Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

1Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

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

2

Slovenia in pictures Area: 20,273 km2

Population: 2.0 million Capital city: LjubljanaLanguage: Slovenian; also Italian and Hungarian in nationally mixed areas Currency: EURO, €Member of EU - 1 May 2004

EU Presidency for 2008


http://epi.yale.edu/CountryScores

Environmental Performance Index (EPI)

Slovenia has rank 15

4

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


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


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

7

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).

8

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

9

3 X 3 Sustainability Matrix


Nature Sustainability

Eco-centric 3

Strategies Expanded- 2 anthropozentric 3 Sufficiency 2 Consistency Narrow 1 1 Efficiency anthropozentric

1 2 3 Principle of Justice, Etics Just Reward for Work

Respect for Private Property Fair Distribution of Goods

(M. F. Jischa, Chem. Eng. Technol. 21, 1998)

1

8

27

Figure 1: Diagonal as a measure of sustainability

10

Environmental Aspects


Environmentally friendly innovation

In addition:

Material brought into the environment < Carrying capacity of

the ecosystem ->min emission of pollutant

Consummation rates of renewables

Their regeneration rates ->

max renewables

Non-renewable resources only if future generation would not be compromised ->

min non-renewables

->Multiobjective

approach

<

(Voss, 1994)

Environmental constraints Opt. Criteria

11

MINLP Model Formulation for Different Levels of Innovations:


a) max z = cTy + f(x) – e(x) b) s.t hi(x) = 0 c) gi(x) 0 d) Biy + Cix bi x X = x Rn: xLO x xUP y Y = 0,1m

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

i Levels }

12

Sustainable and Integrated (Bio)chemical Supply Chain Synthesis


Fig.??(Marquardt Wolfgang, Lars Von Wedel, and Birget Bayer.AspenWorld 2000, Orlando, FL, 2000)

18

r

Sustainability27

Figure 2: Diagonal as a measure of sustainability

13

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)


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.

Extension:

14

Challenges Related to the Manifolds Nature of the Synthesis Problems


Many complex interactions SimultaneousSimultaneous

Discrete and continuous decisions MINLPMINLP

Uncertainty FlexibilityFlexibility

Dynamic systems MIDNLP, MIDNLP, multiperiodmultiperiod

Rule-based decisions Logic-based Logic-based

Multicriterial MultiobjectiveMultiobjective

Features Approach

15

Simultaneous Synthesis and Heat Integration - Methanol Example Problem


Process synthesis and:• sequential HEN synthesis: - 1,192,000 $/yr (loss!)• simultaneous HI by Duran-Grossmann’s model: - 292,000$ $/yr (loss!)• simultaneous HEN synthesis by Yee’s model:

• Yee, Grossmann, Kravanja (1990) 1,845,000 $/yr (profit!).• Kravanja and Grossmann (1994) 2,613,000 $/yr (profit!)

Figure 3: Methanol process and HEN superstructure

Figure 4: Optimal process scheme with HI HEN

16

Table 1: Types of optimization problems and models


Equations Linear Nonlinear Difference Differential Model Steady state Multiperiod Dynamic Example Continuous process Life cycle Batch

process Certainty variables

Nominal

Continuous, x LP NLP e.g. e.g. discrete, y 0-1 ILP INLP logical Y DisLP DisNLP x, y MILP MINLP Mul. MINLP Dyn. MINLP x, Y MDisLP MDisNLP Uncertain par. Flexible

Kravanja Z., 2003, Chem. Biochem. Eng. Q. 17 (1), 1-3.

Different Modeling Complexities


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

http://www.gamsworld.org/minlp/solvers.html

18

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

19

MIPSYN and Logic Based OA


Or when NLP is not imroving

20

MIPSYN flowchart


Topology

P_STRUCT.DAT

Components

P_ COMPON.DAT

User’s modules

MY_MODEL.DAT

Data

P_DATA.DAT

Model generator

MIPSYN Libraries:

AP/OA/ER - Process modules

M/D - Components properties

NLP initializer

Simple simulator

Solution

P_OPTIMUM.RES

Procedure overview

P_B.RES

GAMS

NLP solvers: CONOPT, MINOS, SQP

MILP solver: CPLEX, OSL,

21

Applications


Chemical Engineering(MIPSYN)

NLP optimization • Process sybsystems • Flowsheets

MINLP synthesis:• Reactor networks• Separator networks• Heat exchanger networks• Overall HI process flowsheets

