Transcript Slide 1

The Development of an Advanced Systems
Synthesis Environment: Integration of MI(NL)P
Methods and Tools for Sustainable Applications
Zdravko Kravanja
University of Maribor,
Faculty of Chemistry and Chemical Engineering,
Smetanova 17, 2000 Maribor, Slovenia
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
1
Slovenia
in
pictures
Area: 20,273 km2
Population: 2.0 million
Capital city: Ljubljana
Language: Slovenian; also
Italian and Hungarian in
nationally mixed areas
Currency: EURO, €
Member of EU - 1 May 2004
EU Presidency for 2008
2
Environmental Performance Index (EPI)
http://epi.yale.edu/CountryScores
Slovenia has rank 15
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Outline
• Introduction
• Process Synthesis and Sustainability, Challenges
• Capabilities of an EO Modular MINLP Process
Synthesizer MIPSYN
• Aplications
• Conclusion
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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But the creative
principle resides
in mathematics.
In a certain
sense, therefore,
I hold true that
pure thought can
grasp reality, as
the ancients
dreamed.
Albert Einstein
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Key idea for today and
tomorrow
In (bio)chemical supplay chain the traditional
use of optimization techniques and tools is
not sufficient
unless its efficiency and applications are
consistently upgraded with
sustainable principles
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Creative Principles of Mathematical
Programming
Optimality
Competitive advantage
Feasibility
Constraints satisfied
Integrality
Simultaneous considerations
Creative principles of MP enables:
• Creation of new knowledge and
• New innovative solutions
Study of solutions enables one to get new insights,e.g.
simultaneous HI also reduces raw material usage
(Lang, Biegler, Grossmann, 1988).
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Introduction
Incentives for sustainable development
• Main problems that have to be circumvented:
– Population growth
– Limited resources
– Environmental and society destruction
• How prevent the worming for 2oC in the next 2
decades?!
• Answer: Sustainable development
• New role of PSE: Sustainable PSE of paramount
importance
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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3 X 3 Sustainability Matrix
(M. F. Jischa, Chem. Eng. Technol. 21, 1998)
Nature
Sustainability
27
Eco-centric
3
8
Strategies
Expandedanthropozentric
2
Narrow
anthropozentric
1
3
1
Sufficiency
2 Consistency
1 Efficiency
1
2
3
Principle
Just Reward for Work
Respect for Private Property
Fair Distribution of Goods
of Justice, Etics
Figure 1: Diagonal as a measure of sustainability
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Environmental Aspects
(Voss, 1994)
Environmental constraints
Material brought into
the environment
Consummation rates of
renewables
<
Carrying capacity of
the ecosystem
<
Their regeneration
rates
Non-renewable resources only if future generation
would not be compromised
In addition:
Environmentally friendly innovation
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
Opt. Criteria
->
min emission
of pollutant
->
max
renewables
->
min nonrenewables
->
Multiobjective
approach
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MINLP Model Formulation for Different
Levels of Innovations:
a)
b)
c)
d)
max z = cTy + f(x) – e(x)
s.t hi(x) = 0
gi(x)  0
}  i Levels
Biy + Cix  bi
x  X = x  Rn: xLO  x  xUP 
y  Y = 0,1m
a) Objective function as a real-world economic function (cost benefit approach):
Max Profit = Production income - Raw material cost - Utility cost
- Investment cost – Environmental loss
b) Equality constraints: mass and energy balances, design equations
c) and d) Inequality constraints: product specifications, operational, environmental
and feasibility constraints, logical disjunctive constraints for selection of
sustainable alternatives
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Sustainable and Integrated (Bio)chemical
Supply Chain Synthesis
r
27 Sustainability
8
1
(Marquardt Wolfgang, Lars Von Wedel, and Birget Bayer.
Fig.??
AspenWorld
2000, Orlando, FL, 2000)
Figure 2: Diagonal as a measure of sustainability
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Sustainable Product-Process Synthesis
“Synthesis is the automatic generation of
design alternatives and the selection of
the better ones based on incomplete
