Energy 203 (2020) 117800
Contents lists available at ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
Design and performance analysis of a novel Transcritical Regenerative
Series Two stage Organic Rankine Cycle for dual source waste heat
recovery
Anandu Surendran, Satyanarayanan Seshadri*
Energy and Emissions Research Group (EnERG), Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 2 February 2020
Received in revised form
9 April 2020
Accepted 4 May 2020
Available online 8 May 2020
A Transcritical Regenerative Series Two stage Organic Rankine Cycle (TR-STORC) is proposed to improve
the efficiency of existing Series Two stage ORC (STORC) architecture by combining supercritical heating
in the high pressure (HP) stage and partial evaporation with regeneration in the low pressure (LP) stage.
Exhaust gas and jacket water from a stationary IC engine is used as the primary and secondary heat
source respectively. Using cyclopentane as working fluid, system exergy performance is analysed for a
range of heat source temperatures and for different ratios of heat available between the heat sources. At
lower HP evaporator pressures, lower values of vapour outlet temperatures lead to maximum power
output. For a wide range of heat ratios and temperatures, TR-STORC delivers improved exergetic performance over STORC and pre-heated ORC. It is the recommended choice for all scenarios of dual source
heat recovery. For the engine design point, TR-STORC delivers increased power output by up to16% and
23% than STORC and pre-heated ORC respectively. TR-STORC maintains exergetic superiority for all the
working fluids investigated with maximum net power outputs exceeding STORC by15e34% and preheated ORC by 15e52%.
© 2020 Elsevier Ltd. All rights reserved.
Keywords:
Organic rankine cycle
Waste heat recovery
Two stage evaporation
Dual heat sources
Regeneration
Transcritical
Credit Author Statement
Anandu Surendran, Anandu Surendran is responsible for doing
the research and preparing the draft of the manuscript for submission, Satyanarayanan Seshadri, is the research guide, responsible for directing the study, revising the manuscript and
verification of outputs.
1. Introduction
Waste heat recovery from low and medium temperature heat
sources using Organic Rankine Cycles (ORC) is well known since
ORCs offer much simpler cycle architecture compared to other
systems. Typical applications of ORCs involve two or more heat
sources at the same site with different temperatures and heat
contents. Combined solar-geothermal systems [1e3], IC engines
[4e7] and waste heat streams in process industries and refineries
* Corresponding author.
E-mail addresses: anandusurendran@smail.iitm.ac.in (A. Surendran), satya@
iitm.ac.in (S. Seshadri).
https://doi.org/10.1016/j.energy.2020.117800
0360-5442/© 2020 Elsevier Ltd. All rights reserved.
[8] are the typical cases where more than one heat source has the
potential for waste heat recovery through ORCs.
One of the extensively studied applications of ORCs utilizing
more than one heat source is the internal combustion (IC) engine.
In IC engines, combined heat recovery from the high temperature
exhaust gases and low temperature jacket water using ORCs has
been extensively researched with studies focusing on the simplest
ORC architecture, the preheated single stage ORC. Many of these
studies, such as Vaja et al. [9] concluded that it is possible to recover
only a fraction of the heat from the low temperature jacket water.
Yu et al. [10] reported 75% utilization of engine exhaust gas with
only 9.5% use of jacket water heat for a preheated ORC using R245fa
as working fluid. Underutilization of the secondary heat source in
pre-heated ORCs led to the development of dual-loop ORCs in
which the primary and secondary heat sources are utilized by two
separate high and low temperature loops (HT and LT) with separate
working fluids and expanders. Studies on dual loop ORCs focused
more on identifying working fluids and new cycle architecture
modifications to improve the system exergetic efficiency [11e15].
Shu et al. [11] reported that up to 96.8% utilization of jacket water
heat in dual loop ORCs. Supercritical regenerative dual loop
2
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Nomenclature
Cp
E
Ex
H
I
KA
M
P
Q
S
T
U
V
W
constant pressure specific heat (kJ/kg K)
specific exergy (kJ/kg)
exergy (kJ)
specific enthalpy (kJ/kg)
irreversibility (kW)
total thermal conductance (kW/K)
mass flow rate (kg/s)
pressure (kPa)
heat transfer rate (kW)
specific entropy (kJ/kg K)
temperature (K)
utilization rate of heat source (%)
volumetric flow rate (m3/s)
power (kW)
Greek symbols
hI
thermal efficiency (%)
hex
exergetic efficiency (%)
he
expander isentropic efficiency (%)
hp
pump isentropic efficiency (%)
configurations were found to perform better than traditional dual
loop ORC by Wang et al. [5]. Other improvements on dual loop ORCs
focused on three stage regenerative layouts [14] and methods such
as graphene addition to enhance heat transfer properties of jacket
water [12]. However, dual loop ORCs still needed two separate
expanders with different working fluids leading to higher heat
exchanger requirements associated with the cascaded heat rejection. These layouts render dual loop ORCs economically uncompetitive for waste heat recovery applications.
As opposed to dual loop, a dual pressure (two stage) systems
have been developed recently. These systems in which the heat
source is cascaded into two different pressure levels/stages have
shown improved exergetic efficiency compared to single pressure
ORCs. Two architectures are possible in this layout. The working
fluid can be split into two streams and fed to the high- and lowpressure evaporators separately, referred to as the Parallel Two
Stage ORC (PTORC). Another possibility is to split the working fluid
stream after pre-heating. The HP evaporator in this case will be in
series with the preheater which handles the entire working fluid
flow rate. This configuration is referred to as the Series two stage
ORC. For Low temperature heat sources, STORC presented higher
exergetic performance over PTORC and it should be preferred over
single stage ORCs [16e19]. Li et al. [20] proposed an improved
STORC that coupled supercritical and subcritical heat absorption
processes. For heat source temperatures above 135 C, the modified
cycle was able to generate 20.4% increased power output than
subcritical STORC. Unlike dual loop ORCs, induction turbine layouts
are possible in two stage systems in which the HP and LP turbine
stages can be connected in series. The HP turbine exhaust mixes
with the LP evaporator vapour before entering the LP turbine stage.
A comparative assessment of induction turbine layout and two
separate turbine layout by Li et al. [21] concluded that the former
leads to a 0.3e5.4% increase in power output along with a 34.2%
decrement in specific investment cost.
