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COMBINED EXERGY AND PINCHANALYSIS FOR OPTIMAL ENERGY
CONVERSION TECHNOLOGIES
INTEGRATION
François Marechal, Daniel FavratLaboratory for industrial energy systems
Institute of energy SciencesEcole Polytechnique fédérale de Lausanne
mailto:francois.marechal@epfl.ch
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Content
Process integration technique
Minimum energy requirement
Exergy analysisProcess integration
Integration of the energy conversion system
Analyse the energy requirementHeat pumpsCombined heat and power
Optimal integration
Graphical representation
Results
2
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Process integration vs system
3
3
Energy
Transformation
Processes
Waste treatment
Productionsupport
Rawmaterials
EnergyProductsBy-products
Energy Water - solvent
Waste heatEmissions
Environment Air
Water Solids
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Process integration
Hot & cold composite curves
Minimum energy requirementHot
Cold
Refrigeration
Heat recovery
4
REFRIGERATION
(EATRECOVERY
(OTUTILITY
COOLINGUTILITY
250
300
350
400
450
500
550
600
0 5000 10000 15000 20000 25000 30000
T ( K )
Q(kW)
Cold composite curveHot composite curve
K7
K7
K7
K7
$4MINDTmin/2
DTmin/2
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Carnot composite curves
5
(OT
5TILITY
#OLD
5TILITY
2EFRIGERATION
(EAT
RECOVERY
1K7
#ARNOTCOMPOSITECURVES
HOTCOMPOSITEHOTCOMPOSITECORCOLDCOMPOSITECORCOLDCOMPOSITE
44
%XERGYLOSTCORRESPONDINGTOTHE$4MINOFTHEHOTSTREAMS
%XERGYDELIVEREDBYTHEHOTSTREAMSTOTHESYSTEM
%XERGYREQUIREDBYTHECOLDSTREAMSOFTHESYSTEM%XERGYLOSTCORRESPONDINGTOTHE$4MINOFTHECOLDSTREAMS
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6
Table 3Exergy of the hot and cold process composite curves
Energy Exergy Exergy Name
Total ∆T mincorrected
Hot streams [kW] 20291.0 5521.4 5352.4 Eq hota
below T 0 [kW] 1709.0 131.5 151.2 Eq hotr
Cold streams[kW] 20197.0 4599.3 4650.1 Eq colda
below T 0 [kW] 0.0 0.0 0.0 Eq coldr
∆T min losses [kW] - 381.2
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Carnot Grand composite curve
7
#(0
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 2000 4000 6000 8000 10000 12000
( 1 - T 0 / T )
Q(kW)
Carnot Grand composite curve
200
250
300
350
400
450
500
550
600
0 500 1000 1500 2000 2500 3000
T ( K )
Exergy (kW, T0 : 298.1K)
Exergy requirement as a function of the temperature
2EFRIGERATION
K7
#OLDUTILITY
K7 #OLDUTILITY
K7
2EFRIGERATION
K7
(EATPUMPING
%XERGYBALANCEK7
(EATPUMPING
#(0
(OTUTILITY
K7
(OTUTILITY
K7
Exergy requirementCarnot Grand composite
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Requirements
8
Table 2Minimum energy and exergy requirements of the process
Energy Exergy Name
Heating [kW] +6854 +567 E heat
Cooling [kW] -7145 - 1269 E cool
Refrigeration [kW] +1709 + 157 E frg
Balance [kW] -550
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-0.2
0
0.2
0.4
0.6
0.8
1
-2000 0 2000 4000 6000 8000 10000 12000
1 - T 0 / T ( T 0 = 2 9 8 K )
Q(kW)
Process composite curve
Utility composite curve
-INIMUM%NERGY2EQUIREMENTABOVETHEPINCHPOINT
Exergy requirement
Exergy requirement above the pinch
9
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Exergy by combustion
10
-0.2
0
0.2
0.4
0.6
0.8
1