information”
A. W. Westerberg (1991)
Extension:
Sustainable product-process synthesis is the automatic
generation of design candidates and the multiobjective
selection of the better ones based on the creative
postulation of sustainable alternatives integraly
accross the whole chemical supply chain.
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Challenges Related to the Manifolds Nature
of the Synthesis Problems
Features
Approach
Many complex interactions
Simultaneous
Discrete and continuous decisions
MINLP
Uncertainty
Flexibility
Dynamic systems
MIDNLP, multiperiod
Rule-based decisions
Logic-based
Multicriterial
Multiobjective
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Simultaneous Synthesis and Heat
Integration - Methanol Example Problem
Figure 3: Methanol process
and HEN superstructure
Figure 4: Optimal process
scheme with HI HEN
Process synthesis and:
• sequential HEN synthesis:
• simultaneous HI by Duran-Grossmann’s model:
• simultaneous HEN synthesis by Yee’s model:
• Yee, Grossmann, Kravanja (1990)
• Kravanja and Grossmann (1994)
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
- 1,192,000 $/yr (loss!)
- 292,000$ $/yr (loss!)
1,845,000 $/yr (profit!).
2,613,000 $/yr (profit!)
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Different Modeling Complexities
Table 1: Types of optimization problems and models
Equations
Model
Example
Certainty
variables
Continuous, x
discrete, y 0-1
logical Y
x, y
x, Y
Uncertain par.
Linear
Nonlinear
Steady state
Continuous process
Difference
Multiperiod
Life cycle
Differential
Dynamic
Batch
process
e.g.
e.g.
Mul. MINLP
Dyn. MINLP
Nominal
LP
ILP
DisLP
MILP
MDisLP
NLP
INLP
DisNLP
MINLP
MDisNLP
Flexible
Kravanja Z., 2003, Chem. Biochem. Eng. Q. 17 (1), 1-3.
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Incentives for the development of MP-based
tools for process synthesis:
• Several general MINLP solvers
www.gamsworld.org/minlp/solvers.html
• Logic-based solver LOGMIP
(Vecchietti and Grossmann, 1997)
• Global MINLP Optimizer BARON
(Sahinidis, 2000)
• Almost no tool specialized in MINLP synthesis
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Capabilities of Mixed-Integer Process
SYNthesizer MIPSYN
Extension of PROSYN-MINLP
•
•
•
•
•
Kravanja, Z. and I.E. Grossmann, Computers chem. Engng.,1990
Kravanja, Z. and I.E. Grossmann, 1994
Robustnes:
– Interactive vs. Automated mode of execution
– NLP initialization by a simple flowsheet simulation
– Different NLP and MILP optimizers
Efficient handling of process superstructures
– M/D strategy with alternative decomposition schemes of the superstructure
– Multilevel MINLP strategies
Efficient handling of models:
– Data- and topology independent modeling
– Convex-hull and alternative convex-hull modeling formulation
– Model generation from modules of process units and interconnection nodes
– Simultaneous heat integration
Algorithmic power:
– Different extensions of the OA algorithm
– Different convexifications to prevent poor local solutions
– Integer-infeasible path optimization
Higher-level capabilities:
– Multiobjective synthesis
– Multiperiod synthesis
– Flexible synthesis in the presence of uncertain parameters
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MIPSYN and Logic Based OA
Or when NLP
is not imroving
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MIPSYN flowchart
Topology
Components
Data
User’s modules
P_STRUCT.DAT
P_ COMPON.DAT
P_DATA.DAT
MY_MODEL.DAT
Model generator
MIPSYN
Libraries:
AP/OA/ER
- Process modules
M/D
- Components properties
NLP initializer
Simple simulator
GAMS
Solution
P_OPTIMUM.RES
NLP solvers: CONOPT, MINOS, SQP
Procedure overview
P_B.RES
MILP solver: CPLEX, OSL,
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Applications
Different levels of problem abstraction and application
•
•
•
More general MINLP solver
Process synthesizer
Synthesizer shell for different domains
Chemical Engineering
(MIPSYN)
Mechanical Engineering
(TOP)
NLP optimization
• Process sybsystems
• Flowsheets
NLP optimization
• Timbes trases
• Composite floor systems
MINLP synthesis:
• Reactor networks
• Separator networks
• Heat exchanger networks
• Overall HI process flowsheets
MINLP synthesis of mechanical
structures:
• Gates for hydropower dams
• Steel frames
• Steel buildings
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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PROSYN-MINLP verion
