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.