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Thermo-economic optimization of Regenerative Organic Rankine Cycle for waste heat recovery applications
Energy Conversion and Management 87 (2014) 107–118
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Thermo-economic optimization of Regenerative Organic Rankine Cycle for waste heat recovery applications Muhammad Imran a,b,⇑, Byung Sik Park b,a, Hyouck Ju Kim b,a, Dong Hyun Lee b, Muhammad Usman a,b, Manki Heo a,b a b
Energy System Engineering, University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 305-333, Republic of Korea Energy Efficiency Research Division, Korea Institute of Energy Research, 152 Gajeong-ro, Yuseong-gu, Daejeon 305-343, Republic of Korea
a r t i c l e
i n f o
Article history: Received 8 January 2014 Accepted 30 June 2014
Keywords: Waste heat recovery Organic Rankine Cycle Thermo-economic optimization Regenerative cycle
a b s t r a c t Organic Rankine Cycle (ORC) is low grade and waste heat conversion technology. The current article deal with the thermo-economic optimization of basic ORC and regenerative ORC for waste heat recovery applications under constant heat source condition. Thermal efficiency and specific investment cost of basic ORC, single stage regenerative and double stage regenerative ORC has been optimized by using Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Maximum thermal efficiency and minimum specific investment cost were selected as objective functions and relative increase in thermal efficiency and cost has been analyzed taking the basic ORC as base case. The constraint set consist of evaporation pressure, superheat, pinch point temperature difference in evaporator and condenser. The optimization was performed for five different working fluids. The optimization result show that R245fa is best working under considered conditions and basic ORC has low specific investment cost and thermal efficiency compared to regenerative ORC. R245fa is low boiling organic fluid, which has high degree of thermal stability and compatible with common construction materials of ORC. The average increase in thermal efficiency from basic ORC to single stage regenerative ORC was 1.01% with an additional cost of 187 $/kW while from basic ORC to double stage regenerative ORC was 1.45% with an average increase in cost of 297 $/kW. The sensitivity analysis was also performed to investigate the effect of operating conditions which show that evaporation pressure has promising effect on thermal efficiency and specific investment cost. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Low grade and waste heat conversion technologies can reduce environmental impacts caused by fossil fuels [1]. The low grade and waste heat can be recovered by using Organic Rankine Cycle (ORC). The waste or low grade heat is utilized in evaporator to vaporize the low boiling point organic fluid. These high pressure vapors expand through expander and produce power. The low pressure vapors at expander outlet are condensed in the condenser. The working fluid is pumped back to evaporator and cycle repeats again. ORC is mature energy conversion technology and extensive research has been carried out in last two decades related to ORC [2]. The ORC research can be broadly classified into working fluids selection, applications of ORC, expanders design and modeling, simulation and design tools for ORC, and design and optimization ⇑ Corresponding author at: Energy Efficiency Research Division, Korea Institute of Energy Research, 152 Gajeong-ro, Yuseong-gu, Daejeon 305-343, Republic of Korea. Tel.: +82 42 860 3162; fax: +82 42 860 3756. E-mail address: [email protected] (M. Imran). http://dx.doi.org/10.1016/j.enconman.2014.06.091 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.
of ORC [3]. The major applications of ORC system include geothermal, solar, biomass, ocean thermal energy and waste heat recovery [4]. The average thermal efficiency of ORC system vary from 0.02 to 0.11, small systems lower than 5 kW have lower thermal efficiency [5–8]. Thermal efficiency of ORC system depends on system components, working fluid, and operating conditions of heat source, sink and cycle. Parametric optimization was used to analyze the effect of operating conditions and to find the optimum operating range of operating conditions for maximum value of thermal efficiency, exergy efficiency and net power. The parametric optimization and comparative study of ORC was conducted by [9] using genetic algorithms for ten working fluids. The working fluid R236EA has highest exergy efficiency of 35.43% with net power of 169.6 kW and thermal efficiency of 12.37%. The objective function was exergy efficiency and the decision variables were turbine inlet temperature and pressure. The similar study for maximum exergy efficiency for basic, single stage regenerative and double stage regenerative was carried out by [10] for six working fluids under the decision variables of turbine inlet temperature, pressure
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Nomenclature A b Bo D Dh f G L _ m Nc n h Nu P Pr 0 q Q Re T t W W x HPCD LMTD VPCD DT ifg
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 (kg s1) 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) terminal temperature difference (K) enthalpy of vaporization (kJ kg1)
and mass fraction. Results show that double stage regenerative ORC has highest exergy efficiency than basic ORC. The working fluid R11 has highest exergy efficiency, 0.56 for double stage regenerative, 0.55 for single stage regenerative and 0.50 for basic ORC. The optimization study of turbine inlet temperature and superheat for regenerative ORC system was carried out by [11]. Result indicate that the working fluid R123 had better performance than R134a at evaporation pressure of 2.5 MPa. Another study for parametric optimization of regenerative ORC was conducted by [12] using bees colony and artificial neural network. Results show that for regenerative ORC system, there exist an optimum bleed pressure to feed heater where thermal efficiency, exergy efficiency and net power was maximum. Lower and higher value of bleed pressure result in decrease in thermal performance of regenerative ORC. Cost is major barrier for commercialization of small scale ORC systems, therefore form last few years cost optimization of ORC system is being invested together with thermal performance. Energetic and economic investigation of ORC applications was investigated by [13]. Result show that waste heat recovery from biogas digestion plants with 7500 h of operation with 7% interest rate cost around 5:65c€= kW h. Thermo-economic environmental optimization of diesel waste heat recover using ORC was performed by [14] for four different working fluids. The optimization was performed using genetic algorithm to maximize thermal efficiency and minimize total annualized cost. Working fluid R123 and R245fa has highest thermal efficiency of 0.51 and lowest total annualized cost of 86,253 $/kW. Similar studies for economic assessment and techno-economic optimization had been performed for space heating, cooling, desalination ORC, biomass ORC and solar ORC systems [15–21]. Genetic algorithm is among one of the major optimization tool for
k U SIC PPTD
thermal conductivity (W m1 K1) overall heat transfer coefficient (W m2 K1) specific investment cost ($/kW) pinch point temperature difference (°C)
Greek letters b Chevron Angel (Degree) q density (kg m3) l viscosity (kg s1 m1) gtu isentropic efficiency of turbine a convective heat transfer coefficient (W m2 K1) g 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
ORC system along with other artificial intelligent optimization techniques [10,22–27]. The previous studies are primarily related to thermal and economic optimization of basic ORC for various applications. A few studies are carried out for thermal optimization of regenerative ORC systems [11,12]. The assessment and optimization of conversion of basic ORC into regenerative ORC and relative increase in cost is not yet discussed. The current work intends to present the comparative and feasibility of regenerative ORC with reference to basic ORC in terms of thermal performance and cost at their optimum performance point. The results will be helpful to visualize the relative increase in cost and thermal efficiency of basic ORC conversion to regenerative ORC, considering the basic ORC as the base case. The effect of evaporation pressure, pinch point temperature difference and superheat will help to choose the optimum operating range for minimum cost and maximum thermal efficiency for basic and regenerative ORC system.
2. Methodology The thermodynamic and economic models of basic ORC, single stage regenerative ORC and double stage regenerative ORC was written in MATLAB. The program was written in function format which include the decision variables saturation pressure, superheat, the pinch point temperature difference in evaporator and condenser respectively. Maximum thermal efficiency and minimum specific investment cost were declared as objective functions. The program was written in MATLAB. For each iteration, the cycle components were redesigned for new value of decision variables and then thermal and economic performance was evaluated. The
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process repeated until the there was no further increase in thermal efficiency and decrease in specific investment cost within logical bounds of decision variables. The working fluid properties were calculated by REFPROP using subroutines in MATLAB. 3. System description
constant pressure from process 1 to 2 in evaporator and then expands in turbine from process 2 to 3. The working fluids is condensed in condenser and reject heat at constant pressure during process 3 to 4 and finally pumped back to evaporator during process 4 to 1. The heat received by working fluid in the evaporator
_ r ½h2 h1 Q eV ¼ m The ORC system consists of four major components, evaporator, turbine, condenser and pump. The real time isentropic efficiency of turbine and pump varies between 0.60 to and 0.85, so considering real time application, the pump and turbine are modeled on the basis of isentropic efficiency of 0.65 and 0.75 respectively. Condenser and evaporator have chevron type plate heat exchanger, the geometry of heat exchangers is shown in Fig. 1 and geometrical parameters in Table 1. The working fluids for ORC are characterized by low boiling point, low heat of vaporization, high vapor density and high molecular weight. Five different working fluids are considered for optimization, the properties of working fluids are shown in Table 2.
