applications of mathematical programming in sustainable · pdf file(utilities: cooling water,...

1Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009

Gonzalo Guillén-Gosálbez

Department of Chemical Engineering

Universitat Rovira i Virgili, Tarragona, Spain

Applications of mathematical programming

in sustainable process engineering and

systems biology


Spatial scalefm pm nm mm mm m km Gm

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Biology, physics,

chemistry

Engineering

Management

Current scope of Chemical Engineering

Scope of the work



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Biology, physics,

chemistry

Engineering

Management

Sustainable process

engineering


Limited scope: focus at the plant levelReduce environmental impacts locally at the expense of increasing burdens somewhere

else in the chemical supply chain.

Traditional performance indicators in chemical process design (Beamon, 1998)

• Economic

• Non-economic objectives

Maximize profit

Minimize cost

. . . Maximize Customer satisfaction

Maximize Product quality

…

Available tools in Process Systems Engineering

Environmentally conscious process design

(Mizsey, 1994; El-Halwagi, 1997; Cabezas et al., 1997; etc.)

P-1


1 2 2

TO

TA

L

2

Importance of covering the entire life cycle…

Available tools in PSE

1 12 1T

OT

AL

TO

TA

L

3 3 3 3 Total impact

(entire SC)Local impact (each echelon)

ObjectiveDevelop a framework for the design and planning of sustainable chemical processes:

• Cover the entire life cycle impact (holistic view of the system)


SCM in Process Systems and Chemical Engineering

Raw material extraction

Manufacturingplant

Manufacturing plant

Manufacturing plant

Retailer

Warehouse

Retailer

Customer

Customer

Customer


Manufacturingplant

Manufacturing plant

Manufacturing plant

Retailer

Warehouse

Retailer

Customer

Customer

Customer

supply chain network

othersfinances

Single site

Supply chain(Enterprise-wide optimization

time

horiz

on &

spa

tial s

cope

control production

StrategySC configuration

OperationSC planning and coordination: production, logistics, distribution

TacticSC planning

Supervisory controlMonitoring, fault

diagnosis

Local controlUnit coordination &

local control

Global supervision

Operational accounting

Strategic financial planning

Production SchedulingDetailed plant production

planning

ExecutionSystems and equipment

execution

Production Planning

StrategyPlant design,

retrofit

equipment

P-1

production line

manufacturing plant


Design of sustainable hydrogen supply chains

• Given are:� Demand of hydrogen� Investment and operating costs� Available technologies and potential locations (i.e., grids)� GHG emissions associated with the SC operation

• The task is to determine the optimal SC configuration

• In order to minimize cost and environmental impact

?

Design of SCs for hydrogen production (Almansoori and Shah, 2006)


Technology 1

Technology P

Technology 1

Technology P

Digt

Production Plants

Storage Facilities

Markets

CPL

gpt

NPL

gpt

CST

gst

NST

gst

... ... ...

Qigg’lt

Tech. 1

Tech. S

...

...

...

Tech. 1

Tech. S

Location 1

Location G

Methodology: superstructure

Superstructure

Mathematical representation that embeds all possible logistic alternatives

MILP

Mass balance equationsCapacity constraintsObjective function equations


Mathematical formulation (I)

� Capacity constraints

(production and storage)

Production facilities

Storage facilities

Integer variables

Integer variables

� Mass balances (defined for every

grid)


Mathematical formulation (II)

� Objective function: Total discounted cost

Transportation links

Binary variables

Facilities capital cost

Facilities operating costTransportation capital costTransportation operating cost


Environmental aspects based on LCA (Eco-Indicator 99)

LCA

(ISO 14040 series on LCA)

LCA

(ISO 14040 series on LCA)

Objective strategy to evaluate the environmental loads associated with a product, process or activity

Objective strategy to evaluate the environmental loads associated with a product, process or activity

by quantifying energy and materials used and waste released

by quantifying energy and materials used and waste released

It includes the ENTIRE LIFE CYCLE of the productIt includes the ENTIRE LIFE CYCLE of the product

to evaluate opportunities to do improvements

to evaluate opportunities to do improvements

Combine LCA with optimization tools(Azapagic et al., 1999; Mele et al., 2005;

Hugo and Pistikopoulos, 2005;

