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Multiobjective Optimization of Energy-Environmental Systems
Fengqi You Chemical and Biological Engineering
Northwestern University Evanston / Chicago, IL 60208
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA
Optimization for Energy and Sustainability
• Complex Energy-Environmental Systems Involve complex interactions and are usually highly coupled Require integrated systems analysis & optimization
• Optimization involves multiple objectives Three dimensions of Sustainability*
− Economics − Environmental impacts − Social benefits
Other objectives − Uncertainty & risk, responsiveness − Energy efficiency and energy payback time …
* Grossmann, I. E., & Guillén G, G. (2010) Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes. Computers & Chemical Engineering, 34 (9), 1365-1376.
Motivation
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 2
Two Example Applications
Optimization for Oil Spill Response Operations
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 3
Two Example Applications
Optimization for Oil Spill Response Operations
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 4
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Motivation
Cellulosic Biofuels
Corn Biofuels
Biodiesel Other
Renewables
Production Volume Energy Act 2007 Requirement
(Energy Independence and Security Act of 2007; Biomass Multi Year Program Plan, EERE, U.S. DOE, 2012 )
EthanolBiodiesel
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 5
Biomass-to-Biofuels Supply Chain
• Why does the biomass-to-biofuels supply chain matter? A Link between “sustainable” biomass feedstock and biofuel products Integrated systems analysis of all components is necessary Must be overall economically, environmentally and socially sustainable Special characteristics different from other supply chains
− Some biomass feedstocks (e.g. corn stover) have seasonal supply − Feedstock may deteriorate with time after harvesting – inventory control − Diverse conversion pathways for biorefineries … …
Feedstock Production
Feedstock Logistics
Biofuels Production
Biofuels Distribution
Biofuels End Use
(National Biofuels Action Plan, U.S.DOE, 2008; Biomass Multi Year Program Plan, EERE, U.S. DOE, 2012 )
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 6
• Maximizing the economic, environmental and social performance Given: time periods, cost data, potential locations and conversion technologies, weather condition, feedstock and water availability, harvesting and transportation capacity, feedstock properties, demand, incentives Decisions: network design, facility location, technology selection, capital investment, production levels, inventory control, and logistics management
Problem Statement – Design of Biofuels Supply Chains
Harvesting sites Collection Facilities Demand Zones Biorefineries
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 7
Challenges
• Major Challenges: How to capture the characteristics of biofuel supply chains?
− Biomass: deterioration, seasonality, preprocessing and storage − Biofuels: various conversion pathways/technologies, intermodal network
How to effectively integrate all the elements of the biofuel supply chain across temporal and spatial scales How to quantify the environmental impacts and social performance? How to tradeoff the economic, environmental and social objectives?
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 8
Process/SC Design
Inventory Control
Planning & Scheduling
Multi-Objective
Design SC from Farm to Fuel Retailer, and design Biorefinery process
Coordinate the supply, production and distribution of biomass & biofuel
For seasonal supply of biomass and uncertain demand of biofuels
Economic, environmental (LCA: field-to-wheel), social (EIO: job∙year)
Biofuels Supply Chain Techniques
1 2 3 4 5 6 7 8 9 10 11 12
Production
Inventory
Harvest
Activity Levels under Seasonal Biomass Supply
Centralized Processing Distributed Processing
Phase of LCA and Two Dimension Pareto Curve
Integrated Approach
Various Uncertainties
Uncertainty Many uncertainties due to feedstock supply and fuel product demand/price
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 9
• Objective: Minimize: Total annualized cost Minimize: Total GHG emission (life cycle assessment: GREET model @ ANL) Maximize: Total job • year created (economic input-out analysis: JEDI model @ NREL)
• Constraints: Flow /inventory balance constraints
− Flow balance at the harvesting sites − Inventory balance at collection facilities − Inventory balance at the biorefineries − Flow balance at the demand zones
Investment and financial constraints − Biorefinery construction cost − Government incentives − Annualized investment cost
Flow capacity constraints − Flow capacity in weight − Biomass flow capacity in volume
Harvesting and production constraints − Biomass availability constraints − Harvesting capacity constraints − Biomass conversion constraints − Water usage constraints − Byproduct production constraints