Very few studies have explored the waste heat recovery application of two stage ORC with dual heat sources where maximum
heat source utilization is desired. For an unlinked dual heat source
(solar and geothermal), Li et al. [22] showed that STORC is able to
generate the highest power output when heat source temperatures
D
n
difference
specific volume (m3/kg)
Subscripts
cond
condenser
evap
evaporator
exp
expander
in
inlet
max
maximum
out
outlet
P
primary heat source
pre
preheater
S
secondary heat source
wf
working fluid
1,2,3,4,5,6,7,8 state points
Acronyms
HP
LP
ODP
ORC
VFR
high pressure
low pressure
ozone depletion potential
organic Rankine cycle
volumetric flow ratio
are less than 140 C. Chen et al. [23] analysed a PTORC system for IC
engine heat recovery. PTORC resulted in 8% increased net power
output and 18% lower heat exchanger volume as compared to dual
loop ORC. Rech et al. [24] analysed the performance of subcritical
and supercritical parallel two stage ORC (PTORC) layouts over single
stage ORCs. PTORC layout with supercritical evaporation in the HP
stage, with a thermal efficiency of 12.6% delivered the best performance. Zhi et al. [25] also reported a 12.02% increase in engine
power output for the same architecture using R1233zd as working
fluid. Surendran et al. [26] compared the performance of subcritical
STORC and PTORC architectures using induction turbine layouts
over single stage pre-heated ORC for engine heat recovery utilizing
both exhaust gases and jacket water. When design constraints were
imposed, STORC architecture presented the system performance
over PTORC and pre-heated ORC. STORC was also able to deliver
high improvements in power output over single stage pre-heated
ORC when the heat content in the low temperature source (jacket
water) was significantly higher than that in the exhaust gases.
PTORC showed improved performance only for specific heat source
conditions. SOTRC was recommended for dual source heat recovery
than PTORC, pre-heated ORC and dual loop ORC.
From the above studies, adopting STORC using an induction
turbine layout seems promising for dual source heat recovery,
especially when significant heat is available in the low temperature
heat source. However, the thermal efficiency of STORCs is still lower
than single stage ORCs. Also, the condenser in the STORC still has to
remove a large portion of heat in de-superheating the working fluid
at the condenser inlet. Therefore, development of next generation
ORCs for multiple source heat recovery need to be focused on
advancing the basic STORC architecture by minimizing its disadvantages. One way of improving the system thermal efficiency is to
adopt a supercritical evaporation process in the HP evaporator as
suggested by Li et al. [20]. However, this would lead to further increase in superheat at the turbine exit when dry fluids are
expanded across such high pressure ratios. Use of recuperators,
with or without turbine bleeding could lead to improved thermal
efficiencies for regenerative ORCs operating with a single heat
source [27]. However, for two stage ORCs, the increased heat
exchanger requirements coupled with a decrease in heat source
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
utilization renders the use of recuperators unattractive. Studies on
partial evaporating ORCs for single heat source applications by
Lecompte et al. [28] reports higher heat extraction and power
output for low temperature heat sources. Partial evaporating ORC
outperformed the transcritical ORC by up to 25.6% in second law
efficiency, while the transcritical ORC outperformed the sub-critical
ORC by up to 10.8%. However, use of partial evaporation requires
two-phase expanders in the LP stage that could further increase the
cost of the system.
In this study, a new two stage ORC named Transcritical Regenerative STORC (TR-STORC) is proposed as an improvement to the
existing STORC architecture focusing on dual source heat recovery.
TR-STORC adopts a supercritical evaporation in the HP stage and
partial evaporation of working fluid in the LP stage. Full evaporation
of LP stage fluid is achieved by the regenerative use of superheated
vapour exiting from the HP turbine. This combination of supercritical heating in the HP stage and partial evaporation and
regeneration in the LP stage can improve the thermal match and
can also achieve increased heat source utilization. Exhaust gas and
jacket water from a 2.97 MW natural gas IC engine are the heat
sources. Influence of cycle parameters are analysed and optimized
performances for a range of operating conditions are evaluated.
Constrained optimization using Genetic Algorithm is carried out for
various operating conditions and the cycle performance is
compared with STORC and the basic pre-heated ORC architecture.
2. System description
2.1. Waste heat sources
The heat source in this study is a natural gas fired 4 stroke
turbocharged 20 cylinder engine. At engine design point, the primary heat source consists of high temperature exhaust gases
(705 K, 4.591 kg/s). The primary heat source composition is O2
17.3%, N2 59.3%, CO2 12.9% and H2O 10.5% by mass. Hot jacket water
(363 K, 14 kg/s) acts as the secondary heat source. In order to
explore a wide range of IC engine conditions, the primary and
secondary heat source temperatures and mass flow rates are varied
in this study.
2.2. Cycle architecture and working principle
The layout of the RT-STORC is the same as that of STORC with the
exception of the regenerator as an additional component. STORC
adopts sub-critical evaporation process in the HP evaporator and
achieves full evaporation of working fluid in the LP evaporator (see
Fig. 1). T-s diagram of STORC and single stage pre-heated ORC (see
Fig. 2) are given for reference. In pre-heated ORC, the pressurised
working fluid is pre-heated by the secondary heat source and fully
evaporated by utilizing heat from the primary heat source.
Fig. 3 shows the layout and T-s diagram of TR-STORC. The system
consists of a high pressure (HP) evaporator, a low pressure (LP)
evaporator, a regenerator, a high pressure pump, a low pressure
pump, a two stage induction turbine and a condenser. The high
pressure and low pressure evaporators recover heat from the primary and secondary heat sources respectively. The sub-cooled
working fluid from the condenser is pressurised to an intermediate pressure by the LP pump (9e1) and is fed to the LP evaporator.
In the LP evaporator, the working fluid absorbs heat from the secondary heat source (1-2-3) and is partially evaporated (two phase).
The HP pump pressurises a part of the saturated liquid working
fluid is to a supercritical pressure (2e4). This pressurised working
fluid then absorbs heat from the primary heat source in the HP
evaporator and generates high pressure supercritical vapour (4e5).
