OPTIMISATION OF DIESEL AND

GASOLINE BLENDING OPERATIONS

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy

In the Faculty of Engineering and Physical Sciences

2016

Shixun Jiang

Centre for Process Integration

School of Chemical Engineering and Analytial Science

 Table of Contents

Table of Contents ......................................................................................................... 2

List of Figures .............................................................................................................. 5

List of Tables ................................................................................................................ 6

Abstract ........................................................................................................................ 8

DECLARATION ........................................................................................................ 10

Copyright Statement .................................................................................................. 11

Acknowledgement...................................................................................................... 13

Chapter 1 Introduction ............................................................................................... 14

1.1 Diesel ................................................................................................................... 14

1.2 Diesel production................................................................................................ 19

1.3 Hierarchy of decision making for diesel production ....................................... 22

1.3.1 Distinguishing between planning and scheduling ........................................ 23

1.3.2 Definition of planning ..................................................................................... 23

1.3.3. Definition of scheduling ................................................................................. 24

1.3.4 Relation of planning and scheduling ............................................................. 24

1.4 Challenges in diesel production blending ........................................................ 25

1.5 Objective of this work ........................................................................................ 28

1.6 Structure of the thesis ........................................................................................ 28

Chapter 2 Existing Work on Diesel Blending Optimization ...................................... 30

2.1 Introduction ........................................................................................................ 30

2.2 Diesel fuel technology......................................................................................... 30

2.2.1 Diesel engine .................................................................................................... 30

2.2.2. Diesel fuel properties...................................................................................... 31

2.3 Predictions of diesel blending properties ......................................................... 38

2.4 Methods for diesel blending optimisation ........................................................ 38

2.5 Planning and scheduling methods in refineries ............................................... 39

2
2.5.1 Refinery planning............................................................................................ 39

2.5.2 Scheduling ........................................................................................................ 43

2.5.3 Time Representation ....................................................................................... 47

2.5.4 Process sequences ............................................................................................ 49

2.6 Summary ............................................................................................................. 52

Chapter 3 Modelling and Optimisation of Diesel Blending Planning ....................... 54

3.1 Introduction ........................................................................................................ 54

3.1.1 Diesel blending................................................................................................. 54

3.1.2 Diesel blending Methods ................................................................................. 56

3.1.3 Motivation ........................................................................................................ 57

3.2 Model development ............................................................................................ 58

3.2.1 Mathematical modelling ................................................................................. 58

3.2.2 Model validation.............................................................................................. 66

3.3 Solution strategy ................................................................................................. 67

3.4 Case study ........................................................................................................... 69

3.5 Summary ............................................................................................................. 74

Nomenclature ............................................................................................................. 75

Chapter 4 Scheduling of refinery diesel blending ...................................................... 77

4.1 Introduction ........................................................................................................ 77

4.2 Problem definition.............................................................................................. 78

4.3 Mathematical model .......................................................................................... 80

4.4 Solution algorithm.............................................................................................. 83

4.5 Case study ........................................................................................................... 85

4.5.1 Basic information ............................................................................................ 85

4.5.2 Solving process ................................................................................................ 87

4.6 Summary ............................................................................................................. 91

Nomenclature ............................................................................................................. 93

Chapter 5 Modelling and Optimisation of Gasoline Blending Scheduling ............... 95

3
5.1 Introduction ........................................................................................................ 95

5.1.1 Gasoline ............................................................................................................ 95

5.1.2. Gasoline blending ........................................................................................... 95

5.2 Existing gasoline property correlations ........................................................... 98

5.2.1 Octane number ................................................................................................ 99

5.2.2 RVP................................................................................................................. 100

5.2.3 Boiling range.................................................................................................. 101

5.3 Mathematical model ........................................................................................ 101

5.3.1 Planning model .............................................................................................. 102

5.3.2 Model validation............................................................................................ 104

5.3.3 Scheduling model .......................................................................................... 105

5.4 Case study ......................................................................................................... 106

5.5 Summary ........................................................................................................... 112

Nomenclature ........................................................................................................... 114

Chapter 6 Conclusions and future work ................................................................... 116

6.1 Conclusions ....................................................................................................... 116

6.2 Future work ...................................................................................................... 117

References ................................................................................................................ 119

Appendix A Diesel blending optimization in GAMS ........................................... 127

Appendix B Diesel blending scheduling optimization in GAMS ............................ 152

4
 List of Figures

Figure 1.1 Diesel and Petrol Sales in UK (UKPIA, 2015)................................. 15

Figure 1.2 A modern Refinery (chevron, 1998) ................................................. 22

Figure 1.3 Hierarchical management levels ....................................................... 25

Figure 2.1 A typical diesel engine(Chevron,1998) ............................................ 31

Figure 2.3 Discrete-time representation ............................................................. 48

Figure 2.4: Continuous-time representation ....................................................... 49

Figure 2.5 Example of State-Task Network ....................................................... 50

Figure 2.6 Example of State-Task Network ....................................................... 51

Figure 3.1 Diesel blending ................................................................................. 56

Figure 4.1 Illustration of a blending problem .................................................... 78

Figure 4.2 Solving Algorithm ............................................................................ 84

Figure 4.3 Inventories of feedstocks during the blending process ..................... 90

Figure 4.4 Inventory of products during the blending process .......................... 90

Figure 4.5 Gantt Chart for the scheduling result ................................................ 91

Figure 5.1 A schematic of the gasoline blending streams .................................. 96

Figure 5.2 Inventory of products ...................................................................... 111

Figure 5.3 Inventory of feedstocks .................................................................. 111

Figure 5.4 Gantt Chart for the scheduling result .............................................. 112

5
 List of Tables

Table 1.1 U.S. requirements for diesel fuel oils ................................................. 17

Table 1.2 Diesel Fuel Requirements in Europe .................................................. 17

Table 1.3 Temperate climate grades of diesel fuel in Europe ............................ 18

Table 1.4 Arctic climate grades of diesel fuel in Europe ................................... 18

Table 1.5 Selected specifications of diesel fuel for motor vehicles ................... 19

Table 3.1 Blending ratio ..................................................................................... 67

Table 3.2 Measured properties of blending components and product ............... 67

Table 3.3 the regressed coefficients for the boiling range.................................. 67

Table 3.4 Feedstock availability and properties ................................................. 70

Table 3.5 Product specifications ........................................................................ 70

Table 3.6 Parameters regressed for boiling range prediction ............................. 71

Table 3.7 Properties of each product .................................................................. 72

Table 3.8 Comparison between two results of the proposed model and LP model

.................................................................................................................... 72

Table 3.9 Comparison of linear result CFPP and Validated CFPP ..................... 73

Table 4.1 Feedstock properties ........................................................................... 86

Table 4.2 Product specifications ........................................................................ 86

Table 4.3 Inventory and daily requirements of products.................................... 87

Table 4.4 The First Blending Recipe from the NLP model................................ 88

Table 4.5 New Productions by the MILP model ................................................ 88

Table 4.6 Productions properties of the optimal solution .................................. 89

Table 5.1 Applied models for nonlinear properties .......................................... 104

Table 5.2 Gasoline blending model validation ................................................. 105

Table 5.3 Properties of streams and additives .................................................. 107

Table 5.4 Product specifications and prices ..................................................... 108

Table 5.5 Inventory and daily requirements of products.................................. 108

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Table 5.6 Detailed product composition and production ................................. 110

Table 5.7 Blended product properties (nonlinear blending) ............................. 110

7
 Abstract

Diesel, one of the main petroleum products, is widely used in industry and

transportation. Only high quality diesel product can survive in the more and more

competitive market. The optimization methodology for diesel production and

management is critical to refineries’ profitability.

LP/MIP models have been applied in diesel blending planning and scheduling in the

last decades. With the benefits of reducing the model scale and computing efforts,

LP/MIP models lead to operation results with inaccurate property estimation and

profit loss due to the accuracy loss in the linearisation of blending models. To

improve model accuracy, more accurate property prediction models for diesel

blending should be incorporated into the refinery planning and schedule methods to

improve decision making procedure in the case of scheduling for diesel blending,

where academic effort is almost absent.

A model for planning of refinery diesel streams is developed to optimise the diesel

production of a refinery. Nonlinear blending models are applied to calculate blending

properties more precisely than conventional linear models. Due to the large number

of equations and variables, it may be generated to an infeasible solution if the given

initial points are not good enough. To avoid this situation, a solution algorithm is

proposed. Based on the NLP planning model, a model for scheduling diesel blending

is developed. In order to improve the model accuracy, nonlinear blending

correlations are used, which lead to a complicated MINLP problem that cannot be

solved by existing MINLP solver directly. A robust solution algorithm is proposed in

this thesis to help optimizing the MINLP problem. A case study of diesel production

blending scheduling is introduced to illustrate how to model a diesel blending

scheduling problem and the efficient and reliability of the solution algorithm.

8
Besides, the proposed MINLP model and the solution algorithm can be extensively

applied to other processes in a refinery, such as gasoline blending. Once gasoline

blending models are taken into account, the model can be modified to optimize the

gasoline blending scheduling problem.

9
 DECLARATION

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.

Shixun Jiang Manchester, 2016

10
 Copyright Statement

The author of this thesis (including any appendices and/or schedules to this thesis)

owns any copyright in it (the “Copyright”) and he has given The University of

Manchester the right to use such Copyright for any administrative, promotional,

educational and/or teaching purposes.

Copies of this thesis, either in full or in extracts, may be made only in accordance

with the regulations of the John Rylands University Library of Manchester. Details

of these regulations may be obtained from the Librarian. This page must form part of

any such copies made.

The ownership of any patents, designs, trademarks and any and all other intellectual

property rights except for the Copyright (the “Intellectual Property Rights”) and any

reproductions of copyright works, for example graphs and tables (“Reproductions”),

which may be described in this thesis, may not be owned by the author and may be

owned by third parties. Such Intellectual Property Rights and Reproductions cannot

and must not be made available for use without the prior written permission of the

owner(s) of the relevant Intellectual Property Rights and/or Reproductions.

Further information on the conditions under which disclosure, publication and

exploitation of this thesis, the Copyright and any Intellectual Property Rights and/or

Reproductions described in it may take place is available from the Head of School of

Chemical Engineering & Analytical Science.

11
Dedicated to my dearest parents and wife

12
 Acknowledgement

I would like to express my sincere appreciation to my supervisor, Dr. Nan Zhang,

who provides continuous guidance, support and advice throughout the period of my

research. Without his persistent help, this dissertation would not have been possible.

I sincerely thank School of Chemical Engineering and Analytical Science, and

Centre for Process Integration, for providing an extraordinary academic environment

for me to do my research.

My deepest thank to my wife, my parents and all my other family members, for their

love and company through my life.

I would like to give special thanks to Dr. Luyi Liu and other colleagues and teachers

from CPI for their kind help and cheerful spirit.

13
 Chapter 1 Introduction

1.1 Diesel

The name ‘diesel’ comes from the German inventor and mechanical engineer who

invented diesel engine. Today, diesel engines are used worldwide for transportation,

manufacturing, power generation, construction, and farming. Their success comes

from their efficiency, economy, and reliability. Sales of on-road diesel fuel in the U.S.

rose from 32 billion gallons in 1999 to over 37 billion gallons in 2004, an increase of

nearly three percent annually. In UK, road diesel fuel sales increase from 11 billion

litres in 1988 to 28 billion litres in 2013 (Vandervell, 2015). Over the period to 2030,

energy analysts forecast that diesel demand will continue to grow and petrol demand

to decline, albeit both at a much slower rate than that seen in the last decade (IHS,

2013).

