Purdue University
Purdue e-Pubs
International Refrigeration and Air Conditioning
Conference
School of Mechanical Engineering
1990
Estimation of Thermodynamic Properties of Nonazeotropic Refrigerant Mixtures and Application to
the Heat Pump System
S. T. Ro
Seoul National University
M. S. Kim
Seoul National University
T. S. Kim
Seoul National University
K. S. Cho
Seoul National University
Follow this and additional works at: http://docs.lib.purdue.edu/iracc
Ro, S. T.; Kim, M. S.; Kim, T. S.; and Cho, K. S., "Estimation of Thermodynamic Properties of Non-azeotropic Refrigerant Mixtures
and Application to the Heat Pump System" (1990). International Refrigeration and Air Conditioning Conference. Paper 125.
http://docs.lib.purdue.edu/iracc/125
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NON·AZ EOTROP IC REFRIG ERANT
ESTIMA TION OF THERM ODYNA MIC PROPER TIES OF
SYSTEM
MIXTUR ES AND APPLIC ATION TO THE HEAT PUMP
Cho
Sung Tack Ro, Min Soo Kim, Tong Seop Kim aod Kwao Sbik
y
Departm ent of Meehanical Engineering, Seoul National Universit
Seoul, 151-742, KOREA
ABSTRA CT
non-azeotropic refrigerant mixtures using
Thermod ynamic propenie s are estimated fot the selected binmy
Calculations have been made for eight different
the Peng-Robinson equation of state and mixing rules.
l14, Rl3Bl/R l52a, Rl3Bl/R l2, R22/R1S2a
mixtures including Rl3B11R ll4, R221Rll 4, Rl21Rll 4, Rl52a/R
and R22/Rl4 2b.
mixtures have been chosen to calculate
In this Study, the binary interaction coefficients of the
vapor-liquid equilibria. A con-elation is proposed
thermodynamic properties, such as enthalpy, entropy and the
between dipole moments of each pure refrigerant.
to relate the binary interactio n coefficient with difference
ntal data and they give reasonably good
experime
existing
til=
with
The calc~tlated val~tes are compared
prepared fot a panie~~Jar composition of
are
diagrams
y
re-entrop
temperam
agreements. Pressure-enthalpy and
each refrigerant mixmre.
to simulate the perfotma nce of a heat p11mp
The simple method of property calculation makes it possible
2a, R22/Rl4 2b, and Rl3Bl/R l52a as
R22/R15
4,
R221Rll
including
mixtures
nt
using non-azeotropic refrigera
working fluids.
can be obtained by varying the mixt~tre
The sim~tlated results show that the capacity modulati on
ot. The variation of the coefficient of
compress
type
ent
displacem
a
with
p11mp
composition in a heat
·
system.
mixt~tre
tropic
non-azeo
a
in
performance is also stlldied
NOMEN CLATUR E
c~,:
~~
"
coefficients
conStant pteSSUre specific heat at ideal gas state
f~tgacity
enthalpy
:
kij : binary interactio n coefficient
p : pressure
heat transferr ed
Q
gas constant
R
entropy
s
temperat ure
T
specific volume
IV: compression work
mole fraction of the liq~tid phase
X
mole fraction of the vapor phase
."
compressibility factor
z
Greek leners
a. : coefficient related to the
eq~tation
of state
"" : dipole moment
Subscript
b
c
~
H
j
L
o
w
brine
critical value, condense r
evaporat ot
high temperat~tre side
inlet, i compone nt
j compone nt
low temperat~tre side
standard state, o~ttlet
water
1. INTROD UCTION
working fluids for simulation and effiCient
It is importan t to estimate the thermody namic properties of
proper working fluid muSt be chOsen for
The
p~tmps.
beat
and
ors
refrigerat
as
operation of thermal systems such
s of those working fluids should be
propertie
ynamic
-thermod
the
and
system
the best performa nce of the
correctly evaluated.
th= higher perfottnance of heat pumps
The research and development have been progressed to achieve
ropic: mixtures. The purpose of
non-azem
including
flltids
wotking
of
mixtures
the
utilizing
and refrigerators by
refrigerant mixtures to simulate the
tropic
non·azeo
binary
of
s
propertie
namic
thermody
this study is to estimate
perfonna nce of the systems.
may ~. ~assified into performance
The main advantages of non-azeorropic refrigerant mixt11~
by ~III_'Zillg t~ ~ean temperatll~e
achieved
can~
former
The
].
control[2
capacity
enhancem ent[l] and the
charactenstlcs of ghdmg temperat ure 10
the
by
s1nk
ot
somce
heat
the
and
fluid
working
the
difference betwo=en
404
the non-azeotropic mixtures< The latter profit of non-aze
otropic refrigerants is obtained by changing the mixture
rauo during the operation.