This vapour is then expanded to LP evaporator pressure through the
3
HP stage of the induction turbine (5e6). The entire vapour exiting
the HP stage then mixes with the partially evaporated working fluid
from the LP evaporator inside the vapour regenerator which acts as
a constant pressure mixing vessel. The vapour incoming vapour is
thoroughly mixed with the two phase fluid leading to full evaporation of the LP working fluid thereby producing low pressure
saturated vapour (at 3-300 and 6e300 ). In the LP turbine stage, the
vapour is expanded to condenser pressure (300 -7). The mechanical
work from the turbine is converted to electrical power by the
generator. The superheated vapour exiting the turbine is then desuperheated (7e8) and condensed to saturated liquid in the
condenser (8e9), thereby completing a cycle.
In this study, cyclopentane is used as the working fluid since
many studies have reported cyclopentane as the best working fluid
for high temperature ORC applications [29e31]. The main properties of cyclopentane are listed in Table 1.
3. System modelling
3.1. Thermodynamic model
The ORC system is evaluated based on the following
assumptions:
1. All processes are at steady state. Pressure drop and heat transfer
from the pipelines is neglected. Changes in kinetic and potential
energy of the working fluid is negligible
2. All heat exchangers are counter flow type. For gaseliquid heat
exchangers, pinch point temperature difference (DTevap,HP) is set
at 20 K and for liquideliquid heat exchangers, this value is set at
10 K (DTevap,LP)
3. Both LP and HP turbine stages have same isentropic efficiency of
70%. The isentropic efficiency of 80% is set for the LP and HP
pumps
4. The mixing process in the vapour regenerator is perfectly
adiabatic
5. Temperature rise of cooling water is limited to 5 K (Tsink,
in ¼ 298 K, Tsink, out ¼ 303 K)
6. Ambient temperature (T0) and pressure (P0) are assumed to be
298 K and 0.1 MPa respectively
7. Primary heat source carrier pressure is 101.3 kPa. Cooling limit
on primary heat source (TP,min) is restricted to 373 K so as to
prevent corrosion due to acid droplet formation
The thermodynamic model equations are shown in Table 2.
The temperature profiles of the hot and cold fluids in the heat
exchangers are determined using the discretized heat exchanger
model in Larsen et al. [33]. The discretized heat exchanger model
represented in Fig. 4 is better equipped to predict the exact location
of the pinch point since the temperature profiles in some cases are
curved rather than being straight lines. This is particularly true for a
finite heat capacity source undergoing isobaric cooling [34], and for
working fluids undergoing supercritical heating processes [35].
Based on numerical simulations, discretization with N ¼ 50 for
evaporators and N ¼ 15 for the condenser is adequate to have an
accuracy of 1 W power output.
The mass flow rate mwf1in the HP loop is computed based on an
iterative approach with the pinch point temperature difference and
the primary heat source cooling limit as constraints. The vapour
fraction of the working fluid at the outlet of LP evaporator and the
pinch point temperature difference determines the mass flow rate
mwf2. The condenser mass flow rate msink is also determined using
the same approach. The mass flow rate mwf2 and vapour fraction
are then iterated in a nested loop so as to achieve a saturated
vapour condition at the outlet of the vapour regenerator. This
4
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Fig. 1. STORC layout.
ensures full evaporation of working fluid from the LP loop. A
thermal model is developed in MATLAB using thermo physical data
of working fluids from REFPROP® 9.1database [32]. Energy and
mass balances are then applied across each components (as a
control volume) to determine the system characteristics.
3.2. Thermo-economic parameters
Thermo-economic parameters and their calculations are listed
in Table 3. In order to get a comprehensive estimate of the heat
exchanger cost, the total thermal conductance (KA) values are
calculated. Using the logarithmic mean temperature difference
(LMTD) method [36], the KA requirements for the LP evaporator
and condenser can be computed by finding out the KA values corresponding to the preheater, evaporator, superheated/sub-cooled
sections separately. For the HP evaporator, the working fluid is
heated to supercritical states where the thermodynamic properties
are varying. Therefore, the LMTD approach between the inlet and
outlet of the evaporator cannot be directly applied in the case of HP
evaporator. An alternative solution proposed by Lazova at al [35] is
adopted in this case. The enthalpy change is minimal across the
discretized sections (N ¼ 50) and the KA values for each of the
discretized sections of the HP evaporator are calculated separately.
Total KA value is obtained as the sum of KA values of each discretized section of the heat exchanger. Stage VFR is an estimate of
the change in fluid volume during expansion in each stage and is
used to determine the limit on stage isentropic efficiency. The mass
averaged turbine size parameter gives an indication of the cost and
size of the turbines required.
4. Results
4.1. Influence of HP evaporation pressure and vapour outlet
temperature
Fig. 5 presents the effect of HP evaporation pressure and HP
vapour outlet temperature on net power output, LP vapour fraction
(at state point 3), thermal efficiency and heat source utilization
rates. At lower evaporator pressures, lower values of vapour outlet
temperatures lead to maximum work output. This is due to the
increased first stage turbine work owing to lower superheated
temperatures at the outlet of HP turbine as well as higher mass flow
rates in the HP loop. As the HP stage pressure increases, the net
power output also increases for a given LP stage evaporating temperature (or pressure). This is due to the increase in pressure ratio
across the HP turbine. The optimum vapour fraction in the LP
evaporator outlet decreases with the increase in vapour outlet
temperature in the HP stage. This can be attributed to the increased
degree of superheat available at the exit of the HP turbine at higher
vapour outlet temperatures. Also, for higher HP stage pressures, the
optimum vapour fraction is higher for a given vapour outlet temperature due to the decrease in available superheat at exit of HP
turbine. The primary heat source utilization remains almost constant with vapour outlet temperature (see Fig. 5c). The peaks in
secondary heat source utilization correspond to maximum mass
flow rates in the pre-heater section of LP evaporator. In Fig. 5d, the
variation in thermal efficiency is a direct result of the variation in
net power output and heat source utilization rates for various
vapour outlet temperatures and pressures.
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
5
Fig. 2. (a) T-s diagram of STORC (b) T-s diagram of single stage pre-heated ORC.
