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Computers and Chemical Engineering 28 (2004) 871896

A general modeling framework for the operationalplanning of petroleum supply chains

Srgio M.S. Neiro a,1, Jos M. Pinto a,b, ,2

a Department of Chemical Engineering, University of So Paulo, 05508-900 So Paulo, SP, Brazilb Department of Chemical Engineering and Chemistry, Polytechnic University, Brooklyn, NY 11201, USA

Abstract

In the literature, optimization models deal with planning and scheduling of several subsystems of the petroleum supply chain such asoileld infrastructure, crude oil supply, renery operations and product transportation. The focus of the present work is to propose a generalframework for modeling petroleum supply chains. As a starting point, processing units are modeled based on the framework developed byPinto et al. [Computers and Chemical Engineering 24 (2000) 2259]. Particular frameworks are then proposed to storage tanks and pipelines.Nodes of the chain are considered as grouped elementary entities that are interconnected by intermediate streams. The complex topologyis then built by connecting the nodes representing reneries, terminals and pipeline networks. Decision variables include stream ow rates,properties, operational variables, inventory and facilities assignment. The resulting multiperiod model is a large-scale MINLP. The proposedmodel is applied to a real-world corporation and results show model performance by analyzing different scenarios. 2003 Elsevier Ltd. All rights reserved.

Keywords: Petroleum complex; Supply chain management; Mixed-integer optimization

1. Introduction

Companies have been forced to overstep their physicalfrontiers and to visualize the surrounding business environ-ment before planning their activities. Range vision shouldcover all members that participate direct or indirectly in thework to satisfy a customer necessity. Coordination of thisvirtual corporation may result in benets for all members of the chain individually. Beamon (1998) denes such virtualcorporation as an integrated process wherein a number of business entities (suppliers, manufacturers, distributors andretailers) work together in an effort to acquire raw materi-als, convert them into specied nal products and deliverthese nal products to retailers. Under another point of view,Tan (2001) states that there is a denition of supply chainmanagement (SCM), which emerges from transportation andlogistics literature of the wholesaling and retailing indus-try that emphasizes the importance of physical distributionand integrated logistics. According to Lamming (1996) , this

Corresponding author. Tel.: + 1-718-260-3569;fax: + 1-718-260-3125.

E-mail address: [email protected] (J.M. Pinto).1 Tel.: + 55-11-3091-2237; fax: + 55-11-3813-2380.2 Tel.: + 1-718-260-3569; fax: + 1-718-260-3125.

is probably where the term supply chain management wasoriginally used.

According to Thomas and Grifn (1996) , current researchin the area of SCM can be classied in three categories:BuyerVendor, productiondistribution and inventorydis-tribution coordination. The authors present an extensive lit-erature review for each category. Vidal and Goetschalckx(1997) present a review of mixed integer problems (MIP)that focuses on the identication of the relevant factors in-cluded in formulations of the chain or its subsystems andalso highlights solution methodologies.

Bok, Grossmann, and Park (200 0) present an appli-cation to the optimization of continuous exible processnetworks. Modeling considers intermittent deliveries, pro-duction shortfalls, delivery delays, inventory proles and job changeovers. A bi-level solution methodology is pro-posed to reduce computational expense. Zhuo, Cheng, andHua (2000) introduce a supply chain model that involvesconicting decisions in the objective function. Goal pro-gramming is used to solve the multi-objective optimizationproblem. Perea, Grossmann, Ydstie, and Tahmassebi (2000)and Perea-Lpez, Grossmann, and Ydstie (2001) present anapproach that is capable of capturing the dynamic behaviorof the supply chain by modeling ow of materials and infor-mation within the supply chain. Information is considered

0098-1354/$ see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.compchemeng.2003.09.018


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872 S.M.S. Neiro, J.M. Pinto/ Computers and Chemical Engineering 28 (2004) 871896

Nomenclature

Indices: p propertys streamt time period

u, u unitv operating variable

Sets:PI u properties of the inlet stream of unit uPO u,s properties of outlet stream s of unit uSO u outlet streams of unit uT time periods {t | t = 1, . . . , NT }Uco product tanks at renery sites dedicated to

supply local marketUdem product tanks that present direct demand

from a consumerU f petroleum tanksUI u units whose outlet streams feed unit uUnc product tanks at renery sites that

supply local and other marketsUO u,s units that are fed by stream s of unit uUp product tanksUpipe units that represent pipelinesUport petroleum tanks that store the crude

oil from suppliersUpu processing units at renery sitesU r product tanks at reneriesUS u ordered pairs unit/stream ( u , s) that

feeds unit u

U tank all storage tanks of the supply chainVO u operating variables of unit u

Parameters:Cinvu,t inventory cost of tank u at time period t Cpetu,t price of petroleum u (u Uport) at

time period t Cpu,t sale price of product u (u Up )

at time period t Cru xed operating cost coefcient of unit uCtu transportation cost for pipeline uCvu,v variable coefcient cost of

the operating variable v of unit u

Demu,t demand of product u at time periodt (u Up )

PFLu,p,t lower bound of inlet property p of unit uat time period t

PFUu,p,t upper bound of inlet property p of unit uat time period t

Propu,s,p standard property value p of theoutlet stream s from unit u

QFLu lower bound for feed ow rate of unit uQFUu upper bound for feed ow rate

of unit u

QGain u,s,v ow rate gain of outlet stream s of unitu due to operating variable u

QSLu lower bound for outlet ow rate of unit uQSUu upper bound for outlet ow rate of unit uV Lu,v lower bound for operating variable v of

unit uV Uu,v upper bound for operating variable v of unit u

Variables I u,s,p,t mixture indices of property p of

stream s of unit u at time period t PFu,p,t property p of the feed stream at unit u

at time period t PSu,s,p,t property p of the outlet stream s at

unit u at time period t QFu,t feed ow rate of unit u at time period t QSu,s,t outlet ow rate of stream s at

unit u at time period t Qu ,s,u,t ow rate of stream s between

units u and u at time period t Volu,t inventory level of tank u at

time period t V u,v,t operating variable v of unit u at time

period t yu,s,u ,t binary variable which assumes 1 if

tank u is chosen to supply u with s attime period t ; 0 otherwise

Processing unit:

CDi atmospheric distillation column iDEPROP C3/C4 separation unitFCC i uid catalytic cracking unit iHTi hydrotreatment unit iPDA propane-deasphalting unitSOLV i solvent distillation column iUCi bun unit iUFN naphtha fraction unitUMTBE unit for MTBE productionURA aromatic reform unitURC catalytic reform unitUVGA alcoholization unitVDi vacuum distillation column i

Product tank:PBEN pool of benzenePC3 pool of C3PC4 pool of C4PDIL pool of kerosene for dilutionPDILT pool of dye diluentPDIN pool of regular dieselPDMA pool of maritime dieselPDME pool of metropolitan dieselPDO pool of decanted oil


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S.M.S. Neiro, J.M. Pinto / Computers and Chemical Engineering 28 (2004) 871896 873

PEXFO pool of fuel oil (exportation type)PFO1A pool of fuel oil (type 1A)PFO1B pool of fuel oil (type 1B)PFO4A pool of fuel oil (type 4A)PGC pool of fuel gasPGLA pool of jet gasolinePGLE pool of exportation gasolinePGLN pool of gasolinePGLP pool of LPGPJFUEL pool of jet fuelPLCO pool of light fuel oilPMTBE pool of MTBEPMTU pool of mineral terpentinePNAL pool of light naphthaPNAP pool of naphthaPNAT pool of treated naphthaPOC pool of fuel oilPOCBV pool of BV fuel oil

POCP pool of premium fuel oilPPGC pool of petroleum green bunPPQN pool of petrochemical naphthaPRAT pool of ATRPSOLB pool of rubber solventPTOL pool of toluenePXIL pool of xylene

