 2nd case, the net power is maximized and SIC is minimized under given operating conditions and corresponding exergy efﬁciency is calculated. The results are shown in Table 13. Exergy efﬁciency optimization results in higher exergy efﬁciency and SIC than net power. As it can be seen from Table 13, for BCORC case, when the exergy efﬁciency is optimized it corresponding to 51.23% exergy efﬁciency for SIC of 2423$/kW and net power of 75.22 kW. However, when the same cycle is optimized for net power, the net power is 83.69kw for SIC of 2340$/kW and exergy efﬁciency of 45.65%. There exist a trade-off between the exergy efﬁciency, net power and cost. Sensitivity analysis is performed for the working ﬂuid R245fa for each ORC conﬁguration. The effect of the evaporation temperature,

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Fig. 12. Effect of evaporation temperature on sic and exergy efﬁciency.

condensation temperature, pinch point temperature difference in the evaporator, and the degree of superheat on the exergy efﬁciency and the speciﬁc investment cost were also investigated. Fig. 12 shows the effect of the evaporation temperature on the speciﬁc investment cost and the exergy efﬁciency of BCORC, RCORC, and RGORC. The increase in the evaporation temperature results in an increase of the exergy efﬁciency while the SIC decreases at ﬁrst

and then increases. When the evaporation temperature is increased, the mass ﬂow rate of the working ﬂuid decrease gradually, as a result the exergy destruction decreases in the evaporator. The increase in the evaporation temperature enables more enthalpy difference across the expander and reduces the ﬂow rate. However, the enthalpy difference increases faster than the decrease

Fig. 13. Effect of condensation temperature on exergy efﬁciency and sic.

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in mass ﬂow rate, which leads to an increase in the net power output at ﬁrst. Since exergy efﬁciency is affected by both the net power output and the total exergy destruction. Therefore, the exergy efﬁciency increases due to the increase in the net power and decrease in the exergy destruction. However, at the elevated evaporation temperature, the increase in the exergy efﬁciency is not so sharp due to the decrease in the net power. Moreover, with the increase of the evaporator outlet temperature, the mean heat transfer temperature difference in the evaporator increases, resulting in a decrease in the heat transfer area, which leads to the reduction of the system investment cost. The comprehensive effect of the decreasing system investment cost and the increasing net power output results in the sharp decrease in SIC with the evaporation temperature at ﬁrst. With the further increase of the evaporator outlet temperature, the decreasing net power output becomes gradually obvious, and thus the SIC increases afterward. There exist an optimum evaporation temperature, where the exergy efﬁciency is maximum and SIC is minimum. At 115 C the SIC was minimum, ~2000$/kW and exergy efﬁciency was maximum, 44%. Therefore, the evaporation temperature of 115 C can be considered as the optimum evaporation temperature for R245fa under considered conditions. The effect of the condensation temperature on the SIC and the exergy efﬁciency of each ORC conﬁguration is shown in Fig. 13. When the condenser temperature varies from 25 C to 40 C, the exergy efﬁciency decreases from 38.12% to 33.32% (12.6%) for the BCORC, from 44.57% to 38.08% (14.56%) for the RCORC, and from 48.74%e40.08% (17.54%) for the RGORC. At the higher condensation temperature, the difference between the exergy efﬁciency of the BCORC and the RCORC or the RGORC decreases signiﬁcantly. The increase of the condenser pressure results in a decrease of the mass ﬂow rate and enthalpy drop across the expander. Therefore, the net power reduces considerably with the increase in the condensation temperature. The exergy destruction in the condenser also decreases with the increase in the condensation temperature. The decrease in the net power is sharp as compared to decrease in the

exergy destruction. Therefore, a decrease in the net power dominate over the decrease in exergy destruction and as a result the exergy efﬁciency decreases. However, the SIC of the BCORC presents an increment from 2595 to 2714 $/kW (4.38%), from 2735 to 2882 $/kW (5.10%) for RCORC, and from 2891 to 3069 $/kW (5.80%) for RGORC. The mean heat transfer temperature difference in the condenser increases with the increase in the condensation temperature, resulting a decrease in the heat transfer area of the condenser, which leads to a reduction of the system investment cost. However, the effect of the decreasing the net power output outweigh that of the decreasing system investment cost. As a result, the SIC exhibits an increasing trend with the condenser temperature. Fig. 14 show the effect of the superheat on the SIC and the exergy efﬁciency of the BCORC, the RCORC, and the RGORC. The increase in the degree of superheat results in the slight increase in the exergy efﬁciency and the SIC. An increase in the degree of the superheat enables more enthalpy difference in the expander and less mass ﬂow rate through the expander, while the effect of the decreasing mass ﬂow rate is greater than the increasing enthalpy difference in the expander, resulting in the decrease in the net power output. However, as the degree of superheat increases, the exergy destruction in the evaporator decreases. Although, an increase in the degree of superheat enables more enthalpy difference in the expander and less mass ﬂow rate, the effect of the decreasing mass ﬂow is greater than the increasing enthalpy difference in the expander, resulting in the decrease in the net power output. Therefore, the SIC increases due to the decrease in the net power of ORC system. The exergy efﬁciency of the BCORC was increased from 38.51% to 41.36% (6.87%) with an increase of the SIC from 2545 to 2671 $/kW (4.71%), exergy efﬁciency of the RCORC was increased from 39.71% to 44.21% (10.16%) with an increase of the SIC from 2685 to 2840 $/kW (5.45%), and exergy efﬁciency of the RGORC was increased from 42.23% to 46.58% (19.33%) with an increase of the SIC from 2841 to 3028 $/kW (6.18%). Fig. 15 show that effect of the pinch point temperature difference in the evaporator on the SIC and