4.2. Influence of LP evaporation temperature
In Fig. 6, the effect of LP evaporation temperature (T3) on net
power output, thermal efficiency and secondary heat source utilization rate are shown. At lower values of T3, very high utilization of
secondary heat source is achieved due to the increased mass flow
rate of working fluid in the LP loop (see Fig. 6a). However, the
irreversibility associated with mixing of superheated vapour and
partially evaporated working fluid from the LP evaporator increases
with decrease in LP evaporation temperature. Also, at lower values
of T3, the thermal efficiency of the LP stage decreases resulting in
lower net power outputs (see Fig. 6b). Thus, for a given HP stage
pressure and vapour outlet temperature, there exists an intermediate value of T3 that maximises the net power output.
4.3. System optimization and performance comparison
For the TR-STORC, the optimization parameters are the HP stage
pressure, the vapour outlet temperature T5, the LP evaporation
temperature T3 and the condensing temperature Tcond. The range of
6
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Fig. 3. (a)TR-STORC layout (b) T-s diagram of TR- STORC.
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
7
Table 1
Thermo-physical properties and environmental data of cyclopentane [32].
Working fluid
Molecular mass (g/mol)
Normal boiling point(K)
Critical temperature (K)
Critical pressure (MPa)
GWP
ODP
Cyclopentane
70.133
322.40
511.69
4.515
11
0
Table 2
Thermodynamic model equations.
Parameter
Equations
HP evaporator heat transfer (kW)
Qevap HP ¼ mwf 1 :ðh5 h4 Þ ¼ Cpp :mp :ðTp;in Tp;out Þ
LP evaporator heat transfer (kW)
Total heat input (kW)
Total mass flow rate of working fluid (kg/s)
Energy balance in vapour regenerator
Condenser heat transfer (kW)
Q evapLP ¼ mwf 2 :ðh3 h2 Þ þ mwf :ðh2 h1 Þ ¼ Cps :ms :ðTs;in Ts;out Þ
Q total ¼ Q evapHP þ Q evapLP
mwf ¼ mwf1 þ mwf2
mwf :h3} ¼ mwf1 :h6 þ mwf2 :h3
Q cond ¼ mwf :ðh7 h9 Þ ¼ Cpw :mw :ðTsink;in Tsink;out Þ
HP pump work (kW)
Wpump;HP ¼ mwf 1 :ðh4 h2 Þ=hp
LP pump work (kW)
Wpump;LP ¼ mwf :ðh1 h9 Þ=hp
HP expanderwork (kW)
LP expander work (kW)
Net power output (kW)
Thermal efficiency (%)
Total primary heat available (kW)
Total secondary heat available (kW)
Utilization rate of primary source (%)
Utilization rate of secondary source (%)
Exergy rate of primary heat source (kW)
Exergy rate of secondary heat source (kW)
Irreversibility in HP evaporator (kW)
Irreversibility in LP evaporator (kW)
Wexp;HP ¼ mwf1 :ðh5 h6 Þ:he
Wexp;LP ¼ mwf :ðh3} h7 Þ:he
Wnet ¼ ðWexp;HP þ Wexp;LP Þ ðWpump;HP Wpump;LP Þ
hI ¼ Wnet =Q total
QP;total ¼ CpP :mP :ðTP;in T0 Þ
QS;total ¼ CpS :mS :ðTs;in T0 Þ
Up ¼ Qevap 1 =QP;all
US ¼ Qevap 2 =QS;all
Irreversibility in turbines (kW)
Irreversibility in pump (kW)
Irreversibility in vapour regenerator (kW)
Internal second law efficiency (%)
External second law efficiency (%)
Second law efficiency (exergetic efficiency) (%)
ExP ¼ mP eP ¼ mP :ðhP h0 T0 ðsP s0 ÞÞ
ExS ¼ mS eS ¼ mS :ðhS h0 T0 ðsS s0 ÞÞ
Ievap;HP ¼ mP :ðhP;in hp;out T0 ðsP;in sP;out ÞÞ mwf1 :ððh5 h4 T0 ðs5 s4 ÞÞ
Ievap;LP ¼ ms :ðhs;in hp;out T0 ðss;in ss;out ÞÞ mwf2 :ððh3 h2 Þ T0 ðs3 s2 ÞÞ mwf :ððh2 h1 Þ T0 ðs2 s1 ÞÞ
Iexp;HP ¼ mwf1 :ððh5 h6 Þ T0 ðs5 s6 ÞÞ Wexp;HP
Iexp;LP ¼ mwf :ððh3} h7 Þ T0 ðs3} s7 ÞÞ Wexp;LP
Iexp ¼ Iexp;HP þ Iexp;LP
Ipump;HP ¼ Wexp;HP mwf 1 :ððh4 h2 Þ T0 ðs4 s2 ÞÞ
Ipump;LP ¼ Wexp;LP mwf :ððh1 h9 Þ T0 ðs1 s9 ÞÞ
Ipump ¼ Ipump;HP þ Ipump;LP
Iregen ¼ mwf 2 :ððh3 h0 Þ T0 ðs3 s0 ÞÞ þ mwf1 :ððh6 h0 Þ T0 ðs6 s0 ÞÞ mwf :ððh3} h0 Þ T0 ðs3} s0 ÞÞ
hex;int ¼ Wnet
ððExP;in ExP;out Þ þ ðExS;in ExS;out ÞÞ
hex;ext ¼ ððExP;in ExP;out Þ þ ðExS;in ExS;out ÞÞ
ðExP þ ExS Þ
hex ¼ Wnet=
ðExP þ ExS Þ
Fig. 4. T-Q diagram for the heat absorption process in TR-STORC.
optimization parameters along with the cycle design constraints
are shown in Table 4. The maximum operating temperature of the
working fluid or the maximum allowable temperature based on
pinch conditions is set as the limit on the vapour outlet temperature. Condenser pressure is kept above atmospheric pressure to
prevent air leakage into the system. Volumetric flow ratios (VFR) of
both HP and LP turbine stages are constrained within 50 so that
each stage would require only single rotors and high stage efficiency (70e80%) can be maintained [37].