Stream:ASFR asphalt residueATR atmospheric residueBEN benzene

C3 propaneC3C4 C3/C4 mixtureC4 butaneCN bun naphthaCRAN cracked naphthaDAO deasphalted oilDILT dye diluentDIN regular dieselDMA maritime dieselDME metropolitan dieselDO decanted oil from FCCFDSOL1 bottom solvent from SOLV1FDSOL2 bottom solvent from SOLV2GC fuel gasGLN gasolineHD heavy dieselHGO bun heavy gas oilHK hydrotreated keroseneHN heavy naphthaHNU heavy naphtha from UFNHTD hydrotreated dieselHTOL heavy tolueneJFUEL jet fuelK kerosene

LALC light alcoholLCO light fuel oilLD light dieselLGO bun light gas oilLN light naphthaLNU light naphtha from UFNMTBE methyl terc butyl etherOC fuel oilPGC petroleum green bunRAF ranateRFOR reformRNU naphtha for reform from UFNSOLB rubber solventTOL tolueneTPSOL1 top solvent from SOLV1TPSOL2 top solvent from SOLV2VGO gas oil mixtureVR vacuum residue

XIL xylene

as perturbation of a system control whereas material owsare considered to be control variables. Therefore, this ap-proach is able to react on time and to coordinate the wholesupply chain for changing demand conditions. Similarly,Ydstie, Coffey, and Read (2003) apply concepts from dy-namics and control in the management of highly distributedsupply chains. Important aspects of the supply chain prob-lem are captured in a graph representation, such as topology,

transportation, shipping/receiving and market conditions,assembly/disassembly, storage of assets, forecasting andperformance evaluation. Song, Bok, Park, and Park (2002)present a design problem of multiproduct, multi-echelonsupply chain. Transportation cost is treated as a continuouspiecewise linear function of the distance and a discontinu-ous piecewise linear function of the transportation volume,whereas installation costs are expressed as a function of the capacity. Feord, Jakeman, and Shah (2002) propose anetwork model whose main objective is to decide whichorders should be met, delayed or not to be delivered.

The petroleum industry can be characterized as a typicalsupply chain. All levels of decisions arise in such a supplychain, namely, strategic, tactical and operational. In spiteof the complexity involved in the decision making processat each level, much of their management is still based onheuristics or on simple linear models. According to Forrestand Oettli (2003) , most of the oil industry still operates itsplanning, central engineering, upstream operations, rening,and supply and transportation groups as complete separateentities. Therefore, systematic methods for efciently man-aging the petroleum supply chain must be exploited. In thenext section, the petroleum supply chain scope is describedas well as recent developments found in the literature con-cerning its subsystems.


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2. Petroleum supply chain

The petroleum supply chain is illustrated in Fig. 1.Petroleum exploration is at the highest level of the chain.Decisions regarding petroleum exploration include designand planning of oil eld infrastructure. Petroleum may

be also supplied from international sources. Oil tankerstransport petroleum to oil terminals, which are connectedto reneries through a pipeline network. Decisions at thislevel incorporate transportation modes and supply plan-ning and scheduling. Crude oil is converted to products atreneries, which can be connected to each other in orderto take advantage of each renery design within the com-plex. Products generated at the reneries are then sent todistribution centers. Crude oil and products up to this levelare often transported through pipelines. From this levelon, products can be transported either through pipelines ortrucks, depending on consumer demands. In some cases,products are also transported through vessels or by train.

In general, production planning includes decisions such asindividual production levels for each product as well as op-erating conditions for each renery in the network, whereasproduct transportation focuses on scheduling and inventorymanagement of the distribution network.

Products at the last level presented in Fig. 1 are actuallyraw materials for a variety of processes. This fact indicatesthat the petroleum supply chain could be further extended.However, this work deals with the petroleum supply chainas depicted in Fig. 1.

Sear (1993) was probably the rst to address the supplychain management in the context of an oil company. The

author developed a linear programming network model forplanning the logistics of a downstream oil company. Themodel involves crude oil purchase and transportation, pro-cessing of products and transportation, and depot operation.Escudero, Quintana, and Salmeron (1999) proposed an LPmodel that handles the supply, transformation and distri-bution of an oil company that accounts for uncertainties

Fig. 1. General petroleum supply chain (PSC).

in supply costs, demands and product prices. Dempster,Pedron, Medova, Scott, and Sembos (20 00) applied astochastic programming approach to planning problems fora consortium of oil companies. First, a deterministic multi-period linear programming model is developed for supply,production and distribution. The deterministic model is then

used as a basis for implementing a stochastic programmingformulation with uncertainty in product demands and spotsupply costs. More recently, Lasschuit and Thijssen (2003)point out how the petrochemical supply chain is organizedand stress important issues that must be taken into accountwhen formulating a model for the oil and chemical industry.

Important developments of subsystems of the petroleumsupply chain can be found in literature. Iyer, Grossmann,Vasantharajan, and Cullick (1998) developed a multiperiodMILP for planning and scheduling of offshore oil eldinfrastructure investments and operations. The nonlinearreservoir behavior is handled with piecewise linear approx-imation functions. A sequential decomposition techniqueis applied. Van den Heever and Grossmann (2000 ) pre-sented a nonlinear model for oileld infrastructure that in-volves design and planning decisions. The authors considernon-linear reservoir behavior. A logic-based model is pro-posed that is solved with a bilevel decomposition technique.This technique aggregates time periods for the design prob-lem and subsequently disaggregates them for the planningsub-problem. Van den Heever, Grossmann, Vasantharaan,and Edwards (2000) addressed the design and planning of offshore oileld infrastructure focusing on business rules.A disjunctive model capable to deal with the increasedorder of magnitude due to the business rules is proposed.

Ierapetritou, Floudas, Vasantharaan, and Cullick (1999)studied the optimal location of vertical wells for a givenreservoir property map. The problem is formulated as alarge scale MILP and solved by a decomposition techniquethat relies on quality cut constraints. Kosmidis, Perkins, andPistikopoulos (2002) described an MILP formulation for thewell allocation and operation of integrated gas-oil systems


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whereas Barnes, Linke, and Kokossis (2002) f ocused on theproduction design of offshore platforms.

Cheng and Duran (2003) f ocused on the crude oil world-wide transportation based on the statement that this elementof the petroleum supply chain is the central logistics thatlinks the upstream and downstream functions, playing a cru-

cial role in the global supply chain management in the oilindustry.At another level of the supply chain, Lee, Pinto,

Grossmann, and Park (1996) concentrated on the short-termscheduling of crude oil supply for a single renery. Ms andPinto (2003) and Magalhes and Shah (2003) focus on thecrude oil supply scheduling. The former developed a de-tailed MILP formulation comprised of tankers, piers, storagetanks, substations and reneries, whereas the latter addressesa scheduling problem composed of a terminal, a pipeline, arenery crude storage area and its crude units. Pinto, Joly,and Moro (2000) and Pinto and Moro (2000) focused on therenery operations. The former work focuses on productionscheduling for several specic areas in a renery such ascrude oil, fuel oil, asphalt and LPG whereas the latter ad-dresses a nonlinear production planning. Jia and Ierapetritou(2003) concentrate on the short-term scheduling of reneryoperations. Crude oil unloading and blending, productionunit operations and product blending and delivery are rstsolved as independent problems. Each sub-system is mod-eled based on a continuous time formulation. Integrationof the three sub-systems is then accomplished by applyingheuristic based Lagrangean decomposition. Wenkai and Hui(2003) studied similar problem to that addressed by Jia andIerapetritou (2003) and propose a new modeling technique

and solution strategy to schedule crude oil unloading andstorage. At the renery level, units such as crude distillationunit and uidized-bed catalytic cracking were modeled anda new analytical method was proposed to provide additionalinformation for intermediate streams inside the renery.

Ponnambalam, Vannelli, and Woo (1992) developed anapproach that combines the simplex method for linearprogramming with an interior point method for solving amultiperiod planning model in the oil renery industry. Stillat the production planning level, Liu and Sahinidis (1997)presented a fuzzy programming approach for solving apetrochemical complex problem involving uncertainty inmodel parameters. Bok, Lee, and Park (1998) addressed theproblem of long-range capacity expansion planning for apetrochemical industry.