In this study, the well-known Peng-Robinson equation
of state is chosen to evaluate the thermodynamic
properties of the non-azeotropic refrigerant mixture
s and the conventional mixing rule is also applied.
The
calculation of enthalpy and entropy of the mixture makes
it possible to analize ·rhe performance of the specifie
d
heat pump cycle quantitatively.
The calculation covers the pure components of R13Bl.
R22, Rl2, R152a and R114; and the binary
mixtures of R13Bl /Rll4, R22/Rl l4, R12'Rl l4,
Rl52a/ Rll4, Rl3Bl/ Rl52a, Rl3Bl/ Rl2. R22/R152a
R22/Rl42b.
and
.
.
A rest rig has been assembled and experiment are
in progress to measure perfonnance of a heat pump
with various mixtures. In this report. we present only
the result of ealcularion and analysis.
2. CALCULATION OF THERMODYNAMIC PROPE
RTIES
2 1 EQuation of State
In this study, Peng-Robinson equation of state is chosen
for the ealculation of the thermodynamic
properties of refrigerants since it predicts the properti
es reasonably well and makes the calculation relativel
y
simple, especially for the case of mixing parametetli.
The mixing rule is required to evaluate thermodynamic
properties of refrigerant mixtures, and the procedure
for applying mixing rules will be much complicated
when
a complex form of equation of state is used.
Peng-Robinson equation of state is well-known in
the literature[3]. The working equations are simply
repeated here for the completeness of the paper.
p = ...!!!._ _
a(T)
v-b
v(v+b ) + b(v-b ) '
(1)
(2)
b =
R T<
o.on so-- .
(3)
p<
By using the compressibility factor Z, the cubic equatio
n of the following form is obtained.
z3- (l-B)z 2 + (A.- 3Jl-- 2B)Z- (AB -B 2 -B 3) ~ 0,
(4)
where
Pv
aP
Z=-
bP
A = - - , B .. - .
RT
(5)
Rlrl
RT
As usual, a(T) is expressed as follows.
a(T) = l
T
+
T<
(l - -)(m + n-).
(6)
T.
T
Two parametetli, m and n can be determined from
the experimental data of the saturated states. In
this
procedure, the fugacity equality condition is introduc
ed
are taken from ASHRA E's vapor pressure relation[4] to find m and n. Experimental data for vapor pressure
for pure refrigerants.
2 2 Mixjnz Ruh: and Prapen y CaleuJatign
The equation of state for mixtures can be completed
by assigning the proper mixing parametetli for the
components. The conventional mixing rules are applied
in this study[SJ.
a= 'X.'I.x1:riafi,
i j
(7)
b ~ "Zl:.xtxjbij.
i j
a11
-
(8)
(1 - ku)"lla1a1 ,
"
bl
(9)
+ bj
b.. = (1 - k l j ) - - .
"
2
(10)
In rhe present calculation, £ for rhe interaction parame
ter bij is treated as zero.
11
405
e for enthalpy, h, entropy, s, and fugac:iry, J, are
With Peng-R obinson equatio n of state, the formula
as
summarized
v - (V'Z- 1)b
da(T)
1
--[a( T)- T--] ln
,, + (V'Z + l)b
dT
2V'Zb
h = h0
+
s- s0
+ R I n - - - - - - - - I n v + (V'Z +
2V'Zb tiT
RT
v- b
1
da(T)
+ RT(Z-
,. - (V'Z - l)b
1)
T
(12)
'
da1
Oc;"ci 1,., da 1
1
da(T)
a.-).