Diesel fuel is a mixture of hydrocarbons obtained from oil petroleum. Its boiling

points are normally in the range of 150 to 380°C. It is produced from oil refineries

by refining and converting crude oil into various hydrocarbon fractions. The

beginnings of the oil refining industry date back to 1859, when crude oil was

discovered in Pennsylvania. The first product refined from crude was kerosene,

which was used as lamp oil (Chevron 1998). Since only a fraction of the crude could

be refined into kerosene, quantities of petroleum by-products were wasted. These

petroleum by-products attracted the attention of Rudolf Diesel, the inventor of

compression ignition reciprocating engine. Although the original design by Rudolf

didn’t work, the engine concept was re-designed by other engineers, resulting in a

successful prototype in 1895. Both the engine and the fuel still bear the name of

Diesel.

14
Nowadays, diesel has become one of the most important petrol products due to its

high and increasing demand globally. From Figure 1.1, sales of diesel in UK have

been steadily increasing for the last twenty years, with demand exceeding 27 billion

litres in 2014. Meanwhile, Sales of petrol have been falling since reaching a peak of

33 billion litres in 1990, which was equivalent to 73% market share of transport fuels.

Till the end of 2014, sales of petrol have fallen to below 17 billion litres. However,

after barring a short decline period in 2008 and 2009 due to the economic recession,

sales of diesel has increased to around 27 billion litres till the end of 2014.

Figure 1.1 Diesel and Petrol Sales in UK (UKPIA, 2015)

15
The increasing in diesel sales in UK is part of a Europe-wide trend, which has

largely been fiscally driven for over two decades (UKPIA, 2015). In 2004, petrol

sales were 4 billion litres greater than those of diesel, whilst annual registration of

new diesel vehicles was still only one third of the total vehicle fleet. A key reason for

this relatively slow uptake had been the lack of any tax advantage for diesel, which is

taxed at the same rate as petrol. However, with the advances achieved in diesel

engine performance leading to improved fuel efficiency relative to petrol, combined

with changes in company car personal tax policy and VED (Vehicle Excise Duty)

rates, consumers in recent years have increasingly favoured diesel cars. Today,

approximately 53% of new registered vehicles in the UK are diesel fuelled (up from

49% in 2013), and over 61% of the 44 billion litres of road fuels sold in 2014 was

diesel.

For diesel engine technical and environmental reasons, there are strict diesel fuel

specifications including many property requirements. In U.S., the ASTM D975

standard covers seven grades of diesel. The specifications are presented in Table 1.1.

Grade No.1 –D and No.2 –D both are consisted of 3 sub-grades: S5000, S500 and

S15. The ASTM D975-04 edition of the standard first adopted the ‘Sxxx’ designation

to distinguish grades by sulfer content. The S5000 grades correspond to the “regular”

sulfer grades, the previous No. 1-D and No. 2-D. S500 grades correspond to the

previous “Low Sulfer” grades (D975-03). S15 grades are commonly referred to as

“Ultra-Low Sulfer” grades or ULSD in which the maximum requirement for sulfur

content 15 ppm.

European Union Directive sets specifications for fuels to be used in Europe. For

compression ignition engine fuels, the technical properties regulated by this directive

include: cetane number, sulfer content, polycyclic aromatic hydrocarbons, density

and some distillation characteristics, which are presented in Table 1.2.

16
 Table 1.1 U.S. requirements for diesel fuel oils

Property Test Method No.1-D No.2-D No.4-D

Flash Point, °C , min D 93 38 52 55
Water and sediment, % vol, max. D 2709 0.05 0.05 -
D 1796 0.5
Distillation temperature, °C, D 86
90% Volume Recovered:
min 282
max 288 338
Kinematic Viscosity, mm 2/s at 40°C D 445
min 1.3 1.9 5.5
max 2.4 4.1 24.0
Ash, % mass, max. D 482 0.01 0.01 0.1
Sulphur, ppm ,max D 5453 15 15 -
Copper Strip Corrosion Rating D 130 No.3 No.3 -
Cetane Number, min D 613 40 40 30
Cloud Point, °C, max D 2500 Varies Varies -
Ramsbottom carbon residue, max D 524 0.15 0.35 -
Lubricity, 60°C,max D 6079 520 520 -

Table 1.2 Diesel Fuel Requirements in Europe

Diesel Specification Parameter Units Limits Test Method

Cetane Number 51.0 minimum EN ISO 5165
Cetane Index 46.0 minimum EN ISO 4264
Density at 15°C kg/m3 820 minimum to 845 EN ISO 3675
maximum EN ISO 12185
Polycyclic Aromatic Hydrocarbons % (m/m) 11 maximum EN 12916
Sulphur Content mg/kg 10.0 maximum EN ISO 20846
EN ISO 20847
EN ISO 20884
Flash Point °C >55 EN ISO 2719
Carbon Residue (on 10% Dist. Residue) % (m/m) 0.30 maximum EN ISO 10370
Ash Content % (m/m) 0.01 maximum EN ISO 6245
Water Content mg/kg 200 maximum EN ISO 12937
Total Contamination mg/kg 24 maximum EN 12662
Copper Strip Corrosion (3 Hours at 50°C) class 1 EN ISO 2160
Oxidation Stability g/m3 25 maximum EN ISO 12205
Lubricity, WSD at 60°C μm 460 maximum EN ISO 12156-1
Viscosity at 40°C mm2/sec 2.00 minimum to EN ISO 3104
4.50 maximum
Fatty Acid Methyl Esters (FAME) Content % V/V 5 maximum EN 14078

Besides, to provide options for different climates, the EN 590 standard specifies six

Temperature Climate Grades of diesel fuel (Grade A...F) which differ in the Cold

Filter Plugging Point (CFPP) value (Table 1.3). In addition, there are five Arctic

17
Classes of diesel fuel (Class 0...4) characterized by different properties (Table 1.4).

Each country shall detail requirements for a summer and winter grade, and may also

include intermediate or regional grades as justified by national climate conditions.

Table 1.3 Temperate climate grades of diesel fuel in Europe

Characteristics Class A Class B Class C Class D Class E Class F Units

CFPP 5 0 -5 -10 -15 -20 ℃
Density at 15 ℃ 820 - 860 820 - 860 820 - 860 820 - 860 820 - 860 820 - 860 kg/m³
Viscosity at 40 ℃ 2 - 4.5 2 - 4.5 2 - 4.5 2 - 4.5 2 - 4.5 2 - 4.5 mm2/s
Cetane index 46 46 46 46 46 46
Cetane number 49 49 49 49 49 49

Table 1.4 Arctic climate grades of diesel fuel in Europe

Characteristics Class 0 Class 1 Class 2 Class 3 Class 4 Unit

CFPP -20 -26 -32 -38 -44 ℃
Cloud point -10 -16 -22 -28 -34 ℃
Density at 15 ℃ 800 - 845 800 - 845 800 - 845 800 - 840 800 - 840 kg/m³
Viscosity at 40 ℃ 1.5 - 4.0 1.5 - 4.0 1.5 - 4.0 1.4 - 4.0 1.2 - 4.0 mm2/s
Cetane index 46 46 45 43 43
Cetane number 47 47 46 45 45

In China, different specifications have been allocated to different regions due to

climate varying and economic reasons. Regulation GB 17691-2005 specified

emission limits for China III-V stages, but included fuel specifications for the China

III stage only. Faced with the lack of official fuel standards to ensure availability of

ultra-low sulphur fuels that were necessary to enable emission technologies at the

China IV/V stages, the Ministry of Environmental Protection adopted regulation

GWKB 1.2-2011 which regulated sulphur and polyaromatics as toxics. Selected

specifications are shown in Table1.5.

18
 Table 1.5 Selected specifications of diesel fuel for motor vehicles

China III China IV China V

Sulfur content, mg/kg ≤ 350 ≤ 50 ≤ 10
Cetane number, min-max 50-53 47-51
Polyaromatic hydrocarbons, % (m/m) ≤ 11 ≤ 11 ≤ 11

For sulfer content, the limit was set as 50 ppm in several cities in 2008. From 2013,

the State Council issued a timetable for upgrading fuel quality nationwide. . By the

end of 2014, automotive diesel fuel sulfer will be set at 50 ppm (China IV) and by

the end of 2017, sulfer limits for automotive gasoline and automotive diesel will be

10 ppm maximum (China V). Diesel fuel standards for China V were required to be

issued by July 2013. In April 2015, the State Council advanced timeline for 10 ppm

gasoline and diesel fuel by one year making it nationwide available by January 2017.

In the globalized world today，the products form a refinery may serve several regions.

Refiners need to acquaint the varying specifications in different regions. For instant,

the cetane number limit in U.S. is 40, but in Europe it is 51, which is similar in

China. The specification differences in various regions may influence the diesel

process and marketing decisions for a refinery.

1.2 Diesel production

Refining is the process of converting crude oil into high value products. The main

processes adopted in a refinery are the following:

Separation processes: Crude oil is separated into hydrocarbon streams boiling at

different temperatures by a process of distillation in the Crude Distillation Unit

(CDU).

19
The products that are obtained directly from CDU are called straight-run products

(e.g., straight-run diesel). The material that is too heavy to vaporize under

atmospheric distillation is removed from the bottom of the column (atmospheric

bottoms). The atmospheric bottoms can be fractionated further by a second

distillation carried out under reduced pressure. The lower pressure in the distillation

column allows some of the heavier components to be vaporized and collected. This

process is called vacuum distillation; the distillated product is called vacuum gas oil

(VGO), and the bottoms product is called vacuum residue.

Upgrading processes: These processes improve the quality of selected component

streams depending on their use, by using chemical reactions to remove compounds

present in trace amounts that give the material an undesirable quality, such as

hydrotreating to remove sulfer. Otherwise the bulk properties of the streams are not

changed.

Conversion processes: These processes fundamentally change the molecular

structure of the feedstock streams, usually by “cracking” large molecules into small

ones. Examples of these process units are Fluidized Catalytic Cracking Unit (FCCU),

Hydrocracking unit (HC) and Delayed Coking Unit (DCU).

The primary aim of the FCCU is to convert streams suitable for the gasoline pool;

however, one product stream, light cycle oil (LCO), is often blended into diesel fuel.

Before blending, LCO undergoes subsequent hydrotreating to lower sulfer content

which makes the LCO more stable and suitable for adding to diesel fuel. To meet the

15 ppm sulfer requirement in Euro 5 , LCO undergoes subsequent hydrotreating to

lower sulfer content.

Hydrocracking is another major conversion process. It is similar to catalytic cracking

because it uses a catalyst, but the reactions take place under a high pressure of

20
hydrogen. The primary feed to the hydrocracking unit is VGO. During

hydrocracking, large VGO molecules are cracked into smaller molecules by either

cleaving carbon-carbon bonds or by plucking out sulfer and nitrogen atoms from

-carbon-sulfer-carbon- and -carbon-nitrogen-carbon- molecular linkages. Because of

the high hydrogen pressure used in hydrocracking, hydrogen is added to the

fragmented molecular ends formed by either cleaving carbon-carbon bonds or by

extracting sulfer and nitrogen linkage atoms; in addition, rings of some aromatic

compounds are saturated with hydrogen during the hydrocracking process. Kerosene

and diesel form a large percentage of the product from a hydrocracker. These

products are nearly devoid of sulfer and nitrogen and are enriched in hydrogen.