Mechanical Engineering(TOP)

NLP optimization • Timbes trases • Composite floor systems

MINLP synthesis of mechanical structures:

• Gates for hydropower dams• Steel frames• Steel buildings

Different levels of problem abstraction and application• More general MINLP solver

• Process synthesizer

• Synthesizer shell for different domains

22

PROSYN-MINLP verion


23

MipSyn β Version


24

Multilevel-hierarchical MINLP Synthesis


Combination of the hierarchical strategy and MINLP superstrucutre approach

(Kravanja and Grossmann;1997)

MINLP 1: RCT network:- Detailed RCT network model- Simple SEP model - Simultaneous heat integration

MINLP 3: HEN synthesis- Fixed RCT/SEP structure- Detailed RCT and SEP modules- Staged HEN synthesis model

Tagret HI

Identify SEP tastks

Tagret HI

Identify process streams

HI

Identify SEP tastks

Profit UB

LB

STOP if

UP≈LB

LoopMINLP 2: SEP/RCT network:- Detailed RCT models- Detailed SEP models- Targeted heat integration

25

MINLP 1: Initial Reactor Network and Simplified Separation Superstructure


HDA example

26

MINLP 1 – Optimal Solution


Identified separations

Targeted HI

Upper Bound 6.505 M$/yr

27

MINLP 2: Detailed RCT and Identified SEP


28

MINLP2: Optimal Solution


Identified hot and cold

streams

Targeted HI

Upper Bound 5.892 M$/yr

29

MINLP 3: HEN Synthesis within Fixed Flowsheet


Lower Bound 5.201 M$/yr

30

MINLP II resolved: UB = 5.240 M$/yr

MINLP III: LB = 5.201 M$/yr

STOP

OPTIMAL SOLUTION:


MINLP 2 Resolved

Since UP≈LB →

31

Multilevel Synthesis of Mechanical Structure


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

LINKED MULTILEVEL HIERARCHICAL STRATEGY (LMHS)

SYNTHESIS OF ROLLER HYDRAULIC STEEL GATEHydroelectric Project Blanda, Iceland

(S. Kravanja, A. Soršak, Z. Kravanja; 2003)

32

Optimal Structures


4000 mm

4600 mm

4120 mm

30 30 10 10 10 30 30

100 100 100 100 100 100 100

28245 1079.5 1079.5 1079.5 1079.5 282 45

4972

414

25

479

40

Optimal solution: 8804 €Self-manufacturing costs of the erected gate: 13498 €35% net profit

19622 y !

33

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.

34

MINLP Synthesis Under Uncertainty


• Integration over space of Θ – stochastic optimization: EC or EP• 2NP feasibility constraints + 5NP Gaussian quadrature points

Total: 2NP+ 5NP

max P(y,x,d,) max wi Pi (y, xi, d, i) y,x,d i

s.t. h(y, x, d, ) = 0 s.t. hi (y, xi, d, i) = 0

g(y, x, d, ) 0 gi (y, xi, d, i) 0 i QP

xX, dD, TH xi X, d D, i TH

y0,1m y 0,1m discretization

- problem multiperiod problem

Answer: Simplified approach

35

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)

36

Apriory Identification of Critical Points and Minimal Set of Feasibility Constraints


fx

, , ,

fx

fx

dLO UP

fx

min ( , , , , )

s.t. ( , , , , ) 0

( , , , , ) 0( , , )

, , , , 0,1

ix z d

m

C y x z d M d

h y x z d

g y x z dd g x z

x z d R y

Drawback: approximative

Advantages:

• Model size depend on the number of design variables

• Robust

• Can be applied to complex large-size process models

Maximization of di

NLPi

No ≤ ND (less than ND/5)

37

Approximate Stochastic Optimization


Approximate expected objective

function in CBP

Assure flexibility of design in min

No CP

Enforce approximate trade-offs

CBP

,

CBP c

CBP cC

CBP cd d,

LO

min ( , , )

s.t. ( , , ) 0 ( , , ) 0

( , , ) 0 ( , , ) 0 1,...,

( , ) ( , )

; , ,

x d

k k k

k k k

k k k

k

C x d

h x d h x d

g x d g x d k n

d g x d g x

d d x x d R

38

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

Level 2 Level 3

Significant reduction of problem's

size!