-2000 0 2000 4000 6000 8000 10000 12000
1 - T 0 / T ( T 0 =
2 9 8 K )
Q(kW)
Process composite curve
Utility composite curve
-INIMUM%NERGY2EQUIREMENTABOVETHEPINCHPOINT
Exergy combustion
Exergy requirement
E x e r g y l o
s s e s c h i m n e y
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Exergy composite Heat exchange losses
11
-0.2
0
0.2
0.4
0.6
0.8
1
-2000 0 2000 4000 6000 8000 10000 12000
1 - T 0 / T ( T 0 = 2 9 8 K )
Q(kW)
Process composite curve
Utility composite curve
-INIMUM%NERGY2EQUIREMENTABOVETHEPINCHPOINT
Exergy loss -Heat exchange
Exergy requirement
Exergy loss combustion
E x e r g y l o s s e s c h i m n e
y
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Exergy composite -self-sufficient pockets
12
-0.2
0
0.2
0.4
0.6
0.8
1
-2000 0 2000 4000 6000 8000 10000 12000
1 - T 0 / T ( T 0 = 2
9 8 K )
Q(kW)
Process composite curve
Utility composite curve
-INIMUM%NERGY2EQUIREMENTABOVETHEPINCHPOINT
Exergy loss -
Heat exchange
Exergy requirement
Exergy loss combustion
Process Exergy
E x e r g y l o
s s e s c h i m n e y
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CHP : define the steam network
13
200
300
400
500
600
700
800
9001000
1100
1200
0 2000 4000 6000 8000 10000 12000
T ( K )
Q(kW)
Grand composite curve
Grand composite curve
˙ E = qc
T v " T cT v
#c
" T v " T
c( )
$
%
&
& &
'
(
)
) ) = AT v
#c
" T v " T
c( )
q c
T v
T c
[1]! F. " Marechal and B. " Kalitventzeff. Identification the
optimal pressure levels in steam networks using integratedcombined heat and power method. Chemical Engineering
Science, 52(17):2977–2989, 1997.
mfuel ∗ LHV fuel =QMER +
nCHP i=1 E i
ηcomb
Fuel consumption
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Technology w with nominal flow
T outw,i , P outw,i , mw,i, xw,i
T inw,i, P inw,i, mw,i, xw,i
q w = mw,i(hinw,i − houtw,i)
Hot/cold streams
Mechanical power/electricity
Costs
C 1w, C 2w, CI 1w, CI 2w
ew
Integration of the energy conversion system
14
(OT 5TILITY K73ELF SUFFICIENT
0OCKET
#OLD UTILITY K7
2EFRIGERATION K7
HEATPUMPS
'
A S T U R B
I N E
(IGHPRESSURESTEAM
W
# O M B
U S T I O
N
W
W
W
-EDIUMPRESSURESTEAM
,OWPRESSURESTEAM
2EFRIGERATIONCYCLE
/RGANIC2ANKINECYCLE
(OTSTREAMS#OLDSTREAMS0ROCESSSTREAMS
4+
W
&UEL
&UEL
f w
yw
Level of usage of w
Buy/use technology w ?
Decision variables
Creative engineers ?
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MILP formulation
15
minRr,yw,f w,E +,E −
(
nw
w=1
C 2wf w + C el+E +−C el−E
−) ∗ t
+
nw
w=1
C 1wyw +1
τ
(
nw
w=1
(CI 1wyw + CI 2wf w))
nw
w=1
f wq w,r +
ns
s=1
Qs,r + Rr+1 −Rr = 0 ∀ r = 1,...,nr
Rr ≥ 0 ∀r = 1,...,nr; Rnr+1= 0; R1 = 0
nw
w=1
f wew +E + − E c ≥ 0
nw
w=1
f wew +E + − E c − E − = 0
fminwyw ≤ f w ≤ fmaxwyw yw ∈ {0, 1}
E +≥ 0;E
−
≥ 0
Subject to : Heat cascade constraints
Electricity consumption Electricity production
Feasibility
Energy conversion Technology selection
Operating cost
Fixed maintenance
Investment
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Application
16
Energy Exergy
Heating (kW) +6854 +567
Cooling (kW) -6948 - 1269
Refrigeration (kW) +1709 + 157
Maximum energy recovery
Hot Utility :6854 kWSelf sufficient"Pocket"
Ambient temperature
Cold utility :6948 kW
Refrigeration :1709 kW250
300
350
400
450
500
550
600
0 2000 4000 6000 8000 10000 12000
T ( K )
Q(kW)
.
.
.
.
.
.
.