The extent of conversion is the most significant difference between hydrotreating

and hydrocracking. “Conversion” is defined as the difference in amount of

unconverted oil between feed and product divided by the amount of unconverted oil

in the feed. Unconverted oil is defined as material that boils above a specified

temperature. For vacuum gas oil (VGO), a typical specified temperature is around

343°C. Conversion in hydrotreaters is less than 15 wt%, while conversion in

hydrocrackers and mild hydrocrackers exceeds 20 wt%.

The vacuum residue can be processed in a Coker Unit that thermally cracks the long

chain hydrocarbon molecules in the residual oil feed into shorter chain molecules

that forms the Coker Light Gas Oil (CLGO), which can either be blended into diesel

directly or be refined to be a diesel product.

In a modern refinery (Figure 1.2), diesel intermediates can be produced from various

operating units such as CDU (crude oil distillation unit), catalytic cracking,

hydro-treater, hydro-cracker and delayed coker etc. Various streams from different

units with different specifications can be classified to diesel. However, not all

streams within the required carbon atom numbers (C10-C23) and boiling ranges (150℃
21
-370℃) of diesel from the units can be blended to meet the quality requirements for

market. Compared with the standard specifications, some of the diesel streams have

superior properties and others have inferior properties.

According to particular blending ratios, the diesel streams with inferior properties

can be blended to diesel products that meet standard specifications.

Figure 1.2 A modern Refinery (chevron, 1998)

1.3 Hierarchy of decision making for diesel production

Production of diesel in an oil refinery is a complicated process, due to a long

processing chain with a large number of processes involved, various grades of diesel

22
products, fluctuated market demands, and comprehensive quality requirement.

Different operations could make significant influence in total profit. Therefore,

decision making in refinery diesel production has a significant implication on its

profitability.

The hierarchy of decision making mainly consists of three levels: planning for the

higher level, scheduling at the intermediate level and advanced control at the lower

level (Gupta, 2008). In a refinery, the planning level provides targets for the

scheduling operations and the scheduling provides targets for the advanced

control/regulatory control. Whereas, the advanced control sends feedback to the

scheduling model and the scheduling sends feedback to the planning model.

Feedbacks come from monitoring the results of processes and will reflect the effects

of planning and scheduling operations. According to which, refiners change the

recipes to optimize the operations for the maximum profit

1.3.1 Distinguishing between planning and scheduling

Planning is essential for successful scheduling as it provides the activities and targets

required to be met in the scheduling operations. The result of scheduling operations

could help refiners to modify planning. Planning is forecast driven to which

scheduling is order driven with a further explanation presented in the definitions of

each expression (Kelly and Mann, 2003).

1.3.2 Definition of planning

Planning is essential for successful scheduling as it provides the activities and targets

required to be met in the scheduling operations. The result of scheduling operations

could help refiners to modify planning. Planning is forecast driven to which

scheduling is order driven with a further explanation presented in the definitions of

23
each expression (Kelly and Mann, 2003).

1.3.3. Definition of scheduling

Planning of a refinery contains the long-term aspects, which normally takes months,

in which refiners operate equipment, crude oils and products. It is the first step to run

a refinery to maximize the process efficiency. In planning stage, specifications and

quantities of demanded products are provided to refiners. Refiners process the

product requirements with the refinery condition (feedstocks’ properties and

quantities, producing capacity, operation conditions etc.). By solving mathematical

models, a feasible production plan (properties, quantities and compositions of

products) is obtained.

1.3.4 Relation of planning and scheduling

The business area hierarchy in any industry consists of long-term planning,

short-term scheduling and process control. The hierarchical management levels are

shown in Figure 1.3 with the longest planning horizon at the top which shortens

rapidly while moving down to the process control level. On the other hand, the

reliability of information and their detail increases from the top to the bottom in the

hierarchy. The complex planning and scheduling tasks are broken into simpler ones

that can be solved at each stage separately. Three levels in the hierarchy are

connected in a way that the results of each level are forwarded to the next level.

24
 Figure 1.3 Hierarchical management levels

In long-range planning horizon, refiners deal with feedstocks and products according

to the market demand and environmental regulations. A planning horizon normally

lasts 1-3 months while a scheduling period is generally 1 week. The optimal process

variable values are transferred to the short-term scheduling level in which the time

horizon is counted by week, and the due date of each product should be met.

Afterwards, parameters of each process are derived on the base of scheduling recipe.

The processes can be operated with the help of the parameters, which comes to the

process control level. To sum up, the operating instructions are based on the three

levels. A design which is optimized in all the three levels can be called optimised.

1.4 Challenges in diesel production blending

The refining industry today has to comply with both higher product quality

specifications and more stringent environmental regulations regarding emissions and

25
waste productions. This means that refineries are now faced with the pressure of

reducing emissions that arise from its operations. Product specifications are always a

highly charged subject, due to the interests of environmental pressure groups,

refiners, governments, consumers and engine manufacturers. However the

interaction of these groups makes the predictions of future trends difficult. In old

days, many refiners used to consider product blending as a linear problem but the

need to comply with the environmental restrictions and the demand for higher grades

of petroleum products enforce refiners to solve the scheduling problem in more

accurate ways.

Table 1.2 shows diesel fuel standards in Europe. The minimum cetane number of

diesel product has been driven up slowly due to the requirement of new technology

in the engine designs, which in turn requires higher grade diesel to produce lower

emissions. This is one of the major problems that refiners face as high cetane blend

stocks are limited in conventional refineries.

Particulate emissions, as heavy diesels tend to produce higher particulate emissions,

is the core reason for the need to reduce specific gravity and ASTM 95% temperature.

This increases the problems that refiners face as this further put limitation on the use

of catalytic cracker light cycle oil.

The need for reduction of PAH (Polycyclic aromatic hydrocarbons) is due to the

possible formation of benzene, which is carcinogenic, from incomplete combustion.

This in turn increases the use of straight run blend stocks as possible blending stock.

The quality improvements, emission reduction, performance improvement to

facilitate the advanced engine design and fuel economy are the main reason behinds

the pressures imposed on the specifications (Simon 2001). Refiners face difficulties

in practically meeting the tight specifications with existing blend stocks and limiting

26
the cut range of blend stocks. Hence, product yield and profit are reduced due to the

increment in the production of lower valued products.

The planning and scheduling of diesel production blending are very important in

diesel producing processes. The intermediate streams have different properties. They

need to be processed before enter diesel product market because they cannot

compliance with the requirements. Blending is one of the most commonly used

processes in a refinery. Refiners simulate the blending process and predict the

product properties to obtain a blending ratio. In previous works, researchers simplify

the blending process by linearization the blending property correlations. Through

linearization, the blending problem can be solved directly but linear correlations can

lead to an inaccurate result, which will cause dissatisfying of product specifications

and property loss.

Since 2000, diesel specification has become more and more strict. The minimum

cetane number of diesel has been driven up slowly due to the requirement of new

technology in the engine designs, which in turn requires higher grade diesel to

produce lower emissions. This is one of the major problems that refiners face as high

cetane blend stocks are limited in conventional refineries. Particulate emissions, as

heavy diesels tend to produce higher particulate emissions, is the core reason for the

need to reduce specific gravity and ASTM 95% temperature. This increases the

problems that refiners face as this further put limitation on the use of catalytic

cracker light cycle oil. The need for reduction of polynuclear aromatics is due to the

possible formation of benzene, which is carcinogenic, on incomplete combustion.

This in turn decreases the use of straight run blend stocks as possible blending stock.

Due to the stringent quality requirements, it is critical for refiners to improve the

diesel blending operation to decrease property loss and increase profit.

27
In recent years, oil refineries are increasingly concerned with improving the planning

of their operations. Many commercial software for refinery production planning,

such as RPMS and PIMS, are based on linear models. It was interpreted as general

trends that don’t allow to use more complex models and nonlinear mixing rules

(Moro el al. 1998). In the new century, due to the pressure from more stringent

specifications and competitors, refiners and researchers started to put more emphasis

on developing new nonlinear models which formulate refinery processes more

precisely.

1.5 Objective of this work

As mentioned before, the diesel product specification has become more stringent.

Therefore, refiners are pursuing more efficient operation by deploying mathematical

models for higher accuracy and optimality that can reduce profit loss. Since the

nature of diesel blending is nonlinear, linear models in property prediction will lead

to inaccuracy. A model that applies nonlinear correlations to predict properties in

diesel blending planning and scheduling is developed. On account of the complexity

of diesel blending problem, the nonlinear model in planning and mixed-integer

nonlinear model in scheduling are difficult to solve. To overcome the difficulty, a

feasible solution algorithm to solve and optimise the MINLP planning and

scheduling problems is proposed. Besides, this model can be extended to other

process of a refinery. In this work, it will be modified to optimise a gasoline

production blending scheduling problem to demonstrate the applicability of the

model.

1.6 Structure of the thesis

In Chapter 2, current approaches for diesel planning, scheduling and blending are

28
reviewed. The basic features for each approach, as well as its advantages and

drawbacks, are briefly discussed.

In Chapter 3, an NLP model for diesel blending problem is introduced. Nonlinear

correlations in property estimation for different properties which are limited in

environmental regulations are applied.

In Chapter 4, a new MINLP model has be built for the scheduling problem of diesel

blending, and a robust solving algorithm is proposed to optimize it.

In Chapter 5, the proposed model can also be extended to gasoline blending

scheduling problem. The extending process and how the model works will be

presented.

Finally in Chapter 6, conclusions are drawn for this research work together with

recommendations for future research work.

29
 Chapter 2 Existing Work on Diesel Blending Optimization

2.1 Introduction

In this chapter, existing researches on diesel fuel and production processes are

discussed. As diesel production processes are attached to refineries, the planning and

scheduling methods for refinery operations are reviewed, especially for those that are

related to diesel blending.

2.2 Diesel fuel technology

2.2.1 Diesel engine

Diesel engines have become increasingly common as a power plant source for

providing motive power both in highway and non-highway transportation systems

and also for industrial applications. In the last two decades, diesels have expanded

their preserve from traditional heavy duty applications such as buses and trucks to

even light duty passenger cars, where their operation is almost indistinguishable

when compared to traditionally used gasoline powered engines, while conferring

their advantages of better thermal efficiency and fuel economy. This has led to a

spurt in demand for diesel fuel globally, as a result of which increased middle

distillate or diesel production is the main objective of most refineries

Diesel engines most commonly use a four-stroke operating cycle (see Figure 2.1). In

the first stroke (intake stroke), the intake valve opens while the piston moves down

from its highest position in the cylinder (closest to the cylinder head) to its lowest

position. This draws air into the cylinder in the process. In the second stroke

(compression stroke), the intake valve closes and the piston moves back up the

cylinder. This compresses the air and, consequently, heats it to a high temperature,
30
typically in excess of 540°C (1,000°F). Near the end of the compression stroke, fuel

is injected under high pressure up to 30,000 psi (200 MPa or 2,000 bar) into the

combustion chamber through a fine nozzle. The injection system is designed to

produce a fine spray of small fuel droplets that will evaporate quickly in order to

facilitate rapid mixing of fuel vapour and air.

