Tesis Tamara Cassio

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CranfieldUNIVERSITY

Cassio R. Tamara

Oil Refinery Scheduling

Optimisation

School of Engineering

Department of Process & Systems

Engineering

MSc Thesis


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Cassio R. Tamara Oil Refinery Scheduling Optimisation

MSc Process & System Engineering Cranfield University 2003

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CranfieldUNIVERSITY

School of Engineering

Department of Process & System Engineering

MSc Thesis

Academic Year 2002-2003

Cassio R. Tamara

Oil Refinery SchedulingOptimisation

Supervisor: Dr. Zhigang Shang

September 2003

This thesis is submitted in partial fulfilment of the requirements for theDegree of Master of Science

Cranfield University, 2003. All rights reserved. No part of this publication may be

reproduced without the written permission of the copyright owner


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ABSTRACT

Nowadays, the development of global competition has been one of the main factors

that have driven the efforts toward the optimisation development. Therefore, oil

refineries have been encouraged to be restructured for competing successfully in this

new scenario with low profit margin, tighter environmental regulations and more

efficient plant operation. However, many years and a lot of human and computational

efforts have been dedicated to improve the techniques applied for the overall refinery

optimisation. Good developments have come successfully operating at the planning

level; but developing and solving rigorous overall plant optimisation models at the

production scheduling level still are at research stage and much more work must bedone to continue improving in this field through the involvement of difficult tasks due

to the mathematical complexity of the models which have the compulsory use of a

large quantity of equations and variables that hugely increase the size of the problem.

This Thesis presents a new generic mixed integer linear programming model for

optimising the scheduling of crude oil unloading, inventories, blending and feed to oil

refineries that usually unload several kinds of crude oils with different compositions.The objective function of the model consists on minimising the operational cost

generated during the mentioned operation. Case studies are presented and compared

each other illustrating the capabilities of the model to solve operation scheduling

problems in this area and to support future expansion projects for the system as they

happen in real situations. The solution involves optimal operation of crude oil

unloading, optimal transfer rates among equipments in accordance with the pumping

capacities and tank volume limitations, optimal oscillation of crude oil blended

compositions and fulfilment of the oil charging demand per process unit.


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ACKNOWLEDGEMENT

In memory of my father.

I still remember when I left my country far away from here, with my wife and my two little

children to come to Cranfield, full of hopes and wishes, with the only purpose to study and fulfil

my major dream attending and completing post grade studies abroad in a well known university

as Cranfieldis known. It was a difficult decision to come to the UK with limited resources in the

middle of my professional productive career, with more than 15 years of continuous work in an

oil refinery from Ecopetrol.

I would like to give my thanks to my wife Norma, my daughter Natalia and my son Sebastian for

staying with me during the long months living and sharing together busy and happy moments,

as well as uncertain times. Moreover, I really appreciate the constant prayers of my mother and

my wife during all our stay here.

Furthermore, I would like to give my thanks to Colfuturo which gave me the financial support for

my tuition fees and part of my living expenses. On the other hand, despite the policies and the

difficult moments encountered by Ecopetrol and my country, I really appreciate the tireless and

willing support from the oil refinery manager Mr. Antonio Escalante searching for economical

approval to cover the financial support given by Colfuturo . Thanks also to Mrs Martha

Espinosa, Mr Carlos Bustillo, Mr Jorge Villalba and other important people at the high staff and

board level that were supporting the process.

Finally, I really appreciate the advice and support from Dr. Zhigang Shang for encouraging meto improve the quality and value of my Thesis and his high motivation towards my research.

Furthermore, I would also like to give my thanks to Professor Mike Sanderson, Mrs Linda

Withfield and Mrs Janet Dare for all their kind support and help from the Process and System

Engineering Department during this very important year of my life. From Mr Ivor Rhodes, I

thank him for patiently keeping me on the waiting list to come to Cranfield for three years.

Cassio Tamara, Cranfield, 28th August 2003


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TABLE OF CONTENTS

Chapter 1. INTRODUCTION.......................................................................................1

1.1 Oil Refinery Optimisation....................................................................................1

1.2 Other facts and Developments about Oil Refinery Optimisation. .......................31.3 Present Work........................................................................................................6

Chapter 2. OVERVIEW OF SCHEDULING OPTIMISATION ..................................8

2.1 Scheduling General Concern. ..............................................................................8

2.2 Crude Oil Inventory Scheduling Optimisation. ...................................................9

2.3 Review of Production Scheduling Developments .............................................10

Chapter 3. PRODUCTION SCHEDULING PROBLEM DEFINITION....................13

3.1 Problem Definition.............................................................................................13

3.2 Optimisation Model Formulation Introduction..................................................16

3.3 Model Mathematical Formulation. ....................................................................21

3.3.1 Vessel Arrival and Departure Operation Rules. .........................................22

3.3.2 Material Balance Equations for the Vessel.................................................243.3.3 Material Balance Equations for the Storage Tank. .....................................25

3.3.4 Material Balance Equations for the Charging Tank. ..................................27

3.3.5 Material Balance Equations for Component k in the Storage Tank. ..........28

3.3.6 Material Balance Equations for Component k in the Charging Tank.........29

3.3.7 Operating Rules for Crude Oil Charging to Crude Distillation Units. .......30

3.3.8 Problem Solving Direction. ........................................................................30

3.4 Chapter Summary. ............................................................................................33

Chapter 4. MODEL REAL TEST................................................................................35

4.1 Introduction........................................................................................................36

4.2 Example 1 Results and Analysis........................................................................37

4.3 Example 2 Results and Analysis........................................................................424.4 Example 3 Results and Analysis........................................................................49

4.5 Chapter Summary ..............................................................................................55

Chapter 5. MODEL APPLICATION TO A PRACTICAL CASE..............................57

5.1 Presentation of Case 1........................................................................................58

5.2 Scheduling Alterations of Case 1.......................................................................66

5.3 Bigger Scheduling Alteration of Case 1. ...........................................................72

5.4 Effect of Not Control Oil Sulphur Content Applied to Case 1..........................78

5.5 Effect of Not having Tank Inventory Cost for Case 1. ......................................81

5.6 Effect Caused by a High Reduction in Changeover Cost for Case 1.................82

5.8 Chapter Summary. .............................................................................................82

Chapter 6. MODEL APPLICATION TO CASES WHERE THE SYSTEM

EQUIPMENT LIMITATIONS ARE HIGHLIGHTED. .............................................84

6.1 Case 2, Effect of Increasing the Vessel Unloading Volume..............................84

6.2 Scheduling Alteration of Case 2. .......................................................................91

6.3 Case 3, Effect of a High Increase in Unloading Cost. .......................................95

6.4 Case 4, Effect of CDU Shut Down. ...................................................................98

6.5 Chapter Summary. ...........................................................................................101

Chapter 7. MODEL APPLICATION TO CASES WHERE THINKING EITHER IN

REVAMP OR CHANGE EQUIPMENT IS POSSIBLE...........................................103

7.1 Cases 5 and 6, Increasing Capacity of Charging Tanks...................................103

7.2 Case 7, Effect of Changing Pumping Rate Capacity. ......................................112


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7.3 Case 8, Increasing Capacity of Storage Tanks.................................................116