The cycle parameters are optimized using Genetic Algorithm
(GA) with net power output as the objective function. The interplay
between various cycle parameters in TR-STORC results in a highly
nonlinear behavior of net power output as seen from the cycle
parameter studies (see Fig. 4 a). GA works well as an optimization
technique for highly nonlinear problems and is based on Darwinian
survival of fittest principle. A four dimensional array [T5,PHP evap, T3,
Tcond] within the specified ranges in Table 4 is generated during the
start of each evaluation. The net power output can then be
expressed as a function Wnet ¼ f [T5, PHP evap, T3], which is then
maximized. Constraints in VFRare imposed by means of penalty
function method, wherein the net power output is penalized if the
stage VFR is found to exceed 50. Input parameters to GA are shown
in Table 5. The optimized cycle performance of TR-STORC is then
compared with an optimized STORC and pre-heated ORC for
various heat source conditions.
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A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Table 3
Thermo-economic parameter calculations.
Parameter
Equations
LP evaporator
Log mean temperature difference LMTD (K)
DTlm ¼ ðDTmax DTmin Þ=
KA calculation (kW/K)
KA ¼ Q=
KA HP evaporator (kW/K)
KA LP evaporator (kW/K)
HP evaporator
Heat transfer in the ith section
lnðDTmax =DTmin Þ
DTlm
KAevapHP ¼ KAevap HP;pre þ KAevap HP;evap
KAevapLP ¼ KAevap LP;pre þ KAevap LP;evap
Qevap HP;i ¼ mwf 1 :ðhiþ1 hi Þ
LMTD across the ith section
DTlm;i ¼ ðDTmax;i DTmin;i Þ
KA HP evaporator (kW/K)
i¼50
P
lnðDTmax;i =DTmin;i Þ
KAevapHP ¼
i¼1
Condenser
KA Condenser (kW/K)
Total KA requirements (kW/K)
Expander parameters
HP expander stage VFR
LP expander stage VFR
Mass averaged VFR
Q evap HP; i
DTlm;i
KAcond ¼ KAcond;sub þ KAcond;cond þ KAcond;superhet
KAtotal ¼ KAevap1 þ KAevap2 þ KAcond
V5
V30
V 00
VFRLP ¼ 3
V7
m
VFRHP þ mwf VFRLP
VFR ¼ wf1
mwf þ mwf 1
VFRHP ¼
Turbine size parameter SP (m)
mwf 1
SP ¼
ðmwf1 v30 Þ1=2
ðmwf v7 Þ1=2
þ mwf
ðmwf1 ðh6 h3s0 ÞÞ1=4
ðmwf ðh300 h7s ÞÞ1=4
mwf þ mwf1
Fig. 5. Effect of HP stage pressure and vapour outlet temperature on (a) Net power output (b) Optimum vapour fraction in the LP evaporator (c) Utilization rates of heat sources (d)
Thermal efficiency. LP evaporation temperature is set to 343 K.
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
9
Table 5
Specified input parameters to the genetic algorithm.
GA parameters
Value
Population size
Maximum generations
Constraint tolerance
Function tolerance
Elite count
Crossover fraction
20
15
0.01
0.01 kW
2
0.8
4.3.1. Variation with heat source temperatures
In this section, cycle optimization is carried out for different
primary and secondary heat source inlet temperatures. A parameter f is introduced, which is the relative increase in net power
output with single stage pre-heated ORC selected as the baseline.
fpower;TRTORC ¼
Fig. 6. Effect of LP stage evaporation temperature on (a) Net power output (b) Utilization rates of secondary heat source.
Table 4
Optimizing parameters, design constraints for TR-STORC, STORC and preheated ORC.
Optimized Parameters
TR-STORC
Vapour outlet temperature HP stage T5
Pressure in HP stage PHP evap
Evaporation temperature in LP stage T3
STORC
Evaporation temperature in LP stage T3
Evaporation temperature in HP stage T6
Preheated ORC
Evaporation temperature T4
Preheat temperature T2
For all configurations
Condensing temperature Tcond
Constraints
Condenser pressure Pcond
VFR HP turbine
VFR LP turbine
Degree of sub cooling
Range
1.1Tc-600 K
1.1 Pc- 8MPa
323 K - (Ts,ineDTevap,LP)
323 K - (Ts,ineDTevap,LP)
333K-0.9 Tc
Wnet;TRSTORC Wnet;preORC
100
Wnet;preORC
For the temperature ranges investigated, TR-STORC shows superior performance over pre-heated ORC and STORC. TR-STORC
delivers approximately 14%e20% more power output than STORC
(see Fig. 7 a). As the secondary heat source temperature Ts,in increases, the relative increase in power output of TR-STORC and
STORC exceeds that of pre-heated ORC due to the improved thermal
efficiency and temperature matching in the LP stage. In other
words, as the temperature difference between the two heat sources
decreases, STORC and TR-STORC show improved power outputs
over pre-heated ORC. This is due to the improved utilization of
secondary heat source in two stage ORCs which tend to increase
with increase in Ts,in. Both TR-STORC and STORC are able to fully
utilize the primary heat source, and it remains almost constant
irrespective of the change in secondary heat source temperature
(see Fig. 7b). As seen from Fig. 7 c, the internal exergy efficiency of
TR-STORC is higher than STORC owing to the supercritical evaporation process and the regenerative use of superheated vapour. The
external exergy efficiency of TR-STORC is higher than that of STORC
for the case with Tp,inset at 673 K. At 773 K, the fluctuations in
exergy efficiency are due to the reduced heat input from the secondary heat source since more heat is available from the primary
side. Therefore, higher superheat of HP turbine exhaust prevents
more heat to be extracted from the secondary heat source. For both
TR-STORC and STORC, the external and internal exergy efficiency
and thermal efficiency is seen to show a turning behavior at 383 K
due to heat content of the two heat sources reaching almost the
same values, which is described in the following section. In general,
the higher exergy efficiency and thermal efficiency of TR-STORC is a
result of improved internal and external exergy efficiency.