Figure 2.1 A typical diesel engine(Chevron,1998)

2.2.2. Diesel fuel properties

Since diesel fuel mostly serves diesel engine, the initial motivation of research on

diesel fuel properties is to make diesel engine work in a safe and effective way. On

the other hand, diesel, as a product of petroleum, could cause many environment

problems if it is not produced or used in a proper way. The environmental regulation

of diesel fuel has become more and more stringent in recent year. Researches on

diesel properties would benefit more clean and environmental friendly diesel

production.

31
1. Cetane number

The catane number is a measure of how readily the fuel starts to burn (auto-ignite)

under diesel engine conditions. The ignition delay period can be evaluated by cetane

number. To measure cetane number, its ignition performance is compared to two

pure hydrocarbons: n-cetane which is given the number 100 and α

-methynaphthalene which is given the number 0. If a diesel fuel behaves like a

mixture of 60 volume % cetane and 40 volume%α-methynaphthalene, it is given a

number of 60.

The cetane number of a diesel fuel can be measured by ASTM D 613 test method. A

diesel fuel with a higher cetane number has a better performance in ignition by a

shorter ignition delay. A diesel fuel with a higher cetane number can also reduce

combustion noise and increase engine efficiency and power output (Riazi, 2005).

Cetane number also varies systematically with hydrocarbon structure. Normal

paraffins have high cetane numbers that increase with molecular weight. Isoparaffins

have a wide range of cetane numbers, from about 10 to 80. Molecules with many

short side chains have low cetane numbers; whereas those with one side chain of

four or more carbons have high cetane numbers.

Naphthenes generally have cetane numbers from 40 to 70. Higher molecular weight

molecules with one long side chain have high cetane numbers; lower molecular

weight molecules with short side chains have low cetane numbers.

Aromatics have cetane numbers ranging from zero to 60. A molecule with a single

aromatic ring with a long side chain will be in the upper part of this range; a

molecule with a single ring with several short side chains will be in the lower part.

Molecules with two or three aromatic rings fused together have cetane numbers

below 20.
32
2. Diesel Index or Cetane Index

The cetane method of expressing ignition quality presupposes the availability of a

standard engine (Cooperative Fuel Research Engine), reference fuels and also tends

to be somewhat time-consuming and expensive. Hence alternative tests, such as

diesel index and cetane index, are often used for routine control purposes. ASTM

D976 (IP 218) proposed a method of calculating cetane index as follows:

𝐶𝐼 = 454.74 − 1641.416𝑆𝐺 + 774.74𝑆𝐺 2 − 0.554𝑇50 + 97.083(log10 𝑇50)2

(2.1)

where 𝑇50 is the ASTM D86 temperature at 50% point in ℃.

For diesel index, it is defined as :

(𝐴𝑃𝐼)(1.8𝐴𝑃+32)
𝐷𝐼 = (2.2)
100

which is the function of API gravity and aniline point in ℃. Cetane index is

empirically correlated to DI and AP in the following calculation (Riazi, 2005):

CI=0.72DI+10 (2.3)

CI=AP-15.5 (2.4)

3. Viscosity

Viscosity is defined as the ratio of absolute viscosity to absolute density at the same

temperature. In an easier way, viscosity means resistance to flow or movement and

it’s sensitive to temperature. It can be measured by ASTM D 445 test method.

33
In the case of diesel fuels, low viscosity may give rise to:

(1) Leakage of fuel from pumps and injectors.

(2) Abnormal rate of wear of the moving parts of pumps and injectors owing to lack

of lubricity.

(3) Too fine a degree of atomisation with the result that the fuel will not penetrate

sufficiently far into the compressed air in the cylinder to give the food mixing

essential for efficient combustion.

(i4) Overheating of the injector owing to the concentration of the fuel spray and

hence the flame in a relatively small area around the injector nozzle.

However, if the viscosity of the fuel is too high, it will impede the flow of fuel to the

pump, giving rise to poor atomisation and excessive penetration with inefficient

combustion of fuel.

4. Carbon residue

Different fuels have different tendencies to crack and leave carbon deposits when

heated under similar conditions. It measures coking tendency of a fuel and will affect

the engine deposit. Heavier fractions with more aromatic contents have higher

carbon residues while volatile and lighter fractions such as naphthas and gasolines

have no car- bon residues. There are two older methods to measure carbon residue,

Ramsbottom (ASTM D 524) and the Conradson (ASTM D 189). The relationship

between these methods are also given by the ASTM D 189 method. There is a more

recent test method (ASTM D 4530) that requires smaller sample amounts and is

often referred as micro-carbon residue (MCR) and as a result it is less precise as a

practical technique

34
5. Sulphur content

Sulphur content is significant because it governs the amount of sulphur oxides formed

during combustion. Water from combustion of fuel collects on the cylinder walls,

whenever the engine operates at low jacket temperatures. Under such conditions,

sulphurous and sulphuric acids are formed, which attack the cylinder walls and piston

rings, promote corrosion and thus cause increased engine wear and deposits. These

effects can to some extent be overcome by the use of lubricants containing alkaline

additives. If the diesel fuel is refined from a very high sulphur crude, it may become

necessary to desulphurise it before marketing.

Sulphur content is also an important index for environmental organizations. In

Europe, the sulphur content of diesel fuel specifications has decreased from 0.2 w%

in 1993 to 0.001w% in 2009.

Sulphur content can be measured by ASTM D 129.

6. Ash content

Ash is a measure of the incombustible material present in a fuel and is expressed as a

percentage of the weight of the fuel sample. In the case of distillate fuels, it usually

consists of rust, tank scale or sand, which settles out readily. Blends of distillate and

residual fuel, e.g. LDO may additionally contain metal oxide derived from oil

soluble and insoluble metallic compounds. Ash is significant because it can give rise

to deposit problems such as abrasion, malfunctioning of injectors and high

temperature corrosion, particularly with residual fuels.

Ash content can be measured by ASTM D 482.

35
7. Pour Point

The pour point of a fuel is the lowest temperature at which it will pour or flow when

chilled under prescribed conditions. It is a very rough indication of the lowest

temperature at which a given fuel can be readily pumped. However, since practical

conditions are quite different from those under which the laboratory test is conducted,

many fuels can be pumped at temperatures well below their laboratory pour point.

Test procedures for measuring pour points of petroleum fractions are given under

ASTM D 97 (ISO 3016 or IP 15) and ASTM D 5985 methods.

8. Cold Filter Plugging Point

The cold filter plugging point (CFPP) is defined as the highest temperature at which

the fuel, when cooled under prescribed conditions, either will not flow through the

filter (45 microns) or will require more than 60 seconds for 20 ml to pass through.

This is the temperature at which wax crystals begin to cause blockage of filters.

CFPP can be tested by ASTM D 6371.

9. Freezing Point

The freezing point of diesel describes a temperature at which it changes state from

liquid to solid. It can be tested by ASTM D 2386.

10. Cloud Point

The cloud point is the lowest temperature at which wax crystals begin to form by a

gradual cooling under standard conditions. At this temperature the oil becomes cloudy

and the first particles of wax crystals are observed. Cloud point is another cold

36
characteristic of diesel under low temperature conditions. The standard procedure to

measure the cloud point is described under ASTM D 2500.

The four properties above can all represent diesel performance in a cold weather. In

Europe and China, CFPP is used to grading the diesel fuel products to indicate the

suitable weather of a diesel fuel.

11. Aniline Point

Aniline point of a petroleum fraction is defined as the minimum temperature at

which equal volumes of aniline and the oil are completely miscible. Method of

determining aniline point of petroleum products is described under ASTM D 611 test

method.

The value of aniline point gives an approximation for the content of aromatic

compounds in the oil, since the miscibility of aniline, which is also an aromatic

compound suggests the presence of similar (i.e. aromatic) compounds in the oil. The

lower the aniline point, the greater is the content of aromatic compounds in the oil as

obviously a lower temperature is needed to ensure miscibility.

12. Flash Point

The flash point of a diesel is the lowest temperature it will ignite. Therefore, the

flash point of a fuel indicates the maximum temperature that it can be stored without

serious fire hazard. This has no bearing on performance but is important largely from

the point of view of safety in handling the fuel and minimum values are usually

specified in the specification.

There are several methods of determining flash points of petroleum fractions. The

Closed Tag method (ASTM D 56) is used for petroleum stocks with flash points

37
below 80 ℃. The Pensky-Martens method (ASTM D 93) is used for all petroleum

products except waxes, solvents, and asphalts.

As reviewed, a diesel fuel has a number of properties that measure ignition

performance, environmental influence and safety. Since so many properties should

be considered, it greatly increases the difficulty in optimizing diesel blending.

2.3 Predictions of diesel blending properties

Property estimation is the key part of diesel blending problem. Among the properties

that we need to consider, many of them are not linear depend on the composition,

which means quality loss and prediction error will occur if linear correlations are

directly used. Researchers have done a quantity of works on predicting product

property in a more accurate way.

For properties such as carbon residue, sulphur content, ash content, linear addition is

suitable for property prediction of blending diesel oil. But for the calculation of

cetane number, CFPP, freezing point, flash point, pour point, cloud point, viscosity,

and distillation range, linear addition is not suitable. For these properties, the

nonlinear blending models will be demonstrated in Chapter3.

2.4 Methods for diesel blending optimisation

Compared to gasoline blending problem, there is very few academic publication

available for diesel blending. A planning model for refinery diesel production is

addressed by Moro, Zanin and Pinto (1998). In order to achieve an optimal solution,

this model applied nonlinear blending predictions methods to calculate production

properties. However, it only concerns 5 properties in product specifications,

including density, flash point, boiling range, cetane number and sulphur content.

38
Due to the more stringent environment regulations, it cannot meet the requirements

of current diesel blending situations. On the other hand, since the Moro’ model

focuses on planning of diesel production, it didn’t optimize the production blending

process.

The common industrial perception for the diesel blending problem is that it is

considered as simpler than the gasoline blending problem, with less nonlinear

behavior in property mixing. Therefore, most research effort for refining product

blending is focused on gasoline. As a common approach, the diesel blending

problem is mostly treated as a linear problem, which can be dealt with in overall

refinery LP optimization.

Therefore, the techniques for refinery diesel blending optimization are reviewed in

the context of overall refinery planning and schedule in the next section.

2.5 Planning and scheduling methods in refineries

The configuration of a refinery is one of the most complicated industrial systems.

There are a lot of processes including separation processes, upgrading processes and

conversion processes. Every process has a number of equipment, such as reactors,

distillation columns, heat exchangers, pumps, etc. Raw materials are turned into

various higher value petroleum products. Refiners plan and schedule their operations

according to income of crude oil and requirement of market with specifications

satisfied.

2.5.1 Refinery planning

2.5.1.1 The objective of refinery planning

39
In the oil refining industry many products are produced from only one feedstock

(crude oil) and the values of these products are in the same order of magnitude and

this result as a complex economics of petroleum refining. Also cheaper products can

be improved by upgradation processes. This makes it difficult to calculate the

straightforward production cost. The aim of the optimization process is not only to

achieve a single optimum operating point but also to understand the economics and

price structure of a refinery. In simple mathematical terms, the refinery optimization

can be expressed as:

Objective function:

Maximize profit = Product sale – Material cost – Operating cost

Subject to:

 Process operations (e.g. kinetics, temperatures, pressures, flowrates)

 Process connections

 Various limitations (e.g. throughput, storage, product specifications, market

demand, raw material availability, environmental regulations)

 Resource utilisation (e.g. power, steam, hydrogen)

 Operation policy (e.g. allocation of the storage tanks, loading and unloading
procedure of tanks, product grade transition policy in pipeline), etc.