Production capacity constraints − Biorefinery capacity level constraints − Piece-wise installation cost constraints − Maximum production rate constraints − Collection facility capacity constraints
Nonnegative and integrity constraints
Choose Discrete (0-1), continuous variables
Multi-Objective Mixed-Integer Programming Model Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 10
• Economic objective Measured by annualized total cost
Economic Objective: Cost Minimization
Incentives
Transportation Cost
Inventory Cost Preprocessing Cost Byproduct credit
Feedstock cost
Production cost
Capital Investment
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 11
Environmental Objective: Assessment Based on LCA • Environmental Objective
Measured by GHG emissions (converting to CO2 - equivalent) Farm-to-pump life cycle assessment
− Data from Argonne GREET Model (Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation Model)
− Integrate LCA with multi-objective optimization
GHG emissions
Suboptimal Solutions
B A
C Annu
alize
d To
tal C
ost
Infeasible Solutions
Combined with Multi-Objective Optimization
Automatically search alternatives for improvement
Optimal Solutions (Pareto Curve) PHASE I
Goal and Scope
PHASE II Inventory Analysis
PHASE III Impact Assessment
PHASE IV Interpretation
Life Cycle Assessment
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 12
Social Objective: Maximizing the Local Job Created • Social Objective
Measured by accrued local jobs (full-time equivalent for a year) Integrate the MILP with NREL JEDI Model
− Jobs and Economic Development Impact Model − A state level input-output (IO) model to identify the local economic
impacts (the number of jobs that will accrue to the state or local region) from the construction and operations of a project
− IO analysis evaluates and sums the impacts of a series of effects in multiple industry sectors affected by the change in expenditure
− Using state specific multipliers and personal expenditure patterns data derived from the IMPLAN Professional Model©.
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 13
Biomass Feedstock Supply System
Major issues considered (in the mixed-integer programming model) − Feedstock availability, geographical distribution and seasonality − Harvesting site locations, harvest capacity, weather variability − Transportation network and modes, distance, intermodal transportation − Biomass density, weight and volume capacity, preprocessing and storage
Major output − When, where, which biomass should be harvested? − How, when, how much to transport the feedstocks? − Where, how much and how long should the biomass be stored? − When, where and what type should the feedstocks be preprocessed? − What should be the optimal capacity of collection/storage facilities?
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 14
Integrated Biorefineries
Major issues taken into account − Potential locations and conversion pathways, transportation connectivity − Production capacity, techno-economics, government incentives and policy − Feedstock handling, water usage and availability, byproducts
Approach: Link MILP model with techno-economic models (NREL) − ASPEN models for feedstocks and technologies with different capacities
Major output − Number, size, location and technologies − Amounts of ethanol and byproducts − Biomass Feedstock and water usage − Production and inventory levels
Cellulosic Biomass
Biochemical Conversion
Thermochemical Conversion
hydr
olysis
Sugar/Starch Biomass
Pret
reat
ment
Lignin residue
Distillation
Hydrotreating/ Hydrocracking
MeOHsynthesis
Gas cleanup & conditioning
F-T synthesis
WGS
C5/C6Fermentation
Sugar cane
Corn grain
Agricultural Residues
Wood
Energy Crops
Gasification
Pyrolysis
Combustion
Syn-gas
Crude Ethanol Ethanol
Methanol
Char, etc.
Bio oil
F-T liquid
Hydrogen
Gasoline/Diesel
Heat & Power
(based on Huber et al., 2006) Some Pathways for the Production of Biofuels
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 15
Biofuel Distribution System
Major issues considered (in the mixed-integer programming model) − Transportation connectivity, intermodal transportation − Network capacity, transportation types, policy − Demand, spatial distribution, vehicles and engine technologies − Environment, inventory control of ethanol, blending delay
Major output − When, how much to transport the biofuels from biorefineries to blending
facilities and demand zones? − Which transportation mode to be used for the deliveries? − What is the maximum optimal distribution distance for different
transportation mode (truck vs. dedicated ethanol pipeline)?
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 16
Cost
Emission Smallest Emission
Min Optimal Cost
Largest Emission
Max Optimal Cost
Minimize: Cost + ε∙ Emission (ε = 0.001)
Minimize: Emission
ε- constraint Method
Impossible!