The work of turbine, taking isentropic efficiency gtu of turbine into consideration
_ r gtu ½h2 h3 Wt ¼ m
The schematic and temperature entropy diagram of basic ORC is shown in Fig. 2. The working fluid receives heat from heat source at
ð2Þ
The heat rejected by the working fluid in the condenser
_ r ½h2 h3 Q con ¼ m
ð3Þ
The work done by pump
Wp ¼
_ r ½h1 h4 m
ð4Þ
gpu
Thermal efficiency of the basic ORC system
gth ¼
3.1. Basic ORC
ð1Þ
Wt Wp Q eV
ð5Þ
3.2. Single stage regenerative ORC cycle In single stage regenerative ORC system, some amount of the working fluid is taken out between two stages of expansion and used as feed heater before evaporator. The schematic and temperature entropy diagram is shown in Fig. 3. Single regenerative ORC system has an extra pump and feed heater compared to basic ORC system. The fraction of mass flow rate into the feed heater
x1 ¼
½h2 h1 ½h5 h1
ð6Þ
The heat received by working fluid
_ r ½h4 h3 Q eV ¼ m
ð7Þ
The work of turbine during expansion at stage 1 and stage 2
_ r gtu ½h4 h5 W t;1 ¼ m _ r ð1 x1 Þ gtu ½h5 h6 W t;2 ¼ m
ð8Þ
The heat rejected by the working fluid in condenser
_ r ð1 x1 Þ ½h6 h7 Q con ¼ m Fig. 1. The geometry of evaporator and condenser.
ð9Þ
The work of both pumps, before and after feed heater
W p1 ¼ Table 1 Geometry of heat exchanger.
W p2 ¼
Parameter
Value
Parameter
Value
Effective length Effective width Corrugated pitch
1.25 m 0.55 m 0.01 m
Plate spacing Plate thickness Chevron angel
0.003 m 0.0005 m 60°
_ r ð1 x1 Þ ½h1 h7 m
gpu _ r ½h3 h2 m
ð10Þ
gpu
Thermal efficiency of the single stage regenerative ORC
gth ¼
W t W p fW t;1 þ W t;2 g fW p1 þ W p2 g ¼ Q eV Q eV
ð11Þ
Table 2 Properties of working fluids. Working fluid
Molar mass (kg/kmol)
Critical pressure (MPa)
Critical temperature (K)
ODP
GWP
Type
R245fa R123 R11 R141b R134a
134.05 152.93 137.37 116.95 102.03
3.64 3.66 4.40 4.46 4.06
427.2 456.8 471.1 305.2 374.2
0.0 1.3 45 0.086 0.0
950.0 0.012 1.000 700 1550
Dry Isentropic Isentropic Isentropic Wet
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Fig. 2. Schematic and TS diagram of basic ORC system.
Fig. 3. Schematic and TS diagram of single stage regenerative ORC system.
_ r ½h6 h5 Q eV ¼ m
3.3. Double stage regenerative ORC cycle In double stage regenerative ORC system, some amount of the working fluid is taken out between 1st and 2nd stage of expansion, and between 2nd and 3rd stage of expansion in turbine. This working fluid is then as feed heaters before evaporator. This results in decrease in evaporator load and consequently thermal efficiency of system improves. The schematic and temperature entropy diagram is shown in Fig. 4. Double stage regenerative ORC has 2 extra pump and 2 feed heater compared to basic ORC. The fraction of mass flow rate into the feed heater 1 given by
x1 ¼
½h4 h3 ½h7 h3
ð12Þ
The fraction of mass flow rate into the feed heater 2
x2 ¼
½h2 h1 ½h8 h1
The heat received by working fluid is in evaporator
ð14Þ
The work of turbine during expansion at each stage
_ r gtu ½h6 h7 W t;1 ¼ m _ r ð1 x1 Þ gtu ½h7 h8 W t;2 ¼ m _ r ð1 x1 x2 Þ gtu ½h8 h9 W t;3 ¼ m
ð15Þ
The heat rejected by the working fluid
_ r ð1 x1 x2 Þ ½h9 h10 Q con ¼ m
ð16Þ
The work of pump
W p1 ¼
W p2 ¼ ð13Þ W p3 ¼
_ r ð1 x1 x2 Þ ½h1 h10 m
gpu _ r ð1 x1 Þ ½h3 h2 m
gpu _ r ½h5 h4 m
gpu
ð17Þ
M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118
111
Fig. 4. Schematic and TS diagram of double stage regenerated ORC system.
Thermal efficiency of the two stage regenerative ORC system
Wt Wp Q eV fW t;1 þ W t;2 þ W t;3 g fW p1 þ W p2 þ W p3 g ¼ Q eV
gth ¼
2
ð18Þ
For each new iteration, each component is redesigned for new values of decision variables. Turbine and pump are designed on basis of isentropic efficiency while heat evaporator and condenser are designed on basic of LMTD method. The iterative design process of evaporator and condenser is shown in Fig. 5. The evaporator is divided into three sections, preheater, evaporator and superheater and each section is designed separately. The heat transfer area of each section is redesigned for each iteration. The total heat transfer area is sum of these three sections. Similar approach is adopted for condenser. Evaporator and condenser designed is based on pressure drop limitation of less than 5% of inlet pressure for working fluid. 4.1. Single phase
ð19Þ
Log mean temperature
DT max DT min lnðDT max =DT min Þ
ð21Þ
The single phase Nusselt No. correlation for heat source in plate heat exchange [28]
0:646 6b Nuw ¼ 0:724 Re0:583 Pr0:33
p
ð22Þ
The Single phase Nusselt No. correlation for R245fa in plate heat exchanger [29]
ar;sp
kf lm 0:14 Re0:78 Pr0:33 ¼ 0:2092 Dh lwall
ð24Þ
f ¼
C Rep
ð25Þ
4.2. Two phase For the two phase section, the Log Mean Temperature Difference (LMTD)
LMTDtp ¼
DT max DT min lnðDT max =DT min Þ
ð26Þ
The two phase overall heat transfer coefficient
1 1 tp 1 ¼ þ þ U aw kp ar
ð27Þ
0:3 0:4 2 Nu ¼ Ge1 ReGe eq Boeq Pr
ð28Þ
where as
ð20Þ
The overall heat transfer coefficient of single phase
1 1 tp 1 ¼ þ þ U sp aw kp ar;sp
4fNcG L 2qDh
The Nusselt No. correlation for R245fa evaporation in plate heat exchanger [30]
The heat transfer in the single phase section
LMTDsp ¼
DP ¼
The single phase frictional pressure drop factor for both cold and hot side [28]
4. System modeling
Q sp ¼ U sp Asp LMTDsp
The single pressure drop for both cold and hot side consist of only frictional pressure drop, the pressure drop due to elevation and port pressure loss is neglected for single phase.
ð23Þ
0:041 Pco p 2:83 Ge1 ¼ 2:81 b ; Dh 2 0:082 Pco p 0:61 b Ge2 ¼ 2:81 Dh 2
ð29Þ
The equivalent Reynolds number and boiling number are given by
Reeq ¼
Geq Dh
lf
2 !0:5 3 q q00 f 5 ; Boeq ¼ ; Geq ¼ G4ð1 xÞ þ x Geq ifg qg
ð30Þ
While two phase frictional factor [30] 4 f ¼ Ge3 ReGe eq
ð31Þ
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Fig. 5. Layout of design procedure of evaporator and condenser.
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
where as
5:27 Pco p 3:03 Ge3 ¼ 64710 b ; Dh 2 0:62 Pco p 0:47 b Ge4 ¼ 1:314 Dh 2
2
DP f ¼ ð32Þ
For R245fa condensation in plate heat exchanger [31]
Nu ¼
0:3 0:4 6 Ge5 ReGe eq Boeq Pr
ð33Þ
ð38Þ
The pressure drop due to acceleration
DPac ¼ G2r x
vg vf
ð39Þ
where as Gr is channel flow area
Gr ¼
where as
0:041 Pco p 4:5 Ge5 ¼ 11:22 b ; Dh 2 0:23 Pco p 1:48 b Ge6 ¼ 0:35 Dh 2
4fNcG L 2qDh
mr b Nc W p
ð40Þ
The change in the pressure due to elevation
DPelev ¼ g qm Le ð34Þ
ð41Þ
The port pressure drop
1:5 G2r v m 2
While two phase frictional factor for condensation pressure drop is [31]
DPport ¼
8 f ¼ Ge7 ReGe eq
For real time analysis, all four components of pressure drop are considered in two phase.