Flexibility analysis ot the final optimal solution

39

Synthesis of Flexible Heat Integrated Methanol Process


Structure alternatives:• Two feeds• One- or double stage compression of the feed• Two reactors • One- or double stage compression of the

recycle stream• 8 y

HEN:

• One-stage MINLP model

• 4 hot and 2 cold process streams partitioned into several segments

• 38 y for the selection of the matches

From Kravanja, Z., Grossmann, I. E. (1990).Updated prices

40

Level 1: Deterministic Non-flexible Synthesis at the Nominal Conditions


– Profit of 37.37 MUSD/yr

– Not feasible if small deviations in the uncertain parameters

from the nominal values

MINLP I

HEN: 2 HEs and 2 coolers

41

Flexible MINLP Synthesis


27 uncertain parameters: Gauss distribution, 6 σ interval

• Raw material prices (2)• Temperature of the feeds (2)• Pressure of the feeds (2)• Conversion parameters for reactors (2)• Compression efficiency (1)

• Product demand (1)• Heat transfer coefficients (9)• Price for methanol (1)• Composition of the feeds for H2

and CO (4)• Utility prices (3)

• Only 4 critical vertices !!!• Profit reduced from 37.37 to 33.04 MUSD/a• The same optimal structure as deterministic one

MINLP Level 2: Flexible MINLP synthesis at nominal condition

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

42

Comparison


Mode DeterministicMINLP I

Flexible – nominalMINLP 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

No of simultaneous points 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

43

Multiobjective Sustainable Process Synthesis


Strength:• Simultaneous approach • Numerous interactions exploited

Drawback:• Richness of the solution depends on

the abundance of alternatives

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

Novak Pintarič and Kravanja, 2005

44

Solution of the Multiobjective Multilevel MINLP Problem


econ econ econ env

econ

max (1 )

s.t.

Design or Synthesis Model

0 1

w RSI w RSI

w

a) Weighted sum method:

b) -constraint method

econ

env

max

s.t.

Design or Synthesis Model

RSI

RSI

where:

Relative environmental index:

m, m, m, ,env ,0 0 0 0

m, m, m, ,

mass usage energy usage water usage polution indicators

1

j

k n c olj c

k IS l EC n WC j PIM c IC o OSk l n c o

q q qRSI PF

N q q q

Relative economic index:

econ 0

PBRSI

PB

45

Solution of the Multiobjective MINLP HDA Case Study


Fig. 8: Basic process superstructure

1st economic-based MINLP step

46

HDA Case Study 1st Economic-based MINLP Step


Fig. 2: Economically optimal process flowsheet – base case

PW W1 W2Profitk$/yr

EkJ/kg

Mkg/kg

Wkg/kg

GWkg CO2/kg

Hkg/kg

Xtot

HIQC = 4.203

QH = 05579 0 1.2451 0.3370 0.0078 1.0011 0.9995


Fig. 9: Superstructure, enlarged by sustainable alternatives

Recycling of diphenyle

Heat integration

HDA Case Study 2st Multiobjective Sustainable MINLP Step


Scalar parametric optimization:

0,70

0,80

0,90

1,00

1,10

1,20

0,60 0,70 0,80 0,90 1,00 1,10 1,20 1,30 1,40 1,50 1,60

GEI

Rel

ativ

e pr

ofit

Fig. 10: “Pareto curve” obtained by scalar parametric optimization

Size of NLPs:1400 variables1300 constraints

Size of MILPs:55 binary, 2004 c. variables up to 2040 constraints

1/4h CPU on 1.8 GHzIntel Pentium M processor 1G RAM

HDA Case Study (Cont.) 2st Multiobjective Sustainable MINLP

Step

Very good solutions !

Relative environmental index

R

elat

ive

prof

it


• 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.

Multiobjective Sustainable Process Synthesis


xLO∙y ≤ xs ≤ xUP∙y:

Declared: 0 ≤ xs ≤ xUP

xf + (xLO – xf)y ≤ xa ≤ xf + (xUP – xf)y

Declared: xLO ≤ xa ≤ xUP

y=1xUP

y=0 xLO

xS,LO=0 xS,UP= xUP

y=0,1

0

xUPxLO

Xa,LO=xLO xa,UP= xUP

Fig1.a: In conventional discrete/continuous formulation

Fig.1b: In alternative discrete/continuous formulation

Translation of variables(Ropotar and Kravanja; 2008, 2009)