7.4 Chapter Summary. ...........................................................................................120

Chapter 8. CONCLUSIONS AND FUTURE WORKS ............................................122

8.1 Conclusions......................................................................................................122

8.2 Future Works. ..................................................................................................123BIBLIOGRAFY.........................................................................................................125

APENDIX A ..............................................................................................................127

A.1 Example 1 Computer hardcopy output ...........................................................127



A.4 Case 1 Computer hardcopy output..................................................................143


A.6 Case 3 Computer hardcopy output.................................................................156


APENDIX B ..............................................................................................................170


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LIST OF FIGURES

Figure 1.1- The cycle of refining operations. ................................................................3

Figure 1.2 - Optimisation Efforts for improving profitability .....................................5

Figure 3.1 - Problem Representation. ..........................................................................13Figure 4.1 Oil flow network for example 1. .............................................................38

Figure 4.2 Example 1. Storage tank optimal volume variation. ...............................40

Figure 4.3 Example 1. Charging tank optimal volume variation..............................40

Figure 4.4 Example 1. Optimal feeding to the crude distillation unit. Solid bars:

Blended oil X ; Blank bar: Blended oil Y. ...........................................................41

Figure 4.5 Example 1. Optimal component concentration variation in charging

tanks. ....................................................................................................................41

Figure 4.6 Example 1. Optimal results from the existing model (right side). ..........42

Figure 4.7 Oil flow network for example 2. .............................................................43

Figure 4.8 Example 2. Storage tank optimal volume variation. ...............................46

Figure 4.9 Example 2. Charging tank optimal volume variation.............................46Figure 4.10 Example 2. Optimal feeding to the CDU 1. Dashed bars: blended oil 2;

solid bars: blended oil 3. ......................................................................................47

Figure 4.11 Example 2. Optimal feeding to the CDU 2. Blank bars: blended oi1 1;

Dashed bars: blended oil 2; solid bars: blended oil 3. .........................................47

Figure 4.12 Example 2. Optimal concentration variation of component 1 in charging

tanks. ....................................................................................................................48

Figure 4.13 Example 2. Optimal concentration variation of component 2 in charging

tanks. ....................................................................................................................48

Figure 4.14 Example 2. Optimal results from the existing model. ..........................49

Figure 4.15 Oil flow network for example 3. ...........................................................50

Figure 4.16 - Example 3. Storage tank optimal volume variation. ..............................53Figure 4.17 - Example 3. Charging tank optimal volume variation. ..........................53

Figure 4.18 - Example 3. Optimal feeding to the CDU 1. Dashed bars: blended oil 2;


Figure 4.19 - Example 3. Optimal feeding to the CDU 2. Blank bars: blended oil 1;


Figure 4.20 Example 3. Optimal results from the existing model. ...........................55

Figure 5.1 Oil Flow Next Work for the Oil Refinery. ..............................................57

Figure 5.2 - Case1. Storage tank volume variation results. .........................................62

Figure 5.3 - Case1. Charging tank volume variation results........................................62

Figure 5.4 - Case 1. Feeding to the crude distillation unit results. Solid bars: blended

oil 1; blank bars: blended oil 2.............................................................................63

Figure 5.5 - Case 1. Crude oil sulphur content variation results in charging tanks.....65

Figure 5.6 - Case1a. Storage tank volume variation results. .......................................68

Figure 5.7 - Case1a. Charging tank volume variation results......................................68

Figure 5.8 - Case1a .Crude oil sulphur content variation results in charging tanks. ...69

Figure 5.9 - Case1b. Storage tank volume variation results. .......................................71

Figure 5.10 - Case1b. Charging tank volume variation results....................................71

Figure 5.11 - Case1b. Crude oil sulphur content variation results in charging tanks. .72

Figure 5.12 - Case1c. Storage tank volume variation results. .....................................74

Figure 5.13 - Case1c. Charging tank volume variation results....................................75


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Figure 5.14 - Case 1c. Feeding to the crude distillation unit results. Solid bars:

blended oil 1; blank bars: blended oil 2. ..............................................................75

Figure 5.15 - Case1c. Crude oil sulphur content variation results in charging tanks. .76

Figure 5.16 - Case 1d. Storage tank volume variation results. ....................................79

Figure 5.17 - Case1d. Charging tank volume variation results....................................80Figure 6.1 - Case 2. Storage tank volume variation results. ........................................87

Figure 6.2 - Case 2. Charging tank volume variation results.......................................88


oil 1; blank bars: blended oil 2.............................................................................89

Figure 6.4 - Case 2. Crude oil sulphur content variation results in charging tanks.....91

Figure 6.5 - Case 2a. Storage tank volume variation results. ......................................92

Figure 6.6 - Case 2a. Charging tank volume variation results.....................................93

Figure 6.7 - Case 2a. Feeding to the crude distillation unit. Solid bars: blended oil 1;

blank bars: blended oil 2. .....................................................................................94

Figure 6.8 - Case 2a. Crude oil sulphur content variation results in charging tanks. ..95

Figure 6.9 - Case 3. Storage tank volume variation results. ........................................96Figure 6.10 - Case 3. Charging tank volume variation. ...............................................97

Figure 6.11 - Case 3. Feeding to the crude distillation unit. Solid bars: blended oil 1;

blank bars: blended oil 2. .....................................................................................97

Figure 6.12 - Case 4. Storage tank volume variation results. ......................................99

Figure 6.13 - Case 4. Charging tank volume variation results...................................100

Figure 6.14 - Case 4. Feeding to the crude distillation unit. Solid bars: blended oil 1;

blank bars: blended oil 2. ...................................................................................100



Figure 7.3 - Case 5. Charging tank volume variation results.....................................105Figure 7.4 - Case 6. Charging tank volume variation results.....................................106


oil 1; blank bars: blended oil 2...........................................................................107



Figure 7.7 - Case 5. Crude oil sulphur content variation in charging tanks. .............110

Figure 7.8 - Case 6. Crude oil sulphur content variation in charging tanks. .............110

Figure 7.9 - Case 7c. Storage tank volume variation results. ....................................114

Figure 7.10 - Case 7c. Charging tank volume variation. ...........................................114

Figure 7.11 - Case 8. Storage tank volume variation results. ....................................117

Figure 7.12 - Case 8. Charging tank volume variation results...................................118Figure 7.13 - Case 8. Feeding to the crude distillation unit results. Solid bars: blended



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LIST OF TABLES

Table 4.1 - Comparisons of optimal results with an existing model. ..........................36

Table 4.2 - System information for Example 1............................................................39

Table 4.3 Example 1. Optimal unloading starting date for vessels. .........................39Table 4.4 - System information for Example 2............................................................44

Table 4.5 Example 2. Optimal unloading starting date for vessels. .........................45

Table 4.6 - System information for Example 3............................................................51

Table 4.7 Example 3. Optimal unloading starting date for vessels. .........................51

Table 5.1 - Case 1. Input data summary. ....................................................................60

Table 5.2 - Case 1. Unloading start and finish results. ................................................61

Table 5.3 - Case 1.Vessel volume variation (bbl x 1,000) results. ..............................61

Table 5.4 - Case 1. Results for volumetric flow rate (bbl x 1,000) per day from vessels

to storage tanks. ...................................................................................................64

Table 5.5 - Case 1. Results for volumetric flow rate (bbl x 1,000) per day from storage

tanks to charging tanks.........................................................................................64Table 5.6 - Case 1a. First change of arriving schedule. ...............................................66