Ross (2000) f ormulated a planning supply network modelon the petroleum distribution downstream segment. Re-source allocation such as distribution centers (new and ex-isting) and vehicles is managed in order to maximize prot.Delivery cost is determined depending on the geographiczone, trip cost, order frequency and travel distance for eachcustomer. Iakovou (2001) proposed a model that focuses onthe maritime transportation of petroleum products consider-ing a set of transport modalities. One of the main objectivesof this work was to take into account the risks of oil spill

incidents. Magato, Arruda, and Neves (2002) propose anMILP approach to aid the decision-making process forschedule commodities on pipeline systems. On the productstorage level, Stebel, Arruda, Fabro, and Rodrigues (2002)present a model involving the decision making process onstorage operations of liqueed petroleum gas (LPG).

As a major conclusion of the previous paragraphs, onlysubsystems of the petroleum supply chain have been studiedat a reasonable level of detail. The reason is the resultingcomplexity when parts of the chain are put together withinthe same model. Nevertheless, logic-based approacheshave shown potential to efciently model and solve largesystems without reducing problem complexity ( Trkay &Grossmann, 1996;Van den Heever & Grossmann, 1999;Vecchietti & Grossmann, 2000 ). This fact, allied to the de-velopment of new powerful computers and changing busi-ness necessities provide motivation to increase the scope of petroleum supply chain modeling.

Therefore, the present work develops an integratedmodel for a petroleum supply chain that can be applied toreal-word problems. A set of crude oil suppliers, reneriesthat can be interconnected by intermediate and nal productstreams and a set of distribution centers compose the systemconsidered in this work. Distribution through pipelines isdened from petroleum terminals to reneries and from re-neries to intermediate terminals or directly to distributioncenters.

The paper is organized as follows: the problem statementis given in Section 3, followed by the mathematical modelsfor processing units, storage tanks, pipelines and the op-timization model for the entire petroleum supply chain in

Section 4 . An illustrative example for a simplied reneryis presented in Section 5. Section 6 presents the petroleumsupply chaincase study, and the results obtained by ap-plying the proposed modeling framework. Computationalresults are discussed in Section 7. Finally, conclusions andresearch needs are discussed in the last section.

3. Problem statement

3.1. General problem

According to Lasschuit and Thijssen (2003) , there isgreat appeal that the supply chain of oil and chemicalindustry involve the horizontal integration across depart-mental divisions and coupled coordination of the layers of strategic, planning, scheduling and operational execution(vertical integration). This whole context is usually de-scribed by massive amount of operational data and decisionmaking processes that comprise feedstock, manufacturing,exchange and blending across supply, distribution, termi-nals and depots, and into demand, channel segmentation.It will be clearly veried, in the next section, that the casestudy to be addressed in this work clearly points towardsthe stated requirements.


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Fig. 2. Supply chaincase study.

3.2. Case study

The case study considered in this work partially representsthe real-world petroleum supply chain planning problem of Petrobras (Brazil). Petrobras has 59 petroleum explorationsites among which 43 are offshore, 11 reneries that arelocated along the countrys territory and a large number of facilities such as terminals and pipeline networks. Renerysites are concentrated mainly in southern Brazil where 7sites are found, 4 of which represent 47% of the companysprocessing capacity. These reneries are located in the mostimportant and strategic consumer markets. Therefore, thepresent work addresses the supply chain comprised of these4 reneries, namely: REVAP, RPBC, REPLAN and RE-CAP (Fig. 2). Five terminals compose the storage facilities,

Fig. 3. Crude oil supplycase study.

namely: SEBAT, SEGUA, CUBATAO, SCS and OSBRA;and a pipeline network for crude oil supply and another forproduct distribution compose the transportation facilities.The petroleum and product storage and distribution facilitiesare considered to be organized as detailed in Figs. 3 and 4,respectively. Reneries are supplied with petroleum bytwo main pipeline branches. The OSVAT segment connectsreneries REVAP and REPLAN to the SEBAT terminal,whereas the OSBAT segment connects reneries RPBC andRECAP to the same terminal. Terminals between extremenodes are required in case intermediate storage is neededor pumping capacity is limited.

Crude oil is acquired from a variety of suppliers andits properties strongly depend on supplier origin, which re-sult in different petroleum types. Twenty petroleum types


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Fig. 4. Products storage and distributioncase study.

are considered to supply the complex. The overall chargeis supplied through SEBAT whereby it is then distributedto the terminals and reneries as described in the previousparagraph. Since petroleum types from different supplierspresent distinct properties, every petroleum type is storedat an assigned petroleum tank that is also dedicated. There-fore, SEBAT holds twenty petroleum tanks as shown inFig. 3. Ten oil types are potentially supplied to RECAP andthe remaining 10 are potential suppliers to REVAP, RPBCand REPLAN. Reneries and terminals also contain tank farm that store each of the petroleum types, according toFig. 3.

The whole complex is able to provide 32 products tolocal markets. Six products may be also transferred tosupply the demand from other regions. Transfer is accom-plished by either vessels or pipelines. In case the formeris selected, products are sent to the SEBAT or CUBATAOterminals, whereby products are shipped. In case of trans-fer through pipeline, products are sent to the OSBRAterminal, whereby they are pumped. Demands from otherregions are imposed at the tanks of the transshipmentterminals.

In analogy to petroleum types, different products are alsostored at dedicated tanks, so that every renery and terminalcontains a set of storage tanks for products. Fig. 4 presentsthe two types of product tanks. The black tanks representproducts that supply only the local market, whereas the graytanks represent products that supply either market, local andfrom other regions.

The problem is then to develop an optimization model forthe planning of the above described petroleum supply chainthat accounts for multiple time periods. Decisions involveselection of oil types and their transportation plan, produc-tion levels respecting quality constraints as well as operatingvariables of processing units at reneries and product distri-bution plan and inventory management along the planninghorizon.

4. Mathematical models

The petroleum supply chain presented in the previoussection can be broadly described through three classes of elements that are classied according to their function inthe chain. The next three sections present the mathemati-cal model of each element highlighting their particularitiesand Section 4.4 presents the petroleum supply chain modelbased on these three classes of elements.

4.1. Processing unit model

Processing unit is dened as a piece of equipment thatis able to physically or chemically modify the material fedinto it. According to this denition, processing units are allthose that compose the renery topology and are modeledbased on the general framework developed by Pinto andMoro (2000) for a single renery, as shown in Fig. 5. Gen-erally, stream s1 from unit u1 is sent to unit u at a owrateQu 1,s 1,u,t at time period t . The same unit ( u1) can senda variety of its outlet streams to unit u given by the set{s1, s 2, . . . , sNS 1}. The set US u contains ordered pairs thatrepresent all streams from every unit that feeds unit u. Mix-ture is always accomplished before feeding. Variable QF u,t denotes the resulting feed stream owrate for unit u at timeperiod t . Every stream is characterized by a set of proper-ties {p 1, p 2, . . . , pNP }. Relevant properties at the inlet andoutlet streams are given by the sets PI u and PO u,s , respec-tively, whereas the variables PF u,p,t and PSu,s,p,t denote theproperty values of the inlet and outlet streams at time periodt , respectively. The unit feed is converted into a set of prod-ucts SO u = { s 1, s 2, . . . , s N }. Variable QS u,s,t representsthe outlet owrate of every stream s that leaves unit u at timeperiod t . Since an outlet stream can be sent to more than oneunit (UO u,s = { u 1, u 2, . . . , u N }) to further processing orstorage, there is a splitter assigned to every outlet stream.Different outlet streams may be characterized by specic


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Fig. 5. Model framework for units.

property sets, for instance PO u,s 1 = { p 1, . . . , p NP} andPO u,s N = { p 1, . . . , p NP}. Processing at unit u canbe inuenced by a set of operating variables VOu ={v1, v 2, . . . , v NV }. Every operating variable correspondsto a decision variable V u,v,t . Therefore, based on the vari-ables and sets dened so far and on the framework depictedin Fig. 5, the following equations can be considered tomodel each processing unit u Upu , where Upu is theset of processing units that compose each of the renerytopologies:

QFu,t =(u ,s) US u

Q u ,s,u,t u Upu , t T (1)