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MipSyn β Version
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Multilevel-hierarchical MINLP Synthesis
Combination of the hierarchical strategy and MINLP
superstrucutre approach
(Kravanja and Grossmann;1997)
Tagret HI
Identify SEP
tastks
Tagret HI
Profit
UB
Identify
process
streams
HI
LB
Identify SEP
tastks
MINLP 1: RCT network:
- Detailed RCT network model
- Simple SEP model
- Simultaneous heat integration
MINLP 2: SEP/RCT network:
- Detailed RCT models
- Detailed SEP models
- Targeted heat integration
MINLP 3: HEN synthesis
- Fixed RCT/SEP structure
- Detailed RCT and SEP modules
- Staged HEN synthesis model
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
Loop
STOP if
UP≈LB
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MINLP 1: Initial Reactor Network and
Simplified Separation Superstructure
HDA
example
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MINLP 1 – Optimal Solution
Identified
separations
Targeted HI
Upper Bound
6.505 M$/yr
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MINLP 2: Detailed RCT and Identified SEP
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MINLP2: Optimal Solution
Identified
hot and cold
streams
Targeted HI
Upper Bound
5.892 M$/yr
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MINLP 3: HEN Synthesis within Fixed
Flowsheet
Lower Bound
5.201 M$/yr
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MINLP 2 Resolved
MINLP II resolved: UB = 5.240 M$/yr
MINLP III: LB = 5.201 M$/yr
Since UP≈LB
→
STOP
OPTIMAL SOLUTION:
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Multilevel Synthesis of Mechanical Structure
SYNTHESIS OF ROLLER HYDRAULIC STEEL GATE
Hydroelectric Project Blanda, Iceland
(S. Kravanja, A. Soršak, Z. Kravanja; 2003)
LINKED MULTILEVEL HIERARCHICAL STRATEGY (LMHS)
Superstructure :
• 2 main gate element
• 4 to 6 horizontal girders
• 5 to 9 vertical girders
MINLP1: topology optimization
•
relaxed standard dimensions
•
OAs accumulated for MINLP2
MINLP2: simultaneous topology and standard
dimension optimization
•
discrete standard dimension
•
OAs accumulated for MINLP3
MINLP3: simultaneous topology, standard and
rounded dimension
•
optimization and pre-screening
•
10 discrete dimensions on each side from
the optimal solution of MINLP2
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Optimal Structures
19622 y !
4300
25
479
1868
575
414
100
414
40
133
10
25
120 571
194
10
30
40
94 91
4120 mm
4600 mm
194
10
4000 mm
30 552
40
572 30
419
10
20
10
4100 mm
4000 mm
180
10
566
2232
180
10
568
180
10
516
91
200
10
Optimal solution: 8804 €
Self-manufacturing costs of the erected gate: 13498 €
35% net profit
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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30
10
100
282
10
100
1079.5
10
100
1079.5
30
100
1079.5
100
1079.5
30
100
282
4972
32
45
Optimal Synthesis Under Uncertainty
•
Statement:
Engineering problems have in the practice much larger numbers of
uncertain parameters than we can handle rigorously
•
Consequences:
•
•
•
Flexible but suboptimal (safety factors)
Optimal at nominal conditions but may be inoperable
Motivation:
The synthesis and design of flexible and optimal engineering
structure
•
Goal:
An automated and robust strategy for problems with up to 100 of
uncertain parameters.
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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MINLP Synthesis Under Uncertainty
max P(y,x,d,)
max  wi Pi (y, xi, d, i)
y,x,d
s.t.
i
h(y, x, d, ) = 0
g(y, x, d, )  0
xX, dD,  TH
s.t. hi (y, xi, d, i) = 0
gi (y, xi, d, i)  0
i QP
xi X, d D, i TH
y 0,1m
y0,1m
discretization
 - problem
•
•
multiperiod problem
Integration over space of Θ – stochastic optimization: EC or EP
2NP feasibility constraints + 5NP Gaussian quadrature points
Total: 2NP+ 5NP
Answer: Simplified approach
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Minimal Set of Feasibility Constraints
Definition: Critical points are those the worst combinations of uncertain
parameters that determine optimal oversizing of design variables
needed to achieve desired flexibility
•
Extreme vertex points when the problem is convex
No 2NP
•
A priory determination of Critical Points
(Novak Pintarič and Kravnja, 2008)
•
•
Sequential scanning of all vertex points
Without sequential scanning of all vertex points
–
–
–
KKT based method (rigorous)
Iterative method
Approximate non-iterative method
No = ND
•
