quantitative methods for strategic investment planning in the oil-refining industry
TRANSCRIPT
Brenno C. Menezes
Postdoctoral Fellow
Technological Research Institute
São Paulo, SP, Brazil
Jeffrey D. Kelly
CTO and Co-Founder
IndustrIALgorithms
Toronto, ON, Canada
Ignacio E. Grossmann
R. R. Dean Professor of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA, US
Lincoln F. L. Moro
Senior Consultant
PETROBRAS
São Paulo, SP, Brazil
IAL
Quantitative Methods for Strategic Investment
Planning in the Oil-Refining Industry
CMU, Pittsburgh, Oct 2nd, 2015.
Strategic Planning in PETROBRAS: PLANINV (LP)
No Process Design Synthesis Quantitative Methods
Process Design Optimization (MILP)
2
Delayed Coker
AtmosphericDistillation
CMU, Pittsburgh, Oct 2nd, 2015.
What, Where, When to Invest?
Simplified Process Models +NLP
ProcessingBlending
Quantitative Methods for Strategic Investment
Planning in the Oil-Refining IndustryBrenno C. Menezes, Ignacio E. Grossmann, Lincoln F. L. Moro and Jeffrey D. Kelly
3
Space
Time
Supply Chain
Refinery
Process Unit
second hour day month year
RTOControl
on-line off-line
Scheduling
Operational Planning
Tactical Planning
Strategic Planning
SimulationPetrobras
NLP Optimization Commercial (Aspentech)
LP Optimization Petrobras
Operational Corporate
week
Decision-Making Tools in PETROBRAS (in oil-refining)
Current Strategic Planning Methodology in PETROBRAS
Strategy
- Increase the supply by one refinery
Refinery Operational Planning
- Simulate the Refinery Process Design
Supply Chain Strategic Planning
- Test the refinery best scenarios in the home-grown global investment tool (LP)
Financial Strategy
- Find the best set of competing investments regarding their capital flow
Strategy Decision
- Invest or not in the supply increase
NPV
Net Present Value
4
Refinery Operational Planning
- Simulate the Refinery Process Design
Financial Strategy
- Find the best set of competing investments regarding their capital flow
Capital resource constraints and
uncertainties in product demands
Find the Process Design (MILP)
Max NPVNPV=Sales-Costs
Invest. Costs:*QF+*Y
Strategy
- Increase the supply by one refinery
Supply Chain Strategic Planning
- Test the refinery best scenarios in the home-grown global investment tool (LP)
Strategy Decision
- Invest or not in the supply increase
MINLP
MILP+
NLP
5
Proposed Strategic Planning Methodology in PETROBRAS
NLP in Blending and Processing
Challenges
All Brazilian Refineries
Multi-site MINLP Models
Project Staging
Processing Models
Aggregated Approach (single refinery)
GCIP using sequence-dependent setups
PDH to solve MILPs and NLPs
ISW Distillation ModelDBCTO Distillation Model
How it is addressed
𝐲𝐞=expansion of an existing unit
𝐲𝐞𝐫,𝐮,𝐧,𝐭 𝐐𝐄𝐮𝐋 ≤ 𝐐𝐄𝐫,𝐮,𝐧,𝐭 ≤ 𝐲𝐞𝐫,𝐮,𝐧,𝐭 𝐐𝐄𝐮
𝐔
𝐐𝐂𝐫,𝐮,𝐧,𝐭 = 𝐐𝐂𝐫,𝐮,𝐧,𝐭−𝟏 + 𝐐𝐄𝐫,𝐮,𝐧,𝐭 𝐞𝐱𝐩𝐚𝐧𝐬𝐢𝐨𝐧: 𝐮, 𝐧 𝐞𝐱𝐩
𝐐𝐅𝐫,𝐮,𝐧,𝐭 ≤ 𝐐𝐂𝐫,𝐮,𝐧,𝐭 𝐮, 𝐧 𝐞𝐱𝐩
QF= operational flow Q𝐄= expanded capacity QC= total capacity
Capital Investment Planning (CIP) Formulation
(R,U,N,T) R=RefineryU=Unit typeN=Number of a unit typeT=Time
Crude diet
ISW
Processing
Blending
ON
QC=QCt-1+QNEW MILP
QF≤QC LP
INVREF
OPREF
𝐐𝐂𝐫,𝐮,𝐧,𝐭 = 𝐐𝐂𝐫,𝐮,𝐧,𝐭−𝟏 + 𝐐𝐈𝐫,𝐮,𝐧,𝐭−𝟏 𝐢𝐧𝐬𝐭𝐚𝐥𝐥𝐚𝐭𝐢𝐨𝐧: 𝐮, 𝐧 𝐢𝐧𝐬
𝐲𝐢𝐫,𝐮,𝐧,𝐭 𝐐𝐈𝐮𝐋 ≤ 𝐐𝐈𝐫,𝐮,𝐧,𝐭 ≤ 𝐲𝐢𝐫,𝐮,𝐧,𝐭 𝐐𝐈𝐮
𝐔
Maximize: NPV = DemandSales - SupplyCosts - OperatingCosts - InvestmentCosts
Subject to:
Where:
Sahinidis et. al., CACE, 13, (1989) and Sahinidis & Grossmann, CACE, 15, (1991).