Puigjaner and Guillén-Gosálbez, 2008)


Environmental damage assessment: Global warming

2. Translate emissions into damage (Eco-indicator 99: damage to human health caused by

climate change)

• Human health: DALYs (Disability Adjusted Life Years)

Damage factors translate life cycle inventory into impact

Transportation tasks

Production (raw materials, energy

consumption and direct emissions)

1. Calculate the emissions and feedstock requirements (Life Cycle Inventory :

analysis from the cradle to the grave)

Storage

(compression of hydrogen)


Environmental Impact

Cost

Bi-criterion MILP with economic and environmental concerns

Epsilon constraint method:

Solve a set of single objective problems for different values of ε

Epsilon constraint method

Bi-level decomposition algorithm

Guillén-Gosálbez, Mele and Grossmann, 2009)


Pareto set

Environmental improvements are achieved through structural changes in the network

• Replace steam reforming by

biomass

• Do not use compressed gaseous

hydrogen (too expensive)


Extreme solutions

Steam methane reforming

Coal gasification

Biomass gasification

LH tanker truck

LH railway tank car

CH tube trailer

CH railway tube car

1 2

3 4

5 6

7 8

9 10 11

12 13 14

15 16 17 18

19 20 21

22 23

Production

Transportation

Cryogenic spherical tank (LH)

Pressurized cylindrical vessel (CH)

Storage

54

8

8

19

11

29 41 7

31

23 45 23

47 40 18

21 48 136

1210

6

18

2

1 1

1

1 1

3 3 1

3 4 3

2 4 3

2 4 8

1

2

1 2

3 4

5 6

7 8

9 10 11

12 13 14

15 16 17 18

19 20 21

22 23

1

1

1 1

2 2 1

2 3 1

1 3 3 1

1 3 6

1

5

10

6

17 16

5

8

37 6

21

26

28

19

40 21

1643 35

44 123

119

7

1

1

Minimum cost: more centralized network (economies of scale)

Minimum impact: more decentralized network (reduces transportation emissions)


SCM in Process Systems and Chemical Engineering


Manufacturingplant

Manufacturing plant

Manufacturing plant

Retailer

Warehouse

Retailer

Customer

Customer

Customer


Manufacturingplant

Manufacturing plant

Manufacturing plant

Retailer

Warehouse

Retailer

Customer

Customer

Customer

supply chain network

othersfinances

Single site

Supply chain

time

horiz

on &

spa

tial s

cope

control production

StrategySC configuration

OperationSC planning and coordination: production, logistics, distribution

TacticSC planning

Supervisory controlMonitoring, fault

diagnosis

Local controlUnit coordination &

local control

Global supervision

Operational accounting

Strategic financial planning

Production SchedulingDetailed plant production

planning

ExecutionSystems and equipment

execution

Production Planning

StrategyPlant design,

retrofit

equipment

P-1

production line

manufacturing plant


ConclusionsHydrodealkylation of toluene

Hydrodealkylation of toluene: superstructure taken from Kocis and Grossmann (1986)


Mathematical formulation

Objective function (cost and environmental impact)

Process equations:• Non-linear performance of the system (mass and heat balances)• Sizing equations

Design specifications (linear inequalities)

Continuous variables:• Flows• Operating conditions (pressures, temperatures, etc.)• Sizes of equipments

Discrete variables (logical decisions denoting the potential existence of process units)

The synthesis problem with environmental concerns can be formulated as a multi-objective mixed integer non linear problem (mo-MINLP):


2. Translate emissions into damage (11 impacts aggregated into 3 damage categories)

• Human health: DALYs (Disability Adjusted Life Years)

• Ecosystem quality: PDF·m2·yr (Potentially Disappear Fraction of Species)

• Resources: MJ surplus energy · kg-1

Production of raw materials Direct emissions from

the process

Energy generation

(utilities: cooling water, steam, etc.)

Phase II: Inventory analysis

1. Express the life cycle inventory as a function of some continuous variables:

Continuous variables (pressures, temperatures, flows, etc.)