4.3.2. Variation with heat ratio
Typically, in dual source applications, one of the heat sources
would have heat content higher than the other. For such cases, heat
ratio is defined as the ratio of heat available from the primary heat
source to the secondary heat source can be defined as:
Q P mP CpP TP;in TP;out min
¼
Q S mS CpS TS;in TS;out min
373K-0.9 Tc
323 K- (Ts,ineDTevap,LP)
Qr ¼
313e353 K
The relative increase in power output over pre-heated ORC of
TR-STORC and STORC is seen to increase with decrease in heat ratio
(See Fig. 8a). For all heat ratios, TR-STORC outperforms STORC and
the effect is seen to increase at higher heat ratios. At lower heat
ratios (Qratio<1), there is more heat is available from the secondary
heat source, which the two stage architectures are able to utilize
better when compared to pre-heated ORC. At Qratio<1, this
1.20 bar
50
50
5K
10
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
improved secondary heat source utilization of two stage layout is
the primary reason for the increased work output of STORC and TRSTORC over pre-heated ORC. The improvement in power output of
STORC approaches that of pre-heated ORC as the available heat in
the primary heat source increases. This is because for higher heat
ratios, improved utilization of secondary heat source does not
contribute much to the improvement in power output. However, in
the case of TR-STORC, at higher heat ratios, the lower irreversibility
associated with the supercritical heat transfer process in the HP
evaporator leads to improved performance. For lower heat ratios,
the two stage architecture with partial evaporation and the
regenerative use of superheated vapour in TR-STORC is able to
achieve higher internal exergy efficiencies (see Fig. 8c) which also
manifests as high thermal efficiency (see Fig. 8b). For the heat ratios
investigated, TR-STORC delivers 14e16% and 18e28% increased
power output than STORC and preheated ORC respectively. Close to
heat ratio of 1, the primary and secondary heat content is almost
the same. Therefore, TR-STORC utilizes minimum heat from the
secondary heat source (see Fig. 8d) while maximising the internal
efficiency by means of regeneration. Heat is drawn from the secondary heat source almost entirely in the preheater leading to the
working fluid having a very low vapour quality at state point 3. The
remaining heat from the superheated vapour is used in the
regenerator to fully evaporate the fluid in the LP evaporator. This
leads to a high internal efficiency of TR-STORC at heat ratios close to
1, and the lowest utilization of secondary heat source leads to
coupled lowest external exergy efficiency. At heat ratios higher
than 1, higher mass flow rate associated with the higher utilization
of primary heat source in the HP loop leads to improved utilization
of secondary heat source in the pre-heater. This explains the further
increase in Us at higher heat ratios. Due to this, a similar effect is
seen in the external and internal efficiency plots.
For all the heat ratios investigated, the primary heat source
utilization rate is seen to remain the same at 80% for both TR-STORC
and STORC. The utilization of secondary heat source in the case of
TR-STORC is lower than that of STORC for heat ratios around 1 and is
seen to rise for higher ratios (see Fig. 8d). The utilization of superheat from the HP turbine exhaust allows for less heat to be
withdrawn from the LP evaporator at heat ratios close to 1. External
efficiency also being a measure of heat absorption from the sources
follows the same trend. The effective utilization of the superheat
also explains the higher internal second law efficiencies of TRSTORC corresponding to the same heat ratios.
The optimization results for selected heat ratios along with the
thermo-economic parameters are listed inTable 6. Preheated ORCs
are unable to utilize more heat due to pinch limitations in the series
connected preheater and evaporator, the heat exchanger KA requirements also remain the same irrespective of heat ratio. The
higher KA values associated with TR-STORC are due to the lower
LMTD values associated with the supercritical evaporation process
coupled with higher mass flow rates in partial evaporation. At
higher heat ratios, supercritical heat transfer in the HP evaporator is
dominant and therefore leads to higher KA requirements. However,
it should also be noted that KA values are not an accurate estimate
of the heat exchanger cost. This is particularly true for supercritical
heat transfer, since the strong variations in thermo-physical properties of the working fluid leads to similar variations in heat
transfer coefficient [38], obscuring the variation of heat exchanger
area. Detailed heat exchanger area calculations are required to estimate the exact area requirements which are beyond the scope of
the present study. VFR values of HP turbine stage are particularly
11
high for TR-STORC when compared to STORC and pre-heated ORC.
This is due to the expansion from supercritical pressures to the LP
evaporator pressures in TR-STORC. LP stage VFR values are significantly lower than HP stage for both STORC and TR-STORC. This is
due to the small pressure ratio across the LP turbine. Furthermore,
in preheated ORC, the restricted heat transfer resulting in the same
mass flow rate of the working fluid coupled with a constant pressure ratio across the turbine leads to a constant turbine size
parameter. As for TR-STORC, the turbine size parameters are comparable to that of preheated ORC and STORC for most of the cases
investigated, indicating that the turbine cost would remain roughly
the same.
4.3.3. Component irreversibility distribution
Fig. 9 presents the characteristics of exergy destruction in TRSTORC and STORC for various heat ratios. Compared to STORC,
TR-STORC is able to decrease the irreversibility associated with the
high temperature heat transfer process in the primary side. The HP
evaporator in STORC accounts for 29e41% of the total component
irreversibility. For TR-STORC, the same process irreversibility accounts for only 15e22% of the total. The LP evaporator and preheater together accounts for 3e11% and 2e10% share in component irreversibility in TR-STORC and STORC respectively. The exergy
loss associated with the pre-heating and LP evaporation process is
seen to decrease with increase in heat ratio. This is due to the lower
heat content in the secondary heat source at higher ratios which in
turn leads to less exergy input to these components.
The condenser has the maximum share in component irreversibility ranging from 31 to 41% in TR-STORC and 32e39% in
STORC for the heat ratios investigated. For working fluids such as
cyclopentane used in this study, higher condensing temperature of
328 K is set by the lower limit on condenser pressure (1.20 bar).
Condenser losses could be reduced to a great extent by utilizing
fluids that condense at lowering the condensing temperatures.
Exergy loss in the turbines account for 17e21% in STORC whereas
this is reduced in TR-STORC to 13e19%. However, for TR-STORC the
pumps results in higher irreversibility of 9e13% when compared
with STORC where this ranges only from 3 to 5%. The high pressure
pumping process required to achieve supercritical evaporation is
the major source of increased pump irreversibility. This cannot be
avoided in the case of TR-STORC since the higher power output and
thermal efficiency gains of TR-STORC are inherently dependent on
the supercritical evaporation process. For STORC, the mixing process irreversibility is negligible (less than 2%). Whereas for TRSTORC, the mixing process in the vapour regenerator of TR-STORC
contributes 11e14% of total component irreversibility, remaining
largely unchanged with heat ratio. Improving the thermodynamics
of the regenerative mixing process could lead to further increase in
heat to power conversion efficiency of TR-STORC.