T1 T2
Take an investment decision (binary)
Count on the additional production
Project executionFormulation Improvements:- Project Execution
year- Installations
- NLP Operational Layer
Q𝐈= installed capacity
𝐲i= installation of a new unit
⋀ 𝐮, 𝐧 𝐢𝐧𝐬
−𝟏 t=[1,tend]
t=[1,tend]
t=[1,tend-1]
N
….tend
t=[1,tend]t=[1,tend-1]
8
Options to Formulate the Problem
1st- NLP Operational ProblemZ=profit ($/d) and QFu=unit throughputs to control capacity expansion
2nd- MINLP Strategic Problem (NLP Operational Problem Embedded)Z=NPV ($) and QEu,t and QCu,t to control capacity expansion
3rd- MILP Strategic Problem + NLP Operational Problem (Phenomenological Decomposition Heuristics)Z=NPV ($) and QEu,t, QIu,t and QCu,t to control capacity expansion and installation
Crude Diet
Processing
Blending
- Crude
- Cuts/Final Cuts
- Final Products
NLP
Strategic
Operational
MILP
QFu,t ≤ QCu,t link constraint
Full Space Problem MINLP
Aggregated Approach (single refinery)
Multi-Site Approach
9
REDUC
RPCC
REPLAN
REPARRPBC
REGAP
REVAP
RLAM
LUBNOR
REMAN
RECAP
PREMIUM I
PREMIUM II
RNEST
REFAP
2,013
2,408
3,380
-972
2013 2016 2020 2020
Crude Distillation
CapacityOil Products
Demands
Deficit
RNEST:Train 1 - 115 kbpd - Nov/14
Train 2 - 115 kbpd - May/15
COMPERJ-1:
Train 1 - 165 kbpd - Apr/15
PREMIUM I:Train 1 - 300 kbpd - Oct/17
Train 2 - 300 kbpd - Oct/20
PREMIUM II:
300 kbpd - Dec/17
COMPERJ-2:
Train 2 - 300 kbpd - Jan/18
Refineries in Construction: Refineries in Conceptual Project:
Existing
In Construction
In Conceptual Project
PETROBRAS
Refineries:
Source: PETROBRAS, 2013
in kbpd
COMPERJ-1COMPERJ-2
Aggregated Approach (single refinery)
FK
FLD
ATR
CDUC1C2
C3C4
SW2
VR
VDU
N
K
LD
HD
LCO
DO
HTD
HTK
FCC
D1HT
KHT
CLN
CHN
CLGO
CHGO
CMGO
D2HT
DC
REF
LCNHT
CLNHT
PQN
C1C2
C3C4
HCN
LCN
C1C2
C3C4
FN
FHD
GLN
(GLNC)
MSD
HSD
JET
LSD
HTCLN
HTLCN
FO
REFOR
C1C2 FG
LPGC3C4
LVGO
HVGO
00
ASPR
DAO
PDA
RFCC
SW3
SW1
C1C2
C3C4
HCCO
Crude
HCCD
HCCK
HCCN
HCC
USD
COKE
H2
COKE
LSDimp
GLNimp
(GLNA)
ETH
For RNEST
JETimp
LPGimp
ST
GOST
LNST
HNST
REBRA
4.2% p.a.