Efficient MINLP model formulations

xs = xa – xf(1 – y)

y = 0 → xa = xf

y =1 → xa = xs

51

Alternative logic-based OA algorithm


NLP subproblem:

g gs.t. ( ) 0h x

a a g g

,

min ( )k

lik

lik ik

i D k SD forY true

Z c f f

x x

g g g( )A bx

r g a r( , )A bx x

LO a UP

a

a

( ) 0

( ) 0

for

0

ik

ik

lik ik k ik

ik

h

A

c i D ,k SD Y true

c

x

x

x

x x

[Y: xs = xa]

• NLP are solved only for currently selected alternatives• No singularities -> robustnes significantly improved


Alternative Logic-based OA Algorithm:Translation of OA MILP Master Problem

a g

Tg g

T g

g g g

g g

r g s r

min

s.t.

( ), 1,...,

( ) 0

( )

( )

( , )

ik ik iki k

l l lx

l l lx

Z c y

f fl L

h h

A b

E e

A b

x x x x

x x x x

x

y

x x

ss

s

s

Ta s a

Ta a

T s

T

g s

g a

LO g UP

, 1,...,

, , 0,1

0 , ,

ikik

ik

ikik ik

lx ik ik

l l lx ik ik ik

lx ik

l l lx ik ik ik

mn

ik k

xLOy xx

x xUPy

A b y

f

f f y

h

h h y l L

R

i D k SD

X

x

x x

x x x

x x

x x x

x x x y

x x x

xs = xa – xf(1 – y)

s

a g

Tg g

T g

g g g

g g

r g a r

aa

f f

a f

min

s.t.

( ), 1,...,

( ) 0

( )

( )

( ( , )

///////////////////////////////

)

)

1

/

,

(

ik ik iki k

l l lx

l l lx

ikik

ikik ik ik

x

Z c y

f fl L

h h

A b

E e

A b

xx xUP x y

A y b y

x

x

x x x x

x x x x

x

y

x

X

x

x y

x

Ta f

f

Ta a

Ta a

T

T

g

g a

L

a

a

a

LO a UPU

f

O P

T

g

f

( )

( ) , 1,...,

, , 0,1

0 , ,

,

lik ik

l l lx ik ik ik

lx ik

l l lx ik ik ik

mn

ik k

lx ik

lx ik

f

f f y

h

h h y l L

R

i D S

f

h

k D

x

x

x x

x

x x

x

x x

x

x x x

x x

x

x

x

x x x

y

xx x

(CCH-MILP) (ACH-MILP)

xf =xLO

53

Comparision


0

1

2

3

4

5

6

small moderate large

Eff

icie

ncy

(CPU

CC

H/C

PUA

CH

)

Problem size

Reactor network

HEN

Allyl chlorideM

ILP

NLP

MIL

PN

LPM

ILP

NLP

MIL

PN

LPM

ILP

NLP

MIL

PN

LP

MIL

PN

LPM

ILP

NLP

MIL

PN

LP

40 ys 32 ys 172 ys

184 ys

249 ys100 ys

600 ys

371 ys

400 ys

Figure 5: Efficiency in solving MILP and NLP master problems vs. problem size


mn

y

RXXx

yxg

yxh

xfycZ

1,0

,

0),(

0),(

s.t.

)(min T

EO ext

TEO ext

EO EO ext

ext EO ext

EO EO ext

ext EO ext

EO ext

EO ext

EO EO ext ext

min ( , )

s.t.

( , , ) 0

( , , ) 0

( , , ) 0

( , , ) 0

,

,

0,1

n

n n

Z c y f x x

h x x y

h x x y

g x x y

g x x y

x x x X R

X X X

x X R x X R

y

m

extEO nn

n

EO EO ext

ext EO ext

( , , ) 0

( , , ) 0

h x x y

h x x y

0),( yxh

ext EO

TEO EO

EO EO EO

EO EO EO

EO EO

min ,

s.t.

( , , , ) 0

( , , , ) 0

0,1

n n n

m

Z c y f x Φ x

h x Φ x y y

g x Φ x y y

x X R R

y

),( EOext yxΦx

What if models are too large and compex to be solved in EO environment?

Answer: Hybrid models

Hybrid Modeling and Solution Environment for Disjunctive Models

55

Reactive-Distillation Superstructure (ETBE)


Feed 2

Cond.

Reb.

Dist.

prod.

Feed 1

Feed 2

Cond.

Reb.

Dist.

prod.

Feed 1

Feed 2

Cond.

Reb.

Dist.

prod.