- - = -::::::::..-,..)(1- kq)(- -) •· (-a.i + 1 tiT
tiT
a 1a 1
2 1i
tiT
da 1
D
m1
= - Td - n;
(11)
p
c;
+ J-dT
1)b
+ fc 0 dT,
(13)
Td
r'
(14)
lf/'Q
z + (V'Z + l)B
b,
A.
b,
J,
-)In
In-= -(Z-1 ) -ln(Z -B)- - - · ( - - (V'Z - 1)B
b
a
2V'28
b
x1P
taken from ASHRA E(4].
are
state
gas
ideal
ln the above equatio ns, data for the spedfic heat at
(15)
z-
Cgc:fficieot
2 :>. Vapor- Ljgujd Eguj!jbriym and Bjnazy Jnrerag jon
rule on the conditio n that the fugacities for liquid
Vapor-liquid equilibrium state can be found by phase
in vapor
given pressure and tt:mperature, composition ratios
and vapor phases are the same. In this study, with
one of
and tempera ture data and the composition ratio in
and liquid states are found. When =ither of pressure
ces of fugacities
differen
the
until
DS
unknOW
find
to
ed
perform
liquid and vapor p~ are given, iterations are
reach the order of 10- in eq. (15).
are taken from various literatures: Rl3B1/ Rl14[ 6],
E:<perimental data for the refrigerant milnures
R12[10 ], Rl3Bl/ R152a[ ll], R22/R1S2a and
Rl3B1/
114[9],
R152a/R
R22/R114[7, 8], R12/R114[1],
d to give the reference values of /z and s to
adjuste
are
(12),
and
(11)
eqs.
in
s
R22iR142b. The values h 0 and 0
ant and at bubble point for refrigerant
refriger
pure
for
state
liquid
d
saturate
at
be 200 k.llkg and 1 k.l/kgK
mixtures at T .. 0°C.
j;s
2 4 Calculated Results of Theanqd,marnU; Prqpert
1. With these values, vapor pressures of pure refrigerants
Table
in
shown
are
n
and
m
of
values
ed
Estimat
ble to
]. Systematic deviations appears but it is accepta
dara[l4
E
ASHRA
with
ed
compar
and
ed
are calculat
are also
EnthalpY and entropY of saturate d liquid and vapor
ions.
applicat
of
range
the
within
data
the
utilize
point or
s larger as the tempera ture reaches close to critical
compared with ASHRAE data. The error become
region.
ture
tempera
lower
quid
each refrigerant mixture from the data of vapor-li
The binary interaction coefficients are found for
calculated and
between
ce
differen
the
ing
minimiz
by
ned
of
equilibrium. In this study, ku is determi
tempera ture and mole fraction. The calculated values
experimentally measur ed pressure for a state of given
to be a weak function
seems
ku
1%.
about
within
is
pressure
in
n
deviatio
k'i. are given in Table 2. The average
data are
ed binary interaction coefficients from ~ntal
ot tempera ture and mole fraction. The calculat
ents in mixtures. The following
compon
the
of
ts
momen
dipole
in
ces
differen
of
as
plotted in Fig. 1 as a function
experimental data are not enough for substanees such
interpolating relation may be used to estimate ku when
R22iR142b and R22JR152a.
(16)
kq ~ c1(61.zf + czla111 + c 3 ,
(17)
c 1 "' 0.0197931, c1 "' 0.0204207, c 3 "' 0.0016696 .
ium relations for pressure, tempera ture and mole
Figure 2 shows some of the vapor-liquid equilibr
well with the experimental data. In spite of the
agree
results
ted
CalCIIia
phases.
vapor
and
fractions of liquid
and bubble points are well predicted. Figure 3
point
dew
state,
of
n
equatio
obinson
Peng-R
of
simple form
the results calculated with the aids of R<ioult's
shows
and
klj,
ter.
parame
ion
intet:lct
the
of
indicates the effect
rule.
-7
are calculll:ted f~ refrig~t mixtures. Figures 4
Thermo dynami c propenies of enthalp y and entropy
s at a specific rmxture rano, say, 50/50 mass frac:non
diagram
tropy
ture-en
tempera
and
lpy
e-entha
show pressur
1S2a respectively.
for R22iR114, R22iR152a, R22/R142b and Rl3Bl/R
406
Table 1 Calculated values of m and n in eq. (6) for
several refrigerants
0.!2
Rl52a/Rl14
D.!O
Refri~~:erant
R13Bl
R22
R12
R152a
R142b
Rll4
m
il
0.4380
0.4909
0.4666
0.6990
0.6789
0.5129
0.1992
0.2212
0.1887
0.1212
0.1031
0.2424
- - Eq.(16)
0.08
\
R1:21R114
0.06
Rl3Bl!Rl52a
~':;>
o.o.