10
Conceptual Projects under reevaluation
Refinery Unit Capacities and Models
FK
FLD
ATR
CDUC1C2
C3C4
SW2
VR
VDU
N
K
LD
HD
LCO
DO
HTD
HTK
FCC
D1HT
KHT
CLN
CHN
CLGO
CHGO
CMGO
D2HT
DC
REF
LCNHT
CLNHT
PQN
C1C2
C3C4
HCN
LCN
C1C2
C3C4
FN
FHD
GLN
(GLNC)
MSD
HSD
JET
LSD
HTCLN
HTLCN
FO
REFOR
C1C2 FG
LPGC3C4
LVGO
HVGO
00
ASPR
DAO
PDA
RFCC
SW3
SW1
C1C2
C3C4
HCCO
Crude
HCCD
HCCK
HCCN
HCC
USD
COKE
H2
COKE
LSDimp
GLNimp
(GLNA)
ETH
For RNEST
JETimp
LPGimp
ST
GOST
LNST
HNST
Total Capacity in thousands of m3/d
𝐐𝐒𝐅𝐂𝐂,𝐬 = 𝐐𝐅𝐅𝐂𝐂 𝐘𝐅𝐂𝐂,𝐬 + ∆𝐘𝐅𝐂𝐂,𝐬,𝐂𝐂𝐑 . 𝐏𝐅𝐅𝐂𝐂,𝐂𝐂𝐑 − 𝐏𝐅𝐅𝐂𝐂,𝐂𝐂𝐑 + ∆𝐘𝐅𝐂𝐂,𝐬,𝐑𝐗𝐓 𝐑𝐗𝐓𝐅𝐂𝐂 + ∆𝐘𝐅𝐂𝐂,𝐬,𝐂𝐅𝐓 𝐂𝐅𝐓𝐅𝐂𝐂
𝐐𝐒𝐏𝐃𝐀,𝐀𝐒𝐅𝐑 = 𝐐𝐅𝐏𝐃𝐀 𝟏 − 𝐄𝐗𝐓𝐏𝐃𝐀𝐏𝐅𝐇𝐓,𝐬 = 𝐏𝐅𝐇𝐓 𝟏 − 𝐒𝐄𝐕𝐇𝐓
Pinto et al, 2000; Neiro and Pinto, 2004
Non-convex bilinearities
𝑽𝑷𝒄 =
𝒄𝒓𝑸𝒄𝒓,𝑪𝑫𝑼 𝒎𝒄=𝒎𝒄𝒊 𝒄
𝒎𝒄𝒇 𝒄𝑽𝒄𝒓,𝒎𝒄𝒀𝒄𝒓,𝒎𝒄
𝒄𝒓𝑸𝒄𝒓,𝑪𝑫𝑼 𝒎𝒄=𝒎𝒄𝒊 𝒄
𝒎𝒄𝒇 𝒄𝒀𝒄𝒓,𝒎𝒄
∀ 𝒄
𝑴𝑷𝒄 =
𝒄𝒓𝑸𝒄𝒓,𝑪𝑫𝑼 𝒎𝒄=𝒎𝒄𝒊 𝒄
𝒎𝒄𝒇 𝒄𝑴𝒄𝒓,𝒎𝒄𝑮𝒄𝒓,𝒎𝒄𝒀𝒄𝒓,𝒎𝒄
𝒄𝒓𝑸𝒄𝒓,𝑪𝑫𝑼 𝒎𝒄=𝒎𝒄𝒊 𝒄
𝒎𝒄𝒇 𝒄𝑮𝒄𝒓,𝒎𝒄𝒀𝒄𝒓,𝒎𝒄
∀ 𝒄
11
SW3-Cut
SW2-Cut
SW1-Cut
Naphtha
Kerosene
C1C2
IC5
mc40
mc130mc140mc150mc160mc170mc180
mc210mc220mc230
light
heavy
micro-cuts (mc)
cuts (c) final-cuts (fc)
TBP (ºC)
-163.524
27.878
40
130140150160170
180
210220230
mc200200
mc190190
mc240240Light Diesel
crude (cr)
mc100100
mc250250
.
