Process integration Heat exchanger network design

Résumé des concepts déjà exposés
Process integration
Heat exchanger network design
Notes préparées par
Dr Ir François Maréchal
LENI (Laboratoire d’Energétique industrielle, EPFL)
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Offre et demande en énergie : T = f (Q)
Concept de pincement
Bilan thermique sur un intervalle de T
Calcul de la cascade thermique -> MER
Le point de pincement : propriétés
3 règles à respecter
Les courbes composées
Nombre minimum d’échangeurs
Influence de la valeur de ∆T minimum
Méthode de design de réseaux
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Le concept du pincement thermodynamique
Producteurs et consommateurs
Besoins thermique
T(°C)
175°
150°
1er principe thermo :
Bilan de chaleur
Producteurs => Flux chauds à refroidir
Consommateurs => Flux froids à réchauffer
Excédent d'énergie
Qualité - Quantité
Tin
cp(T ,P,x)dT = m *cp * (Tout − Tin )
2ème principe thermo :
DT > 0
ch
au
d
Q = m*
Tout
Fl
ux
Qualité
+
Flu
oi
x fr
175°
Heuristique ingénieur :
DT > DTmin
Energie
-> Compromis :
Energie - Capital
Quantité
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150°
100°
70°
Excédent d'énergie
H(kW)
Potentiel
de transfert
nul
Supplément d'énergie
T(°C)
d
H(kW)
Supplément d'énergie
T(°C)
Température
Echange
impossible
100°
70°
175°
150°
Potentiel de
transfert
suffisant
100°
70°
Excédent d'énergie
H(kW)
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1
Identify the Pinch point
Calculating the heat cascade
Minimum Energy Requirement
Rnk+1 = Additional Energy
DHnk
Rk+1 ≥ 0
Flux chauds k
Flux froids k
j k =1
i k =1
m j k cp j k (Tk +1 − Tk ) −
Rk = Rk +1 +
Hot streams
T(°K)
mi k cpi k (Tk +1 − Tk )
Benefit :
∆E=Qh - Qhmin
DTmin
Cold streams
Rk ≥ 0
DHk-1
DH1
Q(kW)
Excess of Energy
Heat recovery
by counter-current heat exchange
R1 = Excess Energy
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Important rules
Approche globale : Energie thermique
+Q1
No hot utility below the pinch point
+Qf
Courbe composée globale
Courbes composées
Utilitaire chaud
Utilitaire chaud
+Qc
T(°C)
T(°C)
Qualité
T(°K)
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Puits de chaleur
DTmin
Utilitaire froid
Q1
Pinch point
Source de chaleur
Q(kW)
Utilitaire froid
Quantité
Q(kW)
Résumé énergétique du procédé
Q1
2 Courbes composées des flux chauds et froids
+Qf
No cold utility above the pinch point
Echange contre-courant global
Objectif énergétique du procédé
DTmin => Point de pincement
+Qc
+Q1
2 sous-systèmes indépendants (puits et source)
Q(kW)
Diagnostique du réseau d’échangeurs
No heat exchange accross the pinch point
Règles pour URE
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2
DTmin sensitivity
Minimum number of units
Pinch point = two independent sub-systems
Number of Independent subsystems above the pinch point
Change of the number of exchangers
Total T
Cost
Number of Independent subsystems below the pinch point
Energy
U min,MER = (N above −1− Sabove ) + (Nbelow −1− Sbelow )
Q
Number of streams above
the pinch point
Number of streams below
the pinch point
T
U min,MER = (N total + N utility −1) + (N pinch −1) − (Sabove + Sbelow )
Number of Independent subsystems below and above the
pinch point
Total number of streams,
including the utilities
Q
Investment
Number of streams crossing
the pinch point
DTmin
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Concepts nouveaux
Summary of the work method
Synthèse du réseau d’échangeurs
TARGETING
process simulation and analysis
utility and thermodynamic cycle
selection and integration
DTmin optimization
SYNTHESIS
heat exchanger network structure
heat exchanger network optimization
heat exchanger network analysis and
selection
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Heat exchangers network synthesis
Pinch point
Two independent sub-systems
Goals
Qhmin
Find a heat exchangers network that satisfies:
- MER
- Minimum number of units
- Minimum investment
- Other criteria
T(°K)
HEAT
SOURCE
- Which hot stream with which cold stream ?
DTmin
- What is the heat exchanged ?
DTmin
- What is the structure : serial or //, ...