Depending upon the amount of details incorporated, the formulations can generally

be classified as planning or scheduling. The planning problem ignores some of the

details such as inventories, operating policy, etc. and focuses on long-term goals

such as production optimization, debottlenecking and retrofitting. On the other hand,

the scheduling formulation considers inventory, dynamic markets conditions and

40
detailed operating strategy; but the scope is limited to shorter time horizon.

2.5.1.2 Refinery planning models

Planning formulation can generally be classified as a linear programming (LP) and a

nonlinear programming (NLP). If all the objective function and constraints are linear,

it is an LP formulation whereas, if any of them are in a nonlinear form, it is an NLP

formulation.

Linear programming is the most popular optimization techniques used by the refiners.

LP formulation requires all relevant possible processing routes to be pre-considered.

The linear programming algorithm calculates the optimum combination of supply,

processing, blending and selling activities that generate the maximum profit. Besides,

the linear programming output can also provide the marginal values of all refinery

flows (that helps to understand the economics), marginal values of constraints such

as product specification (to grasp the impact of the environmental regulation),

marginal values of feedstock (feedstock selection decisions) & products (choice of

product and deciding market) and marginal values of additional processing capacity

(to make retrofitting and debottlenecking decisions). Interpreting the LP output

requires skills and in order to evaluate different scenarios it is necessary to generate

several cases and sub cases (Hartmann, 1999, 2003). By solving a large number of

LPs systematically eliminating the options and providing and optimum solution, a

mixed integer linear programming (MILP) can calculate these different scenarios.

The linear programming techniques for overall refinery optimization are relatively

well developed, represented by commercial software – PIMS from Aspen

Technology (1993) and RPMS from Honeywell. In the meantime, many petroleum

companies have developed their own LP tools in-house. The disadvantage of the

linear programming is that it assumes linear combination of provided options. The

41
refining process models are nonlinear and as a result, linear models cannot describe

the nonlinear aspects accurately.

In order to overcome this defect of the linear programming methods, recursion

techniques are employed. These methods use nonlinear simulation methods to

complement linear programming. In recursion techniques, a number of sequential

executions are required. The nonlinear simulation is performed after execution of LP

and it provides the starting point for the next LP. Although recursion gives more

accurate solutions, it not only increases computing time, but also reduces the

transparency of LP’s value structure and its economic driving forces, and therefore

reduces users’ confidence (Hartmann, 1997).

On the other hand, a rigorous nonlinear programming model for overall plant

operation can be formulated by lumping all the rigorous process models together.

Progress of nonlinear programming in 1990s (Viswanathan & Grossmann, 1993;

Porn, Harjunkoski & Westerlund, 1999) allowed many researchers to use NLP

models for optimization. However, most of the applications are limited to single unit

optimization or a group of units. Moro, Zanin and Pinto (1998) optimized diesel

production in RPBC refinery with considering density, flash point, boiling range,

cetane number and sulphur content. Neiro and Pinto (2004) used NLP based

method for the overall refinery optimization. Li et al. (2005) used integrated CDU,

FCC and product blending models for refinery planning. However, researchers

reported the need for decomposition method that would solve such a large size

problem more efficiently.

Zhang (2000) provided a decomposition method to build a synergy between NLP

based rigorous individual plant optimization and the overall refinery optimization. In

his method, the optimization model has been decomposed into two levels: the site

level (master model) and the process level (sub models). The site level optimization
42
deals with the major refinery aspects such as flow arrangement and the process level

optimization deals with process operating conditions for given flow arrangements. A

feedback procedure is used with the help of marginal values derived from the site

level optimization and iterations between both levels of optimization are performed

until the convergence is achieved. This method provides good understanding of

refinery price values and allows users to use in-house process models. The method is

both mathematically solvable and computationally efficient. However, single period

planning model has limits that it doesn’t consider the time issue and storage element.

It assumes that the refinery doesn’t have a deadline of an order and unlimited

capacity of processes.

2.5.2 Scheduling

The long-term and the plant wide planning problems in the petrochemical industry

have been mainly addressed by mathematical programming techniques (Bodington,

1995). Pure linear programming methods have been used for long-term planning, but

they are not suitable for the short-term scheduling and on-line optimization, since

they are based on simplified correlations, without being able to deal with both

continuous (and often nonlinear) processes and discrete decisions accurately

(Zhang and Zhu, 2000). The mathematical formulation for scheduling problem can

be classified as a mixed integer linear programming (MILP) and a mixed integer

nonlinear programming (MINLP). If all the constraints and objective function are in

linear form, it is an MILP formulation and if any of them is nonlinear, it is an

MINLP formulation.

The combined crude allocation/pooling problem have been examined by Lee et al.

(1996) with the development of a mixed integer linear programming multi-period

model for proposing a short-term crude oil unloading, tank inventory management,

43
and CDU charging schedule. Pinto et al. (2000) presented the results of the

application of a mixed integer optimization model in a similar real world problem. In

their model time is represented by variable length time slots, which corresponds to

crude oil receiving operations (vessels unloading) as well as to periods between two

receiving tasks. Shah (1996) proposed a mathematical programming approach, in

which, tanks may store only one crude type and each CDU runs exactly one crude

type from one tank at a time. In modelling of a refinery process, the calculation of

crude oil mixing generates non-convex bilinear constraints. Some researchers have

proposed techniques to linearise these bilinear constraints. Sherali and Alameddine

(1992) proposed a new reformulation linearisation technique (RLT) and imbedded it

within a provably convergent branch and bound algorithm. This RLT process yields a

LP problem whose optimal value provides a tight lower bound on the optimal value

of the bilinear programming problem. Quesada and Grossmann (1995) applied the

technique proposed by Sherali and Alameddine (1992) to model process networks

consisting of one or several splitters, mixers, and linear process units that involve

multicomponent streams. Although the RLT constraints can sometimes replace

bilinear constraints, this often leads to inconsistent solutions, in particular when

handling storage of multiple oil types.

Glismann and Gruhn (2001) reported an MILP model to optimize recipe of

short-term scheduling and blending process. The product recipe of each period is

redefined by making use of a RTN representation. Although the long-term planning

problem can be modified, the scheduling problem cannot be optimized. Mendez and

Grossmann (2006) presented an approach that can optimize off-line blending and

scheduling of oil refinery operations. Nonlinear correlations are applied for the

property estimation. To avoid solving MINLP problem, an iterative procedure is used.

The correlation factor ‘bias’ is introduced to modify the error between nonlinear and

linear correlations and converge the solution in the iteration procedure. In this model,

44
one of the most important assumptions is that the non-linear properties are a weak

function of the compositions. However, in order to improve the accuracy, some

correlations for non-linear properties are very complex. So the application of this

model will be limited. .

In recent years, A number of review papers on scheduling have been written across

different scientific communities, e.g. Floudas and Lin (2004), Méndez, Cerdá,

Grossmann, Harjunkoski, and Fahl (2006), Li and Ierapetritou, 2008a and Li and

Ierapetritou, 2008b, Maravelias (2012) and Iiro Harjunkoskia (2014).

Although there are little research in diesel blending scheduling can be found in

literatures, researches on crude oil scheduling and production blending can be

referred.

Many papers research scheduling methods based on crude oil operations. In crude oil

scheduling problem, refinery operations involve three main segments: crude oil

storage and processing, intermediate processing, and product blending and

distribution. The crude oil needs to be blended before it arrives refining process,

which is similar to diesel production blending. Li et al. (2011) proposed a novel

unit-specific event-based continuous-time MINLP formation for crude oil operation

scheduling. In which, realistic operational features such as single buoy mooring,

multiple jetties, crude blending and etc. are incorporated. Several examples

illustrated that better solutions are obtained. Li et al. (2012a) proposed a framework

to optimise crude oil scheduling problem under uncertainty including demand

fluctuations, ship arrival delays, equipment malfunction and tank unavailability. The

novel MINLP formulation developed by Li et al. (2012b) and the robust optimisation

frame work developed by Lin et al. (2004) and Janak (2007) are successfully utilized

and applied to develop robust optimisation models. To solve the MINLP optimisation

model, a robust optimisation approach and an extended branch and bound global
45
optimisation algorithm for demand uncertainty are also proposed. Castro and

Grossmann (2014) modelled crude oil operations by generate a Resouce-Task

Network superstructure while extending the scope of a well-known continuous–time

formation to variable recipe tasks with multiple input materials. In this mode, the

objective is gross margin maximisation and can be solved close to global optimality.

The advantage of this model is based on a new single time grid formulation, which is

unlike previously proposed unit-specific and priority-slot specific based models.

Cerdá et al. (2016) proposed a novel continuous-time mixed-integer linear

programming (MILP) formulation based on floating time slots to simultaneously

optimise blend recipes and the scheduling of blending and distribution operations.

This MILP approach is able to find optimal solutions at much lower computational

cost than previous contributions when applied to large gasoline blend problems. Dut

to it features an integrality gap close to zero,

Cao and Gu (2014) proposed an online scheduling model for diesel production of a

real-world refinery. They developed an MINLP model to optimise the operation of

diesel production processes in a refinery. In their model, blending correlations of

viscosity, flash point, and solidifying point are considered as nonlinear. For

solidifying point, the equations are derived according to the experimental data.

Summarily, in the past literatures on blending and scheduling problems, most of the

research regards oil blending as a linear problem. Some works proposed algorithm to

make linear result more close to nonlinear result by correction model. These methods

are more accurate than LP models. But there still are shortcomings. The modified

linear result is still inaccurate comparing with nonlinear result. Besides, the

application of the models is limited due to the assumptions made in the modelling

process.

46
The difficulties in a diesel blending scheduling problem concerns primarily 1)the

large number of property should be considered in the model due to product

specifications, 2) the nature of blending model is nonlinear, which would make the

scheduling MINLP, 3) the large number of constraints and variables including

continuous and discrete ones, 4) complexity of nonlinear correlations, 5)the

difficulty in solving MINLP.

2.5.3 Time Representation

Time representation is a preliminary major issue during the mathematical model

formulation of a scheduling problem. Existing scheduling formulations can be

classified into two main categories: discrete-time models and continuous-time

models.

2.5.3.1 Discrete-time models

Early attempts in modelling the process scheduling problems relied on the

discrete-time approach, in which the time horizon is divided into a number of time

intervals of uniform durations and events such as the beginning and ending of a task

are associated with the boundaries of these time intervals.

Discrete-time scheduling formulations make use of the concept of discretization. The

time horizon is divided into a number of time intervals of uniform durations. The

start/end of a task and other important events are associated with the boundaries of

these time intervals. With such a common reference time grid for all the operations

competing for shared resources, such as equipment items, the various relationships in

a scheduling problem can be formulated as constraints of relatively simple forms.

The basic concept of the discrete-time approach is illustrated in Fig. 2.3

47
 Figure 2.3 Discrete-time representation

The main advantage of the discrete-time representation is that it provides a reference

grid of time for all operations competing for shared resources, such as equipment

items. This renders the possibility of formulating the various constraints in the

scheduling problem in a relatively straightforward and simple manner. In this

research, discrete-time representation is applied due to the complexity of the

blending correlations and the large number of equations and variables.