Table 5.7 - Case 1a. Unloading start and finish results. ..............................................67

Table 5.8 - Case 1b. Second change of the arriving schedule. ....................................69

Table 5.9 - Case1b. Unloading start and finish results. ...............................................70

Table 5.10 - Case 1c. Bigger change of the arriving schedule. ...................................73

Table 5.11 - Case 1c. Unloading start and finish results. ............................................74

Table 5.12 - Case 1c. Vessel volume variation (bbl x 1000) results. ..........................74

Table 5.13 - Case 1c. Results for Volumetric flow rate (bbl x 1,000) per day from

storage to charging tanks. ....................................................................................76

Table 5.14 - Case 1c. Results & comparisons among different crude oil volumes for

storage tank 1. ......................................................................................................77Table 5.15 - Case 1d. Unloading start up and finish results. .......................................79

Table 5.15 - Case 1d. Results for volumetric flow rate in bbl x 1000 per day from


Table 5.16 - Case 1e. Results for volumetric flow rate (bbl x 1,000) per day from

vessels to storage tanks. .......................................................................................81

Table 5.17 Resource summary used to solves cases.................................................82

Table 6.1 - Case 2. Input data summary. ....................................................................85

Table 6.2 - Case 2.Unloading start and finish results. .................................................86

Table 6.3 - Case 2. Vessel volume variation (bbl x 1000) results. ..............................86

Table 6.4 - Case 2. Results for volumetric flow rate (bbl x 1,000) per day from


Table 6.5a - Case 2. Results for volumetric flow rate (bbl x 1,000) per day from


Table 6.5b - Case 2. Results for volumetric flow rate (bbl x 1,000) per day from


Table 6.6 - Case 2a. First change of arriving schedule. ...............................................91

Table 6.7 - Case 2a. Unloading start and finish results. ..............................................92

Table 6.8 - Case 2a. Results for volumetric flow rate (bbl x 1000) per day from


Table 6.9 - Case 3. Unloading start and finish results. ................................................96


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Table 6.10 - Case 3. Results for volumetric flow rate (bbl x 1000) per day from


Table 6.11 - Case 4. Unloading start and finish results. ..............................................99

Table 6.12 Resource summary used to solves cases...............................................101

Table 7.1 - Cases 5 and 6. Unloading start and finish results. ...................................104Table 7.2 - Case 5 and 6. Volumetric flow rate in bbl x 1,000 per day from vessels to

storage tanks.......................................................................................................108


storage to charging tanks. ..................................................................................108


storage tanks to charging tanks ..........................................................................109

Table 7.4a - Case 6. Results for volumetric flow rate (bbl x 1000) per day from




Table 7.5 - Case 6. Comparisons / different charging tank capacities.......................112Table 7.6 - Case 7. Input data summary exception....................................................112

Table 7.7a - Case 7c. Results for volumetric flow rate in bbl x 1,000 per day from


Table 7.7b - Case 7c. Results for volumetric flow rate in bbl x 1,000 per day from


Table 7.8 - Case 8. Unloading start and finish results. ..............................................117

Table 7.9 - Case 8. Results for volumetric flow rate (bbl x 1,000) per day from vessels

to storage tanks. .................................................................................................119


storage to charging tanks. ..................................................................................119Table 7.10b - Case 8. Results for volumetric flow rate (bbl x 1,000) per day from


Table 7.11 - Case 8. Comparisons / different storage tank capacities. ......................120

Table 7.12 Resource summary used to solves cases...............................................121


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NOTATION

CDU Crude Distillation Unit

CDUs Crude Distillation Units

LP Linear Programming

MILP Mixed Integer Linear Programming

MINLP Mixed Integer Non Linear Programming

NLP Non Linear Programming

LPG Liquefied Petroleum Gas

bbl Barrels

v vessel number

i storage tank number

j,y charging tank number

l crude distillation unit number

t time interval number

V vessel quantity along the scheduling horizon

I quantity of storage tanks in the system

J quantity of charging tanks in the system

L quantity of crude distillation units in the system

VE grouping of vessels or tankers

ST grouping of storage tanks

CT grouping of charging tanks

CDU grouping of crude distillation units

COMP grouping of crude oil components

SCH grouping of time intervals

VSimax

storage tank maximum capacity

VSimin

storage tank minimum capacity

VBjmax

charging tank maximum capacity

VBjmin

charging tank minimum capacity

CUv unloading cost of vessel vper unit time interval

CSEAv sea waiting cost of vessel v per unit time interval

CSINVi inventory cost of storage tank iper unit time interval


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CBINVj inventory cost of storage tank iper unit time interval

CCHANGl changeover cost of CDU l

TARRv crude oil vessel arrival date

TLEAv crude oil vessel maximum departure date

PUMPCAPv maximum pumping system capacity per vessel v

PUMPCAPi maximum pumping system capacity per storage tank i

EVv,k concentration of component kin the crude oil vessel v

ESi,k concentration of component kin storage tank i

DMCDUt,l demand of each CDU l per time interval

TOTDMCDUl total demand of each CDU lalong the scheduling horizon

DMBCOj demand of each blended crude oilj along the scheduling horizon

XFv,t binary variable denoting if vessel vstarts unloading at time t

XLv,t binary variable denoting if vessel v finishes unloading at time t

XWv,t binary variable denoting if vessel vis unloading its crude oil at time t

F i,j,t binary variable denoting if storage tank i is feeding charging tanks

D j,l,t binary variable denoting if charging tankj is feeding CDU lat time t

Z j,y,l,t binary variable for the changeover from charging tankj toy

TFv integer variable denoting vessel v unloading initiation time

TLv integer variable denting vessel v unloading completion time

VVv,t continuous variable for crude oil volume vessel v

VSi,t continuous variable for crude oil volume in storage tank i

VBj,t continuous variable for crude oil volume in charging tankj

FVS v,i,t continuous variable for flow rate from vessel v to storage tank i

FSB i,j,t continuous variable for flow rate from st. tank ito ch. tankj

FBC j,l,t continuous variable for flow rate from charging tankjto CDU lFKVS v,i,k,t cont. variable for flow rate of component kfrom vessel vto st. tank i

FKSB i,j,k,t cont. variable for flow rate of component k from st. tank ito ch. tank j

FKBC j,l,k,t cont. variable for flow rate of component kfrom st. tankj to CDU l

VKS i,k,t continuous variable for component k volume in storage tank i

VKB j,k,t continuous variable for component k volume in charging tankj

ES i,k,t continuous variable for component kconcentration in storage tank i

EB j,k,t continuous variable for sulphur concentration in charging tankj


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COST continuous variable for the total optimal operational cost

FVS v,i,tmax

maximum flow rate from vessel vto one storage tank i

FVS v,i,tmin minimum flow rate from vessel v to one storage tank i

FSB i,j,tmax maximum flow rate from storage tank i to one charging tankj

FSB i,j,tmin

minimum flow rate from storage tank ito one charging tankj

FBC j,l,tmax

maximum flow rate from charging tankjto one CDU l

FBC j,l,tmax

minimum flow rate from charging tankjto one CDU l

ESi,kmax

maximum concentration of component kin storage tank i

ESi,kmin

minimum concentration of component kin storage tank i

EBj,kmax

maximum concentration of component kin charging tankj

EBj,kmin minimum concentration of component k in charging tankj


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Chapter 1. INTRODUCTION.