Above pinch point
Drive hot streams to the pinch point without cold utility
Below pinch point
Drive the cold streams to the pinch point without hot utility
Qcmin
Q(kW)
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Above the Pinch point
Corrected temperatures
HEAT
SINK
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Heat exchanger representation
Corrected temperatures
Qhmin
T(°K)
T(°K)
Pinch Pinch heat exchanger
Qhmin
Pinch streams
Pinch streams :
• hot streams ending at the pinch
• cold streams starting at the pinch
HEAT
SINK
Q(kW)
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Pinch
Q(kW)
T
Pinch heat exchanger
:
Allows exchange between
two pinch streams
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Grid representation :
Cp rule
- Streams = horizontals
- Heat exchange = verticals
T
CPh
1
CPhŠCPc
CPc
DTmin
1
9080
60 50
9080 80 90
2030
7080 8070
135125
2535
7080
110100
2.5
140150
3
2
8
CPc
Q
CP
6050
8070
Only for pinch heat
exchangers
Feasibility rules
Heat exchangers network representation
Hot
streams
1
Cold
streams
Pinch
Corrected temperatures
Actual temperatures
2
Hot
stream
2
3
1
Cold
stream
Pinch
Hot
streams
Cold
streams
Pinch
Direction de calcul
Pour l'
échange k(chaud) - r(froid) : au dessus du pincement
mk cpk ≤ mrcpr
n hot
et
i =1,i ≠k
micpi ≤
n cold
j =1, j ≠ r
m jcp j
for pinch exchangers:
Above the pinch point:
Vrai globalement
Pinch
(a)
Pinch
exchangers(b)
Cp hot
Cp cold
Cp cold
Cp hot
Below the pinch point:
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Au dessus du pincement
Split du flux clé si la
règle des cp n’est pas
satisfaite
mrcp r = 1
m2,kcp 2,k = 2 − m1,kcp1,k
Q
Numbers of streams
2
3
T = Tpinch +0,5∆Tmin +
80
90
80
140
Hot
streams
2
3
80
80
90
140
?
1
Direction de calcul
m 1,k cp1,k ≤ 1
Only for pinch heat
exchangers
Feasibility rules
mk cpk = 2
Q
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80
Pinch
135 Cold
stream
1
80
135
Hot
streams
Cold
stream
For pinch exchangers
Above the pinch point:
Number of hot Number of cold
Below the pinch point:
Number of cold Number of hot
Pinch
Above the pinch point: cool down the hot streams without cold utilities.
Q
m1,kcp1,k
--> need one cold pinch stream for each hot pinch stream
Below the pinch point : heat up the cold streams without hot utilities.
--> need one hot pinch stream for each cold pinch stream
Q
T = Tpinch −0,5 ∆TMin +
mrcpr
Split du flux non clé si la règle du nombre de flux n’est pas satisfaite
mrcp r = 1
Direction de calcul : en s'
éloignant du Pinch
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Remaining problem analysis
Heuristic rules
Goals :
Initial problem:
Above the pinch point: cool down the hot streams without cold utilities.
Hot stream : Tic -> Toc
Below the pinch point : heat up the cold streams without hot utilities.
Cold stream: Tif -> Tof
Place a heat exchanger
Toc
Start with pinch exchangers
Rules
Remaining problem
1 - Order the streams by decreasing Cp
-> exchange first between the highest Cp
2 - The heat load is calculated to satisfy the heat load of
one of the two stream involved : "tick-off"
3 - Place the utilities at the end of the streams
T2
T3
Tif
Hot streams: Tic -> T2
: T1 -> Toc
Cold streams: Tif -> T4
: T3 -> Tof
Tic
T1
T4
Tof
If the last heat exchanger
is correctly designed, the
MER should not increase
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The synthesis algorithm
N k ≤ N k −1
yes
CP(k)<CP(k-1)
For pinch point
connexion
Place the exchanger
Tick-off
accept
yes
New data set
140°C
Split {k-1} stream
no
170 °C
20 °C
Split 1 {k} stream
60°C
3 kW/°C
135°C
2 kW/°C
{k} ordered list of Key streams with
decreasing Cp at the pinch point
{k-1} the other streams
suppress
80°C
4 kW/°C
yes
Remaining problem
no
An example: identify the energy requirements
no
All examined
yes
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Key streams :
150°C
30 °C
Above the pinch point : hot streams
Below the pinch point : cold streams
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1.5 kW/°C
Mcp
3 kW/°C
4 kW/°C
2 kW/°C
1.5 kW/°C
Tin
170°C
80°C
20°C
150°C
Tout
60°C
140°C
135°C
30°C
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Pour l’exemple 1
Direction de calcul
Remaining problem
Direction de calcul
80°C
20°C
240 kW Regle des cp + heuristique
140°C
80°C
30°C
90°C
60°C
90°C
4 kW/°C
TIn
20
170
150
80
TOut
135
60
30
140
Echangeur E4
TIn
TOut
80
140
170
90
Mcp
2
3
1.5
4
Mcp
4
3
TIn
20
90
150
TOut
135
60
30
MER0
Mcp
2
3
1.5
MERnew
135°C 2 kW/°C
150°C 1.5 kW/°C
170°C
3 kW/°C
If MER0 = MERnew => Heat exchanger OK
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Pour l’exemple 1
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Loops
240 kW Regle des cp + heuristique
80°C
30 kW
35°C
20°C
30°C
60°C
C
70°C
80°C
90°C
60 kW
90°C
140°C 4 kW/°C
20 kW
H 135°C 2 kW/°C
125°C
Q5+X2
Q3-X2
3
Q2-X2
C
1
5
Q4+X2
2
4
Q2-X2
Q5+X2
150°C 1.5 kW/°C
90 kW
H
Q3-X2
170°C
3 kW/°C
Q4+X2
X2 = min(Q2,Q3,Q4,Q5)
Suppress a heat exchanger !