..
.
-88.599
Heavy Diesel
mc50mc60mc70mc80
mc90
5060708090
C536.059
mc120120
mc110110
mc260mc270mc280
mc310mc320mc330
260270280
310320330
mc300300
mc290290
mc340340mc350350
.
360
.
....
Naphtha-Cut
Kerosene-Cut
light
heavy
Light Diesel-Cut
light
heavy
Heavy Diesel-Cut
mc360
Yie
ld (
%)
Temperature (oF)
Swing-Cut Modeling
𝑸𝑪𝑫𝑼,𝒄 =
𝒄𝒓
𝑸𝒄𝒓,𝑪𝑫𝑼
𝒎𝒄=𝒎𝒄𝒊(𝒄)
𝒎𝒄𝒇(𝒄)
𝒀𝒄𝒓,𝒎𝒄 ∀ 𝒄
𝑸𝑪𝑫𝑼,𝒄 = 𝑸𝒄,𝒇𝒄=𝓵 + 𝑸𝒄,𝒇𝒄=𝒉 ∀ 𝒄 = 𝒔𝒘
Menezes, Kelly and Grossmann, 2013
GRAV, SULF, RVP, T10, T50, T85, T90, T95, AROM, GUM, OLEF, FLASH, CETAN, ANI, VISCO, POUR, CLOUD, PPFC, RCR, ACID, RON, MON
Property Group PF or P base Property Name PF or IPF (Property Index)
Concentration
ACID Mass Acidity𝐏𝐅𝐕𝐨𝐥 =
𝐏. 𝐕𝐨𝐥
𝐕𝐨𝐥GRAV Vol Gravity
SULF Mass Sulfur Content𝐏𝐅𝐌𝐚𝐬𝐬 =
𝐏.𝐆𝐑𝐀𝐕. 𝐕𝐨𝐥
𝐆𝐑𝐀𝐕. 𝐕𝐨𝐥CCR Mass Conradson Carbon Residue
Volatility
DIST Vol Distillation 𝐈𝐏𝐑𝐕𝐏 =
𝟏. 𝟖𝐏 + 𝟑𝟐
𝟓𝟒𝟗
𝟕.𝟖
𝐈𝐏𝐅𝐋𝐀𝐒𝐇 = 𝐞𝟏𝟎𝟎𝟎𝟔.𝟏𝟏.𝟖𝐏+𝟒𝟏𝟓
−𝟏𝟒.𝟎𝟗
RVP Vol (IP) Reid Vapor Pressure
FLASH Vol (IP) Flash Point
Combustion
MON Formula Motor Octane Number𝐏𝐅𝐌𝐎𝐍 =
𝐢
𝐌𝐎𝐍𝐁𝐢. 𝐕𝐨𝐥𝐢RON Formula Research Octane Number
CETAN Formula Cetane Number
Stability GUM Vol Gum𝐈𝐏𝐕𝐈𝐒𝐂 =
log𝟏𝟎 𝐏
log𝟏𝟎 𝟏𝟎𝟎𝟎𝐏
Fluidity
VISC Vol (IP) Viscosity
POUR Vol (IP) Pour Point𝐈𝐏𝐅 =
𝐈𝐏. 𝐕𝐨𝐥
𝐕𝐨𝐥
𝐏𝐅 = 𝐟−𝟏(𝐈𝐏𝐅)
CLOUD Vol (IP) Cloud Point
PPFC Vol (IP) Plug-Flow Filter
Blending Equations
𝐌𝐎𝐍𝐁𝐢 = 𝐌𝐎𝐍𝐢 + 𝐚{(𝐌𝐎𝐍𝐢 −𝐌𝐎𝐍𝐕).[(RON−MON)𝐢−(RON−MON)𝐕]}+b(𝐀𝐑𝐎𝐢 − 𝐀𝐑𝐎𝐕)𝟐+⋯
12
13
Fuel Demand Scenarios for 2020 in Brazil
2020
(Planned)
Thousands of m3/day
unit (u) 2016 GLNC GLNCETH GLNC GLNCETH GLNC GLNCETH GLNC GLNCETH
CDU 372 549.1 550.0 482.4 507.3 590.5 553.3 492.0 467.2 536
VDU 153 242.8 265.0 226.8 246.7 204.5 266.9 205.5 218.2 260
FCC 76 76.0 76.0 79.2 76.0 76.0 90.9 76.0 76.0 76
HCC 10 91.5 98.3 68.4 68.4 53.2 75.6 54.0 93.4 73
RFCC 22 43.7 22.0 22.0 22.0 105.5 22.0 48.8 22.0 22
DC 50 146.2 104.7 106.0 56.3 79.8 92.8 80.5 75.6 100
KHT 15 19.0 17.8 15.0 15.0 25.9 18.9 17.6 15.0 15
D2HT 68 122.4 120.0 109.4 97.2 125.3 117.3 111.0 96.1 135
LCNHT 54 64.6 52.9 54.6 52.9 98.0 62.1 67.4 54.0 54
CLNHT 34 81.9 60.8 61.8 37.0 48.7 55.2 49.1 46.6 62