1.1 Oil Refinery Optimisation.

The encouragement to optimise the production planning in oil refineries comes from

the mid fifties when the first applications of linear programming appeared for crude

oil blending and product pooling. Since then, the potential benefits of optimisation for

process operations have come continuously improving. This phenomenon has been

accentuated by the development of global competition and the emergence of

international markets generated from the eighties. Therefore, the competence has

become hard and many oil refineries and petrochemical industries are being

restructured for competing successfully in this new scenario with requirements of low

profit margin, tighter environmental regulations, and more efficient plant operation.

In addition, unit optimizers have been introduced with the implementation of

advanced control systems, generating significant gains in the productivity of the

plants. These successful results have increased the demand for more complexautomation systems that take into account the production objectives {Zhang 2000}.

However, unit optimizers determine optimal values of the process variables but

simply considering current operational conditions {Pinto, Joly, et al. 2000} within a

plant subsystem.

On the other hand, the optimisation of subsystems in the plant does not assure the

global economic optimisation of the plant. The objectives of individual subsystems in

the plant are usually conflicting among them and as consequence; they contribute to

suboptimal and many times infeasible operations. Furthermore, the lack of

computational technology for production scheduling has been the main obstacle for

the integration of production planning objectives into process operations {Barton,

Allgor, et al. 1998}. This integration would help to foresee and solve all the possible

operation infeasibilities on time.


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Oil refinery managers are increasingly concerned with improving the planning and

scheduling of their operations for achieving better results and increasing the profit

margin. The major factor that makes this labour difficult among others is the dynamic

nature of the economic environment assisted by the continuous changing of markets.

Then, oil refineries must face the potential impact of demand variations for final

product specifications, volumes requested and prices or even be able to explore

immediate market opportunities {Joly, Moro, et al. 2002}.

Furthermore, the most successful refineries are those which closely monitor their

performance, adjust properly their operations and identify the main weakness for

promptly correcting them {Zhang 2000}. There are many decisions involved to

achieve the optimal operation of an oil refinery. From the managerial level, managers

need to decide which crude oils to purchase, which oil blended compositions to

process, which products to produce, which operating rules to follow, which catalyst to

use, which operating mode to use for each process and so on. And from the process

level, operators have to determine and control the detailed operation conditions for

each equipment and subsystem in the plant. Finally, all decisions should interact the

best among each other {Zhang & Zhu 2000}.

Nevertheless, an operation cycle (See Fig. 1.1), has been proposed by {Pelham &

Pharris 1996} for oil refineries to help to integrate the main functions and achieve

profitable manufacturing by producing quality products under a safe operating

margin. The cycle starts with central planning to determine long term and mid-term

operations. Then, scheduling deals with the short term day-to-day operations.

Advanced control and on line optimisation should translate the goals set by planningand scheduling to real time process targets, which should be executed by regulatory

control. Monitoring and analysing the results will provide feedbacks to the initial

decision-making procedure. The cycles should be completed with overall refinery

optimisation. The main task consists of finding the best combination of those

decisions to maximise the overall profit. Since overall refinery optimisation almost

covers all the aspects relating to the profit making refinery operations, this is still

considered one of the most difficult and challenging optimisation tasks.


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Figure 1.1- The cycle of refining operations.

1.2 Other facts and Developments about Oil Refinery Optimisation.

As it was mentioned above since the fifties when linear programming technology

started to produce industrial applications mainly for planning purposes, considerable

research efforts have been applied for oil refinery optimisation. As a result, problems

have been formulated as linear models only because the algebraic applied between

variables are linear or can be closely approximated by linear equations. However, for

process operations which have highly non linear formulations, regarding the kinetics,

thermodynamics, hydromechanics, etc, usually the operation still is manually

controlled based on the operators experience.

The availability of LP-based commercial software for refinery production planning,

such as RPMS (Bonner and Moore, 1979) and PIMS (Process Industry Modelling

System-Bechtel Corp., 1993) have allowed the development of general production

plans for the whole refinery, which can be interpreted as general trends. Then, it is

possible to consider that planning technology is well developed, fairly standard and

widely understood and major changes could not be seen, but evolutionary changes

Planning

Monitoring

Analysis Scheduling

RegulatoryControl

Advanced controland optimisation


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could occur {Pelham & Pharris 1996 }. In fact, nowadays it already has started to

appear interesting particular development for overall plant and oil refinery production

planning using non linear programming (NLP) techniques {Moro, Zanin, et al. 1998};

{Zhang & Zhu 2000} and {Pinto & Moro 2000}. But, there are still few commercial

tools for production scheduling and these have not allowed a rigorous presentation of

plant particularities {Moro, Zanin, et al. 1998}. For that reason, refineries are

developing in-house tools strongly based on simulation in order to obtain essential

information for a given system {Magalhaes, Moro, et al. 1998 } very particular for

each refinery. Then, nowadays the efforts are strongly guided toward the development

of production scheduling packages that represent the particularities of each plant or

system. In addition, the major work expected in the future whether this development

is successful should be the integration in one integrated information system of the

production planning and the scheduling functions, which allow planners and

schedulers to operate from a single workstation using applications that have access to

the same databases.

The current situation is similar as fig. 1.2 shows. Fewer efforts have been required to

achieve the biggest benefits by preparing the strategic planning and even the

production planning using linear programming in a horizon of one month up to one

year or more. Then, linear programming has come addressing the long term planning

optimisation models achieving these objectives with no major problems. If it moves

down in the fig. 1.2; much more efforts have to be applied to increase the profit

margin in much less proportion. These are the cases related with the production

scheduling and the process operation level which should handle period of time from

hourly base to horizon up to 15 days.

On the other hand, there are some books and papers that mention specific applications

based on mathematical programming, which compare continuous LP and formulations

using MILP, MINLP or NLP and point out the low applicability of models based only

on continuous variables and discuss the lack of rigorous models for refinery

scheduling using other formulations. A mixed integer linear program (MILP) is the

extension of the LP model that involves discrete variables that help to greatly expands


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the ability to formulate and solve real-world problems, because logical decisions

(those with variables 0 or 1) can be included. Moreover, in reason of the

combinatorial nature introduced by discrete variables in MILP problems, these have

been very hard to solve. However, MILP and MINLP techniques are essential for

solving optimisation problems in the production scheduling field that mostly relies on

discrete variables.

Figure 1.2 - Optimisation Efforts for improving profitability

In summary, the integration of new technologies into process operations is an

essential profitability factor and this can be achieved by through appropriate planning

and scheduling {Joly, Moro, et al. 2002}. Therefore, the importance of on line

integration of planning, scheduling and control has come increasing. Overall plant and

oil refinery production planning presently continue relying on linear programming,

while process optimisation mainly has used either mixed integer linear (MILP), non

linear (NLP) or mixed integer non linear (MINLP) programming techniques. For

individual process or subsystem optimisations, rigorous models have been used to

optimise detailed operating conditions, such as temperatures, detailed process flow

rates, tank volume fluctuations, pressures, blending range compositions, etc. The

results of this kind of optimisation are much closer to the reality. However, there is

still no proper link so far between an overall plant linear programming (LP)

optimisation and different process optimisations in MILP, NLP or MINLP.


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1.3 Present Work.