The discrete-time models provide a relatively simple way to represent time and

program the processes, and, usually lead to a well-structured mathematical problem.

Nevertheless, there are two main limitations in discrete-time models. First, as the

nature of time is continuous, it is an assumption to model the problem in a discrete

way, which would cause inaccuracy. Second, the duration of a time interval is a

tradeoff problem between accuracy of the problem and difficulty of solving it. If the

time interval is small, the problem can be modeled precisely while the scale of the

model will be relatively large. It is difficult to obtain the solutions. However, if the

time interval is too big, there is an incredible loss of model accuracy and the value

and significance of the model can be very low.

2.5.3.2 Continuous-time models

To overcome the drawback of discrete-time model, continuous-time model have

been researched in the past decade. From the literature, this model can be classified

into two categories. One defines a set of events that are used for all the units and

tasks. All units share same time slots which are continuous. The other one defines

48
event point based on a unit, in which all units have different time points subject and

allowing different tasks to start or end at different time instances in different units in

the same event point.

Figure 2.4: Continuous-time representation

All continuous-time approaches can be classified into two categories based on the

type of processes. The first category of approaches focuses on sequential processes

and the second category aims at the scheduling of general network-represented

processes. The critical differences between these two types of processes is that

sequential processes are order or batch oriented and do not require the explicit

consideration of mass balances, which has important Compared to discrete-time

model, continuous-time model is tougher to be built because of the flexibility in

timing the events but requires less computation to be solved.

2.5.4 Process sequences

2.5.4.1 Sequential processes

In sequential processes, Different products follow the same processing sequence. It

is usually possible to define processing stages, which can be single stage or multiple

stages. There can be only one unit per stage or parallel units at each stage. For this

type of process, batches are used to represent production and it is thus not necessary

to consider mass balances explicitly. At each stage, there can be one or multiple

parallel units. When multiple units are involved, time slots are defined for each unit.

49
2.5.4.2 Network-represented processes

When production recipes become more complex and/or different products have low

recipe similarities, processing networks are used to represent the production

sequences. This corresponds to the more general case in which batches can merge

and/or split and material balances are required to be taken into account explicitly. It

can be classified into state-task network (STN) (Kondili, Pantelides, and Sargent,

1993) and the resource task network (RTN) ((Pantelides, 1994).

 STN

Figure 2.5 Example of State-Task Network

As Figure 2.5 shows, The STN representation of a chemical process is a directed

graph with two types of distinctive nodes: the state nodes denoted by a circle,

representing raw materials, intermediate materials or final products, and the task

nodes denoted by a rectangle box, representing an operation. The fraction of a state

consumed or produced by a task, if not equal to one, is given beside the arch linking

the corresponding state and task nodes.

50
 RTN

RTN describes processing equipment, storage, material transfer and utilities as

resources in a unified way. The RTN representation of the same process as in the

STN example is provided in Fig.2.6. In addition to the resources of materials,

denoted also by circles, the related four pieces of equipment, denoted by ellipses, are

also included. Tasks taking place in different units are now treated as different tasks.

Figure 2.6 Example of State-Task Network

Both STN and RTN can be extended to represent storage vessels and alternative

material locations, as well as different equipment states (e.g. clean, dirty, ready to

process). Both STN and RTN representations were originally used for problems in
51
network environments but have recently been used to address problems also in other

environments (Sundaramoorthy and Maravelias, 2011 and Velez and Maravelias,

2013).

2.6 Summary

In this chapter, the basic information of diesel properties and the existing methods

for diesel blending optimization are reviewed. The following areas of improvement

are identified for optimizing refinery diesel blending operation:

 Even though diesel production from oil refineries plays a significant role of
economic contribution in the refining business, the problem of diesel
blending optimization has not received sufficient attention from the academic
research so far.

 Contradictory to the common perception, the nonlinear property behavior of

diesel blending is not trivial, which will be demonstrated in Chapter 3. More
accurate property prediction methods should be adopted in diesel blending
operation.

 More accurate property prediction models for diesel blending should also be
incorporated into the refinery planning and schedule methods to improve the
overall decision making procedure, especially in the case of scheduling for
diesel blending, where academic effort is almost absent.

To address these shortcomings, a nonlinear diesel blending model is proposed in

Chapter 3 to optimize the recipe of diesel blending problem, and further applied for

refinery planning. In Chapter 4, the nonlinear blending model is incorporated into a

diesel blending scheduling method, for which the overall problem becomes an

MINLP problem. To overcome the difficulty in convergence and ensure the overall

optimality, a solution algorithm is also developed. In Chapter 5, the developed

52
methodology is applied to the gasoline blending problem, in order to further test its

robustness and applicability.

53
 Chapter 3 Modelling and Optimisation of Diesel Blending

Planning

3.1 Introduction

Products blending tries to make use of available components for effective mixing in

order to produce valuable products that meet demands and specifications to achieve

maximum profit (Wu, 2010). Gasoline, diesel, aviation fuel, lubricating oils and

heating fuels are the main products from refinery product blending. Since in normal

conditions, the volumes of products sold by a refiner are very huge. As such, even

savings of a fraction of 1% per unit will lead to a substantial increase in profit.

Furthermore, the demand of refining products has been increasing gradually in the

last years and the trends shows possibility of continuing increase in the foreseeable

future. On the other hand, in recent years, modern refineries have been confronted

with more stringent environment standards and strict requirements of quality

specifications. These situations make the product blending strategy more crucial in a

refinery in order to remain competitive in the global market.

3.1.1 Diesel blending

Diesel blending is a process of blending various refinery components from various

refinery upstream units along with additives to produce different grades of diesel

products. The blending ratio depends on the quality, the quantity and the cost of

available blending streams, the demand and the price of the final products. Selection

of blending components and their proportions in the blended product is a complex

problem. In a refinery, the typical number of diesel blending component stream is

between 6 and 8 (Riazi 2013). The diesel blending component streams are mainly as

following:

54
 Straight Run Diesel from CDU

 Light Cycle Oil (LCO) from FCCU followed by Hydrotreating.

 Coker Light Gas Oil (CLGO) produced from the Coker Unit

 Hydrocracked diesel from HCU

The component properties vary since they come from different processes. For

example, Straight Run Diesel usually has a high cetane number due to high

composition of paraffin while the cetane number of Light Cycle Oil from FCCU is

normally very low because of unsaturation.

Diesel blending is a process of blending various refinery streams produced from

various refinery units along with additives to produce different grades of diesel

products. The blending ratio depends on the quality, the quantity and the cost of

available blending streams, the demand and the price of the final products. Selection

of blending components and their proportions in the blended product is a complex

problem. In a refinery, the typical number of diesel blending component stream is

6-8 (Riazi 2013). These component streams are mainly as following:

 Straight Run Diesel from CDU

 Light Cycle Oil (LCO) from FCCU followed by Hydrotreating.

 Coker Light Gas Oil (CLGO) produced from the Coker Unit

 Hydrocracked streams from HCU

The component properties vary since they come from different process. For example,

Straight Run Diesel usually has a high cetane number due to high composition of

55
paraffin while the cetane number of Light Cicle Oil from FCCU is normally very

low because of unsaturation.

Figure 3.1 Diesel blending

As Figure 3.1 shows, in a blending process, intermediate diesel streams are delivered

to several blending tanks. They are blended according to particular recipes in order

to satisfy the product property requirement. After the blending complete (normally

several hours), the diesel streams are delivered to product tanks, where they are

stored and then transported to markets.

3.1.2 Diesel blending Methods

For diesel blending, there are two general blending methods: continuous blending

and batch blending. Continuous blending, also named in-line blending, is a process

of blending various component streams in a blender continuously, and supplying

products to a product storage tank simultaneously. In continuous blending, samples

of the blend are tested to obtain the sample properties periodically. The feedstock

flow rate is adjusted to ensure the blend meets quality specifications. Continuous

blending is beneficial due to a sequence of operations including: blending, quality

analysis, loading and unloading, which can be accomplished in a single run.

56
In batch blending, various component streams are fed one after another into a

blending tank, until product specifications of a particular grade are all met and the

liquid level reaches the required value. The next run of blending can only be started

after completing the offloading of previous product finishes. Storage tanks for both

blending feedstocks and products are required. Compared to continuous blending, in

batch blending the feed quality can be fairly constant over the time and the products

can be more flexible. However, these benefits are obtained at the expense of higher

storage costs and longer operation cycles.

Commercially, batch blending methods are commonly used that continuous blending

for diesel production. Therefore, this work focuses on developing modelling and

optimisation techniques for batch blending.

3.1.3 Motivation

To achieve a successful operation in most petroleum refineries, product blending is

considered as a key process. As reviewed before, many refiners used to treat diesel

blending as a linear problem. Linearization of blending correlations would simplify

the problem by avoiding considering complex and massive nonlinear correlations.

Therefore, the solution algorithm would be much easier than nonlinear problems.

However, adopting linear blending correlations leads to accuracy loss of predicting

the quality of diesel products. Even though a linear model contains the property

specifications as constraints, it is still possible that the products are unqualified due

to the errors of linear blending correlations, leading to a big profit loss.

On the other hand, diesel product specifications include many properties, such as

density, viscosity, cetane number/cetan index, etc. In the literature, none of the

existing diesel blending models considers all the properties specifications

simultaneously. Such simplification could be applicable to some cases, but cannot be

57
considered for general applications.

Therefore, a diesel blending model with more accurate nonlinear property prediction

correlations and the full coverage of diesel property specifications is highly desirable

to improve refining diesel blending operation.

3.2 Model development

3.2.1 Mathematical modelling

The objective of diesel product blending is to obtain a optimal blending recipe with

maximum profit while satisfying product specifications and market demands.

The key elements in a diesel blending planning and scheduling problem:

Decision variables:

 Amount and type of products produced from different feedstocks.

 Blending recipe of each product.

Major parameters:

 Feedstock properties

 Standard specifications for different types of diesel products.

Major constraints:

 Quality limitation on each product must be satisfied.

 Demand of different grade of diesel must be satisfied.

58
 Mass balance.

Assumptions:

 The composition requirements of products are not considered in this research

 The input bounds of each components stream to each blender are neglected.

 The inventory limits are not considered in the planning model, but will be
considered in the scheduling model in Chapter 4.

3.2.1.1 Objective function

The diesel product blending problem can be formulated as a

Non-Linear-Programming (NLP) problem to maximise the profit. In the model, the

profit is considered as the total price of all the diesel products that are sold to the

market. Mathematical representation of the objective function is described as

follows:

Maximise

𝑃𝑟𝑜𝑓𝑖𝑡 = ∑𝑁𝑃 𝑁𝐹
𝑗=1 𝑃𝑗 ∙ 𝑃𝑟𝑖𝑐𝑒𝑗 − ∑𝑖=1 𝐹𝑖 𝐶𝑜𝑠𝑡𝑖 (3.1)

where 𝑃𝑗 is the production flow for product 𝑗, 𝑃𝑟𝑖𝑐𝑒𝑗 is the market price for

product 𝑗, 𝐶𝑜𝑠𝑡𝑖 is the cost of feedstock 𝑖.

