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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
2Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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Biology, physics,
chemistry
Engineering
Management
Current scope of Chemical Engineering
Scope of the work
3Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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Engineering
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Sustainable process
engineering
4Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
5Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
1 2 2
TO
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Importance of covering the entire life cycle…
Available tools in PSE
1 12 1T
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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)
6Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
SCM in Process Systems and Chemical Engineering
Raw material extraction
Manufacturingplant
Manufacturing plant
Manufacturing plant
Retailer
Warehouse
Retailer
Customer
Customer
Customer
Raw material extraction
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
7Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
8Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
9Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Mathematical formulation (I)
� Capacity constraints
(production and storage)
Production facilities
Storage facilities
Integer variables
Integer variables
� Mass balances (defined for every
grid)
10Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Mathematical formulation (II)
� Objective function: Total discounted cost
Transportation links
Binary variables
Facilities capital cost
Facilities operating costTransportation capital costTransportation operating cost
11Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
12Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
13Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
14Gonzalo Guillén Gosálbez Pittsburgh, 16th November 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)
15Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Extreme solutions
Steam methane reforming
Coal gasification
Biomass gasification
LH tanker truck
LH railway tank car
CH tube trailer
CH railway tube car
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3 4
5 6
7 8
9 10 11
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Production
Transportation
Cryogenic spherical tank (LH)
Pressurized cylindrical vessel (CH)
Storage
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Minimum cost: more centralized network (economies of scale)
Minimum impact: more decentralized network (reduces transportation emissions)
16Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
SCM in Process Systems and Chemical Engineering
Raw material extraction
Manufacturingplant
Manufacturing plant
Manufacturing plant
Retailer
Warehouse
Retailer
Customer
Customer
Customer
Raw material extraction
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
17Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
ConclusionsHydrodealkylation of toluene
Hydrodealkylation of toluene: superstructure taken from Kocis and Grossmann (1986)
18Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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):
19Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
20Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
21Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
22Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
23Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
24Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
25Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
MATLAB(kinetics of fed-batch reactor)
MATLAB(kinetics of fed-batch reactor)
OptimizerNelder-Mead Simplex Method
OptimizerNelder-Mead Simplex Method
Simulation Model(SuperPro Designer)
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)
26Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
27Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Production of bioethanol from sugar cane
Simulation Model(SuperPro Designer)
Simulation Model(SuperPro Designer)
Distillation columns(ASPEN)
Distillation columns(ASPEN)
Fermentation(MATLAB)
Fermentation(MATLAB)
28Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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Biology, physics,
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Engineering
Management
Optimization in systems
biology
Joint collaboration with Albert Sorribas
(Department of Medical Sciences, UdL)
29Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
30Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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)
31Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
32Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
33Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Outer approximation
Novelty:
convex envelopes
• Logarithmic transformation
• Piece-wise linear functions
Pozo, Guillén-Gosálbez, Sorribas, Jiménez, 2009
34Gonzalo Guillén Gosálbez Pittsburgh, 16th November 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
35Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Results: Case study 1
Model data
53
50
518
Variables
RNLP equations
Integer variables
14Continuous variables
40CMILP equations
36Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Results: Case study 2
471
439
4235
Variables
RNLP equations
Integer variables
91Continuous variables
211CMILP equations
Model data
Without tuning of parameters
37Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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??
38Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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…
39Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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
40Gonzalo Guillén Gosálbez Pittsburgh, 16th November 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
41Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
Experimental observations
Minimum costMaximum rate of Trehalose synthesis
Maximum rate of NADPH synthesisMaximum rate of ATP synthesis
Results: Case study 3
(Eisen et al., 1998, Gasch et al., 2000 and Causton et al., 2001)
Adaptation of yeast to heat shock
(Vilaprinyo et al., 2006)
42Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
• 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
43Gonzalo Guillén Gosálbez Pittsburgh, 16th November 2009
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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