Is the DTmin verified or acceptable ?
90 kW
U = 4 + 2 -1 + ( 3 -1) - 1 = 6
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Boucles
Boucles
X=30 kW
240 kW
-X
20°C
30°C
E1
80°C
35°C
E2
90°C
C
60 kW 30 kW
60°C
80°C
140°C 4 kW/°C
20 kW
E3
H 135°C 2 kW/°C
125°C
+X
90°C
150°C 1.5 kW/°C
90 kW
170°C
3 kW/°C
240 kW
80°C
20°C
30°C
E1
65°C
! 5°C
C
150°C 1.5 kW/°C
+30 = 120 kW
170°C 3 kW/°C
70°C
90 kW -30 = 0 kW
60°C
90°C
X=min(Q boucle)
90 kW
E2
140°C 4 kW/°C
20 kW
E3 H 135°C 2 kW/°C
125°C
90 kW
Recalculer les températures
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Comparaisons
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Energy relaxation
Echangeur E1 : Q = 30 kW => 0 kW
Echangeur E2 : Q = 90 kW => 90 kW changement de T
Echangeur E3 : Q = 90 kW => 120 kW changement de T
Path following from hot utility to cold utility
3
Qc+X
Q1-X
C
1
2
5
4
Echangeur E1 : Q = 30kW
UA =
Q
30
=
= 0.571 kW/°C
∆Tlm (90 - 35) − (70 - 20)
90 - 35
ln
70 - 20
Cout = a * (A)b = 1800*
0.571
0.2
0.8
= 4171 CHF
H
Qh+X
Q1-X
4171
= 521 CHF/an
8
X such that DTmin is verified
Energy Penalty !!!
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Chemin
Chemin
X : ∆T = ∆Tmin = 70°C + X
− 65°C = 10 K
1.5
X = ( ∆Tmin − ∆Tobs ) * mc cpc = 5*1.5 = 7.5 kW
240 kW
240 kW
80°C
140°C 4 kW/°C
125°C-X/2 °C
65°C
H 135°C 2 kW/°C
10°C=5°C+X/1.5°C 20 kW+X kW
20°C
90 kW+X kW
30°C
C
150°C 1.5 kW/°C
70°C+X/1.5
120 kW-X kW
90°C
170°C 3 kW/°C
60°C
90 kW
80°C
20°C
65°C
140°C 4 kW/°C
20 kW+7.5 kW=27.5 kW
H 135°C 2 kW/°C
90 kW+7.5 kW=97.5 kW
125-7.5/2=121.5°C
10°C
30°C
C
150°C 1.5 kW/°C
70°C+7.5/1.5=75°C
120 kW-7.5 kW=112.5 kW
60°C
90°C
170°C 3 kW/°C
90 kW
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Comparaison des résultats
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HEN synthesis
Draw backs of the simplified algorithm:
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- multiple solutions
- combinatorial problem
- sequential
Use of mathematical programming:
Heat load distribution:
- which stream pairs exchange heat
- how much
- minimize the number of connections
- satisfies ∆Tmin and MER
Remaining problem : find the HEN structure
*
!