3.2.1.2 Constraints

Material balance for component tanks

𝐹𝑖 = 𝑅𝑖 + ∑𝑗 𝐹𝐵𝑖,𝑗 ∀𝑖 (3.2)

59
 𝐹𝑖 ≤ 𝐹𝑖𝑢𝑝 ∀𝑖 (3.3)

Where 𝐹𝑖 is feedstock of diesel component 𝑖 that can be blended into diesel

products before the blending process starts, 𝑅𝑖 is residue amount of component
𝑖 after the blending process, 𝐹𝐵𝑖,𝑗 is the amount of component 𝑖 which is
blended into product 𝑗 during the blending process. 𝐹𝑖𝑢𝑝 is the available amount
of component 𝑖

a) Material balance for product tanks

𝑃𝑗 = 𝑅𝑗 + ∑𝑖 𝐹𝐵𝑖,𝑗 ∀𝑗 (3.4)

Where 𝑃𝑗 is the amount of diesel product 𝑗 that can be sold to market after the
blending process, 𝑅𝑖 is residue amount of component 𝑗 before the blending
process starts, 𝐹𝐵𝑖,𝑗 is the amount of component 𝑖 blended into product 𝑗
during the blending process.

b) Market demand of each products

𝑃𝑗 ≥ 𝑃𝑗𝑚𝑖𝑛 ∀𝑗 (3.5)

where 𝑃𝑗𝑚𝑖𝑛 is the market demand for product 𝑗

c) Other constraints

𝐹𝐵𝑖,𝑗 = 𝑃𝑗 ∗ 𝑥𝑖,𝑗 ∀ 𝑖, 𝑗 (3.6)

𝐹𝐵𝑖,𝑗 ∗ 𝑑𝑒𝑛𝑖 = 𝑥𝑥𝑖,𝑗 ∀ 𝑖, 𝑗 (3.7)

where 𝑥𝑥𝑖,𝑗 is the mass amount of component 𝑖 in product 𝑗.

𝑃𝑗 ∗ 𝑑𝑒𝑛𝑠𝑗 = 𝑦𝑦𝑗 ∀𝑗 (3.8)

60
where 𝑦𝑦𝑗 is the mass amount of product 𝑗 and 𝑑𝑒𝑛𝑠𝑗 is density of product 𝑗

∑𝑖 𝑥𝑖,𝑗 ∗ 𝑑𝑒𝑛𝑖 = 𝑑𝑒𝑛𝑠𝑗 ∀ 𝑖, 𝑗 (3.9)

𝑤𝑖,𝑗 ∗ 𝑦𝑦𝑗 = 𝑥𝑥𝑖,𝑗 ∀ 𝑖, 𝑗 (3.10)

d) Product specification requirement

For properties that can be predicted by linear correlations

𝑃𝑟𝑗,𝑧 = ∑𝑖 𝑥𝑖,𝑗 ∗ 𝜖𝑧 ∀ 𝑗, 𝑧 (3.11)

𝑃𝑟𝑗,𝑧 = ∑𝑖 𝑤𝑖,𝑗 ∗ 𝜖𝑧 ∀ 𝑗, 𝑧 (3.12)

where 𝑃𝑟𝑗,𝑧 is the value of property 𝑧 of product 𝑗, 𝑥𝑖,𝑗 is volume fraction of

component 𝑖 in product 𝑗, 𝜖𝑧 is the value of property 𝑧 of component 𝑖. 𝑤𝑖,𝑗 is

mass fraction of component 𝑖 in product 𝑗.

Common linear blending properties include

 Sulphur content based on weight fractions of blending components

 Ash content based on weight fractions of blending components

 Carbon residue based on weight fractions of blending components

 Polycyclic aromatic hydrocarbons based on weight fractions of blending

components

For properties that can be predicted by different nonlinear correlations

𝑃𝑟𝑗,𝑧 = 𝑓(𝑥𝑖,𝑗 , 𝜖𝑧 ) ∀ 𝑖, 𝑗, 𝑧 (3.13)

61
On the other hand, a number of properties of interest to the refiners are not additives

and need to be treated non-linearly. The correlations that are applied in this model

are as follows:

 Pour point

Prem B.Semwal and Ram G. Varshney(1994) proposed a correlation to estimate pour

point of blended diesel:

1⁄𝑦 1⁄𝑦
𝑇𝑗 = ∑𝑖 𝑉𝑖𝐴 𝑇𝑖 ∀𝑗 (3.14)

Where 𝑉𝑖 and 𝑇𝑖 are volume fraction and pour point in degrees Rankine of stream
1⁄𝑦
𝑖, respectively, 𝑇𝑗 is the blend pour point in Rankine. 𝐴 and 𝑦 are parameters

to be estimated.

 Cold filter plugging point

Prem B.Semwal and Ram G. Varshney(1994) also proposed a correlation to estimate

cold filter plugging point of blended diesel which is similar to the pour point

correlation:

𝐶𝐹𝑃𝑃𝑗13.45 = ∑𝑛𝑖 𝑉𝑖1.03 𝐶𝐹𝑃𝑃𝑖13.45 ∀𝑗 (3.15)

Where C𝐹𝑃𝑃𝑖 is the cold filter plugging point of the stream 𝑖, 𝑉𝑖 is volume

fraction of stream 𝑖, and 𝐶𝐹𝑃𝑃𝑗 is that of the blend in Rankine.

 Viscosity

The viscosity of the blend of different component streams can be estimated using the

62
Refutas (2000) equation. In this method a Viscosity Blending Number (VBN) of

each component is first calculated and then used to determine the VBN of the liquid

mixture as shown below.

1) Calculate the Viscosity Blending Number (VBN)

𝑉𝐵𝑁𝑖 = 14.534 ∗ ln(ln(𝑣𝑖 + 0.8)) + 10.975 ∀𝑖 (3.14)

where 𝑣𝑖 is the kinematic viscosity at the stipulated temperature in diesel

specifications.

2) Calculate the VBN of the blend

𝑉𝐵𝑁𝑗 = ∑𝑁
𝑖=1 𝑥𝑖 ∗ 𝑉𝐵𝑁𝑖 ∀𝑗 (3.15)

where 𝑥𝑖 is the mass fraction of each component in the mixture

3) Calculate the viscosity

𝑉𝐵𝑁𝑗 −10.975
𝑉𝑗 = exp (exp ( )) − 0.8 ∀𝑗 (3.16)
14.534

 Flash point

Wickey. R. O. and Chittenden, D. H (1963) suggested that the flash point of the

blend should be determined from the flash point indexes of the components as given

below:

2414
𝑙𝑜𝑔10 𝐵𝐼𝐹 = −6.1188 + 𝑇 (3.17)
𝐹 −42.6

where 𝑙𝑜𝑔10 is the logarithm of base 10, 𝐵𝐼𝐹 is the flash point blending index, and

𝑇𝐹 is the flash point in kelvin. Once 𝐵𝐼𝐹 is determined for all components of a

63
blend, the blend flash point index (𝐵𝐼𝐵 ) is determined from the following relation:

𝐵𝐼𝑗 = ∑ 𝑥𝑣𝑖 𝐵𝐼𝑖 ∀𝑗 (3.18)

where 𝑥𝑣𝑖 is the volume fraction and 𝐵𝐼𝑖 is the flash point blending index of

component 𝑖

 Cetane number

The relationship for calculation of cetane number blending index is more

complicated than those for pour and cloud point (Riazi, 2005). In order to control the

model scale and computing cost, in this work, the cetane number prediction of diesel

blending uses linear correlation as follows:

𝑃𝑟𝑗,𝑧 = 𝑥𝑖,𝑗 ∗ 𝜖𝑧 ∀ 𝑖, 𝑗, 𝑧 (3.19)

Where 𝑥𝑖,𝑗 is volume fraction of component 𝑖 in product 𝑗.

 Boiling range

AnASTM-D86 distillation point calculation by the ethyl equation is shown blow

(Ethyl Corporation, 1981):

𝐷86𝑋𝐵 = ∑𝑛𝑖=1 𝑣𝑖 𝐵𝑉𝑥𝑖 (3.20)

𝐺 𝐺
BV𝑥𝑖 = 𝐶0𝑥 + 𝐶1𝑥 𝐴𝑖 + 𝐶2𝑥 𝐴2𝑖 + 𝐶3𝑥 𝐴3𝑖 + 𝐶4𝑥 𝐴𝑖 𝐺𝑖 + 𝐶5𝑥 𝐴𝑖 + 𝐶6𝑥 𝐴2𝑖 + 𝐶7𝑥 𝐺𝑖
𝑖 𝑖

(3.21)

Where 𝐷86𝑋𝐵 stands for the predicted temperature at a given point X, 𝐵𝑉𝑥𝑖 is the

temperature blending value of components i at a desired point X, 𝐴𝑖 is the average

boiling temperature (℃) of component i, 𝐺𝑖 is the components i ASTM severity

64
(T90-T10), and 𝐶0𝑥 − 𝐶7𝑥 are the coefficients for each included D86 distillation

point need to be regressed.

 Cetane Index

As Cetane Index is calculated by ASTM D 976 as follows

𝐶𝐼 = 454.74 − 1641.416𝑆𝐺 + 774.74𝑆𝐺 2 − 0.554𝑇50 + 97.083(log10 𝑇50)2

(3.22)

where 𝑇50 is the ASTM D86 temperature at 50% point in ℃, SG is the special

gravity.

As the product density is assumed blended by linear correlation and boiling range

can be predicted by the models above, the cetane index of the product can be

calculated by equation 3.22

3.2.1.3 Key variables

A diesel blending model should solve the following variables that are very

significant for refiners.

1) Blending ratio

Blending ratio of a diesel blending problem describes how to blend feedstocks into

diesel products. It determines composition and properties of a diesel product.

2) Productivity

The productivity needs to be optimised under the condition of market order

requirements. It is vital to optimising the profit of the blending process.

65
3) Products properties

Products specifications are the key constraints of a diesel blending model. Properties

should satisfy all the specifications. Otherwise, products cannot be delivered to

diesel fuel market. Properties are also the key to optimise the profit of a diesel

blending process. Imprecise property calculation leads to property loss and profit

loss. That's the reason why more and more refiners make efforts to develop and

apply nonlinear model of refining processes, including diesel product blending.

3.2.2 Model validation

A verification case from an Asian refinery is studied to show the accuracy of

properties prediction of blending products. Five blending components are mixed

together to produce the diesel product. Blending ratio in volume is shown in Table

3.1. Measured properties of both blending components and the diesel product,

including flash point, pour point, cold filter plugging point, cloud point, viscosity,

and distillation point, as well as blending ratio, are shown in Table 3.2. The product

properties are calculated by both linear and nonlinear correlations. The calculated

properties are compared with the measured properties of blending product to show

the superiority of the proposed model.

Through Table 3.2, the result from linear model is slightly better than nonlinear when

predicting Cetane Index. For flash point, pour point, CFPP, and distillation point,

nonlinear model gives us much more accurate result. The validation illustrates the

reliability of nonlinear models in diesel blending, which is the significant motivation

of this research.