QSu,s,t = QFu,t f u,s (PFu,p,t ) +u VO u

QGain u,s,v V u,v,t

u Upu , s SO u , p PI u , t T (2)

QSu,s,t =u UO u,s

Q u,s,u ,t u Upu , s SO u , t T

(3)

PFu,p,t =(u ,s) US u Q u ,s,u,t PS u ,s,p,t

(u ,s) US u Q u ,s,u,t u Upu , p PI u , t T (4)

PSu,s,p,t = f u,s,p (QFu,t , PFu,p,t | p PI u , V u,v,t | v VO u )

u Upu , s SO u , p PO u,s , t T (5)

QFLu QFu,t QFUu u Upu , t T (6)

V Lu,v V u,v,t V Uu,v u Upu , v VO u , t T (7)

Eq. (1) describes the mass balance at the mixer of unitu. Eq. (2) denotes the relation of the product ow rateswith the feed ow rate (QF u,t ), feed properties ( f u,s is typ-ically a linear function of PF u,p,t and depends on the unitand outlet stream) and operating variables ( V u,v,t ). Eq. (2)is valid for units whose product yields closely depend onpetroleum type, such as atmospheric and vacuum distilla-tion columns. The other units operate at constant yields,which means that the function f u,s (PFu,p,t ) is replaced bya constant parameter. Therefore, Eq. (2) becomes linearfor these cases. Eq. (3) describes mass balances at mix-

ers. Eq. (4) represents a weighted average that relates prop-erties of the unit feed stream with properties of the inletstreams. There are cases for which property must be re-placed by mixture indices in order to apply Eq. (4) and someproperties must be weighted on a mass basis. In the lattercases, the density of the corresponding stream must multi-ply every term in the numerator and denominator of Eq. (4).Eq. (5) shows the general relationship among outlet proper-ties, feed owrate, feed properties and operating variables.The functional form of Eq. (5) depends on the unit, streamand property under consideration. Most of the outlet prop-erties are considered to be constant values, and thereforeonly a few are estimated. Those are usually properties thatdepend on petroleum types such as sulfur content. Eqs. (6)and (7) denote unit capacity and operating variable domain,respectively.

4.2. Tank model

Tank is dened as a piece of equipment where the only twoallowed operations are mixture and storage of the differentfeed streams. Only physical properties can be modied dueto mixing. There are two types of tanks in the complexas presented in Section 3: Uf represents the set of tanksdedicated to store crude oil, whereas U p represents the set


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Fig. 6. Model framework for tanks.

of tanks dedicated to store nal products. Therefore, the setof tanks in the supply chain is dened as Utank = { Uf Up }.

Terminals are composed only of tanks and some of themare facilities used for temporary storing whereas others areused as transshipment points. Tanks at the transshipmentterminals and at reneries are demanding points. Therefore,Udem is dened as the set tanks that satisfy demand andis contained by the set Up . The following two subsets arecontained by the set Udem : Uco that represents product tanksat renery sites that supply the local market as well as othermarkets, that is, product tanks at renery sites connected tothe distribution pipeline network and Unc that represents theproduct tanks at renery sites that supply only local market.Union of these last two sets corresponds to the set of producttanks from reneries, U r .

The general representation of a tank slightly differs fromthat presented in Fig. 5 . The general modeling framework fortanks is depicted in Fig. 6. Tanks may be fed with multipleinlet streams but there is only one outlet stream associatedwith tanks. According to Fig. 6, the following equations canbe written:

QFu,t =(u ,s) US u

Q u ,s,u,t u U tank , t T (8)

Volu,t = Volu,t 1 + QFu,t Demu,t QSu,s,t u U tank , s SO u , t T (9)

QSu,s,t =u UO u,s

Q u,s,u ,t

u U tank \ Unc , s SO u , t T (10)

yu,s,u ,t QLu Q u,s,u ,t yu,s,u ,t Q

Uu

u U tank \ Unc , s SO u , u UO u,s , t T (11)

PFu,p,t =(u ,s) US u Q u ,s,u,t PSu ,s,p,t

(u ,s) US u Q u ,s,u,t u {Uco Unc} , p PI u , t T (12)

VolLu Volu,t VolUu u U tank , t T (13)

Eq. (8) describes the mass balance at the mixer of tank uat time period t . Eq. (9) denotes inventory variation that de-pends on the inlet stream and on the two outlet streams,Demu,t and QSu,t that denote demand and outlet owrate,

respectively. Note that Eq. (9) presents the two outlet streamterms for tanks u U tank \ Unc . Since tanks u Unc have noconnections with other elements of the supply chain, QS u,s,t in Eq. (9) is dropped in these cases. Moreover, tanks u Uf and tanks u Up \ Udem do not present Dem u,t . Eq. (10)denotes the mass balance at the splitter of tank u. Note thatthe set SO u contains a single stream which can be furthersplit to be sent to pipelines or processing units (in case urefers to petroleum tanks at renery sites). Eq. (11) is neces-sary to avoid transportation of small volumes of petroleumtypes or products through pipelines, or small charges of petroleum types to distillation columns. Eq. (12) estimatesfeed properties for every tank u { Uco Unc}, which rep-resent product tanks at reneries. Properties are not eval-uated at terminals. Instead, product quality boundaries areimposed at product tanks at renery sites. Once propertyconstraints are satised at reneries, they are consequentlysatised at terminals. Eq. (13) denes the inventory variabledomain.

4.3. Pipeline model

Pipeline is dened as a piece of equipment that transportscrude oil and products. Neither physical nor chemical prop-erties are modied during transportation. As hypothesis,


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Fig. 7. Model framework for pipelines.

different petroleum types or products are never mixed whentransported in pipelines. A well-dened interface is assumedto exist between two different products or petroleum types.Therefore, it is considered that there is no property deple-tion due to the direct contact between products or petroleumtypes. Thereby, the general framework for modeling apipeline is to consider it as a group of units in parallel, asdepicted in Fig. 7. Note that every stream fed to the pipelineu passes through it with no contact with other streams.Consequently, the inlet and outlet amounts of every streamare identical. According to Fig. 7 and considering that setUpipe represents pipelines that compose pipeline networksin the complex, the following equations can be written:

QFu,t =(u ,s) US u

Q u ,s,u,t u Upipe , t T (14)

Fig. 8. Simplied REVAP owsheetillustrative example.

QSu,s,t = Q u ,s,u,t (u , s) US u , u Upipe , t T

(15)

QSu,s,t = Q u,s,u ,t u Upipe , s SO u , u UO u,s , t T (16)

QFu,t QFUu u Upipe , t T (17)

Eq. (14) calculates the feed owrate at the pipeline u at timeperiod t . As seen in Fig. 7, pipelines are always supplied bytanks and only tanks are supplied by pipelines. Once a tank is selected to supply pipeline u at time period t (yu1,s 1,u,t =1, for instance), the lot Q u 1,s 1,u,t is sent to it and the sameamount then leaves it as stated in Eq. (15). This equationcorresponds to Eq. (2) of processing units. Eq. (16) denotes


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the mass balance at mixers of pipeline u for every stream s(s SO u ) transported through it. Note that UO u,s denotes aunitary set, since stream s is sent to only one tank. Finally,Eq. (17) denes pipeline capacity.

4.4. Petroleum supply chain model

Models of the elements presented in the previous sectiontake part in the set of constraints that compose the opti-mization problem of the whole complex. The optimizationproblem is then given as stated in problem PSC . The objec-tive function is dened in Eq. (18) where the maximizationof the revenue obtained by the product sales minus costsrelated to raw material, operation, inventory and transporta-tion is determined. The operating cost is represented by anon-linear term that depends on the unit operating mode.If the unit operates at its design condition, a xed cost isincurred. Otherwise, a proportional cost is incurred, whichdepends on the deviation variable V u,v,t . Transportation costdepends on the pipeline segment.