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Heat load distribution
Heat load distribution
T*k+1
Qik
MILP formulation
Qjk
Qjk
Qjk
Qikj
Qikj
Qikj
Minimize the number of connections
T*k
Min
Cold streams j
Hot stream i
yij ,Qikj
nc
Hot stream i in temperature interval k
nc
j =1
Qikj = Qik
j =1
∀i = 1,...,nh;∀k = k1,...,k2
nh
Cold stream j in and above temperature interval k
nh
k2
i=1 r= k
Qirj −
k2
r= k
Q jr ≤ 0
∀j = 1,...,nc;∀k = k1,..., k2
k2
r =k
Qirj − y ijQmax ij ≤ 0
∀j = 1,...,nc;∀i = 1,...,nh
r =k
nc
i =1 j =1
yij ∈ {0,1}
y ij
Qikj = Qik
k2
i=1 r= k
connection between i et j (integer variable)
k2
nh
Qirj −
∀i = 1,...,nh;∀k = k1,...,k2
k2
r= k
Q jr ≤ 0
∀j = 1,...,nc;∀k = k1,...,k2
Qirj − y ijQmax ij ≤ 0
∀j = 1,...,nc;∀i = 1,...,nh
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The synthesis method
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Optimize the heat exchangers network
Calculate the heat load distribution for each section
NLP problem
Multiple solutions using integer cuts
Heuristic rules or user
Min
X , m j , Ai
nu
j =1
( C1
j
+ C2 j mj ) +
Constraints
Heat and mass balances
Rating equations
Specifications :
-> screening and choice of the appropriate
solution
Define the HEN structure
F(X) = 0
Apply feasibility rules and heuristics
Splits and serial exchanges
Bounds and limits
G(X)
Optimize the HEN
Total cost criteria
no DTmin nor MER fixed
1
τ
nex
i =1
(a + b A )
i
i
ci
i
T1o
T2i
T1o
T2i
L
L-V
L
L
L
L-V
A1
L
V
T1i
L
T2o
T1i
V
A3
A2
L
L
T2o
nz i
nzi
Q
n Qi iz
Ai =A= nAAi
z,i ==
U iz∆Tlm iz
z =1
z =1UDTlmi
i=1
i=1
0
X : State variables: pressure, temperature, area, heat exchanged,
...
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Heat exchanger network retrofit
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Heat exchanger network retrofit
Knowing an existing heat exchanger network
Identify which exchangers have to changed
Invest new heat exchangers
Reuse existing exchangers
– Repiping
C1
3
C2
4
2
1) Identifier les échangeurs mal placés
1
• 1 side
– Replace
H1
• 2 sides
C1
– Retube
C2
• Increase area
2) Déconnexion
3) Pinch design
4) Récupération des échangeurs
– Optimise
• Change flowrates (by-pass)
•
PINCH
3
Maximize profit
2
4
1
2
4
1
H1
PINCH
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Heat exchanger reuse
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MINLP problem
If required A A available
=> use a by-pass
=> or accept lower DTmin
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DTmin value
DTmin/2
The DTmin is related to the type of fluids
If heat is exchanged between hot stream j
and cold stream j in the interval i,
Heat exchange:
Q = U A DTlm
the temperature difference will be:
Heat transfer
coefficient
1/U = 1/Uc +1/Uf
Temperature
difference
DT > DTmin/2,j + DTmin/2,k
If A and Q are constant
If U increases : DT decreases
If U decreases : DT increases
=> DTmin is related to the streams involved
-> to the film heat transfer coefficient
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How to handle this situation ?
Choice of DTmin/2 :heuristic rule
Consider stream dependent DTmin/2 for calculating the
heat cascade
DHi =
Nc
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Remaining parameter => 1 DDL
∆Tmin /2 j = K *
Hot streams in the interval i
1
hj
b
Nf
1/sqrt(x)
DTmin/2,j
6
5
4
3
2
1
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
hj
Film heat transfer coefficient
-
Σ Ηj(Ti+1 - DTmin/2,j ) - Ηj( Ti - DTmin/2,j )
j=1
8
7
Σ Ηj(Ti+1 + DTmin/2,j ) - Ηj( Ti + DTmin/2,j)
j=1
9
Cold streams in the interval i
b is the cost exponent in the heat exchanger cost estimation formula
DTmin/2 : typical values :
With DTmin/2,j = contribution of stream j
DTmin/2,j is related to the type of fluid involved
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Liquid state :
2
Fluid phase changes :
1
Vapor state :
4
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Assumptions : constant Cp ?
Solutions
Add new temperatures in the list :
one stream= several segments
Fluid phase changes
2
T
α=0
T
use linearized segments
Potential pinch point if
cold stream
α=1
4
Use rigourous thermodynamic
calculations to evaluate H=f(P,T)
3
1
H
H
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