.
.
,
.
,
.
:
Ref rigerant R717 Ammonia
Reference flowrate 0.1 kmol/s
Mechanical power 394 kW
P T in T out Q !Tmin/2
(bar) ( °K) ( °K) kW (°K)
Hot str. 12 340 304 2274 2
Cold str. 3 264 264 1880 2
,
.
. ,
:
:
,
.
.
.
.
:
Refrigeration: ,
Plow T low Phigh T high COP kWe
(bar ) ( °K) ( ba r) (K) -
Cycle 3 5 354 7.5 371 15 130
Cycle 2 6 361 10 384 12 323
Cycle 0 6 361 7.5 371 28 34
:
−
−
.
,.
.
:
,
.
Heat pumpsFluid R123
Header P T Comment
(bar) (K)
HP2 92 793 superheated
HP1 39 707 superheated
HPU 32 510 c ondensation
MPU 7.66 442 condensation
LPU 4.28 419 cond ensation
LPU2 2.59 402 condensation
LPU3 1.29 380 condensation
DEA 1.15 377 deaeration
Steam cycle
Boiler house : NG (44495 kJ/kg)
Air PreheatingGas turbine : NG (el. eff = 32%)
Hot utility
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New objective function
Thermal exergy :
Chemical Exergy :
Work :
Consider exergy losses
17
MinRr,yw,f w
nw
w=1
Lw =
nw
w=1
(f w ∗ (E +w −
nr
r=1
(Eq −w,r)∆T min − E −w ))
(Eq −w,r)∆T min =
nsw
s=1
Q−s,r ∗ (1−T 0 ∗ ln(
T r+1T r
)
T r+1 − T r)
E +w =nfuel,w
f =1 M f,w∆k0f
E −w
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18
Table 7Exergy balances of the energy conversion technologies per 1000 kJ of services deliv-ered.
Technology Servicenr
r=1 Eq−
w,r (nr
r=1 Eq−
w,r)∆T min∆∆T min
E −w E +w Lw
[kJ ] [kJ ] [kJ ] [kJ ] [kJ ] [kJ ]
Gas turbine Hot stream 485.72 481.05 -4.67 1160.3 3228.98 1587.63
Heat pump 1 Hot stream 48.91 40.14 -8.77 63.08 0 22.94
Heat pump 2 Hot stream 64.09 55.89 -8.2 84.77 0 28.88
Heat pump 3 Hot stream 27.55 18.83 -8.72 34.72 0 15.89
Refrigeration Cold stream 158.23 141.96 -16.27 209.59 0 67.63
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Results
19
Opt Fuel GT CHP Cooling HP
kW LHV kWe kWe kW kWe
1 7071 - - 8979 -
2 10086 2957 9006 -
3 16961 5427 2262 9160 -
4 - - - 2800 485
5 666 - 738 2713 496
Comb. + frg
Comb. + stm + frg
GT + stm + frg
hpmp + frg
hpmp + stm + frg
HP1 : 34 kWe
HP2 : 323 kWeHP3 : 129 kWe
Share between heat pumps
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Balanced composite curves (option 5)
20
200
300
400
500
600
700
800
900
1000
1100
1200
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
T ( K )
Q(kW)
Balanced Grand composite curve
Grand composite
-0.2
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
( 1 - T 0 / T )
Q(kW)
BalancedCarnot Grand composite
(EATEXCHANGESYSTEM
(EATEXCHANGERS
%XERGYLOSSES
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200
300
400
500
600
700
800
900
1000
1100
1200
-1000 0 2000 4000 6000 8000 10000
T ( K )
Q(kW)
Othersheat pumps
-0.2
0
0.2
0.4
0.6
0.8
1
-1000 0 2000 4000 6000 8000 10000
( 1 - T 0 / T )
Q(kW)
Othersheat pumps
Fig. 8. Integrated composite curves of the heat pumps
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Integrated composite curves
22
200
300
400
500
600
700
800
900
1000
1100
1200
-2000 0 2000 4000 6000 8000 10000 12000
T ( K )
Q(kW)
Process composite curveUtility composite
/PTION5TILITYINTEGRATEDCOMPOSITECURVE
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Integrated composite curve : steam network
23
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Visualising the results : Carnot efficiency
24
-0.2
0
0.2
0.4
0.6
0.8
1
-2000 0 2000 4000 6000 8000 10000 12000
1 - T 0 / T
Q(kW)
Option 1 : Carnot composite curves
Process composite curveUtility composite curve
-0.2
0
0.2
0.4
0.6
0.8
1
-2000 0 2000 4000 6000 8000 10000 12000
1 - T 0 / T
Q(kW)
Option 5 : Carnot composite curves
Process composite curveUtility composite curve
Tricks for creative engineers : reduce the green area !