The main purpose of this Thesis out of briefly facilitating the understanding of the

huge work that still is demanding the oil refinery optimisation at the scheduling level,

is to develop for oil refineries a new generic scheduling MILP model for optimising

the total operational cost for all the operation that involves the crude oil unloading,

inventory, blending and feeding to crude distillations units in oil refineries, that is one

of the most critical scheduling work in oil refineries due to the operational and

economic impact that it represents. Then, the model development includes the

scheduling of vessel unloading, storage and inventory control, blending and crude oil

component composition control and feeding to crude distillation units. The model

emphasises along the scheduling horizon to strictly follow all the system restrictions

i.e. crude oil component composition range; maximum pumping rate; continuous

feeding rate to guarantee regular feeding to CDUs and so on.

In addition, chapter 2 presents an overview of scheduling optimisation and briefly

reviews all the quite few developments made for production scheduling in oil

refineries pointing out their main particularities. Chapter 3 describes the problem

definition and presents the mathematical formulation of the new model; also it points

out through the chapter content the main conceptual and mathematical differences

between this new model and the model made by {Lee, Pinto, et al. 1996}.

Particularly, in chapter 4, the new model is tested applying the same conditions given

by the examples indicated by {Lee, Pinto, et al. 1996} to show the advantages of the

new model and the shortcomings of the existing model made by {Lee, Pinto, et al.

1996} comparing both results. The model presented by {Lee, Pinto, et al. 1996} isthe oldest one better illustrated found in the literature for this similar purpose and

have encouraged subsequent developments in this field.

On the other hand, some practical cases are presented along chapters 5, 6 and 7

following the request of one particular oil refinery from ECOPETROL, Colombia;

they have been solved using the model to show its advantages and strengths for

solving other examples with different conditions. However, most of the data and


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conditions used for the cases are close to the reality for whichever oil refinery. For

better understanding of these cases it is recommendable to start reviewing them from

chapter 5. Some examples and comparisons among them are shown to explain the

benefits of the model not only for production scheduling optimisation, also for helping

to discover and solve equipment limitations and to analyse the impact caused by

equipment expansion applications logically inside the production scheduling scheme,

keeping the target of the operational cost optimisation. Some of the example features

ever have been shown so far in any paper. Thus, it is demonstrated through the

examination of the cases that the new model is flexible and could be adapted to solve

similar cases in oil refineries.

Chapter 8 presents the conclusion of the Thesis and future works. Appendix A shows

partial hardcopy outputs from GAMS {Brooke, Kendrick, et al. 1998 } indicating

only the solve summary and the data used in the Thesis for all the three examples

analysed in chapter 4 and for some practical cases analysed in chapters 5,6 and 7.

Normally, one output per exercise involves more than 100 pages showing all the

features of the solving steps to get the optimal solution as well as the solution

summary and data mentioned. On the other hand, appendix B shows as an example,

the model programmed using the software GAMS, specifically for solving case 1.

Other examples and cases were run changing the input data according to the new

conditions and adding or taking away some equations or constraints according to the

model mathematical formulation explained in chapter 3.

Finally, due the handling of a huge amount of equations and variables by the model

for solving these examples and cases; definitely, the documentation was found to beindispensable for the software GAMS{Brooke, Kendrick, et al. 1998 } used to

program the model which helped to assist solving the model equations and

constraints for obtaining the optimal solutions for all the problem conditions.


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Chapter 2. OVERVIEW OF SCHEDULING OPTIMISATION

2.1 Scheduling General Concern.

The scheduling is strongly related to the planning at other levels, and it affects many

types of decisions in the oil refinery. The ability to efficiently construct high quality,

feasible and low cost schedules is therefore crucial for the refinery in order to be

competitive.

The scheduling should be concerned about which mode of operation to use in either

each process plant or each plant subsystem at each point of time, in order to satisfy the

demand for a given set of products. A mode of operation for a process plant is

specified by the combination of products consumed and produced in the process, and

by the yield levels for each of the products. Changeovers between modes of operation

cause disturbances and extra costs to the refinery. Hence, long sequences of the same

mode of operation applying few changeovers are preferred. However, long sequences

imply larger inventory volumes for some products and an increased need for storage

capacity with associate larger holding and capital costs. Thus, there must be a trade-

off between the negatives effects of frequents changeovers (feed switch and start up

costs), and the cost of keeping large inventory volumes {Goethe-Lundgren, Lundgren,

et al. 2002}.

On the other hand, scheduling models are intended to determine the timing of the

actions to execute the plan, taking in account i.e. available storage, arrivals of

feedstock (by vessels or oil pipes) and handling of blending compositions. Theyshould focus on the when to do. They investigate the limitations imposed by space

and time. Then, an accurate description of the initial inventory in all the tanks

(compositions and quantities) and a prediction of all the streams required or presented

in the boundary of the system during the coming days are needed. They should draw

attention to problems encountered in storage (overflow or shortage) and timing

(demurrage). Solving these problems may require rescheduling, reallocation of

storage facilities or even reformulation of another plan {Hartmann 1998} .


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In addition, regarding the scope of the new model developed in this Thesis; the model

is designed to help to solve all the concerns mentioned above related to the scheduling

problem. Moreover, the activities of crude oil unloading, storage, blending and

feeding operations, are considered one of the major bottlenecks in the production

chain in oil refineries and therefore, it is interesting to start assisting with the model to

solve the scheduling concerns from this area where delays imply loss of time and lack

of resources and deliveries ahead of the deadlines may cause excess of inventory. At

the end of the day, every refinery must proceed with efficient schedules regarding

theses activities within their operational planning scope.

2.2 Crude Oil Inventory Scheduling Optimisation.

Typically, an oil refinery receives its crude oil through a pipeline, which is linked to a

docking station where oil vessels or tankers unload. The unloading schedule of these

tankers is usually defined at the corporate level and can not be changed easily {Joly,

Moro, et al. 2002}. Thus, for a given scheduling horizon, the number, type and

arriving and departure times of the oil tankers are known a priori.

This thesis is focused on the production scheduling optimisation of operation modes

concerning crude oil vessel unloading, storage, blending and feed to crude distillation

units (CDUs). The new optimisation model proposes the strategic operation for the

system in accordance with the given conditions and the optimal operational cost

calculated. The strategic operation if it is feasible must follow the proposed suitable

unloading days for vessels and the proposed flow rates among vessels and tanks,

among storage and charging tanks and among tanks and plants for keeping the optimalproduction scheduling given by the model results. Moreover, this model can be used

as a viable tool not only for supporting the shipment planning, also for discovering

system infeasibilities and for strategic decisions concerning investments in storage

and pumping systems.

The purpose is to satisfy the demand while the inventory volumes and the pumping

system capacities are not violated. The shipment plan requires to be realizable in


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terms of production, and a cross checking between the shipment plan and the

corresponding required feeding to plants according to the production schedule should

be done to be sure that the feeding can be done in due time {Goethe-Lundgren,

Lundgren, et al. 2002 }. Moreover, the new optimisation model will help to do this

cross checking and answer whether a shipment plan definitely can match in terms of

production or not.