ð35Þ
ð42Þ
where as
4:17 Pco p 7:75 Ge7 ¼ 3521:1 b ; Dh 2 0:0925 Pco p 1:3 b Ge8 ¼ 1:024 Dh 2
5. Economical modeling
ð36Þ
The heat transfer coefficient of water side [28]
0:646 6b Nuw ¼ 0:724 Re0:583 Pr0:33
p
ð37Þ
Pressure drop in two phase consists of four components; pressure drop due to acceleration of the refrigerant, due to change in
Since by definition the waste heat sources are cost free, so only the cost of components is considered in economical modeling. The cost of piping, working fluid and labour is also not considered during economic modeling. The cost of individual components is calculated by the approach [25] using the appropriate Chemical Engineering Plant Cost Index (CEPCI) for the year 2013. The cost of evaporator and condenser is given by
C HX ¼
527:7 F S C HX B1;HX þ ðB2;HX F M;HX F P;HX Þ 397
ð43Þ
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M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118
where FS is an additional factor for overhead cost, B1,HX and B2,HX are constants for heat exchanger type and FM,HX is the additional material factor for heat exchanger. The FP,HX is the pressure factor for HX is the basic cost of heat exchanger made heat exchanger and C from stainless steel The basic cost of heat exchanger is given by in terms of heat transfer area
n o HX ¼ K 1;HX þ K 2;HX ðlog AHX Þ þ K 3;HX ðlog AHX Þ2 log C
Table 3 Constants for economic modeling.
ð44Þ
where K1,HX, K2,HX, K3,HX are constants for type of heat exchanger. The pressure factor for heat exchanger is 2
log F P;HX ¼ fC 1;HX þ C 2;HX ðlog P HX Þ þ C 3;HX ðlog PHX Þ g
ð45Þ
where C1,HX, C2,HX, C3,HX are constant for heat exchanger type. The total cost of pump is
C PP ¼
527:7 PP B1;PP þ ðB2;PP F M;PP F P;PP Þ FS C 397
ð48Þ
527:7 TR F M;TR FS C 397
ð50Þ
where K1,TR, K2,TR, K3,TR are constants for turbine type. The cost of feed heater is given by
527:7 FH B1;FH þ ðB2;FH F M;FH F P;FH Þ FS C 397
FH ¼ K 1;FH þ K 2;FH ðlog V FH Þ þ K 3;PP ðlog V FH Þ log C
2
o
ð51Þ
2
f1 ðxÞ ¼ Maximize ðgth Þ ¼
0.1557 0.1547 0.00 0.00 0.00 1.12 0.87 1.64 4.20 0.1245 0.00
B1,PP B2,PP FM,PP K1,PP K2,PP K3,PP C1,PP C2,PP C3,PP C1,FH
1.89 1.35 2.20 3.389 0.536 0.1538 0.3935 0.3957 0.00226 0.00
Wt Wp TC
ð55Þ
4g gtu fh2 h3 g fh1gh pu
fh2 h1 g ð56Þ
Subjected to constraints
ð52Þ
5bar PeV 30 bar;
0 Superheat 15 K
6 K PPTDeV 30 K;
6 K PPTDco 30 K
ð57Þ
Genetic algorithm solves the objective function for minimum value, to get the maximum value of thermal efficiency, the function of thermal efficiency is used with negative sign during optimization process. The objective function and constraint for single stage regenerative ORC are given by
ð53Þ
½gtu fh4 h5 g þ gtu f1 x1 gfh5 h6 g
K2,HX K3,HX C1,HX C2,HX C3,HX B1,FH B2,FH FM,FH K1,FH K3,PP C3,FH
4g gtu fh2 h3 g fh1gh pu f2 ðxÞ ¼ Minimize ðSIC Þ ¼ C HX;EV þ C TR þ C HX;CO þ C PP þ C FH
where K1,FH, K2,FH, K3,FH are constants for feed heater type. The pressure factor for feed heater
log F P;FH ¼ fC 1;FH þ C 2;FH ðlog PFH Þ þ C 3;FH ðlog PFH Þ g
1.70 0.96 1.21 2.40 4.66 3.50 2.2659 1.4398 0.1776 0.204 10
f1 ðxÞ ¼ Maximize ðgth Þ ¼
where B1,FH and B2,FH are constants for feed heater type and FM,PP is the additional material factor, FP,HX is the pressure factor for feed HX is the basic cost of feed heater. The basic cost of feed heater and C heater
n
FS B1,HX B2,HX FM,HX K1,HX FM,TR K1,TR K2,TR K3,TR K2,FH C2,FH
The search space is very large for tradition optimization techniques and chances of convergences are low. Therefore the optimization of the regenerative cycle is performed by using Nondominated Sorting Genetic Algorithm-II (NSGA-II) in MATLAB. The multi objective function for Basic ORC is given by
HX is where FM,TR is the pressure and material factor for turbine and C the basic cost of turbine, given by
C FH ¼
Value
6.1. Multi objective optimization
ð49Þ
n o TR ¼ K 1;TR þ K 2;TR ðlog W TR Þ þ K 3;TR ðlog W TR Þ2 log C
Constant
The regenerative ORC is optimized for maximum thermal efficiency and minimum specific investment cost. The decision variables include the evaporation pressure, superheat at turbine inlet, pinch point temperature difference in evaporator and condenser, mass fractions in single stage and two stage regenerative ORC. The selection of these parameters is based on their strong influence on thermal efficiency and specific investment cost.
where C1,PP, C2,PP, C3,PP are constant for pump type. The cost of turbine is given
C TR ¼
Value
6. Thermo-economic optimization
where K1,PP, K2,PP, K3,PP are constants for pump type? The pressure factor for pump is 2
Constant
Specific Investment Cost ¼ SIC ¼
ð47Þ
log F P;PP ¼ fC 1;PP þ C 2;PP ðlog PPP Þ þ C 3;PP ðlog PPP Þ g
Value
The specific investment cost of each configuration is calculated by the relation
ð46Þ
where B1,PP and B2,PP are constants for pump type and FM,PP is the additional material factor, FP,HX is the pressure factor for pump HX is the basic cost of pump. The basic cost of pump is given and C by in terms of pump power
n o PP ¼ K 1;PP þ K 2;PP ðlog W PP Þ þ K 3;PP ðlog W PP Þ2 log C
Constant
h
fh3 h2 g
gpu
i þ f1x1 ggfh1 h7 g pu
fh4 h3 g
h i ½gtu fh4 h5 g þ gtu f1 x1 gfh5 h6 g fh3gh2 g þ f1x1 ggfh1 h7 g pu pu f2 ðxÞ ¼ Minimize ðSIC Þ ¼ C HX;EV þ C TR þ C HX;CO þ C PP þ C FH
ð58Þ
where C1,FH, C2,FH, C3,FH are constant for feed heater type. The value of constants for economic analysis is shown in Table 3. The total cost of components is sum of individuals cost of components
5 bar P eV 30 bar;
TC ¼ fC HX;EV þ C TR þ C HX;CO þ C PP þ C FH g
6 K PPTDeV 30 K; 6 K PPTDco 30 K;
ð54Þ
Subjected to constraints
0 Superheat 15 K 0 x1 0:25
ð59Þ
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The objective function and constraint for two stage regenerative ORC are given by
f1 ðxÞ ¼ Maximize ðgth Þ ¼
The parameters of algorithm and logical bounds of decision variables are shown in Table 4.
gtu ½fh6 h7 g þ f1 x1 gfh7 h8 g þ ð1 x1 x2 Þfh9 h10 g g1pu ½h5 h4 þ f1 x1 gfh3 h2 g þ f1 x1 x2 gfh1 h10 g fh6 h5 g
½gtu fh6 h7 g þ gtu f1 x1 gfh7 h8 g þ gtu ð1 x1 x2 Þfh9 h10 g f2 ðxÞ ¼ Minimize ðSIC Þ ¼ C HX;EV þ C TR þ C HX;CO þ C PP þ C FH
Subjected to constraints
5 bar PeV 30 bar;
0 Superheat 15 K;
0 x1 0:25
6 K PPTDeV 30 K;
6 K PPTDco 30 K; 0 x2 0:25
ð61Þ
h
fh5 h4 g
gpu
i þ f1x1 ggfh3 h2 g þ f1x1 xg2 gfh1 h10 g pu
pu
ð60Þ
Elitism [32] was applied to eliminate the regression in one generation to next generation. The fittest offspring from population were selected and during the optimization process one whole generation was replaced with these offspring to reduce the computational time. The undersize and over size population decrease the quality of final solution. Initially the optimization was performed
Table 4 Genetic algorithm parameters. NSGA-II parameters
Values
Parameter (constraints)
Lower bound
Upper bound
Size of population Objective function tolerance Crossover fraction Mutation fraction Selection process
100 0.001 0.70 0.06 Tournament
Evaporation pressure Superheat PPTD in evaporator PPTD in condenser Mass fraction
5 bar 0 °C 6 °C 6 °C 0
30 bar 15 °C 30 °C 30 °C 0.25
Fig. 6. Layout of multi objective genetic algorithm.
