1. LECTURE DAY 3
Timo Laukkanen

2. What was important in Lecture 2
Problem Table Algorithm (PTA)
Heat Cascade
Grand Composite Curve (GCC)
Pinch violations
Stream grid
Maximum Energy Recovery (MER) Network
Targeting for minimum number of Units

3. What is important in Lecture 3
A LP (linear programming) transshipment model for minimizing utility consumption
A MILP (Mixed Integer Linear Programming) extended transhipment model for minimizing the number of units

4. Different optimization model types

5. Global and Local Optima

6. Convex, Concave and Non-Convex functions

7. Optimization with a mathematical model

8. Sequential Heat Exchanger Synthesis
Problem Data
(streams, cost)
DT min value
Optimization of utilities consumption
LP-transshipment model
Minimization of number
of units
MILP-transshipment model
Optimization of network cost
NLP-superstructure
Result OK?
NO, new DTmin value
YES, STOP

9. Sequential Heat Exchanger Synthesis
LP Model:
Minimum Utility Consumption (Transshipment Model)

10. Temperature Intervals
Tsupply (°C)
Ttarget (°C)
m cp (kW/K) H1
400
120
1.0 H2
250
2.0 C1
160
1.5 C2
100
1.3
∆Tmin = 50°C
Hot Utility: Steam at 450°C
Cold Utility: Water at 20°C
Find the starting temperatures of all streams (and utilities)
Keep one column for hot temperatures and one for cold
Add ∆Tmin to get hot, substract to get cold

11. Hot Utility: Steam at 450°C Cold Utility: Water at 20°C TI 1 TI 2 TI 3
Tsupply (°C)
Ttarget (°C)
m cp (kW/K) H1
400
120
1.0 H2
250
2.0 C1
160
1.5 C2
100
1.3
∆Tmin = 50°C
Hot Utility: Steam at 450°C
Cold Utility: Water at 20°C
450
400
TI 1
350
TI 2
250
200
TI 3
210
160
TI 4
150
100
TI 5 70 20 H1
250 H2 C1 C2
120
120

12. H1 H2 C1 C2 ∆Tmin = 50°C Hot Utility: Steam at 450°C
Tsupply (°C)
Ttarget (°C)
m cp (kW/K) H1
400
120
1.0 H2
250
2.0 C1
160
1.5 C2
100
1.3
∆Tmin = 50°C
Hot Utility: Steam at 450°C
Cold Utility: Water at 20°C
450
400 H1 H2 C1 C2
TI 1 75
350
TI 2
150
225 65
250
200
TI 3 40 80 60 52
210
160
TI 4
120 78
100
TI 5 30 70 20 H1
250 H2 C1 C2
120
120

13. Qs
TI 1 75 C1
225 R1 60
150
TI 2 H1 R2 65 40 80
TI 3 52 H2 C2 78
120 60 R3 60
TI 4 30 R4
TI 5 Qw

14. R = Qs
R = R
R = R
R = R
Qw = R

15. R = Qs
R = R
R = R
R = R
Qw = R
Min Z = Qs + Qw
s.t. R1 – Qs = 75
R2 - R1 = -140
R3 - R2 = 8
R4 - R3 = 102
Qw - R4 = 90
Qs, Qw, R1, R2, R3, R4 ≥ 0

16. General Formulation
index
Sets
Parameters
Variables

17. Interval k
hot process
cold process
hot utility
cold utility

19. Sequential Heat Exchanger Synthesis
Extended LP Transshipment Model

20. Qs
TI 1 75 C1
225 R1 60
150
TI 2 H1 R2 65 40 80
TI 3 52 H2 C2 78
120 60 R3 60
TI 4 30 R4
TI 5 Qw

21. C1
Q112
Q113 H1
R12
Q122
Q123 C2
Q124
R13
R14

24. Energy Balances

26. Sequential Heat Exchanger Synthesis
MILP Transshipment Model
Minimum number of units

27. Simplifactions Hot utilities treated as hot streams
Cold utilities treated as cold streams
Divide the problem at the pinch
Energy balance for temperature intervals:

30. If, then
Either, or