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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


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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



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 )



• 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



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?



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



• 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


• 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



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



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©.



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?



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



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)?



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!


Pareto Curve



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)



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



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


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)



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$MM

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Total Annual Emission (Kton CO2 -eq)

Pareto Curve 1 (Economic vs. Environmental)

Pareto Curve

Good Choice




Case 2 – Cost Effective & “Good Choice” Solutions


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

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Case 2 – Pareto Curve (Economic vs. Social)

Almost linear – the higher expenditure, the more jobs created



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



Time for a break – some “simple” math

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0.10.20.30.4

pdf for a and b 2012 CAPD Annual Meeting, Carnegie Mellon University, Pittsburgh, PA 25

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0.1

0.2

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Problem

Solution

No train is expected to crash …

pdf for x


• 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


Case Study – State of Illinois for Bio-gasoline and Biodiesel


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



• 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


Result of SP Model

N = 1,000 scenarios

E[Cost] = $ 2,822.6 ± 15.6 MM (95% confidence interval)



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



• 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

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0.2

0.3

Conditional Value-at-Risk (CVaR) Downside Risk



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

∈⋅

= +−

≥ − ∈≥ ∈≥

∑



Pareto Curve – CVaR vs. E[Cost] Optimization of Biofuel Supply Chains under Uncertainty


CVaR Optimization of Biofuel Supply Chains under Uncertainty


Downside Risk Optimization of Biofuel Supply Chains under Uncertainty


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


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


Ecological, Economic and Social Impacts of Oil Spills

BP Stock Price in 2010



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



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



Background – Oil Transport & Weathering Processes

Photo-oxidation Evaporation

Spreading Spreading Drift

wind

Dissolution

Dispersion

Emulsification

Biodegradation

Sedimentation



• 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



Background – Cleanup and Coastal Protection Methods Optimization for Oil Spill Response Operations


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



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



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



• 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


• 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)



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:



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



Pareto Curve – Cost vs. Timespan (local optima)

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l Cos

t (M

illio

n $)

Cleanup Time Span (Days)

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C D E F

Coastal ProtectionBurningSkimmingDispersant



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


Fengqi You Chemical and Biological Engineering

Northwestern University [email protected]

http://you.mccormick.northwestern.edu


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