On the other hand, the need for some supporting optimisation tools for the scheduling

is also accentuated by the frequent change in the planning situation. For example, the

shipment plan may change since it is based on forecasts of demand and vessels may

arrive delayed or interchanged. Whenever a change occurs in the shipment plan, a re

scheduling of the involved system needs to be carried out in order to not lose money

stopping the possible operational cost increase by this effect. Moreover, there would

be other non planned situations for instance that could affect the production

scheduling and therefore, a rescheduling also is needed to check if the conditions are

still feasible and the optimal operational cost has not been negatively impacted i.e.

crude oil vessel unloading volume increase; cost alteration in vessel operations and so

on.

In summary, the new optimisation model can be used to evaluate whether a suggested

shipment plan is feasible or not, to evaluate the optimal operational cost incurred by a

particular shipment plant, and to support decisions on whether a shipment plan

should be changed or not. Of great importance to mention, it is also the possibility of

analysing many scenarios and to be able to make fast evaluations of consequences of

sudden changes in shipment plans, proposed changes in some tanks or pumpscapacities, etc.

2.3 Review of Production Scheduling Developments

A good mention of important contributions to the production planning and scheduling

in oil refineries already has been done through chapters 1 and 2. However, regarding

the concern of this Thesis related to the optimal operational scheduling for crude oil


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unloading, inventory , blending and feeding to CDUs, the first MILP works were

reported by {Shah 1996 }and {Lee, Pinto, et al. 1996 }.{Shah 1996} complementarily

mentions that his model could be extended to cover the design of tanks not giving any

practical example about this matter and {Lee, Pinto, et al. 1996 } particularly presents

a better illustrated model than {Shah 1996}, focused on using a continuously feed

following a demand of blended crude oils for charging the CDUs . Other

developments in this area have appeared later by {Pinto, Joly, et al. 2000}; {Joly,

Moro, et al. 2002}; {Goethe-Lundgren, Lundgren, et al. 2002} ; {Mas & Pinto 2003 }

and {Jia, Ierapetritou, et al. 2003 }. {Pinto, Joly, et al. 2000} and {Joly, Moro, et al.

2002} present a MILP problem unloading the crude oil by scheduled batches of

different composition through a single oil pipeline instead unloading from vessels;

moreover, they use only one set of tanks for managing the storage and blending

operations just before feeding the CDUs. {Goethe-Lundgren, Lundgren, et al. 2002}

emphasises the operation modes and formulates a MILP model considering an

example changing storage tank capacities for analysing future investments. {Mas &

Pinto 2003} presents a decomposition strategy applying several MILP models for

each subsystem of a large system analysed which has events too difficult to solve

simultaneously and {Jia, Ierapetritou, et al. 2003 } propose a solution which leads to a

MILP model with fewer binary and continuous variables and fewer constraints saving

computer time; moreover, their model was tested using the same condition data of the

examples of {Lee, Pinto, et al. 1996 }; nevertheless, the results from {Jia, Ierapetritou,

et al. 2003} show that the optimal operational costs have increased for three out of

four examples of {Lee, Pinto, et al. 1996 }; specifically, 8.76 % more for example 1,

10.82% more for example 2 and 1.98 % more for example 4; example 3 presents a

reduction of 3.68 %; but, they do not present any explanation with respect to the costincrease.

On the other hand, considering another section of the oil refinery, few developments

for the production scheduling optimisation have been done for particular process

plants in oil refineries. These applications should involve models developed using

MILP or MINLP techniques. {Joly, Moro, et al. 2002} develops a MINLP model for

managing the production scheduling problem in a fuel oil and asphalt plant including


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its inventory control and distribution; but the MINLP is transformed to a MILP

because no global solution was guaranteed by the convectional MINLP solution

algorithms due to the bilinear terms in the viscosity constraints. {Magalhaes, Moro,

et al. 1998} describes the development of an integrated production scheduling system

(SIPP) for an oil refinery that at the date of the paper publication was in

commissioning. The system integrates other refinery applications and databases and

the MILP optimisation techniques; but they do not refer to any interface done between

the LP-tool at the planning level and the tools used at the scheduling level. Even at the

scheduling level is not mentioned any interface among the applications that works at

this level and the MILP optimisation techniques used. The SIPP user has to apply an

iterative process until the scheduling programme is feasible. Moreover, special care

should be applied to identify is the feasible solution is the optimal. On the other hand,

process units models are presented as steady-state based in the data input from the

LP-planning and instead, tanks and pipelines have transient models. Separately, they

mention an application using MILP techniques to assist the scheduling production of

the LPG area and their future intention to be managed by the SIPP.

Finally, regarding the production scheduling optimisation of finished product

blending , storage and distributions, it has been other developments by {Breiner Avi

& Maman 2001 } and {Jia & Ierapetritou 2003}. {Breiner Avi & Maman 2001}

introduces a MINLP developed system (MPMP) successfully installed in an oil

refinery for managing and optimising the final product blending and storage

production scheduling. The MINLP is extremely difficult to solve satisfactorily and

hence, they use a four step algorithm and separate the MILP from the NLP operation

for solving it. On the other hand, {Jia & Ierapetritou 2003} introduces a MILP modelto manage the operation of gasoline finished products in an oil refinery, specifically

blending, storage and distribution pipelines.


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Chapter 3. PRODUCTION SCHEDULING PROBLEM

DEFINITION.

This chapter presents the problem definition and the mathematical formulation of the

production scheduling optimisation problem for the unloading, storage, blending and

feeding of an oil refinery. The new model will be formulated using general notation

showing the possibility of using the model for a general problem of this matter.

3.1 Problem Definition

The system configuration for this production scheduling optimisation modelcorresponds to a multistage system consisting of vessels, storage tanks, charging

tanks, and CDUs as is illustrated in fig.3.1.

Figure 3.1 - Problem Representation.

For a given scheduling horizon, crude oil vessels arrive to the refinery docking station

which only allows one vessel for unloading. In accordance with the planning level

each vessel will have a reasonable date for leaving that should be at most the date that

the next vessel arrives. The day one vessel arrives could start to unload depending of


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the optimal results recommended by the model in accordance with all the current

conditions of the system analysed. The day one vessel finishes unloading should be up

to one day before its maximum departure date fixed at the planning level; the reason is

because the maximum departure date allowed for the preceding vessel is the same

planned arriving date of the next vessel and potentially this next vessel could start

unloading on the arriving date. Instead {Lee, Pinto, et al. 1996} is not clear in their

model description about the established limit for the vessel departure date after it has

completed unloading. Each time that a vessel rescheduling is done, the maximum

departure dates for vessels are reformulated in accordance with the new arriving dates

for each vessel and both will be new input conditions to the optimisation model for

avoiding basic interferences.

The crude oil is unloaded into storage tanks at the docking station and the problem

considers one pre selected storage tank per vessel that manages the same crude oil

composition of the vessel. Then, the crude oil is transferred from storage tanks to

charging tanks. Each crude oil inside the charging tank must carry out to be within a

range of blended crude oil composition determined at the planning level for the

scheduling horizon. The fulfilment of this blended composition range is made per tank

having in account the material balance of the remaining volume and the different

flows coming in or coming out the tank with their different compositions per time

interval. Then, blended crude oils from charging tanks are charged into the CDUs and

whenever that it is optimally required feed switches are done from one kind of

blended crude oil to another for each CDU. Finally, it is important to mention that

whether a charging tank is feeding a CDU, it must not be fed by any storage tank or

vice versa.