0.02
Table 2 Calculated values of binary interaction
coefficient for several mixtures
Mixture
k ..
l11u.l
R13B1/Rl14
R22/R114
Rl2/R114
R152a/Rl 14
Rl3Bl/R1 52a
R13Bl!R12
0.0104
0.0393
0.0020
0.1047
0.0802
-0.0009
0.15
0.92
!.5
O.Dl
1.77
1.62
0.14
Fig. 1 Relation between I411LI and .1:
11
(141,.. I ; difference between dipole
moments
{Debye), kq : binary interaction coefficient)
3.0
2.5
v
2.5
0
0
.6
2.0
0
5o
30
10
-10
-3o
·c
·c
·c
·c
·c
2.0
v
eo ·c
0
40 'C
0
"'
0
,.
6""
2.0
--
20
0
-20
·c
·c
·c
l.S
!,;.
t.S
6
"-
0..
1.0
1.0
(a) R13Bl!Rl 14
(b) R22/Rl14
Fig. 2 Vapor-liquid equilibria for the non-azeotropic refrigerant mixtures
(Marks represent experimental data.)
407
tS;-----------------------~
kij = 0.0393
klj =
ts,-------------------------~
- - kij "' 0.0333
0
----- ku =
Raoult's rule
--~-----~OL---~-D••
u ------~LO
D.2
D.D
----...J
0.21.-----~-.......
0.0
0.2
0.0
0.8
LO
(b) R22JR152a
(a) R22/Rl14
LOr----------------------~
0.1.-------------------------~
kij = 0.0247
k;i
o
Raoult's rule
- - -
t5
- - - klj = 0.0802
- - - - - ku =
o.s
=0
0
Raoul!'s rule
~·
0.0
------~LO
----------0.0~------~~
0.4
0.2
~0
L---------o.---..0..1. ---------1LO
0.0
~·
0.2
(d) R13Bl!R152a
(c) R22/R142b
Fig. 3 CoPlparison of vapor-liquid equilibria with Raoult's rule (T = 0°C)
408
10. 0.- ---- ---- ---- ,
1.0
c.."'
g
~
;...
.....
0.1
0.01 .____._
100
1~
_.__....__..
zoo zso
..___.._~__,
300
3$0
.ooo •so
h (k.Tikg)
s (kJikgK)
(a) P·h diagram
(b) T-s diagram
Fig. 4 Pressure-enthalpy and temperature-entropy
diagram for the refrigerant mixture R22/R114
(mass fraaion 50!50)
I~Or------------~
1.0
.......
£::
~
.....
0.1
•10
0.01
100
Fig. 5
200
300
.00
....
~L---~--~~--
600
~~~
1.0
1.2
1.• 1.11
1.11
~~~
:a.o :2.2 2.•
h (k.Tikg)
s (k.TikgK)
(a) P·h diagram
(b) T·S diagrnm
~ure-enthalpy and temper ature·e ntropy
diagram for tbe refrigerant mixture R22/R152a
(mass fraction 50/50)
1o.o 1 - - - - - - - - - - - - ,
l.O
.......
.r:
e.....
0.1
-
O.Ot'-::=--'-~-'-:~........_
100
~
:100
_....._._~
.00
~L-~~~-d====~~~
600
0.11
h (k11kg)
Fig. 6
1.0
1.2
u
u
1.8
:2.0
:2.2
s (kJikgK)
(a) P·h diagram
(b) T-s diagram
Pressure-enthalpy and temperature-entropy diagram
for the refrigerant mixture R22IR142a
(mass fraaion 50150)
409
•oo
11.0
360
1.0
g300
~
!