ST 34 81.9 60.8 61.8 37.0 48.7 55.2 49.1 46.6 62
REF 12 37.2 28.6 27.7 16.4 18.1 24.6 20.4 22.7 12
profit (Millions of USD/day) 38.491 29.081 27.384 16.046 27.123 23.100 22.747 20.701
NPV (Billions of USD) - - - - 8.8189 5.5455 11.6236 6.6885
capital invest. (Billions of USD) 34.7730 28.2714 22.5300 14.7968 25.0000 24.5079 19.1699 21.1708 23.1563
no. of equations
no. of continuous variables
no. of discrete variables
no. of non zero elements
no. of non linear elements
CPU (s) 0.561 0.375 0.530 0.484 0.826 7.377 1.080 0.936
1061 2552
Capacities in
(Conceptual
Project)NLP MINLP
2009-2012 trends 4.2% p.a.2009-2012 trends 4.2% p.a.
2020 (Results)
1019
1127
12
4463
460
406
-
1772
Aggregated Approach (REBRA)
CONOPT DICOPT
NLP results
MINLP results
Post-Optimization calculation
2020
(Planned)
Thousands of m3/day
unit (u) 2016 GLNC GLNCETH GLNC GLNCETH GLNC GLNCETH GLNC GLNCETH
CDU 372 549.1 550.0 482.4 507.3 590.5 553.3 492.0 467.2 536
VDU 153 242.8 265.0 226.8 246.7 204.5 266.9 205.5 218.2 260
FCC 76 76.0 76.0 79.2 76.0 76.0 90.9 76.0 76.0 76
HCC 10 91.5 98.3 68.4 68.4 53.2 75.6 54.0 93.4 73
RFCC 22 43.7 22.0 22.0 22.0 105.5 22.0 48.8 22.0 22
DC 50 146.2 104.7 106.0 56.3 79.8 92.8 80.5 75.6 100
KHT 15 19.0 17.8 15.0 15.0 25.9 18.9 17.6 15.0 15
D2HT 68 122.4 120.0 109.4 97.2 125.3 117.3 111.0 96.1 135
LCNHT 54 64.6 52.9 54.6 52.9 98.0 62.1 67.4 54.0 54
CLNHT 34 81.9 60.8 61.8 37.0 48.7 55.2 49.1 46.6 62
ST 34 81.9 60.8 61.8 37.0 48.7 55.2 49.1 46.6 62
REF 12 37.2 28.6 27.7 16.4 18.1 24.6 20.4 22.7 12
profit (Millions of USD/day) 38.491 29.081 27.384 16.046 27.123 23.100 22.747 20.701
NPV (Billions of USD) - - - - 8.8189 5.5455 11.6236 6.6885
capital invest. (Billions of USD) 34.7730 28.2714 22.5300 14.7968 25.0000 24.5079 19.1699 21.1708 23.1563
no. of equations
no. of continuous variables
no. of discrete variables
no. of non zero elements
no. of non linear elements
CPU (s) 0.561 0.375 0.530 0.484 0.826 7.377 1.080 0.936
1061 2552
Capacities in
(Conceptual
Project)NLP MINLP
2009-2012 trends 4.2% p.a.2009-2012 trends 4.2% p.a.