Combination of Critical Points by using set covering problem
No ≤ ND (less than ND/5)
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Apriory Identification of Critical Points
and Minimal Set of Feasibility Constraints
min C ( y fx , x, z , d , )  M  di
Maximization of di
x , z , d ,
s.t.
h( y fx , x, z, d , )  0
g ( y fx , x, z , d , )  0
d  g d ( x, z ,  )
 LO     UP
x, z, d ,  R, y fx  0,1
NLPi
m
Drawback: approximative
Advantages:
No ≤ ND (less than ND/5)
• Model size depend on the number of design variables
• Robust
• Can be applied to complex large-size process models
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Approximate Stochastic Optimization
Approximate
expected objective
function in CBP
Assure flexibility
of design in min
No CP
Enforce
approximate
trade-offs
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Three-level MINLP Strategy for Flexible
MINLP Synthesis
MINLP level 1: Deterministic non-flexible synthesis at the nominal conditions
MINLP levels 2 and 3: Flexible stochastic MINLP synthesis
Flexibility analysis ot the final optimal solution
Level 2
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
Level 3
Significant
reduction of
problem's
size!
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Synthesis of Flexible Heat Integrated
Methanol Process
From Kravanja, Z., Grossmann, I. E. (1990).
Updated prices
Structure alternatives:
•
•
•
•
•
Two feeds
One- or double stage compression of the feed
Two reactors
One- or double stage compression of the recycle
stream
8y
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
HEN:
• One-stage MINLP model
• 4 hot and 2 cold process streams
partitioned into several segments
• 38 y for the selection of the matches
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Level 1: Deterministic Non-flexible
Synthesis at the Nominal Conditions
MINLP I
HEN: 2 HEs and 2 coolers
–
–
Profit of 37.37 MUSD/yr
Not feasible if small deviations in the uncertain parameters
from the nominal values
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Flexible MINLP Synthesis
27 uncertain parameters: Gauss distribution, 6 σ interval
•
•
•
•
Product demand (1)
Heat transfer coefficients (9)
Price for methanol (1)
Composition of the feeds for H2
and CO (4)
• Utility prices (3)
•
•
•
•
Raw material prices (2)
Temperature of the feeds (2)
Pressure of the feeds (2)
Conversion parameters for
reactors (2)
• Compression efficiency (1)
MINLP Level 2: Flexible MINLP synthesis at nominal condition
• Only 4 critical vertices !!!
• Profit reduced from 37.37 to 33.04 MUSD/a
• The same optimal structure as deterministic one
MINLP Level 3: Flexible MINLP synthesis at CBP
• Profit reduced from 33.04 to 32.72 MUSD/a
• The same optimal structure
Flexibility analysis: Flexibility index 1.000
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Comparison
Deterministic
MINLP I
Flexible –
nominal
MINLP II
Flexible at CBP
(Appr.Stohastic)
MINLPIII
Power COMP-2 (MW)
18.49
29.57
29.57
Power COMP-3 (MW)
15.56
27.97
27.98
Power COMP-4 (MW)
3.34
3.34
3.00
Volumen RCT-1 (m3)
72.78
77.42
77.87
A HE1 (m2)
558.56
529.59
529.33
A HE2 (m2)
208.53
402.82
401.01
A Cooler 1 (m2)
518.46
946.48
967.38
A Cooler 2 (m2)
2436.24
2396.71
2368.37
1
5
5
Continuous variables
572
2656
2656
Discret variables
46
46
46
(In)equalities
580
2892
2892
CPU per NLP (s)
 0.1
 2.5
 1.7
CPU per MILP (s)
 0.1
 0.85
 0.6
Mode
No of simultaneous points
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Multiobjective Sustainable Process
Synthesis
Novak Pintarič and Kravanja, 2005
Two-step superstructural MINLP approach
• 1st economic-based MINLP step for basic process
superstructure that comprises technological end economical
alternatives
Base case solution
•
2nd multiobjective MINLP step for sustainable
superstructure, augmented by additional environmental and
other alternatives
Sustainable solution
Strength:
• Simultaneous approach
• Numerous interactions exploited
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
Drawback:
• Richness of the solution depends on
the abundance of alternatives
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Solution of the Multiobjective Multilevel
MINLP Problem
a) Weighted sum method:
max  wecon RSI econ  (1  wecon ) RSI env 
s.t.
b)  -constraint method
Design or Synthesis Model
0  wecon  1
max RSI econ
s.t.
Design or Synthesis Model
RSI env  
where:
Relative economic index:
RSI econ 
PB
PB 0
Relative environmental index:
RSI env
1