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M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118 Table 5 Optimum solution for basic Organic Rankine Cycle. Optimum value of operating parameters
Evaporation pressure (MPa) Superheat (°C) PPTD evaporator (°C) PPTD condenser (°C) Thermal efficiency (%) Specific investment cost ($/kW)
Working fluids R123
R11
R245fa
R141b
R134a
1.2356 3.47 7.57 14.36 7.264 3556
1.3247 2.69 11.95 13.29 7.912 3795
1.6818 1.27 8.34 16.17 6.184 3274
1.1576 3.49 6.41 10.18 7.960 4155
2.7251 4.25 26.55 17.65 6.587 3655
Table 6 Optimum Solution for Single Stage Regenerative Organic Rankine Cycle. Optimum value of operating parameters
Evaporation pressure (MPa) Superheat (°C) PPTD evaporator (°C) PPTD condenser (°C) Mass fraction into feed heater Thermal efficiency (%) Specific investment cost ($/kW)
Working fluids R123
R11
R245fa
R141b
R134a
1.4908 0.00 6.91 16.32 0.21098 8.724 3749
1.4789 0.00 12.44 14.74 0.16450 8.812 3987
1.8287 0.00 8.31 18.69 0.17394 7.028 3453
1.2411 0.00 8.25 9.87 0.18146 8.804 4571
2.921 0.00 24.85 19.25 0.2254 7.241 3845
Table 7 Optimum solution for double stage regenerative Organic Rankine Cycle. Optimum value of operating parameters
Evaporation pressure (MPa) Superheat (°C) PPTD evaporator (°C) PPTD condenser (°C) Mass fraction into feed heater 1 Mass fraction into feed heater 2 Thermal efficiency (%) Specific investment cost ($/kW)
Working fluids R123
R11
R245fa
R141b
R134a
1.4504 0.00 8.71 14.96 0.1544 0.1034 9.204 4057
1.4862 0.00 10.94 13.62 0.0969 0.0937 9.468 4327
1.8024 0.00 13.35 16.58 0.1334 0.0929 7.668 3739
1.2035 0.00 8.14 8.54 0.1125 0.0832 9.316 4960
2.807 0.00 27.85 21.45 0.1325 0.1078 8.047 4185
for three values of population size 80,100,120. The solution at population size of 100 gave the high quality result. The variation in results was 0–0.015. Therefore the population size was chosen 100 for current study. For mutation and crossover fraction, the optimization was carried out for values from 0 to 1 with interval of 0.05. The best quality result are obtained at mutation fraction of 0.06 and crossover fraction of 0.7. The layout of multi objective genetic algorithm is shown in Fig. 6. 7. Results and discussion The result of the thermo-economic optimization for basic ORC, single stage regenerative ORC and double stage regenerative ORC are shown in Tables 5–7 respectively. The application of elitism converge the objective functions to optimum solution reducing the computational time about 9%. Result indicate that the superheat at turbine inlet is not necessary for working fluids under consideration for regenerative ORC. The thermal efficiency for regenerative cycle was higher than the basic ORC while the cost of basic ORC was lower than regenerative ORC system. Considering the Basic ORC as base cost, the average increase in thermal efficiency from basic to single stage regenerative ORC was 1.01% with an additional cost of 187 $/kW while from basic to double stage regenerative ORC was 1.45% with an average increase in cost of 297 $/kW. The SIC was different for different working fluid; R245fa had the lowest cost while R141b had the highest SIC.
The effect of decision variables on the thermal and economic performance of each ORC configuration was also investigated. The sensitivity analysis was performed for working fluid R245fa. The effect of evaporation pressure on the specific investment is shown in Fig. 7. The specific investment cost decreased with increase in evaporation pressure due to increase in net power. Each working fluid correspond to a specific value of evaporation pressure where the net output was maximum and consequently the SIC was minimum. Although the cost of heat exchanger increased with increase in evaporation pressure however it was dominated by the net power produced. With further increase in evaporation pressure after specific value of evaporation pressure the net power decreased and cost of heat exchanger increased, as a result the SIC increased rapidly. The basic cycle had lowest cost and double stage regenerative ORC had the highest cost. Fig. 8 represent the effect of evaporation pressure on thermal efficiency. Thermal efficiency of the ORC increased with increase in evaporation pressure due to increase in net output which indicates an optimum value of pressure ratio. After specific value of evaporation pressure the thermal efficiency decreased due to decrease in net output. The effect of evaporation pressure was promising on thermal efficiency and SIC of ORC. For R245fa, under considered conditions, the optimum evaporation is shown in Fig. 9. The optimum evaporation was between 13 and 16 bar. Each working fluid had a specific range of pressure for maximum thermal efficiency and minimum SIC.
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Fig. 7. Evaporation pressure vs. specific investment cost.
Fig. 8. Evaporation pressure vs. thermal efficiency.
Fig. 10 shows the effect of superheat at turbine inlet on specific investment cost. When the super heat increased, the area of superheater increased and consequently the SIC increased. The slight increase in SIC cost show that the cost of heat exchanger dominated the increase in net power output. Therefore for simple ORC as well as regenerative ORC, the increase in superheat resulted in increase in SIC. The average increase in cost was about 6 $/kW per 1 °C increase in superheat. Fig. 11 shows the effect of superheat on thermal efficiency of ORC. For basic ORC there was no increase in thermal efficiency but the efficiency of regenerative cycle increased 0.5% with an increase in superheat of 15 °C. Fig. 12 shows the effect of pinch point temperature difference on specific investment cost of basic ORC and regenerative ORC. The specific investment cost increased with increase in pinch point temperature. The higher pinch point resulted in decrease in cost of heat exchanger but correspond to lower evaporation pressure and low net power. Therefore the SIC decreased with increase in pinch point temperature difference. The average increase in SIC was 18 $/kW per 1 °C increase pinch point temperature difference.
Fig. 10. Superheat vs. specific investment cost.
Fig. 9. Optimum evaporation pressure for R245fa.
M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118
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capacity increased and consequently thermal efficiency decreased. The low pinch point correspond to high efficiency but high SIC, the higher value of pinch point temperature difference correspond to low thermal efficiency and low SIC.
8. Conclusion
Fig. 11. Superheat vs. specific thermal efficiency.
Thermo-economic optimization of regenerative ORC is performed using multi objective genetic algorithm for constant temperature waste recovery applications. Maximum thermal efficiency and minimum SIC were considered as objective function while evaporation pressure, superheat and pinch point are considered as decision variables. Optimization results are rough approximation of thermal and economic performance of ORC for a capacity range of 30–120 kW. The optimization results show that the average increase in thermal efficiency from basic to single stage regenerative ORC is 1.01% with an additional cost of 187 $/kW while from basic to double stage regenerative ORC is 1.45% with an average increase in cost of 297 $/kW. The SIC cost is different for different working fluid; R245fa has the lowest cost while R141b has the highest SIC. The effect of operating parameters is also investigated which shows that the superheat at turbine inlet results in slight increase in thermal efficiency but significant rise in SIC. Higher pinch point temperature difference results in high SIC and thermal efficiency and low value of pinch point temperature difference corresponds to low thermal efficiency and SIC. The evaporation pressure has promising effect on thermal efficiency and SIC. For each working fluid, the evaporation pressure has specific range for maximum thermal efficiency and minimum SIC. Acknowledgments The authors gratefully acknowledge the financial support provided by the Korea Institute of Energy Research under the title of ‘‘Development of 100 kWe Class ORC Power Generation System Utilizing Low Temperature Geothermal Energy’’ (B4-2461).
Fig. 12. Pinch point temperature difference vs. specific investment cost.
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Fig. 13. Pinch point temperature difference vs. thermal efficiency.