~
f.,
0.1
Fig. 7
h (kJ/kg)
s (kJ/kgK)
(a) P-h diagram
(b) T-s diagram
for the refrigerant mixture Rl3B11Rl52a
Pressure-enthalpy and temperature-entropy diagram
(mass fraction 50/50)
3. ANALYSIS OF HEAT PUMP CYCLE S
1 I fundam ental A<Sumptjons
cycles by using the thermodynamic propenies of
It is possible to perform the simulation of heat pump
ns in
to find the characteristi(S of heat pump operatio
refrigerant mixtures. Various combinations are tried
R221Rl14.
s
include
s
mixture
The
.
capacity
heating
t
modes of constant volumetric flow rate and constan
cycles. It
are the proper combinations to apply to beat pump
R221Rl52a. R22/R142b and R13Bl/R1S2a. These
d liquid state at
saturate
in
is
and
tor
evapora
the
of
ait
the
at
°C
5
is assumed that the fluid is superheated by
the exit of the condenser.
fixed stroke. The efficiency of the compressor is
Compressor is thought to be reciprocating type with
the outlet and the inlet. In this study, the
between
ratio
pressure
the
the
of
assumed to be a simple function
ssor are regarded as a linear function of
compre
the
of
cy
efficien
ssion
compre
the
volumetric efficiency and
except in the condenser and the
transfer
heat
the
and
flow
the
in
drops
pressure
pressure ratio[l2 ]. The
counterflow type between refrigerant and
be
to
assumed
is
e
exchang
heat
The
d.
evaporator are neglecte
ted
ture-entropy diagrams of the cycle are represen
secondary fluid. The pressure-enthalpy and tempera
8.
schematically in Fig.
t Yo!umerric Sow Rate Cycle
3 2 Mpdu!atinn qf Heatina; Capacity jn a Constan
the
dealt with in a heat pump cycle. We assume that
In this section, modulation of heating capacity is
conditions are given
design
and
g
operatin
The
rate.
flow
volume
t
compressor is operated in a mode of constan
beat
and exit of the condenser and the evaporator, overall
for the temperatures of secondary fluids at inlet
follows:
as
ant
refriger
of
rate
flow
transfer coefficient and volume
= 25 °C
- water tempera ture at the condenser inlet (T...:~)
40 °C
water tempera ture at the condenser outlet (T_,) "'"
~ 20 "C
- brine tempera ture at the evaporator inlet (T,.1)
10 °C
brine tempera ture at the evaporator outlet(T,..,) =
= 03 kWfK
overall heat transfer coefficient in the condenser (UA)0
"' 0.3 kWfK.
overall heat rransfer coefficient in the evaporator q~A),
.
1s
volume flow rate of the refrigerant (m) "' 0.002 m
ants in the heat pump by using
refriger
of
states
Iterative method is used to calculate thermodynamic
g the temperature of the refrigerant at the
assumin
with
initiated
is
tion
Calcula
s.
relation
energy balance
and
ned by heat transfer characteristics at the evaporator
condenser ellit. The inlet state of evaporator is determi
the
lations of states at the condenser are performed with
Recalcu
found.
is
~t
ssor
compre
at
state
the
then
design condition of (UA )•.
9 as a function of mass fraction of lower boiler in the
Variations of the heating capacity are shown in Fig.
P) are drawn in Fig. 10 and defined as follows:
ance(CO
perform
of
ents
mixtures. The corresponding coeffici
QH
(18)
COP "'-.
w
410
p
T
It
s
(a) Pressur e-entha lpy diagram
Fig. 8
(b) Temper ature-en tropy diagram
Schematic diagram of heat p11mp cyde
a.o . . - - - - - - - - - - - - - ,
7.0
6.0
Rl3Bl /Rl52a
7.0
R22/R l52a
5.0
8.0
i
::.
4.0
~
0
"
u
01
5.0
3.0
2.0
4.0
Rl3Bl/ Rl52a
1.0
o.o
0.0
0.2
0.4
o.8
0.8
1.0
Mass fraction of lower boiler (R13B l, R22)
Fig. 9
3.0
0.0
0.2
0.4
0.8
0.8
1.0
Mass fraction of lower boiler (R13Bl , R22)
Variatio n of heating capacity with respec:t to Fig.
10 Variatio n of COP with respec:t to the mass
the mass fraction of lower boiler in constan t
fraction of lower boiler in constan t volume
volume flow rate cyde
flow rate cycle
As shown in Figs. 9 and 10, heating capacity, QH,
and COP vary nearly monotonic:ally as the compon
ents of the
mixt11res chang=s. In c:ase of mixtures with R22,
heating capacity decreases while COP increases
by adding
higher boiler to R22. It enables the heat pump
to be operate d to meet required heating load and
higher
perform ance is obtaine d. Similar _result is obtaine d
for the Dlixture of R13Bl/ Rl52a.