Suboptimal Solutions
Pareto Curve
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 17
Case Study – State of Illinois for Cellulosic Ethanol
Resource of agricultural residue
102 Counties − 102 harvesting sites − 102 potential collection facilities − 102 possible biorefinery site locations − 102 blending facilities/demand zones
12 time periods per year (for 20 yrs)
Resource of wood residue Resource of energy crop IL Population density
Three Types of Feedstocks − Agricultural residues, energy crops and wood residues
Two Major Technologies − Biochem. (SSF, SHF) and thermochem. (gasification)
Three Major Transportation Modes − Truck (large & small), train, water (barge & ship)
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 18
Case 1 – Cost-Effective Design (near-term scenario)
Resource of agricultural residue Population density
Supply: 100% of state’s agricultural residue
Demand: 10% of the current fuel usage (E10)
Minimum Cost: $3.663/gal
BiochemicalThermochemical
150 MGY
138 MGY
102 MGY
124 MGY
0500
100015002000250030003500400045005000
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecTo
talF
eeds
tock
Inve
ntor
y (to
n)
Cost Breakdown Feedstock Inventory
35%
30%
17%
8%10% Investment
Production
Transportation
Storage & Handling
Feedstock
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 19
Case Study for County-Level SC of Illinois (Yr 2022 scenario)
Resource of agricultural residue Population density
Supply: 50% of state’s cellulosic biomass – Agricultural residues: corn stover, etc. – Energy crops: switchgrass, miscanthus, etc. – Wood residues : forest and mill residue, urban wood
Demand: 5.594% of 16 BGY (EISA cellulosic biofuel requirement )
Resource of energy crop Resource of wood residue
GHG emissions
Suboptimal Solutions
Annu
alize
d Tot
al Co
st
Infeasible Solutions
Two major conversion technologies (Biochem. and thermochem.) Three major transportation modes (Truck, train, & water) 102 Counties (harvesting sites, plant locations, demand zones) 12 time periods per year (for 20 years)
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 20
5300
5400
5500
5600
5700
5800
5900
6000
22200 22300 22400 22500 22600 22700 22800 22900 23000
Tota
l Ann
ualiz
ed C
ost (
$MM
)
Total Annual Emission (Kton CO2 -eq)
Pareto Curve 1 (Economic vs. Environmental)
Pareto Curve
Good Choice
Suboptimal Solutions
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 21
Case 2 – Cost Effective & “Good Choice” Solutions
Resource of agricultural residue
Population density
Resource of energy crop
Resource of wood residue
Minimum Cost: $3.225/gal
Unit Cost: $3.243/gal
39%
29%
19%
3%10% Investment
Production
Transportation
Storage & Handling
Feedstock
0
500
1000
1500
2000
2500
3000
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Tota
lFee
dsto
ck In
vent
ory
(ton)
Cost Breakdown
Feedstock Inventory
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 22
4000
6000
8000
10000
12000
14000
16000
100000 150000 200000 250000 300000 350000
Tota
l Ann
ualiz
ed C
ost (
$MM
)
Total Accrued Local Job (full time equivalent for a year)
Case 2 – Pareto Curve (Economic vs. Social)
Almost linear – the higher expenditure, the more jobs created
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 23
Remarks
• Unit cost reduce from $3.663/gal in Case 1 to $3.225 in Case 2 Large scale production (near term vs. Yr 2022)
− Economy of scale, shorter average transportation Feedstock diversity
− hedge the seasonality, lower inventory cost, reduce deterioration • Plant locations usually have abundant biomass resource
Reduce cellulosic biomass transportation cost • Investment and production costs contribute ≈70% of total cost
Improving the conversion technologies is the key issue • Maximum social impact is almost proportional to the total cost
Consistent with the government policies and social responsibilities
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 24
Time for a break – some “simple” math
-4 -2 0 2 4 60
0.10.20.30.4