Fig. 13 shows the effect of pinch point temperature difference on thermal efficiency of the ORC. The increase in pinch point temperature difference decreased the thermal efficiency. The increase in pinch point temperature difference result in decrease in evaporation pressure and net power. The evaporator
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Thermo-economic optimization of Regenerative Organic Rankine Cycle for waste heat recovery applications Muhammad Imran a,b,⇑, Byung Sik Park b,a, Hyouck Ju Kim b,a, Dong Hyun Lee b, Muhammad Usman a,b, Manki Heo a,b a b
Energy System Engineering, University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 305-333, Republic of Korea Energy Efficiency Research Division, Korea Institute of Energy Research, 152 Gajeong-ro, Yuseong-gu, Daejeon 305-343, Republic of Korea
a r t i c l e
i n f o
Article history: Received 8 January 2014 Accepted 30 June 2014
Keywords: Waste heat recovery Organic Rankine Cycle Thermo-economic optimization Regenerative cycle
a b s t r a c t Organic Rankine Cycle (ORC) is low grade and waste heat conversion technology. The current article deal with the thermo-economic optimization of basic ORC and regenerative ORC for waste heat recovery applications under constant heat source condition. Thermal efficiency and specific investment cost of basic ORC, single stage regenerative and double stage regenerative ORC has been optimized by using Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Maximum thermal efficiency and minimum specific investment cost were selected as objective functions and relative increase in thermal efficiency and cost has been analyzed taking the basic ORC as base case. The constraint set consist of evaporation pressure, superheat, pinch point temperature difference in evaporator and condenser. The optimization was performed for five different working fluids. The optimization result show that R245fa is best working under considered conditions and basic ORC has low specific investment cost and thermal efficiency compared to regenerative ORC. R245fa is low boiling organic fluid, which has high degree of thermal stability and compatible with common construction materials of ORC. The average increase in thermal efficiency from basic ORC to single stage regenerative ORC was 1.01% with an additional cost of 187 $/kW while from basic ORC to double stage regenerative ORC was 1.45% with an average increase in cost of 297 $/kW. The sensitivity analysis was also performed to investigate the effect of operating conditions which show that evaporation pressure has promising effect on thermal efficiency and specific investment cost. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Low grade and waste heat conversion technologies can reduce environmental impacts caused by fossil fuels [1]. The low grade and waste heat can be recovered by using Organic Rankine Cycle (ORC). The waste or low grade heat is utilized in evaporator to vaporize the low boiling point organic fluid. These high pressure vapors expand through expander and produce power. The low pressure vapors at expander outlet are condensed in the condenser. The working fluid is pumped back to evaporator and cycle repeats again. ORC is mature energy conversion technology and extensive research has been carried out in last two decades related to ORC [2]. The ORC research can be broadly classified into working fluids selection, applications of ORC, expanders design and modeling, simulation and design tools for ORC, and design and optimization ⇑ Corresponding author at: Energy Efficiency Research Division, Korea Institute of Energy Research, 152 Gajeong-ro, Yuseong-gu, Daejeon 305-343, Republic of Korea. Tel.: +82 42 860 3162; fax: +82 42 860 3756. E-mail address: [email protected] (M. Imran). http://dx.doi.org/10.1016/j.enconman.2014.06.091 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.
of ORC [3]. The major applications of ORC system include geothermal, solar, biomass, ocean thermal energy and waste heat recovery [4]. The average thermal efficiency of ORC system vary from 0.02 to 0.11, small systems lower than 5 kW have lower thermal efficiency [5–8]. Thermal efficiency of ORC system depends on system components, working fluid, and operating conditions of heat source, sink and cycle. Parametric optimization was used to analyze the effect of operating conditions and to find the optimum operating range of operating conditions for maximum value of thermal efficiency, exergy efficiency and net power. The parametric optimization and comparative study of ORC was conducted by [9] using genetic algorithms for ten working fluids. The working fluid R236EA has highest exergy efficiency of 35.43% with net power of 169.6 kW and thermal efficiency of 12.37%. The objective function was exergy efficiency and the decision variables were turbine inlet temperature and pressure. The similar study for maximum exergy efficiency for basic, single stage regenerative and double stage regenerative was carried out by [10] for six working fluids under the decision variables of turbine inlet temperature, pressure
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Nomenclature A b Bo D Dh f G L _ m Nc n h Nu P Pr 0 q Q Re T t W W x HPCD LMTD VPCD DT ifg
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 (kg s1) 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) terminal temperature difference (K) enthalpy of vaporization (kJ kg1)
and mass fraction. Results show that double stage regenerative ORC has highest exergy efficiency than basic ORC. The working fluid R11 has highest exergy efficiency, 0.56 for double stage regenerative, 0.55 for single stage regenerative and 0.50 for basic ORC. The optimization study of turbine inlet temperature and superheat for regenerative ORC system was carried out by [11]. Result indicate that the working fluid R123 had better performance than R134a at evaporation pressure of 2.5 MPa. Another study for parametric optimization of regenerative ORC was conducted by [12] using bees colony and artificial neural network. Results show that for regenerative ORC system, there exist an optimum bleed pressure to feed heater where thermal efficiency, exergy efficiency and net power was maximum. Lower and higher value of bleed pressure result in decrease in thermal performance of regenerative ORC. Cost is major barrier for commercialization of small scale ORC systems, therefore form last few years cost optimization of ORC system is being invested together with thermal performance. Energetic and economic investigation of ORC applications was investigated by [13]. Result show that waste heat recovery from biogas digestion plants with 7500 h of operation with 7% interest rate cost around 5:65c€= kW h. Thermo-economic environmental optimization of diesel waste heat recover using ORC was performed by [14] for four different working fluids. The optimization was performed using genetic algorithm to maximize thermal efficiency and minimize total annualized cost. Working fluid R123 and R245fa has highest thermal efficiency of 0.51 and lowest total annualized cost of 86,253 $/kW. Similar studies for economic assessment and techno-economic optimization had been performed for space heating, cooling, desalination ORC, biomass ORC and solar ORC systems [15–21]. Genetic algorithm is among one of the major optimization tool for
k U SIC PPTD
thermal conductivity (W m1 K1) overall heat transfer coefficient (W m2 K1) specific investment cost ($/kW) pinch point temperature difference (°C)
Greek letters b Chevron Angel (Degree) q density (kg m3) l viscosity (kg s1 m1) gtu isentropic efficiency of turbine a convective heat transfer coefficient (W m2 K1) g 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
ORC system along with other artificial intelligent optimization techniques [10,22–27]. The previous studies are primarily related to thermal and economic optimization of basic ORC for various applications. A few studies are carried out for thermal optimization of regenerative ORC systems [11,12]. The assessment and optimization of conversion of basic ORC into regenerative ORC and relative increase in cost is not yet discussed. The current work intends to present the comparative and feasibility of regenerative ORC with reference to basic ORC in terms of thermal performance and cost at their optimum performance point. The results will be helpful to visualize the relative increase in cost and thermal efficiency of basic ORC conversion to regenerative ORC, considering the basic ORC as the base case. The effect of evaporation pressure, pinch point temperature difference and superheat will help to choose the optimum operating range for minimum cost and maximum thermal efficiency for basic and regenerative ORC system.
2. Methodology The thermodynamic and economic models of basic ORC, single stage regenerative ORC and double stage regenerative ORC was written in MATLAB. The program was written in function format which include the decision variables saturation pressure, superheat, the pinch point temperature difference in evaporator and condenser respectively. Maximum thermal efficiency and minimum specific investment cost were declared as objective functions. The program was written in MATLAB. For each iteration, the cycle components were redesigned for new value of decision variables and then thermal and economic performance was evaluated. The
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process repeated until the there was no further increase in thermal efficiency and decrease in specific investment cost within logical bounds of decision variables. The working fluid properties were calculated by REFPROP using subroutines in MATLAB. 3. System description
constant pressure from process 1 to 2 in evaporator and then expands in turbine from process 2 to 3. The working fluids is condensed in condenser and reject heat at constant pressure during process 3 to 4 and finally pumped back to evaporator during process 4 to 1. The heat received by working fluid in the evaporator
_ r ½h2 h1 Q eV ¼ m The ORC system consists of four major components, evaporator, turbine, condenser and pump. The real time isentropic efficiency of turbine and pump varies between 0.60 to and 0.85, so considering real time application, the pump and turbine are modeled on the basis of isentropic efficiency of 0.65 and 0.75 respectively. Condenser and evaporator have chevron type plate heat exchanger, the geometry of heat exchangers is shown in Fig. 1 and geometrical parameters in Table 1. The working fluids for ORC are characterized by low boiling point, low heat of vaporization, high vapor density and high molecular weight. Five different working fluids are considered for optimization, the properties of working fluids are shown in Table 2.