N
 qm, k
 0 
 kIS qm, k
mass usage
l


0
lEC l
energy usage
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
qm, n
q
nWC
0
m, n
water usage

 
jPIM cIC j oOS
qm,c ,o
0
qm,
c ,o

PFj ,c 

polution indicators
44
Solution of the Multiobjective MINLP
HDA Case Study
1st economic-based MINLP step
Fig. 8: Basic process superstructure
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
45
HDA Case Study
1st Economic-based MINLP Step
Fig. 2: Economically optimal process flowsheet – base case
PW
HI
W1
W2
QC = 4.203
QH = 0
Profit
k$/yr
E
kJ/kg
M
kg/kg
W
kg/kg
GW
kg CO2/kg
H
kg/kg
Xtot
5579
0
1.2451
0.3370
0.0078
1.0011
0.9995
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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HDA Case Study
2st Multiobjective Sustainable MINLP Step
Recycling of diphenyle
Heat integration
Fig. 9: Superstructure, enlarged by sustainable alternatives
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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HDA Case Study (Cont.)
2st Multiobjective Sustainable MINLP Step
Relative profit
Relative profit
Scalar parametric optimization:
1,20
Very good solutions !
Size of NLPs:
1400 variables
1300 constraints
1,10
Size of MILPs:
55 binary,
2004 c. variables
up to 2040 constraints
1,00
0,90
1/4h CPU on 1.8 GHz
Intel Pentium M processor
1G RAM
0,80
0,70
0,60
0,70
0,80
0,90
1,00
1,10
1,20
GEIRelative
1,30
1,40
1,50
1,60
environmental index
Fig. 10: “Pareto curve” obtained by scalar parametric optimization
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Multiobjective Sustainable Process
Synthesis
• Alternatives with synergistic effects on economic and
environmental criteria.
• More profitable and less environmentally harmful
solution can be obtained
• Most of alternatives do not show clear trends in their
impacts on economic and environmental indicators.
• Interactions can be very complex and unpredictable.
• Importance of the simultaneous approach to the
sustainable synthesis of process schemes.
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Efficient MINLP model formulations
Translation of variables
(Ropotar and Kravanja; 2008, 2009)
y = 0 → xa = xf
xLO∙y ≤ xs ≤ xUP∙y:
Declared: 0 ≤
xs
≤
y =1 → xa = xs
xUP
xs = xa – xf(1 – y)
y=0
xS,LO=0
xLO
y=1
xUP
xS,UP= xUP
xf + (xLO – xf)y ≤ xa ≤ xf + (xUP – xf)y
Declared: xLO ≤ xa ≤ xUP
y=0,1
Fig1.a: In conventional
discrete/continuous formulation
xLO
0
Xa,LO=xLO
xUP
xa,UP= xUP
Fig.1b: In alternative discrete/continuous
formulation
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Alternative logic-based OA algorithm
NLP subproblem:
min Z l 
 
iDk kSD , for
Yikl true
c
ik
  
 f ika x a
f g ( xg )
s.t. hg ( x g )  0
Ag ( xg )  bg
Ar ( x g , x a )  br
[Y: xs = xa]
hik ( x a )  0
Aik (x a )  0
cik   ik
x LO  x a  x UP
0  cik




l
 i  Dk ,k  SD for Yik  true




• NLP are solved only for currently selected alternatives
• No singularities -> robustnes significantly improved
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
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Alternative Logic-based OA Algorithm:
Translation of OA MILP Master Problem
(CCH-MILP)
(ACH-MILP)



min Z   cik yik  ika   g
i

min Z   cik yik  ika   g
i
k
k
s.t.
s.t.
 g  f  x l    x f  x l  ( x g  x l ) 
 g  f  x l    x f  x l  ( x g  x l ) 
T
T
 
 
h x  xh x
l
l T
 , l  1,..., L


(x  x ) 0
g
l
 
xs = xa – xf(1 – y)
xf =xLO
Ar ( x g , x s )  b r

s
 x  X ik

x  xUPyik
 
f x 
x
a
ik

x s   ika 
 
 
 x hik x

x  xg , xs
x
LO
x x
g
T
  x   f x  x 
 f x ( x  x )  f x  y
 
 

 
x l  f ika x l  yik

T
l
l
ik
n
ik
, l  1,..., L
m
i  Dk , k  SD
UP
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
l T
a
a
ik
l T
a
x ik
l T
a
x ik
l
f
a
ik
f
l
ik
  x  h x  x 
 h x ( x  x )  h x  y
 