2020 (Results)
1019
1127
12
4463
460
406
-
1772
Aggregated Approach (REBRA)
CONOPT DICOPTSimilar Demands
1st stage: Investment decisions (here-and-now)
(for all time period t with investment allowed)
• New process unit yi (installation)
• Revamp of existing unit ye (expansion)
• Size of the installation 𝑄𝐼• Size of the expansion 𝑄𝐸
2nd stage: Operational decisions (wait-and-see)
(for all time period t and scenario sc)
• Yields
• Rates
• Properties
• Unit variables
Multi-Site Approach – PDH (MILP+NLP)
PDH = Phenomenological Decomposition Heuristics = Quantity + Quality Decomposition
MILP = logic + quantity NLP = quantity + quality
17
Multi-Site Approach – PDH (MILP+NLP)
Multi-Site Approach – PDH (MILP+NLP)
Multi-Site Approach – PDH (MILP+NLP)
(in millions of USD)
(in Billions of USD)
Capacity Unit Results(Capacities in Thousands of m3/day)
Project Staging
Three types of capital investment planning (CIP) problems
Project Staging
Motivating example 1: small GCIP flowsheet for expansion
IMPL’s UOPSS Visual Programming Language using DIA
Variable Names:
v2r_xmfm,t: unit-operation m flow variable
v3r_xjifj,i,t: unit-operation-port-state-unit-operation-port-state ji flow variable
v2r_ymsum,t: unit-operation m setup variable
v3r_yjisuj,i,t: unit-operation-port-state-unit-operation-port-state ji setup variable
VPLs (known as dataflow or diagrammatic programming) are based on the idea of "boxes and arrows", where boxes or other screen objects are treated as entities, connected by arrows, lines or arcs which represent relations (node-port constructs). (Bragg et al., 2004)
x = continuous variables (flow f)
y = binary variables (setup su)
j
𝐯𝟐𝐫_𝒙𝒎𝒇𝐦,𝒕 ≥ 𝑳𝑩𝒇𝒎 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ∀ 𝐦, 𝐭 (1)
𝐯𝟐𝐫_𝒙𝒎𝒇𝐦,𝒕 ≤ 𝑼𝑩𝒇𝒎 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ∀ 𝐦, 𝐭 (2)
𝐣∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≥ 𝑳𝑩𝒇𝒎 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ∀ (𝐢,𝐦), 𝐭(3)
𝐣∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≤ 𝑼𝑩𝒇𝒎 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ∀ (𝐢,𝐦), 𝐭(4)
𝐢∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≥ 𝑳𝑩𝒇𝒎 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ∀ (𝐦, 𝐣), 𝐭(5)
𝐢∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≤ 𝑼𝑩𝒇𝒎 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ∀ (𝐦, 𝐣), 𝐭(6)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≥ 𝑳𝑩𝒇𝐣,𝒊 𝐯𝟑𝐫_𝒚𝒋𝒊𝒔𝒖𝐣,𝐢,𝒕 ∀ (𝐣, 𝐢), 𝐭(7)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≤ 𝑼𝑩𝒇𝐣,𝒊 𝐯𝟑𝐫_𝒚𝒋𝒊𝒔𝒖𝐣,𝐢,𝒕 ∀ (𝐣, 𝐢), 𝐭 (8)
j
Semi-continuous equations for units
Semi-continuous equations for streams
Mixer for each i, but using lo/up bounds
Splitter for each j, but using lo/up bounds
𝐣∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≥ 𝑳𝑩𝒚𝐢,𝒎 𝐯𝟐𝐫_𝒙𝒎𝒇𝐦,𝒕 ∀ (𝐢,𝐦), 𝐭(9)
𝐣∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≤ 𝑼𝑩𝒚𝐢,𝒎 𝐯𝟐𝐫_𝒙𝒎𝒇𝐦,𝒕 ∀ (𝐢,𝐦), 𝐭(10)
𝐢∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≥ 𝑳𝑩𝒚𝐦,𝒋 𝐯𝟐𝐫_𝒙𝒎𝒇𝐦,𝒕 ∀ (𝐣,𝐦), 𝐭(11)