4.3.4. Performance at engine design point
The optimized performance of TR-STORC, STORC and pre-heated
ORC at engine design point (see Section 2.1) is shown in Table 7.
Among the three cycle architectures, TR-STORC also has the highest
thermal efficiency and exergy efficiency. The utilization of primary
heat source is almost the same for all the three architectures. STORC
utilizes the secondary heat source to the highest and has higher
heat absorption capacity. However, TR-SORC is able to limit its use
of the secondary heat source (28% less than that of STORC) by utilizing the superheat from the exit of the HP turbine stage in the
vapour regenerator. This ability of TR-STORC to optimize both its
Fig. 7. Relative increase in power output of STORC and TR-STORC over pre-heated ORC (b) Variation in heat source utilization rate (c) Internal exergy efficiency (d) Thermal efficiency (e) External exergy efficiency for various primary and secondary heat source temperatures.
12
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Fig. 8. Variation of (a) relative increase in power output over pre-heated ORC (b) thermal efficiency (c) internal and external efficiencies and (d) utilization rate of secondary heat
source Us for TR-STORC and STORC with heat ratio Qr. Primary and secondary heat sources temperatures are fixed at 673 K and 363 K respectively.
Table 6
Optimized cycle parameters and thermo economic parameters for different heat ratios. Primary and secondary heat source inlet temperatures are set at 673 K and 363 K
respectively.
Qr
Tcond (K)
TR-STORC
0.375 328
0.750 328
1.500 328
2.287 328
STORC
0.375 328
0.750 328
1.500 328
2.287 328
Preheated ORC
0.375 328
0.750 328
1.500 328
2.287 328
Pcond (bar)
Tevap,LP (K)
Pevap,LP (bar)
Tevap,HP (K)
Pevap,HP (bar)
mwf1 (kg/s)
mwf2 (kg/s)
Wnet (kW)
VFRHP
VFRLP
SP (m)
KA (kW/K)
1.2
1.2
1.2
1.2
342
348
349
349
1.85
2.19
2.25
2.25
575
575
570
573
64.03
71.18
68.00
70.68
2.36
2.478
2.509
2.499
4.877
2.056
1.607
1.535
349.0
332.2
324.9
324.5
48.4
49.5
46.0
48.3
1.5
1.8
1.8
1.8
1.23
0.46
0.38
0.37
155.3
190.2
231.6
267.0
1.2
1.2
1.2
1.2
343
345
351
351
1.91
2.03
2.38
2.38
460
460
460
460
21.84
21.84
21.84
21.84
3.273
3.300
3.382
3.382
2.859
1.103
0.190
0.124
301.8
285.2
280.8
279.6
13.9
13.1
11.2
11.2
1.5
1.6
1.9
1.9
0.85
0.46
0.32
0.31
200.5
131.1
99.3
96.6
1.2
1.2
1.2
1.2
e
e
e
e
e
e
e
e
460
460
460
460
21.84
21.84
21.84
21.84
3.387
3.387
3.387
3.387
e
e
e
e
274.8
274.8
274.8
274.8
21.6
21.6
21.6
21.6
e
e
e
e
0.46
0.46
0.46
0.46
117.7
118.0
118.5
119.3
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
13
Table 7
Optimum cycle performances at engine design point.
Parameters
Pre-heated ORC
STORC
TR-STORC
Wnet (kW)
hI (%)
hex (%)
Up (%)
Us (%)
mwf (kg/s)
Tevap,LP (K)
Tevap,HP (K)
Pevap,HP (MPa)
VFRLP
VFRHP
SP
KA (kW/K)
W/KA
280
14.4
14.2
81.5
5.20
3.50
e
460
2.18
e
21.6
0.516
117
2.46
297
12.2
15.0
81.6
18.4
4.85
344
460
2.18
1.6
13.5
0.681
147
2.02
344
15.3
17.4
81.6
13.3
4.84
347
582
6.83
1.7
45.2
0.120
149
2.31
modification to the current STORC is also an alternative to STORC.
Optimized results are compared for two distinct heat ratios (Qr > 1
and Qr < 1). Results shown in Table 8 indicate that R-STORC brings
only marginal improvement (<1%) in performance when compared
to STORC. The expansion of vapour from within the critical pressure
in subcritical cycles results in lower superheat at the exit of the HP
expander. This decreased superheat results in less heat available for
regeneration. On the other hand, for expansion from transcritical
pressures, the resulting superheat is quite high, making more heat
available for regeneration in the vapour regenerator. Transcritical
evaporation combined with utilization of the resulting high superheat is the primary reason for the additional power output of
TR-STORC.
Fig. 9. Component wise irreversibility distribution at optimized conditions for (a) TRSTORC and (b) STORC with heat ratio Qr. Primary and secondary heat sources temperatures are fixed at 673 K and 363 K respectively.
Tevap,LP and vapour fraction in order to match the available superheat leads to higher thermal efficiency. Therefore, TR-STORC delivers the highest power output, which is 16% higher than STORC
and 23% higher than pre-heated ORC. The KA values of TR-STORC
are comparable to that of STORC. The higher KA values of STORC
and TR-STORC can be explained by the higher heat source utilization of the two stage architectures over the single stage pre-heated
ORC. VFR values of TR-STORC being less than 50 implies that the
same two stage induction turbines of STORC with single rotor per
stage can be used.
4.3.5. Performance comparison with regenerative subcritical STORC
A regenerative subcritical STORC (R-STORC), which is a
4.3.6. Performance comparison for various working fluids
The superiority of TR-STORC architecture is further analysed by
comparing the performance for various organic fluids which are
commonly used in high temperature ORC systems. The cycle performances are optimized for each of these working fluids using
Genetic Algorithm and the same constraints and boundary conditions in Table 9.
The maximum net power output of TR-STORC is higher than
STORC and preheated ORC for all the studied working fluids and is
able to generate 15e34% and 15e52% higher power output than
STORC and single stage preheated ORC respectively (see Fig. 10).
The increment in net power output is particularly high for working
fluids such as butane which have sufficiently high maximum
temperatures and lower condensation temperatures corresponding
to the condenser pressure limit. The highest net power output is
obtained for pentane. The lower condensing temperature of
pentane corresponding to the minimum condenser pressure allows
for a considerable reduction in the condenser irreversibility.