1.3 Pertonn apce Enhanr.emgm in a Constant Heating
Camsity Cycle
Similar sim11lations are carried 0111 to find the perform
ance characteristics in a heat pump operate d in a
mode of a consran t heating capacity. A set of operatin
g conditiOI!S are chosen to provide a heating capacity
of 6
kW. They are as follows:
-
water temperat11re at the conden ser inlet (T~) •
Z5 °C
water temperar11re at the conden ser outlet (T..,) "'
45 °C
411
9.0
r---- ----- ---,
00.0~----------~
A : R22/Rl14
B : R22/Rl42b
8.0
C : R22/Rl52a
D : R13B1/R152a
7.0
"
'§
p..
0
~ 16.0
u
c
~
8.0
-6 10.0
>
5.0
4.0 .___
0.0
A
B
C
D
R22/RU4
R22/Rl42b
Rl3Bl/R152a
R22/R152a
5.0
_._""""='__..__.....__........_ __,
o.e 0.8 1.0
0.4
0.2
0.0 .....__ _.__ __.._ _....__ __.__ __,
0.0
0.2
0.4
0.6
0.8
1.0
Mass fraction of lower boiler (R13Bl, R22)
Mass fraction of lowe:r boiler (R13Bl, R22)
with respect
Fig. 11 Variation of COP with respect to the mass Fig. 12 Variation of volume flow rate
to the mass fraction of lower boiler in
fraction of lower boiler in constant beating
constant heating capacity cycle
capacity cycle
brine temPerature at the evaporator inlet (Tb<i) .., 20 °C
brine temperature at the evaporator outlet (T,_) = S °C
beating load (Q") ~ 6.0 kW
The calculation procedures are same as the previous case. However, overall heat transfer coefficients,
UA ,in evaporator and condenser are calculated for each mixture to meet the required heating load.
of
Variations of COP's for four different mixtures are shown in Fig. 11 as a function of mass fraction
with pure
lower boiler component. For all cases, the higher value of COP is obtained with the mixtures than
temperature
components only. The maldmum values of COP appear at the mass fraction where the largest
a peculiar
difference occurs during phase change. In case of R22/Rll4 mixture, a plot of calculated COP's has
was
shape. The peeuliar shape of COP resulted from the fact that the minimum temperature differenee
assigned between refrigerant and heat souree or heat sink in each end of condenser and evaporator.
Fig.
The corresponding volume flow rates of the refrigerants at the inlet of compressor are represented in
rate varies
12 for four different combinations of mixtures in terms of mass fraction of lower boiler. The flow
monotonically but not linearly.
•
•
4. CONCLUDIN G REMARKS
the
Peng· Robinson equation of state is used in order to estimate the thermodynamic properties of
for
refrigerant mixtures. With this equation of state and mmng rules, thermodynamic properties are calculated
the mixtures including R13Bl/Rll4, R22/Rll4, R121Rl14, R1S2a/Rl14, R13Bl/RlS2a, R13Bl1Rl2,
R22IR152a and R22/R142b.
A
Necessary binary interaction parameters are found for each mixture to gencinlize the calculation.
moments
correlation is proposed for the binary interaction coefficients in terms of difference between the dipole
on the
of each pure refrigerant. Pressure-enthalpy and temperature-en tropy diagrams are presented based
calculation for a certain composition ratio of each refrigerant mixture.
oon·
Two types of simulations are carried out to cl!antderizc the perfonnance of the heat pump by using
fluids. The
azeotropic refrigerant mixtures, R221R152a, R22IR142b, R22/R114 and R13Bl/RlS2a as working
compressor
results show that it is pnssible to modulate heating capacity in a heat pump with a displacement rype
of a
and to increase COP in case of a constant heating capacity. These can be achieved by varying composition
mixture and by choosing proper combinations of pure components.
412
ACKNOW LEDGEM E.Nr
The work described in this report was perfonned with financial
assistance from Goldstar Co., Ltd. in
Korea ro Seoul National University.
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2.
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413