𝐢∈(𝐣,𝐢)
𝐯𝟑𝐫_𝒙𝒋𝒊𝒇𝐣,𝐢,𝒕 ≤ 𝑼𝑩𝒚𝐦,𝒋 𝐯𝟐𝐫_𝒙𝒎𝒇𝐦,𝒕 ∀ (𝐣,𝐦), 𝐭(12)
𝐦(𝐦∈𝐮)
𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ≤ 𝟏 ∀ 𝐮, 𝐭(13)
𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝒎′,𝒕 + 𝐯𝟐𝐫_𝒚𝒎𝒔𝒖𝐦,𝒕 ≥ 𝟐 𝐯𝟑𝐫_𝒚𝒋𝒊𝒔𝒖𝐣,𝐢,𝒕∀ 𝒎′, 𝒋 , (𝐢,𝐦) (14)
xX
xX
x
x
j
Several unit feeds(treated as yieldswith lower andupper bounds)
Selection of modesin one physical unit
StructuralTransitions
Project Staging
Constraints Continuous Variables Binary Variables CPU (s) Z (M$)
Big-M 328 124 36 1.8111.841Convex-Hull 394 244 36 0.30
GCIP 929 422 251 0.25
Jackson and Grossmann (2002)
Big-M and Convex-Hull GCIP proposition
.
Oil-refinery network example
Constraints Continuous Variables
Binary Variables
CPU (s)
Z (M$)
GCIP 2005 729 648 0.5 4,285
28
Conclusions
Novelty:
• Aggregated multi-site approach for capacity expansion of a country/company
• Nonlinearities from processing and blending to evaluate the capability
• Includes project execution time (excluding the production from expandedunits during this period)
• Expansion and Installation to control the capacity increment of units
• Phenomenological decomposition (quantity + quality problems segregated)
• More realistic approach (in a quantitative manner) for strategic investmentplanning in the oil-refining industry
29
Impact for industrial applications:
• Realistic formulation to predict investments in oil-refinery units
• Avoids overestimating/underestimating capacity expansion/installation
• Evaluates the capability (not only the capacity) by including nonlinearities
Conclusions
References
All Brazilian Refineries
MINLP Models
Project Staging
Processing Models
Aggregated Approach (REBRA)
GCIP using sequence-dependent setups
PDH to solve MILPs and NLPs
ISW Distillation ModelDBCTO Distillation Model
B.C. Menezes, L.F.L. Moro, W.O. Lin, R.A. Medronho, F.L.P. Pessoa, 2014, Nonlinear Production Planning of Oil-Refinery Units for the
Future Fuel Market in Brazil: Process Design Scenario-Based Model, Ind Eng Chem Res, 53, 4352-4365.
B.C. Menezes, J.D. Kelly, I. E. Grossmann, 2013, Improved Swing-Cut Modeling for Planning and Scheduling of Oil-Refinery
Distillation Units, Ind Eng Chem Res, 52, 18324-18333.
B.C. Menezes, J.D. Kelly, I. E. Grossmann, 2015, Phenomenological Decomposition Heuristic for Process Design Synthesis of Oil-
Refinery Units, Comput Aided Process Eng, 37, 1877-1882.
J.D. Kelly, B.C. Menezes, I. E. Grossmann, 2014, Distillation Blending and Cutpoint Temperature Optimization using Monotonic
Interpolation, Ind Eng Chem Res, 53, 15146-15156.
B.C. Menezes, J.D. Kelly, I. E. Grossmann, A. Vazacopoulos 2015, Generalized Capital Investment Planning using MILP and
Sequence-Dependent Setups, Comput Chem Eng, 80, 140-154.
B.C. Menezes, L.F.L. Moro, I.E. Grossmann, R.A. Medronho, F.L.P. Pessoa, 2014, Production Planning of Oil-Refinery Units for the
Future Fuel Market in Brazil, COBEQ, Florianópolis, Brazil.