pdf for a and b 2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 25
-10 -5 0 5 100
0.1
0.2
0.3
Problem
Solution
No train is expected to crash …
pdf for x
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• Minimizing Cost & Risk for Biofuel SC Design under Uncertainty Given: time periods, cost data, potential locations and technologies, production & transportation capacity, incentives, uncertainty distributions of supply and demand Decisions: network design, facility location, technology selection, capital investment, production levels, inventory control, and logistics management Objective: Minimizing Cost & Risks
Problem Statement
Harvesting Sites Demand Zones Hydrocarbon Biorefineries
Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 27
Case Study – State of Illinois for Bio-gasoline and Biodiesel
Resource of agricultural residue
102 Counties for harvesting sites, potential biorefinery plant locations, and demand zones Three Types of Feedstocks
− Agricultural residues, energy crops, & wood residues 12 time periods per year (for 20 years) ~70,000 uncertain parameters (102×12×20×5)
Resource of wood residue Resource of energy crop IL Population density
Two Major Conversion Technologies
Gasification + FT Synthesis Pyrolysis + Hydroprocessing
Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 28
• Scenario Generation Historical data obtained from Energy Information Administration Forecast using time series method => normally distributed parameters Generate scenarios by Monte Carlo sampling
• Two-stage Decisions
First stage decisions (here-and-now) − Network design, technology selection, capital investment
Second stage decisions (wait-and-see) − Harvesting, production, inventory, transportation, sale
Two-Stage Stochastic Programming Approach Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 29
Result of SP Model
N = 1,000 scenarios
E[Cost] = $ 2,822.6 ± 15.6 MM (95% confidence interval)
Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 30
Multi-cut L-shaped Method
Deterministic Model
Stochastic Programming Model 100 scenarios 1,000 scenarios
# of Binary Var. 408 408 408 # of Cont. Var. 652,296 65,118,126 651,171,126 # of Constraints 30,708 2,939,130 29,379,330
Impossible to solve directly takes >10 hours by using standard L-shaped only 1.5 hours with multi-cut version
Multi-cut Bender’ Decomposition Algorithm Computational Performance
Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 31
• SP model: minimize expected cost (risk-neutral objective) • A few risk measures
Variance (Mulvey et al., 1995) Upper partial mean (Ahmed and Sahinidis, 1998) Probabilistic financial risk (Barbaro et al., 2002) Downside risk (Eppen et al., 1988) CVaR (Rockafellar and Uryasev, 2000)
Risk Management
-10 -5 0 5 100
0.1
0.2
0.3
Conditional Value-at-Risk (CVaR) Downside Risk
Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 32
Multiobjective Optimization Model Formulation
VaR Constraints
CVaR Objective
Economic Objective
Original Constraints ( )
min : [ ]
s.t., ,
Capital Operationss ss S
n
E Cost Cost p Cost
f θ
∈= + ⋅
= ∈
∑
x b x
min : ( , )1
,0,
0
s ss S
Operationss s
s
pCVaR x VaR
Cost VaR s Ss S
VaR
ϕα
α
ϕϕ
∈⋅
= +−
≥ − ∈≥ ∈≥
∑
Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 33
Pareto Curve – CVaR vs. E[Cost] Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 34
CVaR Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 35
Downside Risk Optimization of Biofuel Supply Chains under Uncertainty
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 36
Cellulosic Biomass
TriglyceridesSource
Biochemical Conversion
Thermochemical Conversion
hydr
olysis
Sugar/Starch Biomass
Pretr
eatm
ent
Lignin residue
Transesterification
Distillation
Extraction
Hydrotreating/ Hydrocracking
MeOHsynthesis
Gas cleanup & conditioning
F-T synthesis
WGS
C5/C6Fermentation
Sugar cane
Corn grain
Agricultural Residues
Wood
Energy Crops
Oil Seeds
Gasification
Pyrolysis
Combustion
Syn-gas
Crude Ethanol Ethanol
Methanol
Char, etc.