Problem PSC :

Max Z

=u Udem t T

Cpu,t Demu,t u Uport t T

Cpetu,t QFu,t

u Upu t T

Cru +v VO u

(Cvu,v V u,v,t ) QFu,t

u U f t T

Cinvu Volu,t u Up t T

Cinv u Volu,t

u Upipe t T

Ctu QFu,t (18)

subject to:

Eqs. (1)(7) to represent processing units at reneries; Eqs. (8)(13) to represent petroleum and product tanks; Eqs. (14)(17) to represent pipelines of crude oil and prod-

ucts.

PFLu,p,t PFu,p,t PFUu,p,t

u Upu Uco Unc , t T (19)

QF , QS, Q, Vol R + ; PF, PS, V R ; y { 0, 1}

where Uport is a subset of Uf that represents tanks at the portthat store the purchased crude oil from suppliers. Eq. (19)enforces the idea of imposing bounds on feed propertiesto product tanks at reneries, as well as processing units.The former is usually imposed by environmental regulationsand customer specications, whereas the latter is determinedby limitations on processing unit operation. The completemodel corresponds to a largescale mixed-integer nonlinearprogramming (MINLP) problem, which contains thousandsof continuous variables and hundreds of binary variables

depending on the planning horizon. It is important to notethat the binary variables correspond to the acquisition of crude oil types at every time period as well as the decisionof transfer of streams between the several elements of thechain.

Connections among units from the same renery are ac-

complished according to the scheme depicted in Fig. 5 andthat is illustrated in the next section. Reneries and terminalsare connected according to the scheme depicted in Fig. 7.This means that reneries transfer their products to termi-nals in a tank-pipeline-tank conguration, and vice versa.The same is valid to petroleum transfer. Therefore, there isalways a petroleum tank farm and a product tank farm in thereneries (see Figs. 3 and 4). Only few unit-tank or unit-unitconnections are allowed, as showed in Figs. 1013 . In thiscase, the connection framework follows that of Fig. 5. Itmust be clear that Eq. (3) is responsible for the connectionfrom one unit to another through Eq. (1) or to a tank throughEq. (8). Tanks and pipelines are connected through Eq. (10)that applies to the former and Eq. (14) that holds for thelatter. Finally, products leave a pipeline ( Eq. (16)) to feed atank, as enforced in Eq. (8). In summary, the role of variableQ u ,s,u,t is to connect variables QS u ,s,t and QFu,t .

5. Illustrative example

Application of problem PSC is illustrated by modeling asimplied version of renery REVAP. The owsheet basedon that of Pinto and Moro (2000) is presented in Fig. 8.The renery is composed of an atmospheric distillation col-

umn (CD1), a vacuum distillation column (VD1), a uidizedcatalytic cracking unit (FCC), a propane deasphalting unit(PDA) and a hydrotreating unit (HT3). Atmospheric distil-lation fractionates crude oil into the following hydrocarbonstreams: compounds with 3 and 4 carbon atoms (C3C4),light naphtha (LN), heavy naphtha (HN), kerosene (K), lightdiesel (LD), heavy diesel (HD) and atmospheric residue(ATR). The vacuum distillation column fractionates the ATRstream from CD1 in two streams: vacuum gas oil (VGO)and vacuum residue (VR). The FCC unit produces light cy-cle oil (LCO), decanted oil (DO), cracked naphtha (CRAN)and a light hydrocarbon mixture (C3C4). PDA produces

deasphalted oil (DAO) and asphaltic residue (ASFR), andHT3 improves product quality by reducing sulfur content(HTD) of its feed stream. Products are identied by theirpool names: liqueed petroleum gas (PGLP), interior diesel(PDIN), gasoline (PGLN), petrochemical naphtha (PPQN)and fuel oil (PFO1A). Three crude oil types are availablefor feeding the renery: Bonito, Marlin and RGN.

The production planning considering a planning horizonthat spans two time periods is given as follows. 3

3 Mass balances for the outlet streams are not shown for all units.Fig. 8 clearly shows connections among units.


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5.1. Petroleum tank model

Eqs. (20) and (21) model the outlet streams of petroleumtanks. 4 Since these are simply mass balances and boundconstraints, it is only necessary to dene their valid setsthat are as follows: U f = { Bonito, Marlin, RGN } and T =

{1, 2}.QSu, PT,t = Q u, PT,CD1,t u U f , t T (20)

yu,t 500 QSu, PT,t 15 000 yu,t u U f , t T

(21)

5.2. CD1 model

The CD1 feed is composed of a petroleum mixture thatresults from all petroleum types available ( UI CD1 = Uf ) asstated in Eq. (22):

QFCD1 ,t =u UI CD1

Q u ,PT,CD1 ,t t T (22)

Moreover, feed ow rate must satisfy CD1 operating capac-ity:

14000 QFCD1,t 36 000 t T (23)

Production level depends on the feed ow rate, feed prop-erties and on a single operating variable:

QSCD1,s,t = QFCD1,t PFCD1 ,p,t + QGainCD1 ,s V CD1,V 1,t

s SO CD1 , p PI CD1 , t T (24)

where SO CD1 : {C3C4, LN, HN, K, LD, HD, ATR } andPI CD1 : {YC3C4, YLN, YHN, YK, YLD, YHD, YATR }. El-ements of the set PI CD1 denote yields of the outlet streamsand depend on the petroleum types fed to the distillationcolumn. The operating variable V CD1,V 1,t is the feed tem-perature deviation ( V 1). Distillation column is fed at the de-sign temperature value when V CD1,V 1,t = 0 and it yields thedistance from the design temperature when V CD1,V 1,t = 0.Temperature deviation of the column feed must also satisfythe following design constraint:

10 V CD1 ,V 1,t 10 t T (25)

Feed properties that appear in Eq. (24) are weighted accord-ing to each petroleum type selected to compose the reneryfeed:

PFCD1,p,t =u UI CD1 Q u ,PT,CD1,t Propu ,PT,p

u UI CD1 Q u ,PT,CD1,t p PI CD1 , t T (26a)

4 Outlet streams from petroleum tanks are referred to as PT to denotepetroleum.

where Prop u ,PT,p is a parameter that denotes the property p assigned by the petroleum type u . Properties of the out-let streams can be modied by the operating variable as inEq. (26b) :

PSCD1,s,p,t = PropCD1,s,p + PGainCD1,s,p V CD1,V 1,t

s SO CD1 , p PO CD1,s , t T (26b)Analogously, Prop CD1,s,p is a parameter that denotes theproperty p of the product stream s, and SO CD1 and PO CD1 ,sare dened according to the renery topology and prod-uct stream, respectively. The elements of these sets are notshown for the sake of simplicity, since every stream s SO CD1 denes a set PO CD1 ,s .

Petroleum types characterize both production yields forevery product stream of CD1 and the sulfur content car-ried by each of these product streams. Consequently, sulfuramount strongly depends on the petroleum types fed intoCD1 and must be estimated through a relation that is similar

to Eq. (27a):

PFCD1 ,S,t =u UI CD1 Q u ,PT,CD1 ,t Propu ,PT,S

u UI CD1 Q u ,PT,CD1 ,t t T (27a)

where S denotes sulfur and Prop u ,PT,S is sulfur contentpresent in the petroleum type u .

As seen in Fig. 8 and according to the set SO CD1 pre-sented together with Eq. (24), unit CD1 produces seven out-let streams that are sent to other units for further processingor are sent to tanks where they are mixed with other inter-mediate streams to compose nal products. Therefore, seven

equations in the form of Eq. (3) are generated. For the sakeof illustration, the application of Eq. (3) to the atmosphericresidue stream yields:

QSCD1 ,ATR ,t =u UO CD1,ATR

Q CD1,ATR ,u ,t t T

(27b)

where UO CD1 , ATR = {VD1}. In other words, the ATRstream that leaves CD1 is completely sent to VD1 andtherefore the owrate QCD1 ,ATR ,VD1 ,t also corresponds tothe feed owrate of unit VD1, as seen in Eq. (28a). Fig. 9magnies the connection between these two units and

illustrates the owrate variables involved.