Feed 1

Feed 2

Cond.

Reb.

Dist.

prod.

Feed 1

Feed 2

Cond.

Reb.

Dist.

prod.

Feed 1

Cond.

Reb.

Dist.

prod.

Feed 1

Cond.

Reb.

Dist.

prod.

Cond.

Reb.

Dist.

prod.

Cond.

Reb.

Cond.Cond.

Reb.Reb.

Dist.

prod.

Feed 1Feed 1

• 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

Figure 11: Tray superstructure Figure 12: Column superstructure

Ropotar, Novak Pintarič, Reneaume and Kravanja, 2009

56

Hybride MINLP model in MIPSYN


External FORTRAN:• Liquid and vapor enthalpies • Reaction rate • Equilibrium constant • Mass of catalyst• Tray dimension

EO environment in GAMS:• Objective function• MESH equations for separation trays• MESH equations for reaction trays• By-pass• Logical constraints

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

Hybrid Modeling and Solution Environment for Disjunctive Models

57

Solution for the Hybride System


Process parameters 1-level MINLP with multiple restarts

Multiple level MINLP (2ndlevel)

Multiple level MINLP with constrained integer-cuts (2ndlevel)

Position of the feeds 8, 36 8, 37 10, 37

Position of reaction trays 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

Flow of distillate, mol/s 0.0648 0.0646 0.0642

Flow of product, mol/s 0.0281 0.0282 0.0284

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

Table 2: Solution for three different strategies.

For up to 10 reaction and 50 separation trays:

• 3000 constraints

• 1500 variables

• 150 binary variables

External

• 500 constraints

• almost all variables


Extending Process Synthesizer MIPSYN for the Synthesis of Bioprocesses

• MIPSYN Library extended for modules:MIPSYN Library extended for modules:

• Substrate preparation

• Bioconversion

• Product purification

• Solids drying

• Objective function - maximizing revenue:Objective function - maximizing revenue:

• Without investment

• With investment


Process description from Ramkumar Karuppiah et al., 2008

Optimization of the Corn-based Ethanol

FEED: FEED: Corn Kernels (18 kg/s) PRODUCTS: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


Corn Washing water

Water

glucoamylase

Saccaromycescerevisiae,urea, water

,,

,CO2, O2

DDGS

VOC

Biogas

water

Corn grits

REC-1SPL-2

FEED-9

ADS-1

SPL-4

SPL-3

CDES-1

CADS-1

HEH-5

y1

Superheatedsteam

a-amylase

WASH-1FEED-1 FEED-2

GRIND-1

FEED-3

MXR-1

HEH-1PREMIX-1

FEED-5

FEED-6

FEED-7

HEC-2

MXR-2

LTANK-1

SAC-1

HEC-3

HEH-2

MXR-3

STOR-1

FER-1

STOR-2SPL1-1

MXR1-1

MXR-10

FLOT-1

MECP-1

MXR-8

PRD-1

HEH-3

HEC-4

HEC-7

MXR1-2

MXR1-3

SPL1-2

MECP-2

FLOT-2

HEC-10

BC-1

DRY-1

SPL-5

HEC-8

PRD-9

PRD-6

PRD-8

PRD-7

MXR-9

WWT-1MXR-4

PRD-2

HEH-4

PRD-3

SPL-1

MXR-5

MXR-6

MXR-7

HEC-5

HEC-6

PRD-5

HEH-6 Dry air

FEED-8

PRD-4

Bioethanol

y2

Figure 13: Superstructure of a corn-based ethanol plant

Non heat integrated process:

21.018 M$/yr bioethanol: 5,837 kg/sbiogas: 1,015 kg/sDDGS: 4,174 kg/s.

Heat integrated process:

31.952 M$/yr bioethanol: 5,107 kg/sbiogas: 1,047 kg/s inDDGS: 4,150 kg/s.

Solution with MIPSYN

Sythesis of Bioethanol

61

MINLP Synthesis Biogas Process from Organic and Animal Waste


Figure 14: Superstructure for selecting the optimal processing system for an industrial case study


Figure 15: Optimal solution for the industrial case study of biogas production with NPW of 7.730 MEUR

MINLP Synthesis Biogas Process from Organic and Animal Waste

63

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.


64

THANK YOU


Plenary Lecture, ESCAPE 19, Krakow, Poland, 14 – 17 June 2009

Documents

albert einsteinplenary

simultaneous hi

km2 population

new insights

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eu presidency

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