The work of turbine, taking isentropic efficiency gtu of turbine into consideration
_ r gtu ½h2 h3 Wt ¼ m
The schematic and temperature entropy diagram of basic ORC is shown in Fig. 2. The working fluid receives heat from heat source at
ð2Þ
The heat rejected by the working fluid in the condenser
_ r ½h2 h3 Q con ¼ m
ð3Þ
The work done by pump
Wp ¼
_ r ½h1 h4 m
ð4Þ
gpu
Thermal efficiency of the basic ORC system
gth ¼
3.1. Basic ORC
ð1Þ
Wt Wp Q eV
ð5Þ
3.2. Single stage regenerative ORC cycle In single stage regenerative ORC system, some amount of the working fluid is taken out between two stages of expansion and used as feed heater before evaporator. The schematic and temperature entropy diagram is shown in Fig. 3. Single regenerative ORC system has an extra pump and feed heater compared to basic ORC system. The fraction of mass flow rate into the feed heater
x1 ¼
½h2 h1 ½h5 h1
ð6Þ
The heat received by working fluid
_ r ½h4 h3 Q eV ¼ m
ð7Þ
The work of turbine during expansion at stage 1 and stage 2
_ r gtu ½h4 h5 W t;1 ¼ m _ r ð1 x1 Þ gtu ½h5 h6 W t;2 ¼ m
ð8Þ
The heat rejected by the working fluid in condenser
_ r ð1 x1 Þ ½h6 h7 Q con ¼ m Fig. 1. The geometry of evaporator and condenser.
ð9Þ
The work of both pumps, before and after feed heater
W p1 ¼ Table 1 Geometry of heat exchanger.
W p2 ¼
Parameter
Value
Parameter
Value
Effective length Effective width Corrugated pitch
1.25 m 0.55 m 0.01 m
Plate spacing Plate thickness Chevron angel
0.003 m 0.0005 m 60°
_ r ð1 x1 Þ ½h1 h7 m
gpu _ r ½h3 h2 m
ð10Þ
gpu
Thermal efficiency of the single stage regenerative ORC
gth ¼
W t W p fW t;1 þ W t;2 g fW p1 þ W p2 g ¼ Q eV Q eV
ð11Þ
Table 2 Properties of working fluids. Working fluid
Molar mass (kg/kmol)
Critical pressure (MPa)
Critical temperature (K)
ODP
GWP
Type
R245fa R123 R11 R141b R134a
134.05 152.93 137.37 116.95 102.03
3.64 3.66 4.40 4.46 4.06
427.2 456.8 471.1 305.2 374.2
0.0 1.3 45 0.086 0.0
950.0 0.012 1.000 700 1550
Dry Isentropic Isentropic Isentropic Wet
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Fig. 2. Schematic and TS diagram of basic ORC system.
Fig. 3. Schematic and TS diagram of single stage regenerative ORC system.
_ r ½h6 h5 Q eV ¼ m
3.3. Double stage regenerative ORC cycle In double stage regenerative ORC system, some amount of the working fluid is taken out between 1st and 2nd stage of expansion, and between 2nd and 3rd stage of expansion in turbine. This working fluid is then as feed heaters before evaporator. This results in decrease in evaporator load and consequently thermal efficiency of system improves. The schematic and temperature entropy diagram is shown in Fig. 4. Double stage regenerative ORC has 2 extra pump and 2 feed heater compared to basic ORC. The fraction of mass flow rate into the feed heater 1 given by
x1 ¼
½h4 h3 ½h7 h3
ð12Þ
The fraction of mass flow rate into the feed heater 2
x2 ¼
½h2 h1 ½h8 h1
The heat received by working fluid is in evaporator
ð14Þ
The work of turbine during expansion at each stage
_ r gtu ½h6 h7 W t;1 ¼ m _ r ð1 x1 Þ gtu ½h7 h8 W t;2 ¼ m _ r ð1 x1 x2 Þ gtu ½h8 h9 W t;3 ¼ m
ð15Þ
The heat rejected by the working fluid
_ r ð1 x1 x2 Þ ½h9 h10 Q con ¼ m
ð16Þ
The work of pump
W p1 ¼
W p2 ¼ ð13Þ W p3 ¼
_ r ð1 x1 x2 Þ ½h1 h10 m
gpu _ r ð1 x1 Þ ½h3 h2 m
gpu _ r ½h5 h4 m
gpu
ð17Þ
M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118
111
Fig. 4. Schematic and TS diagram of double stage regenerated ORC system.
Thermal efficiency of the two stage regenerative ORC system
Wt Wp Q eV fW t;1 þ W t;2 þ W t;3 g fW p1 þ W p2 þ W p3 g ¼ Q eV
gth ¼
2
ð18Þ
For each new iteration, each component is redesigned for new values of decision variables. Turbine and pump are designed on basis of isentropic efficiency while heat evaporator and condenser are designed on basic of LMTD method. The iterative design process of evaporator and condenser is shown in Fig. 5. The evaporator is divided into three sections, preheater, evaporator and superheater and each section is designed separately. The heat transfer area of each section is redesigned for each iteration. The total heat transfer area is sum of these three sections. Similar approach is adopted for condenser. Evaporator and condenser designed is based on pressure drop limitation of less than 5% of inlet pressure for working fluid. 4.1. Single phase
ð19Þ
Log mean temperature
DT max DT min lnðDT max =DT min Þ
ð21Þ
The single phase Nusselt No. correlation for heat source in plate heat exchange [28]
0:646 6b Nuw ¼ 0:724 Re0:583 Pr0:33
p
ð22Þ
The Single phase Nusselt No. correlation for R245fa in plate heat exchanger [29]
ar;sp
kf lm 0:14 Re0:78 Pr0:33 ¼ 0:2092 Dh lwall
ð24Þ
f ¼
C Rep
ð25Þ
4.2. Two phase For the two phase section, the Log Mean Temperature Difference (LMTD)
LMTDtp ¼
DT max DT min lnðDT max =DT min Þ
ð26Þ
The two phase overall heat transfer coefficient
1 1 tp 1 ¼ þ þ U aw kp ar
ð27Þ
0:3 0:4 2 Nu ¼ Ge1 ReGe eq Boeq Pr
ð28Þ
where as
ð20Þ
The overall heat transfer coefficient of single phase
1 1 tp 1 ¼ þ þ U sp aw kp ar;sp
4fNcG L 2qDh
The Nusselt No. correlation for R245fa evaporation in plate heat exchanger [30]
The heat transfer in the single phase section
LMTDsp ¼
DP ¼
The single phase frictional pressure drop factor for both cold and hot side [28]
4. System modeling
Q sp ¼ U sp Asp LMTDsp
The single pressure drop for both cold and hot side consist of only frictional pressure drop, the pressure drop due to elevation and port pressure loss is neglected for single phase.
ð23Þ
0:041 Pco p 2:83 Ge1 ¼ 2:81 b ; Dh 2 0:082 Pco p 0:61 b Ge2 ¼ 2:81 Dh 2
ð29Þ
The equivalent Reynolds number and boiling number are given by
Reeq ¼
Geq Dh
lf
2 !0:5 3 q q00 f 5 ; Boeq ¼ ; Geq ¼ G4ð1 xÞ þ x Geq ifg qg
ð30Þ
While two phase frictional factor [30] 4 f ¼ Ge3 ReGe eq
ð31Þ
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Fig. 5. Layout of design procedure of evaporator and condenser.
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
where as
5:27 Pco p 3:03 Ge3 ¼ 64710 b ; Dh 2 0:62 Pco p 0:47 b Ge4 ¼ 1:314 Dh 2
2
DP f ¼ ð32Þ
For R245fa condensation in plate heat exchanger [31]
Nu ¼
0:3 0:4 6 Ge5 ReGe eq Boeq Pr
ð33Þ
ð38Þ
The pressure drop due to acceleration
DPac ¼ G2r x
vg vf
ð39Þ
where as Gr is channel flow area
Gr ¼
where as
0:041 Pco p 4:5 Ge5 ¼ 11:22 b ; Dh 2 0:23 Pco p 1:48 b Ge6 ¼ 0:35 Dh 2
4fNcG L 2qDh
mr b Nc W p
ð40Þ
The change in the pressure due to elevation
DPelev ¼ g qm Le ð34Þ
ð41Þ
The port pressure drop
1:5 G2r v m 2
While two phase frictional factor for condensation pressure drop is [31]
DPport ¼
8 f ¼ Ge7 ReGe eq
For real time analysis, all four components of pressure drop are considered in two phase.