5.3. VD1 model

Since VD1 is fed only with atmospheric residue fromCD1, the inlet variables of VD1 are equal to the outlet vari-ables of ATR stream given by the set of Eqs. (28):

QFVD1,t = Q CD1,ATR ,VD1,t t T (28a)

PFVD1 ,p,t = PSCD1 ,ATR ,p,t p PI VD1 , t T (28b)

Production yields of the outlet streams, as well as the sul-fur content of the inlet stream of the VD1 depend on the


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Fig. 9. Connection between CD1 and VD1 for the illustrative example.

petroleum types supplied to the renery. Therefore, the pro-cedure to determine PI VD1 = { YVGO, YVR, S } is identi-cal to that of unit CD1. Moreover, since there is no relevantoperating variable for VD1, Eqs. (2) and (5) are simplied,respectively, as given in Eqs. (29) and (30) .

QSVD1 ,VGO,t = QFVD1 ,t PFVD1 ,YVGO ,t t T (29a)

QSVD1 ,VR ,t = QFVD1 ,t PFVD1 ,YVR ,t t T (29b)

PSVD1,VGO ,p,t = PropVD1 ,VGO,pp PO VD1,VGO , t T (30a)

PSVD1,VR ,p,t = PropVD1 ,VR ,p p PO VD1,VR , t T

(30b)

where Prop VD1,VGO ,p and PropVD1 ,VR ,p are property valuesof the outlet streams VGO and VR, respectively. Unit VD1operates within the following range:

10000 QFVD1,t 24 000 t T (31)

5.4. PDA model

Since PDA is exclusively fed by VR from VD1 and no op-erating variable is considered, the following equations rep-resent inlet and outlet variables:

QFPDA,t = Q VD1 ,VR ,PDA,t t T (32a)

4000 QFPDA,t 7200 t T (32b)

PFVD1 ,p,t = PSVD1 ,VR ,p,t p PI VD1 , t T (32c)

QSPDA,DAO ,t = Yield PDA,DAO QFPDA,t t T (33a)

QSPDA,ASFR ,t = Yield PDA,ASFR QFPDA,t t T

(33b)

PSPDA,DAO ,p,t = PropPDA,DAO ,pp PO PDA,DAO , t T (34a)

PSPDA,ASFR ,p,t = PropPDA,ASFR ,pp PO PDA,ASFR , t T (34b)

Product ow rates are calculated from constant yield val-ues as shown in Eq. (33). Note that Yield PDA,DAO andYield PDA,ASFR denote xed parameters differently from PFused for CD1 and VD1 units. Eq. (34) holds in the case of properties that do not depend on the properties of the inletstream. Eq. (35) evaluates sulfur content of the productstreams of PDA, which depends on the inlet conditions.

PSPDA,DAO ,S,t = sulfurPDA,DAO PFPDA,S,t t T

(35a)

PSPDA,ASFR ,S,t = sulfurPDA,ASFR PFPDA,S,t t T

(35b)

where sulfur PDA,DAO and sulfurPDA,ASFR are constant pa-rameters.

5.5. FCC model

The FCC feed is composed by the combination of DAOfrom PDA and VGO from VD1 so that feed ow rate is


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determined by Eq. (36) and its operating capacity is ex-pressed by Eq. (37).

QFVD1 ,t = Q VD1 ,VGO,FCC ,t + Q PDA,DAO ,FCC,t t T

(36)

7000 QFFCC,t 12 500 t T (37)Properties of the inlet stream of FCC are calculated throughthe weighted average of properties of the two streams thatcompose the FCC feed:

PFFCC,p,t =

(u ,s) UI FCC Q u ,s, FCC,t PSu ,s, D20,t PSu ,s,p,t

(u ,s) UI FCC Q u ,s, FCC,t PSu ,s, D20,t p PI FCC , t T (38)

where UI FCC = { (VD1, VGO), (PDA, DAO) } and densityPSu ,s,D20, t is used to estimate properties in a mass basis.Product owrates are not inuenced by any operating vari-able, but depend on carbon residue (RCR) fed to FCC re-sulting in a special form of Eq. (2):

QSFCC,s,t = QFFCC,t [Yield FCC,s+ YGain FCC,s (PFFCC ,RCR ,t RCFCC )]

s SO FCC , t T (39)

In Eq. (39), YGain FCC,s is a owrate gain parameter re-lated to the carbon residue property (PF FCC ,RCR ,t ), RCFCCis a constant parameter and SO FCC = { C3C4, CRAN, LCO,ATR}. The parameter YGain FCC ,s may assume either posi-tive or negative values. Properties of the outlet streams arestandard values ( Eq. (40)), with exception of sulfur contentthat is dened according to sulfur content at the inlet of FCC(Eq. (41)).

PSFCC ,s,p,t = PropFCC ,s,p p PO FCC,s , t T (40)

PSFCC ,s, S,t = sulfurFCC ,s PFFCC ,S,t t T (41)

5.6. HT3 model

The unit HT3 is fed by three streams (LD, HD, LCO) thatleave two units (CD1, FCC), so that feed owrate is givenby Eq. (42) whereas the operating capacity is bounded byEq. (43) .

QFHT3 ,t = Q CD1,LD,HT3,t + Q CD1 ,HD,HT3,t + Q FCC ,LCO,HT3 ,t t T (42)

3200 QFHT3,t 7500 t T (43)

Three properties at the inlet of HT3 must be convertedto index form in order to be additive: viscosity (VISCO),ash point (FP) and DASTM 85% (A85), which limits thecontent of heavy fractions that are related to large carbon

Table 1Sets of feed properties for product tanks of the illustrative example

Product tank Set of feed properties ( PI u )

PGLP {PVR, MON }PGLN {PVR, MON }PDIN {FP, A50, A85, S, NC, D20 }

PFO1A {S, VISCO}PPQN

Table 2Volume of petroleum purchased of the illustrative example (m 3)

Tank Time period 1 Time period 2

Bonito 0 1341Marlin 9649 9420RGN 15000 15000

residue and poor color. Their mixture indices are calculatedby Eqs. (44)(46) .

I u ,s, VISCO ,t =log10P u ,s, VISCO ,t

log101000P u ,s, VISCO ,t (u , s) US HT3 , t T (44)

Table 3Production and inventory levels of the illustrative example

Tanks Production level(QFu,t ) (m3)

Inventory level(Vol u,t ) (m3)

Timeperiod 1

Timeperiod 2

Timeperiod 1

Timeperiod 2

PGLP 689 487 2689 2798PPQN 0 0 200 250PGLN 1152 2716 6152 6364PDIN 615 0 11115 11385PFO1A 1632 3061 5232 5730

Table 4Product properties and bounds of the illustrative example

Producttank

Property Lowerbound

Time period Upperbound

1 2

PGLP MON 83 83PVR 5.00 4.96 15

PGLN MON 81 82 82PVR 0.3 1.00 0.55 0.7

PDIN FP 0 0A50 245 279.83 279.78 313A85 300 357.94 358.64 370S 0.14 0.13 0.5NC 40 43.18 43.27D20 0.82 0.82 0.82 0.88

PFO1A S 0.8 0.81 2.5VISCO 0.48 0.45 0.48


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Fig. 10. REVAP owsheet.

Fig. 11. RPBC owsheet.


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I u ,s, FP,t = exp 10006 .1

1.8P u ,s, FP,t + 415 14.0922

(u , s) US HT3 , t T (45)

I u ,s, A85,t =

1.8P u ,s, A85 ,t + 32

549

7.8

(u , s) US HT3 , t T (46)

Once these mixture indices have been determined, propertiesof the inlet stream of HT3 can be evaluated through Eq. (4).The exception is property A85 that must be calculated byEq. (47) .

PFFCC,A85 ,t

= 305 (u ,s) UI FCC Q u ,s, FCC,t I u ,s, A85,t

(u ,s) UI FCC Q u ,s, FCC,t

0.128

17.78 p PI FCC , t T (47)

Outlet ow rate equals inlet ow rate as well as most of the properties at the outlet stream. Exception is made tosulfur content ( S ) and cetane number ( NC ) that depend onan operating variable and are calculated through Eqs. (48)and (49) , where VR HT3,S and VRHT3,CN are constant param-eters. Operating variable range must assume values withinthe interval dened through Eq. (50).

