1. Introduction Process Integration Water distribution Summary
Visualisation and interaction for design
Professor Eric S Fraga
Department of Chemical Engineering
UCL (University College London)
ECOSSE Retrospective Symposium
Edinburgh
17 April 2009
c 2009, All rights reserved.
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2. Introduction Process Integration Water distribution Summary
Process design
Process design should be informed by robust optimisation with
confidence in results. But...
complex non-linear, non-convex,
discontinuous & noisy models, 1500
Cost versus Pressure
1400
1300
combinatorial search space, 1200
Cost (k$/yr)
1100
small, possibly non-convex, feasible 1000
900
regions, and 800
700
600
0 5 10 15 20 25 30 35
ill- or un-defined objective function Pressure (atm)
and constraint equations outside
feasible regions.
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3. Introduction Process Integration Water distribution Summary
The simplest things give me ideas.
Joan Mir´
o
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4. Introduction Process Integration Water distribution Summary
Visualisation and interaction
Computer based tools for design and optimization are
intended for use by non-experts.
Visual representations critical for ease of use.
Interaction can enable engineer to apply own intuition.
Strategy is to combine data analytics, visualisation, and
robust (hybrid) optimisation.
Applications in energy, water, carbon capture, sustainability,
and control.
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5. Introduction Process Integration Water distribution Summary
Heat-integrated process design
Task:
Identify potential
integrations for given
configuration.
Enable process
modification for
better integration.
Help engineer identify
design alternatives.
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6. Introduction Process Integration Water distribution Summary
To simplify complications is the first essential of
success.
George Earle Buckle
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7. Introduction Process Integration Water distribution Summary
Visual representation
For a given process configuration, we can display the hot and
cold streams visually and support interaction, where
x-axis for position independent
duties,
y -axis for temperature, and
hot stream overlapping cold
stream indicates heat integration.
Allow user to manipulate process by moving streams (the tail
wagging dog approach): streams can be moved horizontally for
different integrations and moved vertically or stretched
horizontally to change underlying unit designs.
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8. Introduction Process Integration Water distribution Summary
HEN design algorithm
1 Define list of intervals
A graphical view of ns
process heat requirements I ← {{xa,i } ∪ {xb,i }}
defines left and right 1
end-points for each hot
and cold stream in the
2 For each interval [Ij , Ij+1 ]:
process: 1 Generate list of active streams, A.
2 Sort A from top to bottom using yb values.
3 Generate match for each hot stream
{(xa,i , ya,i )}
immediately above cold stream in A.
{(xb,i , yb,i )} 4 Generate utility match for all other
streams.
i = 1, . . . , ns and
3 Coalesce adjacent similar matches.
x, y ∈ Z+ .
4 Design exchanger for each match.
5 Cost all exchangers and utility use.
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9. Introduction Process Integration Water distribution Summary
Demonstration
www ESF, Patel & Rowe (2001). ChERD 79(7):765–776
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10. Introduction Process Integration Water distribution Summary
Water distribution networks
We wish to design the pipe network for water distribution for a
given configuration with the aim of meeting water demand
with redundancy in the network. A small motivating problem:
7 nodes
8 pipes
1 reservoir
no pumps
Alperovits & Shamir (1977), Water Resource Research 13(6):885-900
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11. Introduction Process Integration Water distribution Summary
The design problem
Given
network layout: connectivity, length (Lk ), set of discrete pipe
diameters, pipe cost;
node demands, Dn ; and,
min
minimum head requirements, Hn .
Determine
diameter of each pipe, dk , chosen from the set of discrete
diameters;
flow amount and direction, Qk ; and,
head (pressure) at each node, Hn
so as to minimise total network cost.
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12. Introduction Process Integration Water distribution Summary
The model
min Cm Lk ykm
k m
subject to:
Qk − Qk = Dn
k∈In k∈On
∆Hk = Hn∈Ik − Hn∈Ok
β
Qk −γ
∆Hk = w Lk dm ykm
CHW m
min
Hn ≥ Hn + En
ykm = 1
m
Indices: k, pipes/connections, n, nodes, and m, pipe
diameters.
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13. Introduction Process Integration Water distribution Summary
Direct optimization
Solved minlp in gams, using dicopt with the cplex milp
solver and a variety of nlp solvers:
Initial Solution (103 $)
Configuration conopt2 conopt3 minos minos5
None 659 655 444 Fails
All flows = 100 441 441 452 452
Initialization affects success of the nlp solvers.
Consider visual and interactive tool for initialization of
subsequent mathematical programming method: hybrid
approach.
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14. Introduction Process Integration Water distribution Summary
Simplicity and complexity need each other.
John Maeda
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15. Introduction Process Integration Water distribution Summary
Discrete optimization
Use of visualization requires mapping from continuous to
discrete space.
Mapping converts MINLP to discrete
programming model ...
... but equality constraints cannot be
satisfied in discrete space.
So we use interval analysis to identify
solutions which are close to feasible in
discrete space.
The discrete model is solved either by the engineer through
interaction or using an embedded stochastic optimisation
procedure.
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16. Introduction Process Integration Water distribution Summary
Interval arithmetic
Changes to model given that node heads are now intervals:
∆Hk = Hn∈Ik − Hn∈Ok
1
β
∆Hk
Qk =
w C Lk γ
βd
k
0 ∈ Qk − Qk − Dn
k∈In k∈On
where indicates an interval value.
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17. Introduction Process Integration Water distribution Summary
Demonstration
www ESF & Papageorgiou (2007), Optimization and Its Applications, Springer, 4:311-332.
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18. Introduction Process Integration Water distribution Summary
Hybrid procedure results
Initial Solution (103 $)
Configuration conopt2 conopt3 minos minos5
None 659 655 444 Fails
All flows = 100 441 441 452 452
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19. Introduction Process Integration Water distribution Summary
Hybrid procedure results
Initial Solution (103 $)
Configuration conopt2 conopt3 minos minos5
None 659 655 444 Fails
All flows = 100 441 441 452 452
Hybrid 419 419 423 419
Behaviour of nlp solvers is more consistent.
The global optimum is found in 3 of the cases.
Solutions obtained are better in all cases.
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20. Introduction Process Integration Water distribution Summary
Summary
To simplify complications is the first essential of
success.
George Earle Buckle
But...
Everything should be made as simple as possible, but
not simpler.
Albert Einstein
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21. Introduction Process Integration Water distribution Summary
Acknowledgements
The following have contributed to the work presented here:
Dr Lazaros Papageorgiou, UCL
Ms Rupal Patel, UCL
Dr Glenn Rowe, Dundee
and the ECOSSE group is to blame for my working in this
field!
http://www.homepages.ucl.ac.uk/~ucecesf/research.html
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