Bio oil
Raw oil Biodiesel
F-T liquid
Hydrogen
Gasoline/Diesel
Heat & Power
Objective: Integration of biorefinery process design with biofuel supply chain optimization • Representation of detailed process
models and operational logistics • Multi-scale and multi-site modeling -
geospatially distributed production facilities and supply chain infrastructure
• Focusing on advanced infrastructure-compatible biofuels, i.e. ‘drop-in’ fuel
Current Work: Multiobjective to Multi-scale Optimization
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 37
High Performance Computation
Optimization Algorithm and Decomposition Methods
No
Initialization
Convergence ? Yes Stop
Solve the | j | MILP relaxation of LRsubproblems of (AP) under Yj=1,
set Vj as the optimal objective
Solve the | j | MILP relaxation of LRsubproblems of (AP) under Yj=1,
set Vj as the optimal objective
Update subgradients
Solve reduced (P) for UB
Update LB
NoYes
Fixed 0-1 variables
• Computational Challenge Problem size for nationwide analysis (3,141 counties)
− 12,564 binary variables − 3,552,527,574 continuous variables − 2,842,407,120 constraints
Current Work: Solving ‘Larger’-Scale Problems
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 38
Two Example Applications
Optimization for Oil Spill Response Operations
Life Cycle Optimization of Sustainable Biofuel Supply Chains
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 39
Ecological, Economic and Social Impacts of Oil Spills
BP Stock Price in 2010
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 40
Motivation
• Hundreds of oil spills (>10,000 gallons) per year1
• Planning the response operations is important but non-trivial The case of Deepwater Horizon/BP Oil Spill
− Costs up to $40 billion2 for cleanup and coastal protection − Many thousands of people and equipments involved
400 -
200 -
300 -
100 -
1970 1980 1990 2000
Num
ber o
f spi
lls
(>10
.000 g
allon
s)
* 1. International oil spill conference 2001 2. BP report, Nov. 2, 2010
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 41
Literature Review
• Very few on oil spill response planning Most modeling papers on oil spill are for oil weathering process Psaraftis & Ziogas (1985), Wilhelm & Srinivasa (1996, 1997), Ornitz & Champ (2003), Gkonis et al. (2007), etc.
• Limitations of previous works Complex interactions between response operations and oil transport and weathering process are neglected
− Integration leads to challenging optimization problem (MIDO) Coastal protection operations have not been taken in account in response planning – it may cost more to protect the coast than cleanup
Only single objective is used – minimizing either time or cost − Multi-objective optimization
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 42
Background – Oil Transport & Weathering Processes
Photo-oxidation Evaporation
Spreading Spreading Drift
wind
Dissolution
Dispersion
Emulsification
Biodegradation
Sedimentation
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 43
• Dynamic Oil Weathering Model Complex physical & chemical phenomena taking place simultaneously Over 50 models exists, mostly are based on semi-empirical approach An example given below (note: oil spill cleanup affects volume and area)
Background – Oil Transport and Weathering Model
Volume balance
Emulsification
Dispersion
Evaporation
Spreading
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 44
Background – Cleanup and Coastal Protection Methods Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 45
Coastal Protection − Oil slick area − Boom availability − Staging area location − Sea & weather condition
Chemical Dispersant − Emulsification degree − Dispersant availability − Weather & sea condition − Regulation
Background – Oil Spill Response Operations
Dispersant Dispersant
Burning Skimmers
Boom
In-situ Burning − Slick thickness − Oil viscosity − Parent oil density − Weather condition
Mechanical (skimming) − Water content − Slick thickness − Weather condition − Hydrodynamics
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 46
Problem Statement • Given:
An oil spill − location & spill amount, oil physical / chemical properties, cleanup target
A set of staging areas − Location, required boom length, life time, deployment rate, unit D&M cost
Sets of mechanical/skimming, in-situ burning, & dispersant cleanup facilities − Availability, response times & costs, operating windows
A set of time periods for the response planning • Major Decisions:
Oil spill cleanup Coastal protection Oil transport & weathering
• Objectives: Min. Cost & Max. Responsiveness
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 47
Challenges • Modeling Challenge
Coastal protection, spill cleanup, oil transport and weathering process − Time-dependent oil physical and chemical properties, hydrodynamics, weather
conditions, facility availability, performance degradation, cleanup operational window, and government regulations