Fig. 12. RECAP owsheet.

PSHT3 ,HTD ,S,t = PFHT3 ,S,t (VRHT3,S V HT3,V1,t )

t T (48)

PSHT3 ,HTD ,CN,t = PFHT3 ,CN,t VRHT3 ,CN V HT3 ,V1,t

t T (49)50 V HT3 ,V1,t 90 t T (50)

5.7. Product tank model

Product tanks for the illustrative example serve local mar-kets and therefore are modeled as such. In this case, Eqs. (8),(9), (12) and (13) are applied. Eqs. (8), (9) and (13) arestraightforward and will not be shown. The complicatingconstraints are those related to feed properties assessment.Table 1 presents the set of feed properties ( PI u ) of eachproduct tank ( u Up ). From the properties listed in Table 1 ,

PVR, MON, A50, and D20 are calculated according toEq. (12) . Properties S and NC are calculated on a mass ba-sis. Therefore Eq. (12) must include the density in the sameway as done in Eq. (38). Properties A85, FP and VISCOfollow the same procedure described for the FCC unit.

The renery model corresponds to a mixed-integer non-linear programming (MINLP) problem, which contains 383variables and 349 equations. Six binary variables are neces-sary for the decision of purchasing crude oil (three for each


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time period). The model was implemented in the modelingsystem GAMS ( Brooke, Kendrick, & Meeraus, 1998 ) andsolved with DICOPT ( Viswanathan & Grossmann, 1990 ).The NLP subproblems were solved with CONOPT2 ( Drud,1994), whereas the MILP master problems were solved withOSL (IBM, 1991 ). Overall, 1.98 CPU seconds were nec-

essary to solve the problem. NLP sub-problems representnearly 75% of total solution time. Table 2 presents results of the amount required of each petroleum type. Table 3 showsproduction and inventory levels for each period and Table 4presents the optimal product properties calculated and theirspecications.

Eqs. (29), (38) and (44)(47) are critical constraints be-cause of their high non-linearity and the wide domain of vari-ables. This fact requires the problem to be carefully scaledand bounded. Another important aspect is that concerningstarting point. Since the formulation results a non-convexNLP problem, different starting points may lead to differentlocal optima. However, computational tests with differentstarting points led to the same solution.

Fig. 13. REPLAN owsheet.

6. Petroleum supply chaincase study

This section is divided in two parts. The rst part presentsfurther details in the description of the targeted petroleumsupply chain whereas the second part presents results anddiscussion obtained through the implementation of problem

PSC for the case study.

6.1. Case study revisited

The previous section illustrated how complex problemPSC can be even for a relatively small example. Actually,even the small example can be further complicated if thetime horizon is extended. For the petroleum supply chain de-scribed in Section 3.2 , renery models follow the same ideapresented in the previous section, except that each renerypresents a particular conguration as well as sets of process-ing units and petroleum and product tanks. Therefore, theapproach is to formulate model for reneries according tothe processing unit and tank models presented in Section 4.


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Fig. 14. Connections of intermediate streams among reneries.

Fig. 15. Comparison of the petroleum distribution for the three cases.


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Terminal models are formulated based on the tank modeland connections among facilities are modeled according tothe pipeline model. Figs. 1013 present topologies of theREVAP, RPBC, RECAP and REPLAN reneries, respec-tively. Symbols used to describe processing units, product

Fig. 16. Interference on the petroleum type selection.

tanks and intermediary streams are described in the notationsection. The REVAP renery is composed of 8 units andhas a processing capacity of 36 000 m 3 per day of crude oilthat is converted in 14 products. The RPBC renery is com-posed of 13 units and has a processing capacity of 27 000m 3


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per day of crude oil that is converted in 15 products. Thetopology of the renery RECAP is as follows: there are4 units with a processing capacity of 8500 m 3 per day of crude oil that is converted in 10 products. The REPLANrenery is composed of 10 units and has a processing ca-pacity of 54 200m 3 per day of crude oil that is converted in

15 products.Besides connections of nal products among reneriesand terminals described in Section 3.2 , connections of in-termediate streams among reneries are also allowed. Suchpossible connections are illustrated in Fig. 14. Units VD1and VD2 from RPBC can either send VGO to be processedat its own FCC unit or send it to the FCC unit from REVAP.Moreover, CD1 from RECAP can either send ATR to be pro-cessed at FCC from its site or send it to FCC from REVAP.Another possibility is to use DO and LCO produced at RE-CAP to compose products at its site or send those streamsto compose fuel oil products at REVAP. Finally, K producedat CD1 at REPLAN may be sent to be processed at HT1 orHT2 at REVAP.

6.2. Results and discussion

In this section, results of the problem PSC are comparedto two other cases in which additional constraints are in-cluded. The model was implemented in the modeling sys-tem GAMS ( Brooke et al., 1998 ) and solved with DICOPT(Visvanathan & Grossmann, 1990). The NLP subproblemswere solved with CONOPT2 ( Drud, 1994 ), whereas theMILP master problems were solved with CPLEX (ILOG,1999).

The original problem is compared to a rst scenario inwhich renery REVAP is assigned lots of certain petroleumtypes and to a second scenario in which the pipeline seg-ment SG-RV of the product distribution network is tem-porarily interrupted for maintenance. The three cases aresummarized as follows:

Case (a) Original problem PSCCase (b) A minimum amount of 10000m 3 for

petroleum type Larab and 8 000 m 3 forpetroleum type Bicudo must be ordered dueto a contract agreement with their suppliers

Case (c) Operation of pipeline segment SGRV isinterrupted for maintenance

The input data is presented in Appendix A . Table A.1presents prices of petroleum types from all possible suppli-ers. Table A.2 presents inventory costs for petroleum andproduct tanks, Table A.3 presents transportation costs forpetroleum and product pipeline networks and Table A.4presents product sale prices and demands for reneries andterminals.

Fig. 15 shows a comparison of the petroleum amountssent to reneries of the complex for the three cases. The nor-

mal font values in the callouts represent results for case (a)the italic values represent results for case (b) and the boldface values represent results for the case (c). It can be seenthat the overall petroleum load for reneries RPBC, RECAPand REPLAN are unaffected by the perturbations imposedon the renery REVAP. Interruption of the pipeline segment

SGRV causes a signicant 10 000m3

drop of the overallpetroleum load to renery REVAP, since product distribu-tion is hindered by the pipeline stoppage. This perturbationcauses also a small impact on the petroleum selection asseen in Fig. 16. For case (b), on the other hand, the impact

Fig. 17. Interference on the production level of renery REVAP.


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Fig. 18. Interference on the production level of renery RPBC.

is doubtless more signicant. Fig. 16 shows the reductionof the load of petroleum types RGN and Cabiun in favor of petroleum types Larab and Bicudo acquirement imposition.

Analyzing the reneries production planning, it can berealized that the additional constraints given in case (b)enforce re-planning of the entire complex, as veried inFigs. 1720 . Comparison between case (a) and case (b) re-veals that the change in petroleum types selection tries tocompensate the disadvantage that case (b) presents with thepartial pre-selection of petroleum types. Actually, for mostof the products planning of the supply chain is not changedat all. The more relevant impacts on production planning are

observed to PDME from REVAP, PDME and PDIN from

Fig. 19. Interference on the production level of renery RECAP.

Fig. 20. Interference on the production level of renery REPLAN.

RPBC, POCBV from RECAP and PDMA and PDIN from

REPLAN. These tanks, with exception of POCBV, are di-rectly connected to the pipeline distribution network. Thismeans that the distribution planning is also altered to ad- just the additional constraints of case (b). The variation forthe POCBV tank can be explained by the connection of theintermediate streams DO and LCO from renery RECAPto renery REVAP (see Figs. 12 and 14). The perturbationcaused by case (c) has smaller effect on reneries produc-tion. Actually, only renery REVAP is directly impacted bythe interruption of pipeline segment SGRV that causes in-crease of the inventory level for some products due to thedecient distribution ( Fig. 21).

Fig. 21. Inventory level for product tanks from renery REVAP underconstraints of case c).