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Carnot integrated composite curves
25
200
300
400
500
600
700
800
900
1000
1100
1200
-1000 0 1000 2000 3000 4000 5000 6000
T ( K )
Q(kW)
Integrated composite curves of the steam network
Others(STMNET)
Mech. power
-0.2
0
0.2
0.4
0.6
0.8
1
-1000 0 1000 2000 3000 4000 5000 6000
1 - T 0 / T
Q(kW)
Carnot integrated composite curves of the steam network
Others(STMNET)Mech. power
%XERGYLOSSESINTHEHEAT
TRANSFERBETWEENSTEAM
CYCLEANDTHESYSTEM
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Energy efficiency
NGCC equivalence of electricity
EU mix for electricity
Exergy efficiency
Comparing results
26
Total2 = mfuel ∗ LHV fuel +(E + −E
−)
ηel
(= 38%(EUmix))
Total1 = mfuel ∗ LHV fuel +(E + −E −)
ηel
(= 55%(NGCC ))
ηex =Eq colda + Eq hotr + E −grid
E + + Eq coldr + Eq hota
−
E + =nfuels
fuel=1
M +fuel∆k0
fuel + E +grid
−
with
L = (1− ηex)(E + + Eq coldr + Eq hota)
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Table 9Energy consumption and exergy efficiency of the diff erent options
Option Fuel E +
gridTotal 1 Total 2 ηec ηex Losses
[kW LHV ] [kWe] [kW LHV ] [kW LHV ] % % [kW]
1 7071.0 371.0 7745.5 8029.7 9.2 34.9 8868.0
2 10086.0 -2481.0 5575.1 3675.1 29.4 44.5 8830.0
3 16961.0 -7195.0 3879.2 -1630.7 43.5 51.3 11197.2
4 0.0 832.0 1512.7 2149.9 49.3 72.4 2408.1
5 666.0 125.0 893.3 989.0 49.6 72.6 1831.6
Results
Comb. + frg
Comb. + stm + frg
GT + stm + frg
hpmp + frg
hpmp + stm + frg
Total2 = mfuel ∗ LHV fuel +(E + −E
−)
ηel(= 38%(EUmix))
Total1 = mfuel ∗ LHV fuel +(E + −E
−)
ηel
(= 55%(NGCC ))
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-20000
-15000
-10000
-5000
0
5000
10000
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
option 1option 2option 3option 4option 5
'RID%LECTRCITYEFFICIENCY
K7
Sensitivity of the grid electricity mix
Comb. + frgComb. + stm + frg
GT + stm + frghpmp + frg
hpmp + stm + frg
−
cfuel(e/kJ )
c−grid
(e/kJ e)
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OPT1 OPT2 OPT3 OPT4 OPT5
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
Conversion
HTX
DTmin conversion
DTmin process
Energy conversion system configurations
E x e r g y l o s s e s ( k W
)
Fig. 6. Exergy losses of the diff erent options
Exergy losses of the options
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OPT1 OPT2 OPT3 OPT4 OPT5
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Conversion
HTX
DTmin conversionDTmin process
Energy conversion system configurations
S h a r e
i n
t h
e
e x e r g y
l o s s e s
Fig. 7. Share of the exergy losses in the diff erent options
Share of the exergy losses
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Conclusions
Energy conversion system integration
Satisfy the process requirement with minimum ressourcesValorise the available process exergy
Combined exergy - Process integration
Analyse the requirements
Opportunities for energy conversion integration (Carnot composite)
Type of technologies
Generate optimal integrated systems
MILP method
Exergy objective
Evaluate & compare solutions
Graphical representations : Carnot composite & area
Integrated composite curves
Exergy efficiency wrt minimum process exergy requirement (+&-)
31