ð35Þ
ð42Þ
where as
4:17 Pco p 7:75 Ge7 ¼ 3521:1 b ; Dh 2 0:0925 Pco p 1:3 b Ge8 ¼ 1:024 Dh 2
5. Economical modeling
ð36Þ
The heat transfer coefficient of water side [28]
0:646 6b Nuw ¼ 0:724 Re0:583 Pr0:33
p
ð37Þ
Pressure drop in two phase consists of four components; pressure drop due to acceleration of the refrigerant, due to change in
Since by definition the waste heat sources are cost free, so only the cost of components is considered in economical modeling. The cost of piping, working fluid and labour is also not considered during economic modeling. The cost of individual components is calculated by the approach [25] using the appropriate Chemical Engineering Plant Cost Index (CEPCI) for the year 2013. The cost of evaporator and condenser is given by
C HX ¼
527:7 F S C HX B1;HX þ ðB2;HX F M;HX F P;HX Þ 397
ð43Þ
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where FS is an additional factor for overhead cost, B1,HX and B2,HX are constants for heat exchanger type and FM,HX is the additional material factor for heat exchanger. The FP,HX is the pressure factor for HX is the basic cost of heat exchanger made heat exchanger and C from stainless steel The basic cost of heat exchanger is given by in terms of heat transfer area
n o HX ¼ K 1;HX þ K 2;HX ðlog AHX Þ þ K 3;HX ðlog AHX Þ2 log C
Table 3 Constants for economic modeling.
ð44Þ
where K1,HX, K2,HX, K3,HX are constants for type of heat exchanger. The pressure factor for heat exchanger is 2
log F P;HX ¼ fC 1;HX þ C 2;HX ðlog P HX Þ þ C 3;HX ðlog PHX Þ g
ð45Þ
where C1,HX, C2,HX, C3,HX are constant for heat exchanger type. The total cost of pump is
C PP ¼
527:7 PP B1;PP þ ðB2;PP F M;PP F P;PP Þ FS C 397
ð48Þ
527:7 TR F M;TR FS C 397
ð50Þ
where K1,TR, K2,TR, K3,TR are constants for turbine type. The cost of feed heater is given by
527:7 FH B1;FH þ ðB2;FH F M;FH F P;FH Þ FS C 397
FH ¼ K 1;FH þ K 2;FH ðlog V FH Þ þ K 3;PP ðlog V FH Þ log C
2
o
ð51Þ
2
f1 ðxÞ ¼ Maximize ðgth Þ ¼
0.1557 0.1547 0.00 0.00 0.00 1.12 0.87 1.64 4.20 0.1245 0.00
B1,PP B2,PP FM,PP K1,PP K2,PP K3,PP C1,PP C2,PP C3,PP C1,FH
1.89 1.35 2.20 3.389 0.536 0.1538 0.3935 0.3957 0.00226 0.00
Wt Wp TC
ð55Þ
4g gtu fh2 h3 g fh1gh pu
fh2 h1 g ð56Þ
Subjected to constraints
ð52Þ
5bar PeV 30 bar;
0 Superheat 15 K
6 K PPTDeV 30 K;
6 K PPTDco 30 K
ð57Þ
Genetic algorithm solves the objective function for minimum value, to get the maximum value of thermal efficiency, the function of thermal efficiency is used with negative sign during optimization process. The objective function and constraint for single stage regenerative ORC are given by
ð53Þ
½gtu fh4 h5 g þ gtu f1 x1 gfh5 h6 g
K2,HX K3,HX C1,HX C2,HX C3,HX B1,FH B2,FH FM,FH K1,FH K3,PP C3,FH
4g gtu fh2 h3 g fh1gh pu f2 ðxÞ ¼ Minimize ðSIC Þ ¼ C HX;EV þ C TR þ C HX;CO þ C PP þ C FH
where K1,FH, K2,FH, K3,FH are constants for feed heater type. The pressure factor for feed heater
log F P;FH ¼ fC 1;FH þ C 2;FH ðlog PFH Þ þ C 3;FH ðlog PFH Þ g
1.70 0.96 1.21 2.40 4.66 3.50 2.2659 1.4398 0.1776 0.204 10
f1 ðxÞ ¼ Maximize ðgth Þ ¼
where B1,FH and B2,FH are constants for feed heater type and FM,PP is the additional material factor, FP,HX is the pressure factor for feed HX is the basic cost of feed heater. The basic cost of feed heater and C heater
n
FS B1,HX B2,HX FM,HX K1,HX FM,TR K1,TR K2,TR K3,TR K2,FH C2,FH
The search space is very large for tradition optimization techniques and chances of convergences are low. Therefore the optimization of the regenerative cycle is performed by using Nondominated Sorting Genetic Algorithm-II (NSGA-II) in MATLAB. The multi objective function for Basic ORC is given by
HX is where FM,TR is the pressure and material factor for turbine and C the basic cost of turbine, given by
C FH ¼
Value
6.1. Multi objective optimization
ð49Þ
n o TR ¼ K 1;TR þ K 2;TR ðlog W TR Þ þ K 3;TR ðlog W TR Þ2 log C
Constant
The regenerative ORC is optimized for maximum thermal efficiency and minimum specific investment cost. The decision variables include the evaporation pressure, superheat at turbine inlet, pinch point temperature difference in evaporator and condenser, mass fractions in single stage and two stage regenerative ORC. The selection of these parameters is based on their strong influence on thermal efficiency and specific investment cost.
where C1,PP, C2,PP, C3,PP are constant for pump type. The cost of turbine is given
C TR ¼
Value
6. Thermo-economic optimization
where K1,PP, K2,PP, K3,PP are constants for pump type? The pressure factor for pump is 2
Constant
Specific Investment Cost ¼ SIC ¼
ð47Þ
log F P;PP ¼ fC 1;PP þ C 2;PP ðlog PPP Þ þ C 3;PP ðlog PPP Þ g
Value
The specific investment cost of each configuration is calculated by the relation
ð46Þ
where B1,PP and B2,PP are constants for pump type and FM,PP is the additional material factor, FP,HX is the pressure factor for pump HX is the basic cost of pump. The basic cost of pump is given and C by in terms of pump power
n o PP ¼ K 1;PP þ K 2;PP ðlog W PP Þ þ K 3;PP ðlog W PP Þ2 log C
Constant
h
fh3 h2 g
gpu
i þ f1x1 ggfh1 h7 g pu
fh4 h3 g
h i ½gtu fh4 h5 g þ gtu f1 x1 gfh5 h6 g fh3gh2 g þ f1x1 ggfh1 h7 g pu pu f2 ðxÞ ¼ Minimize ðSIC Þ ¼ C HX;EV þ C TR þ C HX;CO þ C PP þ C FH
ð58Þ
where C1,FH, C2,FH, C3,FH are constant for feed heater type. The value of constants for economic analysis is shown in Table 3. The total cost of components is sum of individuals cost of components
5 bar P eV 30 bar;
TC ¼ fC HX;EV þ C TR þ C HX;CO þ C PP þ C FH g
6 K PPTDeV 30 K; 6 K PPTDco 30 K;
ð54Þ
Subjected to constraints
0 Superheat 15 K 0 x1 0:25
ð59Þ
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The objective function and constraint for two stage regenerative ORC are given by
f1 ðxÞ ¼ Maximize ðgth Þ ¼
The parameters of algorithm and logical bounds of decision variables are shown in Table 4.
gtu ½fh6 h7 g þ f1 x1 gfh7 h8 g þ ð1 x1 x2 Þfh9 h10 g g1pu ½h5 h4 þ f1 x1 gfh3 h2 g þ f1 x1 x2 gfh1 h10 g fh6 h5 g
½gtu fh6 h7 g þ gtu f1 x1 gfh7 h8 g þ gtu ð1 x1 x2 Þfh9 h10 g f2 ðxÞ ¼ Minimize ðSIC Þ ¼ C HX;EV þ C TR þ C HX;CO þ C PP þ C FH
Subjected to constraints
5 bar PeV 30 bar;
0 Superheat 15 K;
0 x1 0:25
6 K PPTDeV 30 K;
6 K PPTDco 30 K; 0 x2 0:25
ð61Þ
h
fh5 h4 g
gpu
i þ f1x1 ggfh3 h2 g þ f1x1 xg2 gfh1 h10 g pu
pu
ð60Þ
Elitism [32] was applied to eliminate the regression in one generation to next generation. The fittest offspring from population were selected and during the optimization process one whole generation was replaced with these offspring to reduce the computational time. The undersize and over size population decrease the quality of final solution. Initially the optimization was performed
Table 4 Genetic algorithm parameters. NSGA-II parameters
Values
Parameter (constraints)
Lower bound
Upper bound
Size of population Objective function tolerance Crossover fraction Mutation fraction Selection process
100 0.001 0.70 0.06 Tournament
Evaporation pressure Superheat PPTD in evaporator PPTD in condenser Mass fraction
5 bar 0 °C 6 °C 6 °C 0
30 bar 15 °C 30 °C 30 °C 0.25
Fig. 6. Layout of multi objective genetic algorithm.