− Different time representation: discrete (planning) vs. continuous (weathering) − Account for the complex interactions between them (spreading, evaporation,
dispersion, and emulsification v.s. cleanup and boom protection) Multi-Objective Challenge
− Measure of responsiveness − Tradeoff between economic and responsiveness
• Computational Challenge Multi-Objective mixed-integer dynamic optimization (MIDO) problem Non-convex MINLP after discretization based on orthogonal collocation on FEs
− 2,052 discrete variables, 11,482 continuous variables, 14,006 constraints
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 48
• Objective: Min: Total cost (= cleanup cost + coastal protection cost - credit from oil recovery)
Min: Response timespan (= measure of responsiveness)
• Constraints: Cleanup planning constraints
− Availability of mechanical systems − Cleanup rate of skimmers − Availability of burning systems − Operational window of burning sys. − Availability of dispersant systems − Performance of dispersant systems − Chemical dispersant balance − Dispersant availability − Regulation on dispersant application
Nonnegative & integrity constraints
Coastal protection constraints − Coastal protection identification − Boom length balance − Boom deployment constraints − Boom failure constraints
Dynamic Oil weathering model − Spreading process − Evaporation process − Dispersion process − Emulsification process − Viscosity increment − Volume balance
(bilinear terms)
(ODEs)
Multi-Objective Mixed-Integer Dynamic Optimization Model Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 49
• Full discretization based on orthogonal collocation on finite elements* High robustness and efficiency
• Integrating discrete- and continuous-time representation A finite element = a time period (e.g. a day) Oil transport and weathering model use continuous-time formulation Planning model uses multi-period formulation
− Consistent with the real-world practice − Cleanup rate as a piecewise step function
• Challenge: Initialization Resulting model is a large-scale non-convex MINLP
− EX1: 2,052 discrete var., 11,482 continuous var., 14,006 constraints − EX1: Solving the RMINLP directly with any NLP solver leads to infeasibility
Simultaneous Approach for Solving the MIDO
* Biegler et al. (2002); Cuthrell & Biegler (1987)
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 50
Approximate MILP Model for Initialization
ODE (Oil Weathering)
MILP (Response Planning)
Cleanup rate
Volume, area, thickness, viscosity, water content, evaporation rate, dispersion amount, etc.
• The MIDO can be decomposed as an MILP and an ODE system ODE for oil weathering; MILP for response planning
− Bilinear terms in the cleanup planning constraints are now linear if state variables (physical and chemical properties of oil slick) are fixed
Step 1: Solve the ODE with zero cleanup rate (eq. to natural weathering process)
Step 2: Construct the approximate MILP model for initialization − Fix state variables based on the ODE solution, except volume and area
− Compute the percentage of oil removed by natural weathering at time t (δt) − Add the following volume balance constraints to the MILP:
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 51
Case Study – Oil Spill in the Gulf of Mexico
Major Input Data − API = 25, other oil data from ADIOS (NOAA , 2000) − Spill rate: 10,000 m3/day for 42 days − Cleanup target: ≥1,500 m3 on sea surface − Cleanup by mechanical, in-situ burning and
dispersant sys. (C-130, helicopter, vessel) − Drift towards to the shore − 3 staging areas (locations and required booms)
Problem Size (MINLP after discretization) − # of Discrete Variables: 2,052 − # of Continuous Variables: 11,482 − # of Constraints: 14,006
Solution − Direct solution: infeasible for any solver − Proposed approach: ≈ 139CPUs/instance
(CPLEX + KNITRO + DICOPT)
Spill Site
S1
S2 S3
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 52
Pareto Curve – Cost vs. Timespan (local optima)
0
200
400
600
800
1000
1200
70 90 110 130 150 170
Tota
l Cos
t (M
illio
n $)
Cleanup Time Span (Days)
A
B
C D E F
Coastal ProtectionBurningSkimmingDispersant
Optimization for Oil Spill Response Operations
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 53
Remarks
• Summary Various objectives for energy-environmental system optimization
− Economic, environment, social, risk, responsiveness … Key component: finding a suitable quantitative measure Computational challenges lie in:
− Large-scale optimization problems − Handling uncertainties and risks
• Extensions Algae for CCS and biodiesel production Organic photovoltaic systems ($$$, LCA, EPBT) New material and process development for CCS
Conclusion
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 54
Fengqi You Chemical and Biological Engineering
Northwestern University [email protected]
http://you.mccormick.northwestern.edu
2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 55