Furthermore, when compared to working fluids having the same
maximum temperature limit (600 K) such as hexane and cyclopentane, the critical temperature of pentane is the lowest. This
allows pentane to be optimized across a wider range of vapour
outlet temperatures and supercritical pressures leading to
improved net power output. In summary, the regenerative heat use
in TR-STORC allows for improvement in performance of various
working fluids used on ORC systems.
5. Critical remarks and discussion
Previous study on performance of two stage ORCs in dual source
heat recovery by Surendran et al. [26] reported an increment in
performance improvement of STORC over preheated ORC as the
temperature difference between the primary and secondary heat
14
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Table 8
Comparison of TR-STORC with STORC and R-STORC.
Qr
Wnet (kW)
0.75
2.28
STORC
R-STORC
TR-STORC
285.2
279.6
287.8
279.9
332.2
324.6
higher than that of STORC and contribute to the bulk of exergy
destruction. Therefore, future studies on two stage ORCs should be
directed at the use of improved regenerative mixing processes such
as thermal compression that are capable of utilizing vapour
superheat.
Among the different working fluids, although pentane shows
Table 9
Selected working fluids along with their thermo physical properties, maximum and minimum temperatures [32].
Parameters
Critical temperature (K) Molecular mass (g/mol) Critical pressure (MPa) Maximum temperature (K) Condensing temperature at 1.20 bar (K) GWP ODP
Cyclopentane 511.7
Pentane
469.7
Hexane
507.8
Butane
425.1
R365mfca
460.0
a
70.1
72.1
86.2
58.1
148.1
4.52
3.37
3.03
3.80
3.27
600
600
600
575
500
328.0
314.2
347.4
277.2
318.1
11
~20
3
~20
782
0
0
0
0
0
Vapour outlet temperature is varied from 470 to 500 K. Minimum vapour outlet temperature condition of 1.1Tc cannot be applied for R365mfc.
the highest power output, the difference in net power outputs of
cyclopentane and butane when compared to that of pentane in TRSTORC are lower by 3e4% only. Fluids such as butane which
underperforms in STORC and preheated ORC layouts are able to
match with high performing fluids like cyclopentane and pentane
in TR-STORC. This indicates that in TR-STORC, there exists a possibility of selecting several working fluids delivering similar power
outputs. Therefore, other alkanes capable of operating at higher
temperatures, with lower condensing temperatures and which
have molecular stability at supercritical states would qualify as
working fluids for TR-STORC. Furthermore, computer aided molecular design of ORC working fluids as reported by Shilling et al.
[39] and Lampe et al. [40] could be extended to develop stable and
non-flammable working fluids which can match these properties.
6. Conclusions
Fig. 10. Maximum net power outputs of TR-STORC, STORC and single stage pre-heated
ORC at optimized conditions for various working fluids. Primary and secondary heat
sources temperatures are 673 K and 363 K respectively. Qratio is 0.75.
sources decreased. Similar behavior is also shown by TR-STORC in
this study. However, the increment in net power output of TRSTORC over STORC stays with a narrow band14-16%), irrespective
of the temperature difference between the two heat sources. This is
because in TR-STORC, the supercritical HP evaporation coupled
with partial evaporation and regeneration in the LP stage leads to
higher thermal efficiencies and increased mass flow through the LP
turbines. STORC is able to deliver significant performance
improvement only for heat ratios less than 1. Whereas, TR-STORC
delivers improved performance over the entire range of heat ratios investigated, making it a favourable choice for all scenarios of
dual source heat recovery. However, as described in Section 4.3.3,
the constant pressure mixing process in the vapour regenerator
contributes to a significant share in component irreversibility,
almost equal to that of the two pumps combined. This is further
supported by the poor performance improvement of R-STORC over
STORC, seen in Section 4.3.5. This indicates that constant pressure
mixing is a thermodynamically inefficient process that needs to be
replaced for further improvement of the system. In addition to that,
regulating the vapour fraction at the evaporator outlet poses a
challenge, especially from a system control perspective. Furthermore, the condenser and turbine irreversibilities in TR-STORC are
A regenerative two stage ORC architecture that improves on the
existing STORC architecture by combining supercritical heating in
the HP stage with partial evaporation and regeneration in the LP
stage is proposed. Exhaust gas and jacket water from an IC engine
are used as the primary and secondary heat sources for the cycle.
Influence of cycle parameters is analysed and the optimized performances for a range of operating conditions including working
fluids are evaluated. The main conclusions are:
1. At lower evaporator pressures, lower values of vapour outlet
temperatures lead to maximum work output. The vapour fraction in the LP evaporator outlet decreases with the increase in
vapour outlet temperature in the HP stage.
2. Utilization rate of secondary heat source decreases linearly with
LP evaporation temperature. An intermediate LP evaporation
temperature exists that maximises the net power output.
3. STORC delivers significantly higher power output than single
stage pre-heated ORC only for cases with heat ratio less than 1.
TR-STORC is able to deliver increased power outputs for all heat
ratios, ranging between 14-16% and 18e28% when compared to
STORC and preheated ORC respectively.
4. At the engine design point, TR-STORC delivers 16% and 23%
higher power output than STORC and pre-heated ORC
respectively.
5. TR-STORC is able to achieve excellent exergetic performance for
all the working fluids investigated. TR-STORC is able to generate
15e34% and 15e52% higher power outputs than STORC and
single stage preheated ORC respectively.
A. Surendran, S. Seshadri / Energy 203 (2020) 117800
Reduction in vapour regenerator irreversibility by improving the
thermodynamics of the mixing process coupled with reduction in
turbine and condenser irreversibilities are essential to further
enhance the heat to power conversion efficiency of TR-STORC. This
shall be the subject for future studies on two stage regenerative
ORCs.
Declaration of competing interest
Initial results from this study has been presented at the 5th
International Seminar on ORC Power Systems held at Athens,
Greece.
Acknowledgement
The results presented in this paper have been obtained with the
financial support provided by the Department of Science and
Technology (DST), Government of India and the Industrial Consultancy & Sponsored Research, Indian Institute of Technology
Madras.
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