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M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118 Table 5 Optimum solution for basic Organic Rankine Cycle. Optimum value of operating parameters
Evaporation pressure (MPa) Superheat (°C) PPTD evaporator (°C) PPTD condenser (°C) Thermal efficiency (%) Specific investment cost ($/kW)
Working fluids R123
R11
R245fa
R141b
R134a
1.2356 3.47 7.57 14.36 7.264 3556
1.3247 2.69 11.95 13.29 7.912 3795
1.6818 1.27 8.34 16.17 6.184 3274
1.1576 3.49 6.41 10.18 7.960 4155
2.7251 4.25 26.55 17.65 6.587 3655
Table 6 Optimum Solution for Single Stage Regenerative Organic Rankine Cycle. Optimum value of operating parameters
Evaporation pressure (MPa) Superheat (°C) PPTD evaporator (°C) PPTD condenser (°C) Mass fraction into feed heater Thermal efficiency (%) Specific investment cost ($/kW)
Working fluids R123
R11
R245fa
R141b
R134a
1.4908 0.00 6.91 16.32 0.21098 8.724 3749
1.4789 0.00 12.44 14.74 0.16450 8.812 3987
1.8287 0.00 8.31 18.69 0.17394 7.028 3453
1.2411 0.00 8.25 9.87 0.18146 8.804 4571
2.921 0.00 24.85 19.25 0.2254 7.241 3845
Table 7 Optimum solution for double stage regenerative Organic Rankine Cycle. Optimum value of operating parameters
Evaporation pressure (MPa) Superheat (°C) PPTD evaporator (°C) PPTD condenser (°C) Mass fraction into feed heater 1 Mass fraction into feed heater 2 Thermal efficiency (%) Specific investment cost ($/kW)
Working fluids R123
R11
R245fa
R141b
R134a
1.4504 0.00 8.71 14.96 0.1544 0.1034 9.204 4057
1.4862 0.00 10.94 13.62 0.0969 0.0937 9.468 4327
1.8024 0.00 13.35 16.58 0.1334 0.0929 7.668 3739
1.2035 0.00 8.14 8.54 0.1125 0.0832 9.316 4960
2.807 0.00 27.85 21.45 0.1325 0.1078 8.047 4185
for three values of population size 80,100,120. The solution at population size of 100 gave the high quality result. The variation in results was 0–0.015. Therefore the population size was chosen 100 for current study. For mutation and crossover fraction, the optimization was carried out for values from 0 to 1 with interval of 0.05. The best quality result are obtained at mutation fraction of 0.06 and crossover fraction of 0.7. The layout of multi objective genetic algorithm is shown in Fig. 6. 7. Results and discussion The result of the thermo-economic optimization for basic ORC, single stage regenerative ORC and double stage regenerative ORC are shown in Tables 5–7 respectively. The application of elitism converge the objective functions to optimum solution reducing the computational time about 9%. Result indicate that the superheat at turbine inlet is not necessary for working fluids under consideration for regenerative ORC. The thermal efficiency for regenerative cycle was higher than the basic ORC while the cost of basic ORC was lower than regenerative ORC system. Considering the Basic ORC as base cost, the average increase in thermal efficiency from basic to single stage regenerative ORC was 1.01% with an additional cost of 187 $/kW while from basic to double stage regenerative ORC was 1.45% with an average increase in cost of 297 $/kW. The SIC was different for different working fluid; R245fa had the lowest cost while R141b had the highest SIC.
The effect of decision variables on the thermal and economic performance of each ORC configuration was also investigated. The sensitivity analysis was performed for working fluid R245fa. The effect of evaporation pressure on the specific investment is shown in Fig. 7. The specific investment cost decreased with increase in evaporation pressure due to increase in net power. Each working fluid correspond to a specific value of evaporation pressure where the net output was maximum and consequently the SIC was minimum. Although the cost of heat exchanger increased with increase in evaporation pressure however it was dominated by the net power produced. With further increase in evaporation pressure after specific value of evaporation pressure the net power decreased and cost of heat exchanger increased, as a result the SIC increased rapidly. The basic cycle had lowest cost and double stage regenerative ORC had the highest cost. Fig. 8 represent the effect of evaporation pressure on thermal efficiency. Thermal efficiency of the ORC increased with increase in evaporation pressure due to increase in net output which indicates an optimum value of pressure ratio. After specific value of evaporation pressure the thermal efficiency decreased due to decrease in net output. The effect of evaporation pressure was promising on thermal efficiency and SIC of ORC. For R245fa, under considered conditions, the optimum evaporation is shown in Fig. 9. The optimum evaporation was between 13 and 16 bar. Each working fluid had a specific range of pressure for maximum thermal efficiency and minimum SIC.
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Fig. 7. Evaporation pressure vs. specific investment cost.
Fig. 8. Evaporation pressure vs. thermal efficiency.
Fig. 10 shows the effect of superheat at turbine inlet on specific investment cost. When the super heat increased, the area of superheater increased and consequently the SIC increased. The slight increase in SIC cost show that the cost of heat exchanger dominated the increase in net power output. Therefore for simple ORC as well as regenerative ORC, the increase in superheat resulted in increase in SIC. The average increase in cost was about 6 $/kW per 1 °C increase in superheat. Fig. 11 shows the effect of superheat on thermal efficiency of ORC. For basic ORC there was no increase in thermal efficiency but the efficiency of regenerative cycle increased 0.5% with an increase in superheat of 15 °C. Fig. 12 shows the effect of pinch point temperature difference on specific investment cost of basic ORC and regenerative ORC. The specific investment cost increased with increase in pinch point temperature. The higher pinch point resulted in decrease in cost of heat exchanger but correspond to lower evaporation pressure and low net power. Therefore the SIC decreased with increase in pinch point temperature difference. The average increase in SIC was 18 $/kW per 1 °C increase pinch point temperature difference.
Fig. 10. Superheat vs. specific investment cost.
Fig. 9. Optimum evaporation pressure for R245fa.
M. Imran et al. / Energy Conversion and Management 87 (2014) 107–118
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capacity increased and consequently thermal efficiency decreased. The low pinch point correspond to high efficiency but high SIC, the higher value of pinch point temperature difference correspond to low thermal efficiency and low SIC.
8. Conclusion
Fig. 11. Superheat vs. specific thermal efficiency.
Thermo-economic optimization of regenerative ORC is performed using multi objective genetic algorithm for constant temperature waste recovery applications. Maximum thermal efficiency and minimum SIC were considered as objective function while evaporation pressure, superheat and pinch point are considered as decision variables. Optimization results are rough approximation of thermal and economic performance of ORC for a capacity range of 30–120 kW. The optimization results show that the average increase in thermal efficiency from basic to single stage regenerative ORC is 1.01% with an additional cost of 187 $/kW while from basic to double stage regenerative ORC is 1.45% with an average increase in cost of 297 $/kW. The SIC cost is different for different working fluid; R245fa has the lowest cost while R141b has the highest SIC. The effect of operating parameters is also investigated which shows that the superheat at turbine inlet results in slight increase in thermal efficiency but significant rise in SIC. Higher pinch point temperature difference results in high SIC and thermal efficiency and low value of pinch point temperature difference corresponds to low thermal efficiency and SIC. The evaporation pressure has promising effect on thermal efficiency and SIC. For each working fluid, the evaporation pressure has specific range for maximum thermal efficiency and minimum SIC. Acknowledgments The authors gratefully acknowledge the financial support provided by the Korea Institute of Energy Research under the title of ‘‘Development of 100 kWe Class ORC Power Generation System Utilizing Low Temperature Geothermal Energy’’ (B4-2461).
Fig. 12. Pinch point temperature difference vs. specific investment cost.
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Fig. 13. Pinch point temperature difference vs. thermal efficiency.
Fig. 13 shows the effect of pinch point temperature difference on thermal efficiency of the ORC. The increase in pinch point temperature difference decreased the thermal efficiency. The increase in pinch point temperature difference result in decrease in evaporation pressure and net power. The evaporator
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