 

x   x , x  R , y0,1
 x hik x
  x  h  x  y
 R , y 0,1
0   g ,  ika

 x f ika x
xs 
 h x l
 x ik
Ar ( x g ,xs ( x a , y))  b r
Aik x a  x f 1  yik   bik yik
 f a x l
 x ik
l T
 , l  1,..., L


////////////////////////////////  a
 x  X ik
x a  x f  ( xUP  x f ) yik 
Aik x s  bik yik
l T
( xg  xl )  0
E g ( y)  e g
E g ( y)  e g
s
T
Ag ( x g )  bg
Ag ( x g )  bg
xLOyik  x s
 
h xl  xh xl
l T
l T
a
l T
l
f
l
x ik
g
ik
a
n
0   g , ika
x
LO
f
x ik
m
i  Dk , k  SD
x x ,
g
ik , l  1,..., L
UP
x LO  x a  x UP
52
Comparision
6
400 ys
Reactor network
Efficiency (CPUCCH /CPUACH )
5
HEN
Allyl chloride
4
371 ys
3
600 ys
249 ys
100 ys
184 ys
2
40 ys 32 ys
172 ys
small
moderate
NLP
MILP
NLP
MILP
NLP
MILP
MILP
NLP
MILP
NLP
MILP
NLP
NLP
MILP
NLP
0
MILP
NLP
MILP
1
large
Problem size
Figure 5: Efficiency in solving MILP and NLP master problems vs. problem size
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
53
Hybrid Modeling and Solution Environment
for Disjunctive Models
min Z  c T y  f ( x)
s.t .
h ( x, y )  0
g ( x, y )  0
x  X , X  Rn
y  0,1m
h( x, y )  0
hEO ( xEO , xext , y )  0
hext ( xEO , xext , y )  0
n
nEO next
What if models are too large and compex to be
solved in EO environment?
Answer: Hybrid models
min Z  c T y  f ( xEO , xext )
s.t.
hEO ( xEO , xext , y )  0
hext ( xEO , xext , y )  0
g EO ( xEO , xext , y )  0
min Z  c T y  f  xEO , Φ  xEO  
gext ( xEO , xext , y )  0
x   xEO , xext   X  R n
X  X EO
X ext
s.t.
hEO ( xEO , Φ  xEO , y  , y )  0
xEO  X EO  R nEO , xext  X ext  R next
g EO ( xEO , Φ  xEO , y  , y )  0
y   0,1
xEO  X EO  R n next  R nEO
m
xext  Φ( xEO, y)
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
y   0,1
m
54
Reactive-Distillation Superstructure (ETBE)
• Superstructure consists of
– Three sections of alternative trays
– Fixed feeds, condenser and reboiler
– Each tray can be
• Selected for separation
• Selected for reaction or
• By-passed
Ropotar, Novak Pintarič, Reneaume and
Kravanja, 2009
Dist.
Cond.
Feed 1
Feed 2
Reb.
prod.
Figure 11: Tray superstructure
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
Figure 12: Column superstructure
55
Hybrid Modeling and Solution Environment
for Disjunctive Models
Hybride MINLP model in MIPSYN
EO environment in GAMS:
• Objective function
• MESH equations for separation trays
• MESH equations for reaction trays
• By-pass
• Logical constraints
External FORTRAN:
•
•
•
•
•
Liquid and vapor enthalpies
Reaction rate
Equilibrium constant
Mass of catalyst
Tray dimension
MIPSYN enables:
• Execution of NLP subproblem and external sub-model only for existing
trays to reduce the size and prevents numerical problems to occur.
Challenge:
how to handle different hybrid model sizes within
MINLP iterations?
• Initialization of each NLP which increases the model robustness.
• Several strategies to handle nonconvexities
• Miltilevel MINLPs: the next level starts from the optimal solution of
the current level
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
56
Solution for the Hybride System
Table 2: Solution for three different strategies.
Process parameters
1-level MINLP
with multiple
restarts
Multiple level
MINLP
(2ndlevel)
Multiple level
MINLP with
constrained
integer-cuts
(2ndlevel)
For up to 10 reaction
and 50 separation
trays:
8, 36
8, 37
10, 37
3, 5, 7, 9, 11,
13, 15, 18, 36
2, 4, 6, 10,
14, 23, 25,
32, 38, 40
3, 5, 7, 10, 12,
14, 16, 21, 34,
37, 39, 41
Number of
separation trays
37
36
35
• 1500 variables
Flow of distillate,