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Fig. 22. Products feed owrate percentage at terminal SEGUA.

Indeed, distribution planning plays an important role byattempting to balance interferences suffered in the supplychain as observed how reneries react to the constraints im-posed on the system. Likewise, there is an impact on thedistribution facilities. Figs. 2225 show the percentage of each product transferred to terminals, whereas Fig. 26 showsthe total amount to be transported by each product pipelineaccording to the production planning. Again, the values innormal font in the callouts represent results for case (a) thevalues in italics represent results for case (b) and the val-ues in bold face represent results for the case (c). For case(b), it is observed that only little variations are established.For case (c), on the other hand, larger variations can be ob-served. Since all reneries are needed to satisfy the demandrequirements of the whole chain, products from renery RE-

Fig. 23. Products feed owrate percentage at terminal SCS.

VAP are then transferred to terminal SCS whereby transferis accomplished to other terminals. Moreover, product dis-tribution from the other reneries is signicantly altered asseen by Figs. 2225 .

In terms of the objective function, case (a) presents netpresent value 0.5% higher than case (b) and 14% higher thancase (c).

As a conclusion for case (b), pre-selection of somepetroleum types tend to be counterbalanced by selectionof other petroleum types absorbing the disturbing effectat the renery level. A comparison of the petroleum typeselections between case (a) and case (b) really revealsthat there is a great difference in terms of number andamount of petroleum types selected. Such a measure avoidspropagation of the disturbance over other facilities of thecomplex. As a conclusion for case (c), opposite to case (b),disturbance can only be absorbed by the whole distributionsystem.


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Fig. 24. Products feed owrate percentage at terminal CUBATAO.

7. Computational results

Non-linearity in problem PSC appears in constraints (2),(4), (12), (14), (38) and (44)(47) and also the objectivefunction (18). Such equations represent process units orproduct tanks. Therefore, non-linearity is present only at re-nery models. Although terminal models are basically rep-

Table 5Computational results

Case (a) Case (b) Case (c)

Time period 1 Time period 2 Time period 1 Time period 2 Time period 1 Time period 2

Constraints 2304 4607 2306 4611 2304 4607Variables 2544 5087 2544 5087 2544 5087Discrete variables 195 390 195 390 195 390Solution time (CPU s) 116.8 656.2 152 915.6 157.8 2301.5

Fig. 25. Products feed owrate percentage at terminal OSBRA.

resented by product tanks, Eq. (12) is not included in the setof constraints describing these tanks. Instead, product qual-ity constraints are applied at renery product tanks. Productproperties must be within a range established by customerspecications and environmental regulations. Once all re-neries are subjected to the same quality constraints, thereis no need to recalculate properties at terminals, since


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Fig. 26. Pipeline loads of the product distribution network.

mixture of streams of any product from any renery willthen always lie within property boundaries.

Table 5 presents computational results for the three casesconsidering a planning horizon of 1 and 2 time periods inorder to verify the increase in model size as the planninghorizon is extended and the corresponding difference in objective function value among the three cases. It can be ob-served, according to Table 5 , that the number of constraintsof problem PSC (case a)original problem) doubles whentime horizon is doubled, whereas solution time increases

fourfold. Moreover, NLP subproblems consumed 97% of the solution time.

8. Conclusions and future research

In recent years, enterprises have been forced to changetheir management rules from a decentralized management toa context which share of information with other elements thatcompose the supply chain to which they belong has becomevital. Model PSC presented in the present paper has demon-strated to be an efcient tool to assist production planning of a large petroleum supply chain. The whole complex topol-ogy is built through general structures representing process-ing units, storage tanks and pipelines and by connecting theelements of the chain according to the particularities of thesestructures. A small example showed how a renery can bemodeled based on the general structures. The representationof the targeted petroleum supply chain was then analyzedthrough three what-if cases and important characteristics of the system were discussed. The results have demonstratedthe potential of problem PSC to real-world petroleum sup-ply chains and how it can be used to help in the decisionmaking process of the production planning. According tothe presented results different strategies are adopted depend-

ing on the locations and on the amplitude of the disturbanceimposed on the petroleum supply chain. Moreover, it is il-lustrated the necessity of having a coordinated productionplanning in order to balance the dynamic behavior of thewhole supply chain in face of different scenarios.

Since problem PSC presents a structure with localizednon-linearity constraints, it might be protable to employany decomposition method that would result in smallerMINLP and MILP problems. Decomposition methods arenow the main concern of the ongoing research, which would

allow extension of time periods and inclusion of differentscenarios.

Acknowledgements

The authors acknowledge nancial support from FAPESPunder Grant 00/02403-5 and 98/14.

Appendix A

Data for the supply chain case study Tables A.1-A.4 .

Table A.1Prices of petroleum types from all possible suppliers

Petroleum types Cf (US$/m 3)

Lixo 127Bonito 132Larab 139Marab 136Marlin 121RGN 115Cabiun 124


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Table A.1 ( Continued )

Petroleum types Cf (US$/m 3)

Albaco 117Bicudo 123Condoso 118Bonit 127Bonny 132Marli 121RGNE 121Cabiuna 115Albacor 124Brass 115Palanca 124Larabe 118Coso 127

Table A.2Inventory costs at every facility

Tank type Cinv (US$/m3

d)Petroleum Product

SEBAT 0.11 SEGUA 0.23 0.35SCS 0.28CUBATAO 0.25 0.27OSBRA 0.46REVAP 0.12 0.32RPBC 0.12 0.32RECAP 0.12 0.32REPLAN 0.12 0.32

Table A.3Transportation costs for petroleum and product pipelines

Petroleum pipeline Ct (US$/m 3) Product pipeline Ct (US$/m 3)

OBT-I 0.044 SGSB 0.098OBT-II 0.044 SGRV 0.031OVT-I 0.052 SGSC 0.037OVT-II 0.038 SGOB 0.024OVT-III 0.045 SGRC 0.036

SCRV 0.051SCRC 0.085SCOB 0.049SCSG 0.037SCCB 0.042RPCB 0.034OBSC 0.032CBSC 0.042

Table A.4Product sale prices and demands for reneries, terminals and pipelines

Renery REVAP Renery RPBC

Cp(US$/m 3)

Dem(m3)

Cp(US$/m 3)

Dem(m3)

PC3 180 500 PGLP 118 200PC4 100 100 PDIN 230 350PMTBE 100 0 PDME 242 500

Table A.4 ( Continued )

Renery REVAP Renery RPBC

Cp(US$/m 3)

Dem(m3)

Cp(US$/m 3)

Dem(m3)

PGLP 115 130 PDMA 212 300PJFUEL 130 200 PNAP 146 900PPQN 148 600 PNAT 160 158PGLN 149 1000 PPGC 152 600PDIN 210 500 POC 180 1500PDME 230 600 PDO 159 700PDMA 206 200 PGLN 270 500PFO1A 139 800 PGLA 290 500PFO1B 142 50 PGLE 298 200PFO4A 151 4000 PXIL 160 100PEXFO 146 300 PTOL 167 45

PBEN 280 210

RECAP REPLAN

PDIN 132 0 PNAL 128 330PGLP 65 200 PNAP 151 3850PRAT 98 500 PJFUEL 175 100PGC 202 400 PDIL 150 0POCP 144 90 PMTU 180 200PLCO 0 400 PGLN 181 2000PGLN 141 150 PGLP 215 400PSOLB 231 300 PPGC 122 230PDILT 236 200 PDIN 280 2000POCBV 257 90 PDMA 267 500

PDME 254 6000PFO1A 160 1050PFO1B 162 1500PFO4A 158 2800PEXFO 149 990

Terminal SEBAT CUBATAO OSBRA

Cp(US$/m 3) Dem(m3) Cp(US$/m 3) Dem(m3) Cp(US$/m 3) Dem(m3)

PDIN 230 3000 230 4000 230 10500PDME 242 4400 242 3000 242 5500PDMA 226 3000 226 2000 226 5400PGLN 270 6500 270 600 270 1000PJFUEL 175 0 175 200 175 500PGLP 128 800 128 800 128 3600

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