Damage in each impact category (11 impact categories)

Damage in each damage category (3 damage categories)

Eco indicator 99 (add normalization and weighting factors)

Uncertainty


Uncertainty in the emissions

Emissions are described

through discrete distributions

Probabilistic objective:Minimize omega for a given probability level

Target level omegaChance constrained programming

(Charnes and Cooper, 1962)


ConclusionsPareto setGuillén-Gosálbez, Caballero and Jiménez, 2008

• 724 constraints• 710 continuous variables • 13 binary variables • Solved with GAMS 21.33 interfacing with DICOPT

Changes in topology and operating conditions


ConclusionsImpact categories and risk curves

The probability of high Eco-indicator 99 values is decreased

1. Carcinogenic effects on humans (DALYs).

2. Respiratory effects on humans caused by organic substances (DALYs).

3. Respiratory effects on humans caused by inorganic substances (DALYs).

4. Damage to human health caused by climate change (DALYs).

5. Human health effects caused by ionizing radiations (DALYs).

6. Human health effects caused by ozone layer depletion (DALYs).

7. Damage to ecosystem quality (toxic emissions) (PDF·m2·yr).

8. Damage to ecosystem quality (acidification and eutrophication) (PDF·m2·yr).

9. Damage to ecosystem quality (land occupation and land conversion) (PDF·m2·yr).

10. Damage to resources caused by extraction of minerals (MJ surplus energy · kg-1).

11. Damage to resources caused by extraction of fossil fuels (MJ surplus energy · kg-1).

Total Eco99


OptimizerOptimizer

Simulation Model(ASPEN, HYSYS, SuperPro Designer, etc.)

Simulation Model(ASPEN, HYSYS, SuperPro Designer, etc.)

Index calculator(economic, LCA, etc.)

Index calculator(economic, LCA, etc.)

Simulation models for SCM

Combined simulation-optimization approach

Decision variables

(independent variables)

Dependent variables

Use process simulators instead of generic modeling systems…

(Caballero, Milán-Yañez and Grossmann, 2005)


ConclusionsCombined simulation-optimization approach

• Citric acid production

• Pyruvic acid

• Lysine

• Riboflavin

• Cyclodextrin

• Penicilin

• Human serum albumin

• Human insulin

• Monoclonal antibodies

• Alpha-1-antitrypsin

• Antitrypsin

• Plasmid DNA

Biotechnological processes (single product batch processes)

SuperPro Designer

• Batch processes

• Economic performance

• Scheduling

• Short cut methods


MATLAB(kinetics of fed-batch reactor)

MATLAB(kinetics of fed-batch reactor)

OptimizerNelder-Mead Simplex Method

OptimizerNelder-Mead Simplex Method

Simulation Model(SuperPro Designer)


LCA analysisLCA analysis

Combined simulation-optimization approach

Decision variables

(initial concentrations, amount of raw materials, operting times)

Dependent variables

Master problem (MILP, heurist, etc.)Master problem (MILP, heurist, etc.)

Slave problem (NLP)

Number of equipments in parallel

Master problem (de-bottlenecking heuristic)


Production of bioethanol (Fernando Mele, Univ. Tucumán)

Argentina law 26093: 5% of ethanol in gasoline in 2011

Challenge: produce both sugar and ethanol

Decision-support tools to guide the transition process


Production of bioethanol from sugar cane



Distillation columns(ASPEN)

Distillation columns(ASPEN)

Fermentation(MATLAB)

Fermentation(MATLAB)



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Biology, physics,

chemistry

Engineering

Management

Optimization in systems

biology

Joint collaboration with Albert Sorribas

(Department of Medical Sciences, UdL)


Introduction

Variables:

• Enzyme activities

Objective:

• Maximize ethanol synthesis rate

• Metabolite concentrations

Fermentation in S. cerevisiae

(Polisetty et al., 2008)

Biotechnology

• Use of microorganism to produce

biochemical products

• Metabolic network


Mathematical formulation

Velocityvr

Stoichiometric coefficientµir

• Current alternatives

BARON (commercial package)

Computational problems complex networks

Long CPU time

Polisetty et al., 2008

Large optimality gaps

Does not guarantee optimality

• Steady state conditions

• Velocity: power-law

• Objective function

Kinetic orderfrj

Metabolite concentrationXj

Enzyme activityγr

Non-convex

search space

Final product synthesis rate

GMA model

Flux balance analysis (linear representation)

Generalized Mass Action (GMA) model (Voit, 1992) (nonlinear model)