mol/s
0.0648
0.0646
0.0642
• 150 binary variables
Flow of product,
mol/s
0.0281
0.0282
0.0284
External
Reboiler duty, W
4 024
3 687
3 377
Condenser duty, W
4 230
3 895
3 586
Isobutylene
conversion, %
99.36
99.44
99.71
Annual cost, k$/year
8.926
8.809
8.571
Position of the feeds
Position of reaction
trays
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
• 3000 constraints
• 500 constraints
• almost all variables
57
Extending Process Synthesizer MIPSYN for
the Synthesis of Bioprocesses
• MIPSYN Library extended for modules:
• Substrate preparation
• Bioconversion
• Product purification
• Solids drying
• Objective function - maximizing revenue:
• Without investment
• With investment
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
58
Optimization of the Corn-based Ethanol
Process description from
Ramkumar Karuppiah et al., 2008
FEED:
Corn Kernels (18 kg/s)
PRODUCTS: Ethanol (5.81 kg/s)
Distillers Dried Grains with Solubes (4.15 kg/s)
Biogas (1.047 kg/s)
Substructures:
• Feed preparation (washing, grinding, cooking)
• Enzymatic hydrolysis (liquefaction, saccharification) and fermentation
• Ethanol purification (distillation, adsorption)
• Solids drying (centrifugation, floatatition, drying)
Alternatives - Different routes for separation solid – liquid:
• Separation before the beer column
• Separation after the bottom of the beer column
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
59
Corn
FEED-1
Washing water
WASH-1
Sythesis of Bioethanol
,
CO2, O2
PRD-1
FEED-2
y1
MECP-1
FER-1
VOC
HEC-4
GRIND-1
Water
PRD-9
SPL-5
SPL1-1
STOR-2
FEED-3
MXR-8
DDGS
FLOT-1
MXR-1
MXR1-1
MXR1-3
HEH-1
PREMIX-1
Superheated
steam
a-amylase
FEED-5
MXR-10
MXR-2
PRD-8
HEC-10
DRY-1
BC-1
MECP-2
HEC-8
HEH-3
MXR-9
y2
HEC-2
SPL1-2
LTANK-1
FLOT-2
Biogas
HEC-7
HEC-3
PRD-6
MXR1-2
glucoamylase
WWT-1
MXR-4
SAC-1
PRD-7
HEH-2
water
SPL-2
REC-1
Solution with
MIPSYN
Non heat
integrated process:
21.018 M$/yr
bioethanol: 5,837 kg/s
biogas: 1,015 kg/s
DDGS: 4,174 kg/s.
PRD-2
Saccaromyces
,
,
cerevisiae,
urea,
water
FEED-7
MXR-3
Heat integrated
process:
Corn grits
HEH-4
FEED-9
STOR-1
SPL-1
Figure 13:
Superstructure of
a corn-based
ethanol plant
SPL-3
MXR-7
PRD-3
MXR-5
ADS-1
31.952 M$/yr
bioethanol: 5,107 kg/s
biogas: 1,047 kg/s in
DDGS: 4,150 kg/s.
HEC-5
SPL-4
HEC-6
PRD-5
MXR-6
CADS-1
Bioethanol
FEED-8
HEH-5
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
HEH-6
CDES-1
PRD-4
Dry air
60
MINLP Synthesis Biogas Process from
Organic and Animal Waste
Figure 14: Superstructure for selecting the optimal processing system for an industrial case study
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
61
MINLP Synthesis Biogas Process from
Organic and Animal Waste
Figure 15: Optimal solution for the industrial case study of biogas
production with NPW of 7.730 MEUR
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
62
Conclusion
Vision:
In order to prevent global worming and achieve efficiency
and suficiency in production and consumption:
redesign or fundamentaly innovate chemical and
process industries based on sustainability principles
appliead to the whole (bio)chemical supply chain.
The greatest challenge for the PSE community:
Based on the systems approach, to provide engineers
and scientists with powerful concepts, methods and
tools so that they will be able to shape this sustainable
development.
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
63
THANK YOU
Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009
64