In addition, there will be probably special problems that could consider more storage

tanks than crude oil vessels and therefore, vessels have to unload to more than one

storage tank. This situation could be managed by the optimisation model carrying out

a pre established crude oil blended composition range in each storage tank like

charging tanks. Then, storage tanks have to carry out blending material balance

conditions and limitations the same presented in charging tanks i.e. they must not be


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fed by vessels if they are feeding charging tanks or vice versa. Through the model

mathematical explanation, the equations that should be used to solve this particular

problem will be pointed out. This situation makes more difficult the solving solution

as it will be illustrated solving the example 3 of {Lee, Pinto, et al. 1996} in chapter 4.

On the other hand, the new model for the production scheduling optimisation

developed in this Thesis is concerned to meet a feed demand per each crude

distillation unit (CDU) and not concerned instead to meet a fixed demand of a specific

blended crude oil demand for charging the CDUs along the scheduling horizon,

disregarding the allowed charging rate variation per each CDU as {Lee, Pinto, et al.

1996} presents. However, the new model easily can be configured selecting the

properly required solving option depending on the desirable kind of demand for the

problem. Furthermore, to meet a feed demand to each plant does not mean that the

control of charging different blended crude oils will be lost; although, there is not a

fixed amount of blended oil to consume along the scheduling horizon, the manager

could know what kind of blended oil will optimally charge each CDU following its

feed changeovers i.e. either high or low sulphur content crude oil. Moreover, to meet

a feed demand guarantees the stable running of the plant along the scheduling horizon

and a clear understanding of the production planning fulfilment.

Although {Lee, Pinto, et al. 1996} shows in their existing model the operating

constraints for the flow rate variation, it is not clear how they manage the restriction

to total flow rates variation among vessels and tanks and among storage and charging

tanks. This new model totally takes care about this situation that is very important in

real situations in accordance with the pumping system capacities and the real flow

limitations with respect to pumping in parallel to different tanks from one single

source that could be either a tank or a vessel.

On the other hand, {Lee, Pinto, et al. 1996} compares the results from their example 1

and made comparisons between ruled based schedule and optimal schedules.

Regarding this matter, it is understood that ruled based or heuristic schedules are not

the best and therefore, this Thesis is interested not only to find the optimal schedules


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and the optimal operational cost for each situation, also in exploring and analysing

how the optimal operational cost of the system could be improved, for instance

attending one manager concern like this: If there is some money to invest in the

feeding system to plants, what we should do to reduce the optimal operational cost

and simultaneously getting at each time interval (day) the feeding rates to plants

closer or equal to the maximum capacity as well. Finally, it is possible to observe

other own particularities of this new model along the model presentation and

explanation in this chapter.

3.2 Optimisation Model Formulation Introduction

Given the configuration of this multistage system and the arrival time of the vessels,

the equipment capacity limitations and the key component concentration ranges for

crude oils, the problem will focus on determine the following operating variables to

minimise costs:

a. Waiting time for each vessel in the sea after arriving.

b.

Unloading duration time for each vessel.

c. Crude oil unloading rate from vessels to storage tanks.

d. Crude oil transfer and blending rates from storage tank to charging tanks.

e. Inventory volumes of storage and charging tanks.

f. Crude distillation unit charging rates fulfilling the demand per each CDU.

Instead {Lee, Pinto, et al. 1996} sets to fulfil a demand of blended crude oils.

g. Sequence of type of blending crude oil to be charged in each CDU in

accordance with the optimal mode changeovers.

The following are the operating rules that have to be obeyed:

a. In the scheduling horizon each vessel for unloading should arrive and leave

the docking station.

b. If a vessel does not arrive at the docking station, it can not unload the crude

oil.


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c. If a vessel leaves the docking station, it can not continue unloading the crude

oil.

d. The vessel can start unloading the same arriving date.

e.

The vessel can not unload on its maximum departure date. Except for the last

vessel.

f. While the charging tank is charging one CDU, crude oil can not be fed into

the charging tank and vice versa.

g. Each charging tank can feed at most one CDU at one time interval.

h. Each CDU is charged by only one blended crude oil at one time interval.

On the other hand these are the following operating constrains that must be met:

a. Equipment capacity limitations: Tank capacity and pumping rate.

b. Quality limitations of each blended crude oil: Range of component

concentrations in each blended crude oil.

c. Demand per interval of time (day) of each CDU. Instead {Lee, Pinto, et al.

1996}sets up to follow a demand of each blended crude oil for the scheduling

horizon.

The model minimises the operation cost for the total system shown. The model is

formulated using general notation and MILP formulation, showing the possibility of

using the model for a general problem of this matter. In order to develop the multi-

period MILP model, continuous and binary variables are associated with the system

network. The following are the assumptions for the proposed model:

a. Only one vessel docking station for crude oil unloading is considered.

b. The time applied for the changeover are neglected and also the transient flows

generated during either start up or shut down when a changeover is done.

c. Perfect blending is assume for each charging tank while it is being fed by

different crude oils, and additional blending time inside the tank is not

required before it charges the CDU.


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d. The composition of the crude oil is decided by the amount of key components

presented in the crude oil or in the blended crude oil. In general, sulphur is at

least one of the key components for differentiating between crude oils.

A uniformed discretisation is chosen in the given scheduling horizon for the proposed

scheduling model. The selection of the length of each discretised time span involves a

trade off between accurate operation and computational effort. The reviewed cases in

this thesis involve 15 time intervals during the scheduling horizon. Instead, the 3

examples of {Lee, Pinto, et al. 1996}reviewed in this Thesis involve 8, 10 and 12

time intervals respectively.

The optimisation problem involves the following sets, parameters and variables:

Sets

VE= {v = 1, 2... V/ crude oil vessel or tankers}

ST= {i = 1, 2... I/ storage tanks}

CT= {j,y = 1, 2... J/ charging tanks}

COMP= { k = 1, 2... K/ crude oil components}

CDU= {l = 1, 2... L/ crude distillation units}

SCH= {t = 1, 2... T/ time intervals along the scheduling horizon}

Parameters

VSimax

: storage tank maximum capacity.

VSimin

: storage tank minimum capacity.

VBjmax

: charging tank maximum capacity.

VBjmin

: charging tank minimum capacity.

CUv : unloading cost of vessel vper unit time interval.

CSEAv : sea waiting cost of vessel vper unit time interval.

CSINVi : inventory cost of storage tank iper unit time interval.

CBINVj: inventory cost of charging tankjper unit time interval.

CCHANGl: changeover cost of CDUl.


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TARRv: crude oil vessel arrival date to the docking station.

TLEAv: crude oil vessel maximum departure date from the docking station.

PUMPCAPv: maximum pumping system capacity or total flow capacity from each

vessel vto storage tanks.

PUMPCAPi :maximum pumping system capacity or total flow capacity from each

storage tank ito charging tanks.

EVv,k : concentration of component kin the crude oil vessel v.

ESi,k : concentration of component kin the crude oil of storage tank i.

ESi,kmin

: minimum concentration of component k in the blended crude oil of storage

tank i.

ESi,kmax: maximum concentration of component k in the blended crude oil of storage

tank i.

EBj,kmin: minimum concentration of component k in the blended crude oil of charging

tankj.

EBj,kmax

: maximum concentration of component k in the blended crude oil of

charging tankj.

DMCDUt,l : demand of each CDU l per time interval.

TOTDMCDUl : total demand of each CDU l along the scheduling horizon.