Fig. 14. Effect of degree of superheat on sic and exergy efﬁciency.

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489

Fig. 15. Effect of pinch point temperature difference in evaporator on sic and exergy efﬁciency.

the exergy efﬁciency of the BCORC, the RCORC, and the RGORC system. The increase in the pinch point temperature results in the increase of the mass ﬂow rate of the working ﬂuid and therefore, the exergy destruction in the evaporator increases. Furthermore, due to the decrease in the evaporation temperature, the net power also decreases. Due to the decrease in the net power and increase in the exergy destruction, exergy efﬁciency of the ORC system decreases. The exergy efﬁciency decreases from 44.66% to 36.83% (17.53%) for the BCORC, from 48.69% to 40.86% (16.08%) for the RCORC, and from 54.09% to 46.27% (14.45%) for the RGORC. When the pinch point temperature was varied from 3 C to 20 C, the SIC decreases initially and then increases. The increase in pinch point temperature difference results in the decrease in the mean heat transfer temperature difference in the evaporator, resulting a decrease in the heat transfer area of the evaporator, which leads to the system investment cost reduction. At lower pinch point, 3 C to 7.5 C, the net power outweighs the total cost of the system, and SIC decreases. However after 7.5 C, the net power decreases faster than the decrease in the total cost of the system. Therefore, SIC increases with increase in the pinch point temperature difference. There exist an optimum value of pinch point temperature difference for the minimum SIC. For R245fa under considered conditions and pinch point of 7.5 C, the BCORC has the minimum SIC of 2245 $/kW and the exergy efﬁciency of 42.81%, the RCORC has the minimum SIC of 2390 $/kW and the exergy efﬁciency of 46.84%, and the RGORC has the minimum SIC of 2561 $/kW and e the exergy efﬁciency of 52.25%. 8. Conclusion The thermoeconomic model presented in the study aims to optimize the speciﬁc investment cost and the exergy efﬁciency of the basic ORC system, the recuperated ORC system, and the regenerative ORC system. The optimization was performed using Non-dominated Sorting Genetic Algorithm-II and the results are compared at the optimum operating condition of each

conﬁguration. Basic ORC system has the lowest exergy efﬁciency, thermal efﬁciency, and speciﬁc investment cost but highest net power. The regenerative ORC system has the highest exergy efﬁciency and the speciﬁc investment cost. But the net power of the regenerative ORC system is lower than the basic ORC. The results show that for the exergy efﬁciency lower than 45%, the basic ORC is the most suitable conﬁguration based on the lowest value of speciﬁc investment cost. However for exergy efﬁciency higher than 45%, the regenerative ORC is the most suitable conﬁguration based on the lowest value of speciﬁc investment cost. Evaporation temperature has the propitious effect on the exergy efﬁciency and the speciﬁc investment cost for each conﬁguration. For each working ﬂuid, there is an optimum evaporation temperature at which the exergy efﬁciency and the speciﬁc investment cost have the optimum value which depends on the heat and sink source conditions. For R245fa, optimum evaporation temperature is 115 C corresponds to the highest exergy efﬁciency of 54.58% and the lowest speciﬁc investment cost of 2487 $/kW for the regenerative ORC conﬁguration. The design of the evaporator and the condenser based on the optimum pinch point can signiﬁcantly improve exergoeconomic performance of the system. At optimum pinch point temperature difference of 7.5 C, basic ORC system has minimum speciﬁc investment cost of 2245 $/kW and maximum exergy efﬁciency of 42.81%, the recuperated ORC system has minimum speciﬁc investment cost of 2390 $/kW and maximum exergy efﬁciency of 46.84%, and the regenerative ORC system has minimum speciﬁc investment cost of 2561 $/kW and maximum exergy efﬁciency of 52.25%.

Acknowledgment The authors gratefully acknowledge the ﬁnancial support provided by the Korea Institute of Energy Research (B5-2409).

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Comparative assessment of Organic Rankine Cycle integration for low temperature geothermal heat source applications

Comparative assessment of Organic Rankine Cycle integration for low temperature geothermal heat source applications

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