Upper bound

Lower bound

Decompose original problem into two hierarchical levels: a master MILP and

a slave NLP (Bergamini et al., 2005; Polisetty et al., 2008)

original objective function

SRS

Original search spaceConvexified search space

convexified objective function

Starting point

Outer approximation

Master Slave


Lower bound

convexified objective function

Upper bound

original objective function

Outer approximation

Master Slave

Original search space

S

Decompose original problem into two hierarchical levels: a master MILP and

a slave NLP (Bergamini et al., 2005; Polisetty et al., 2008)

Convexified search space

RS


Outer approximation

Novelty:

convex envelopes

• Logarithmic transformation

• Piece-wise linear functions

Pozo, Guillén-Gosálbez, Sorribas, Jiménez, 2009


Case studies (Polisetty et al., 2008)

Case study 1

Maximize ethanol production in

Saccharomyces cerevisiae

Case study 2

Maximize citric acid synthesis

rate in Aspergillus niger

Ethanol

Citric

acid


Results: Case study 1

Model data

53

50

518

Variables

RNLP equations

Integer variables

14Continuous variables

40CMILP equations



471

439

4235

Variables

RNLP equations

Integer variables

91Continuous variables

211CMILP equations

Model data

Without tuning of parameters


Optimization in Evolution studies

Evolutive emergence of design

Understanding adaptation:

• Feasible responses (survival in new conditions)

• Hypothetical optimum (natural selection)

Heat

shock

Oxidation

Other

stresses

Adaptation

Evolution

�Energy

�Protein

�Others

Old

designNew

design

Reverse optimization problem:

• Known: Optimal solution (actual system)

• Unknown optimization problem: Objective function and constraints??


Change-fold

Enzyme j

Change-fold Enzyme i

(1)

(3)

(2)

(4)

(5)

Importance of appropriate set of constraints

Hypothetical feasible regions

• Different sets of constraints lead to different feasible regions (design

principles)

• (3) and (5) do not contain

experimental results

• (4) does not explain all

experimental results

• (1) more restrictive than (2)

• Experimental observations

(comparison):

DISCHARDED!!!

DISCHARDED!!!

PREFERRED…


Feasibility approach (algorithm)1

1

01

−≤− ∑∑∈∈

MyyMs

s

Ms

s

Integer cut:enzyme activity i in interval j

otherwise

Remain identiyinfying and removing feasible regions

Until no more feasible solutions remain

Enzyme activityγr

γr

Guillén-Gosálbez, Sorribas, 2009


Problem statement (Case study 3)

Ribulose-5P

Glcout

Glcin

HXTa

GLKbb

G6PDHd

G6P

F16P

2PEP

2PYR

PYKc

TDHc

PFKc

TPSb

GLY

GOLPYK

GLK

ATP

TDH

TPS

ATPase

PFK

2 Glycerol

+

-

• Global optima different criteria:

Solve reverse optimization problem:

• Feasible enzyme activities:

• PFK

• Fulfill physiological constraints:

• TDH

Adaptation of yeast to heat shock

(Vilaprinyo et al., 2006)

(Others)

• ATP

• NADPH

• Trehalose

Max • CostMin


Experimental observations

Minimum costMaximum rate of Trehalose synthesis

Maximum rate of NADPH synthesisMaximum rate of ATP synthesis


(Eisen et al., 1998, Gasch et al., 2000 and Causton et al., 2001)

Adaptation of yeast to heat shock

(Vilaprinyo et al., 2006)


• Application of optimization tools to emerging areas

• Sustainability: combined approach LCA + optimization

• Systems biology: application of global optimization to metabolic engineering and evolution studies

• PSE provides strong background and powerful tools to address problems of great interest

Conclusions


PhD students

Robert Brunet (sustainable process engineering)

Berhane Gebreslassie (sustainable process engineering)

Andrew Kostin (sustainable process engineering)

Nagore Sabio (sustainable process engineering)

Carlos Pozo (systems biology)

Pedro Copado (systems biology)

Acknowledgments

Research projects

Spanish Ministry of Education

Spanish Ministry of External Affairs

Spanish Ministry of Science and Innovation (MICINN)

Generalitat de Catalonia (Catalonian Government)


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Biology, physics,

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Management

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