DMBCOt,j : demand of each blended crude oilj along the scheduling horizon. It will

be used to solve the examples of {Lee, Pinto, et al. 1996}.

FVS v,i,tmax:maximum crude oil rate from vessel vto one storage tank i.

FVS v,i,tmin:minimum crude oil rate from vessel v to one storage tank i. This variable

is not mandatory to have a value. It could be either 0 or a positive value depending of

the minimum flow restriction for the vessel pumping system that normally is assisted

working in series with the refinery pumping system to storage tanks.FSB i,j,t

max: maximum crude oil rate from storage tank ito one charging tankj.

FSB i,j,tmin

: minimum crude oil rate from storage tank ito one charging tank j. By

default this parameter has a value of 0 as the minimum value. A small optimal flow

rate if it is optimally required could be managed with centrifugal pumps and process

control instrumentation.


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FBC j,l,tmax

: maximum crude oil rate from charging tankjto one CDU l. In general

this value corresponds to the maximum CDU lfeed capacity or it could be adjusted to

a lower value.

FBC j,l,tmin: minimum crude oil rate from charging tank jto one CDU l.This value

could be adjusted to the same valueDMCDUt,l, depending on the problem conditions.

Binary variables

XFv,t : variable to denote if vessel vstarts unloading at time t.

XLv,t : variable to denote if vessel vfinishes unloading at time t.

XWv,t : variable to denote if vessel vis unloading its crude oil at time t.

F i,j,t : variable to denote if the crude oil blended in storage tank iis feeding charging

tanks at time t; otherwise storage tank icould be being fed by vessel v.

D j,l,t : variable to denote if the crude oil blended in charging tankjcharges CDU lat

time t; otherwise charging tankjcould be being fed by storage tanks.

Z j,y,l,t : variable to denote switch of the blended crude oil fed to CDU l from the

charging tankjto the chargingy.

In teger variables

TFv : vessel v unloading initiation time.

TLv : vessel v unloading completion time.

Continuous variables

VVv,t: volume of crude oil in vessel v at time t.

VSi,t: volume of crude oil in storage tank i at time t.

VBj,t: volume of crude oil in charging tankj at time t.FVS v,i,t: volumetric flow rate from vessel vto storage tank i at time t.

FSB i,j,t: volumetric flow rate from storage tank i to charging tankj at time t.

FBC j,l,t: volumetric flow rate from charging tankj to CDU l at time t.

FKVS v,i,t: volumetric flow rate of component k from vessel v to storage tank i at time

t.

FKSB i,j,k,t: volumetric flow rate of component k from storage tank i to charging tankj

at time t.


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FKBC j,l,k,t: volumetric flow rate of component kfrom storage tankj to CDU lat time

t.

VKS i,k,t : volume of component kin storage tank iat time t.

VKB j,k,t : volume of component kin charging tankjat time t.

ES i,k,t : concentration of component k in the blended crude oil of storage tank iat

time t.

EB j,k,t : concentration of component k in the blended crude oil of charging tank j at

time t.

COST : total optimal operational cost.

In itial conditions

VVv, TARRv : initial volume of crude oil vessel at time equal TARRv .

VSi,1 : initial volume of storage tank iat time equal 1 in the start up of the scheduling

horizon.

VBj,1 : initial volume of charging tank j at time equal 1 in the start up of the

scheduling horizon.

ES i,k,1 : concentration of component kin the blended crude oil of storage tank iat

time tequal 1 in the start up of the scheduling horizon.

EB j,k,1 : concentration of component kin the blended crude oil of charging tank jat

time tequal 1 in the start up of the scheduling horizon.

VKS i,k,1 : initial volume of component kin storage tank iat time tequal 1 in the start

up of the scheduling horizon .

VKB j,k,1 : initial volume of component kin charging tank jat time tequal 1 in the

start up of the scheduling horizon.

3.3 Model Mathematical Formulation.

The model focus on minimising the following operation cost of the system for the

operations of crude oil vessel unloading, storage, blending and feeding to crude

distillation units in an oil refinery. Then, this is the main objective equation that

represents the total operation cost of the system:


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V V

COST = [(TLv -TFv + 1) CUv ] + [ (TFv - TARRv ) CSEAv ] +v=1 v=1

I T

[ (VSi,t+ VS i,t+1) CSINVi/2] +i=1 t=1

J T

[ (VB j,t+ VS j,t+1) CBINVj/2] +j=1 t=1

J J L T

(CCHANGl Z j,y,l,t) (3.1)j=1 y=1 l=1 t=1

The above equation is subjected to the following constrains:

3.3.1 Vessel Arrival and Departure Operation Rules.

Each vessel must arrive to the docking station for unloading only once through the

scheduling horizon:

T

XFv,t = 1 , v VE (3.2)t=1

Each vessel leaves the docking station only once through the scheduling horizon:

T

XLv,t = 1 , v VE (3.3)t=1

The unloading initiation time is denoted by the following equation:

T

TFv = tXFv,t , v VE (3.4)t=1

The unloading completion time is denoted by the following equation:

T

TLv = tXLv,t , v VE (3.5)

t=1


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Each vessel must start unloading either after or on the arrival time established at the

planning level:

TFv TARRv , v VE (3.6)

Each vessel must finish unloading up to one interval of time before the maximum

departure time established at the planning level:

TLv < TLEAv , v VE , v V (3.7)

Except for the last vessel:

TLv TLEAv , v = V (3.8)

Minimum duration of the vessel unloading is two time intervals:

TLv - TFv 1 , v VE (3.9)

The preceding vessel must finish unloading one time interval before the next vessel in

the sea arrives and starts to unload:

TFv+1 TLv + 1 , v VE (3.10)

Unloading of vessel vonly will be possible between time TFv and TLv:

T

XWv,t XFv,t , t m , v VE,t=1

m { m= TARRv , TLEAv} (3.11)

T

XWv,t XLv,t , t >m , v VE,t=1

m

{ m= TARRv , TLEAv} (3.12)


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3.3.2 Material Balance Equations for the Vessel.

The crude oil in vessel vat time t+1 must be equal to the crude oil in vessel vat time t

taking away the crude oil transfer from vessel v to storage tank iat time t:

VVv,t= VVv, TARRv , t = TARRv (3.13)

I

VV v,t+1 = VVv,t - FVS v,i,t , v VE , t SCH (3.14)i=1

The crude oil of each vessel vhas different composition. Then, if there is one storage

tank assigned to each vessel, the solution must guarantee that the crude oil from each

vessel vis transferred to the corresponded storage tank iwhich will handle the same

vessel crude oil composition. Then, for this general case, iis equal to v to identify the

respective storage tank for the vessel:

I T I T

FVS v,i,t = FVS v,i,t , v VE,

i=1 t=1 i=1 t=1

i=v(only valid for one side of the equation) (3.15)

If there is more storage tanks than vessels, the problem could consider managing

crude oil blending composition ranges per storage tank and then, each vessel could

optimally unload to several tanks meeting with the pre established blending range for

each storage tank as it was explained above. Whether this is the case, equation 3.15 is

not useful and must not be used for this situation. However, instead the following

equation should be used to control the total flow from each vessel to storage tanks

within a reasonable margin:

I

FVS v,i,t PUMPCAPv , v VE, t SCH (3.16)i=1


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Cassio R. Tamara Oil Refinery Scheduling Optimis

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Tesis Tamara Cassio