66
 Table 3.1 Blending ratio

blending ratio(volume) %
F1 10
F2 30
F3 15
F4 43
F5 2

Table 3.2 Measured properties of blending components and product

Property F1 F2 F3 F4 F5 Linear Nonlinear Measured

Flash Point(℃) 24.0 42.0 83.0 69.0 179.0 60.7 44.4 45.5
Pour Point(℃) -65.0 -50.0 2.5 -5.0 2.5 -23.2 -22.2 -12.5
CFPP(℃) -50.0 -50.0 4.0 -4.0 -1.0 -21.1 -15.5 -8.0
Cetane Index 36.8 48.0 63.4 60.6 57.7 54.8 62.2 55.7
Kinematic Viscosity(40℃),mm2/s 1.284 1.300 4.416 4.858 4.327 3.356 2.110 2.371
10% 137.2 165.4 262.6 256.9 332.2 219.8 204.4 207.5
Distillation
50% 143.8 199.2 301.8 307.9 334.9 258.5 286.4 289.1
(D86)
95% 166.2 254.8 361.6 387.6 349.7 321.0 351.0 348.2

Table 3.3 the regressed coefficients for the boiling range

C0 C1 C2 C3 C4 C5 C6 C7
D10 -0.0504 1.6746 -0.002205 0.000029 -0.12954 -3.34E+03 -5.24E+01 43.67155
D50 3.767599 -4.40E+03 1.67E+01 -0.02055 17.93395 3.89E+06 -3.36E+08 1.15E+04
D90 2.80E+05 -2.61E+03 8.04E+00 -0.008151 9.976215 3.16E+06 -3.36E+08 -9.79E+03

3.3 Solution strategy

After refiners discovered that linear models for the diesel blending problem are not

accurate, they realised that the nature of the problem is a nonlinear problem.

However, the obstacle of development of nonlinear model is the complexity of the

problem. Due to a large number of variables and equations, researchers tried to

simplify the problem to make it easier to solve (Moro el al.1998). In the

simplification, they used linear correlations which resulted in reduced accuracy for

predicting the properties thereby limiting the applications of the model.

67
Due to the complexity of the diesel blending problem, it could be difficult to solve

the nonlinear problem directly. Exponentiation arithmetic is applied in the model of

Pour Point and CFPP estimation. If the planning model is solved directly by the

existing solvers (CONOPT, BARON, MINOS), it would lead to infeasible.

To overcome the solving difficulty, a solution strategy is introduced. Since one of the

key aspects of solving general NLP problems successfully is to provide a feasible

initial point. A solution strategy that emphasised the use of a good initialisation for

nonlinear diesel blending model is presented below.

Mathematically, the Nonlinear Programming (NLP) Problem can be expressed like:

Minimize f(x)

St g(x) ≤ 0

L ≤ x ≤ U

where x is a vector of variables that are continuous real numbers. f(x) is the objective

function, and g(x) represents the set of constraints. L and U are vectors of lower and

upper bounds on the variables.

When solving an NLP problem, it is highly desirable to provide initial values for all

the variables as a starting point. Even though algorithms are different depending on

different solvers, the initial values of variables will influence whether the problem

can be solved or not and the solving time. A poor initial value may lead to more

solving time and infeasible solution from the solver. On the other hand, a good initial

value could allow for much quicker convergence to the optimal solution. However,

due to the complexity of the diesel blending problem, it is difficult to provide a

suitable initial value for all the variables.

68
To improve the efficiency of solving the nonlinear diesel blending model, a multi

modelling and solution method is proposed as follows:

Since there are so many constraints in the diesel blending problem, it is decomposed

into two parts. The first part is the objective function and the most crucial constraints

that are related to the variables in the objective function (Equation 3.1, 3.2, 3.3, 3.6,

3.7, 3.8, 3.9, 3.10 and the mixing correlation of density Equation 3.11). The

following parts consist of other constraints (other equations mentioned in the model)..

By decomposing the model, solving a complex nonlinear problem directly is avoided.

After the first part is solved, which is simple and easy to work out, the variables

those are in the objective function are valued. Then, the second part is added into the

model and solved. Sequentially, the others parts are added into the model and

solved .

Through this method, the solver firstly solves a simple NLP problem to determine

the variables in the first part. The values of the variables will be the initial point

when it comes to the next step. These values are results of a part of the model, so

they are more reliable than predicted arbitrarily.

3.4 Case study

To demonstrate the effectiveness of the proposed blending model, an assumed case

study is shown as follows. The feedstocks properties comes from diesel streams of a

refining processing Chinese Daqing Crude

69
 Table 3.4 Feedstock availability and properties

F1 F2 F3 F4
Avalability(t) 1500 1200 1300 800
Cetane Number 68 34 73 73
Sulphur Content(ppm) 12 8 2 8
-1
Density(g*ml ) 0.867 0.8559 0.8287 0.8162
CFPP(°C) -15 -8 -15 4
2
Viscosity(mm /sec ) 3.8 1.5 4.4 2.7
Ash Content(% (m/m) ) 0.003 0.1 0.01 0.008
PAH(% (m/m) ) 9 13 4 2
Flash Point(°C) 50 70 60 55
10%(℃) 137.2 165.4 262.6 256.9
Distillation(D86) 50%(℃) 143.8 199.2 301.8 307.9
90%(℃) 185.6 266.8 372.3 396.7

Four diesel intermediate feedstocks need to be blended to diesel products that can be

sold directly to the market. Feedstock properties are presented in Table 3.4. Every

product must satisfy the EN 590 diesel fuel product standard and the market

demands simultaneously. The product specification and demands are shown in Table

3.5.

Table 3.5 Product specifications

P1 P2 P3 P4
Cetane Number ≥46 ≥46 ≥46 ≥46
Sulphur Content(ppm) ≤10 ≤10 ≤10 ≤10
Density(g*ml-1) 0.82-0.86 0.82-0.86 0.82-0.86 0.82-0.86
CFPP(°C) 0 -5 -10 -15
2
Viscosity(mm /sec ) 2-4.5 2-4.5 2-4.5 2-4.5
Ash Content(% (m/m) ) ≤0.01 ≤0.01 ≤0.01 ≤0.01
PAH(% (m/m) ) ≤11 ≤11 ≤11 ≤11
Flash Point(°C) ≥55 ≥55 ≥55 ≥55
Price($/t) 1270 1290 1320 1330
Demand(t) 500 900 1150 2150

70
The objective of the diesel blending problem is to generate a local optimal solution

that meets all the specifications and market demand for each product while

maximising the overall profit. For feedstock F2, the cetane number 34 cannot meet

the specification, and the CFPP (cold filter plugging point) 9℃ is not qualified for

product P3 and P4. If it is blended into products, theses inferior properties need to be

compensated for by premium properties from other feedstocks.

The blending ratio of each product is the key variable of the case since it determines

the product properties. To predict the boiling range, parameters in Equation 3.16 and

3.17 are regressed as Table 3.6:

Diesel blending model is to maximize objective function (3.1), subject to constraints

(3.2) – (3.21).

The optimised product properties are shown in Table 3.7.

Table 3.6 Parameters regressed for boiling range prediction

10% 50% 90%

C0 -1.1221800E+03 -6.7706000E+03 -3.1739400E+03
C1 1.7772186E+01 4.2621677E+01 5.8536876E+01
C2 -5.9493070E-02 -5.1265930E-02 -2.5951042E-01
C3 6.5610000E-05 -2.8420000E-05 3.4356000E-04
C4 -4.9407090E-02 -3.0859948E-01 -5.1248600E-02
C5 -1.1602600E+04 -5.5564200E+04 -2.0435300E+04
C6 1.0337340E+06 5.0551080E+06 1.6848850E+06
C7 3.7781577E+01 2.2027610E+02 6.4706280E+01

71
 Table 3.7 Properties of each product

P1 P2 P3 P4
Cetane Number 54.2 52.6 58.7 66.7
Sulphur Content(ppm) 8.076 8.347 9.803 6.794
Density(g*ml-1) 0.836 0.841 0.852 0.846
CFPP(°C) -3.3 -5.0 -10.0 -15.0
Viscosity(mm2/sec ) 2.000 2.000 2.591 3.523
Ash Content(% (m/m) ) 0.009 0.009 0.006 0.007
PAH(% (m/m) ) 7.521 8.354 8.762 6.901
Flash Point(°C) 60.1 60.0 55.0 55.7

From Table 3.7, by adopting the proposed model, the market demands and product

specifications are both achieved, especially CFPP (cold filter plugging point) which

is critical property to winter diesel grades definition. The optimisation result based

on the proposed model is compared with the linear model in which linear correlation

as equation (3.9) is applied to calculate all the products properties.

Table 3.8 Comparison between two results of the proposed model and LP model

P1 P2 P3 P4
Model 1 500 900 1150 2250
Model 2 591 900 1150 2150

In Table 3.8, the production of each product from the two models is different. The

result from the proposed model prefers to produce as much Product 4 as possible.

However, the result from the linear model prefers to produce more Product 1. As

there is difference in the recipe of the two models, the composition and products

properties are also different.

The difference of the two results is due to the difference between the linear

correlations and the nonlinear correlations. The less accurate linear correlations

could make big difference when considering the large amount of petroleum products

72
produced everyday all over the world.

Inaccurate correlation could result in unqualified products, which can lead to not

only a financial penalty, but also potential safety hazard. Even though all the product

properties based on the recipe from the linear model seem to be within the limit,

when validating the product properties with the nonlinear models, some of the

properties exceed the bounds of specifications. In this case, for instance, after

recalculating by nonlinear correlations, the product properties of conventional model

are different compared with those in the linear model result.

Table 3.9 Comparison of linear result CFPP and Validated CFPP

CFPP(°C) Linear result Validated

P1 0.0 -0.8
P2 -5.0 -6.3
P3 -10.0 -11.2
P4 -15.0 -16.2

Table 3.9 illustrates that the difference between the linear result and the validated

property. With the diesel stream CFPP decreasing from 0 ºC to -15 ºC, the

deviation of the linear correlation increase from about 0.8 ºC to about 1.2 ºC. The

relative error of 5.3% cannot be neglected. Due to the inaccurate CFPP prediction,

the linear model leads to a property loss in the products, which would cause a profit

loss. In this case, the total profit optimised by linear model is 7.44 M$. However, the

proposed nonlinear planning model could optimize the profit to 7.69 M$. With better

property estimation methods, the total profit of the blending process is increased by

3.3%.

This case is solved by CONOPT in GAMS 23.5 on Dell M14 (Intel® Core™

2.40GHz) running Windows 10. It contains 161 equations and 133 variables. The

execution time is 0.004s

73
3.5 Summary

Diesel Product blending is one of the most important steps in refining operations.

Most refining products are blended from intermediate process streams. Due to the

varying properties of blending components from upstream units and tightened

product specifications, the diesel product blending problem becomes more

challenging for modern refiners. For predicting diesel blending properties, the

investigation shows that the nonlinear models have better accuracy than the linear

models. The different results of linear models and nonlinear models are validated in

this chapter. To improve the feasibility of the results for diesel blending optimization,

nonlinear models are necessary to predict product properties.

Good initialization is very important to solve NLP problems. In diesel blending

optimisation, due to the large number of variables, it obtains infeasible result from

existing solver to solve this nonconvex NLP model. A solution strategy is introduced

to solve diesel blending optimization problem.

In the case study, a diesel blending problem is solved by the nonlinear model and a

conventional linear model. Compared with the linear model, the nonlinear model can

deliver a more accurate property prediction and a better objective, which is a higher

profit in this problem.

74
 Nomenclature

Sets

𝑖 component index

𝑗 product index

Parameters

C𝐹𝑃𝑃𝑖 cold filter plugging point of the component 𝑖

𝐶𝑜𝑠𝑡𝑖 cost of a component

𝑃𝑟𝑖𝑐𝑒𝑗 price of a product

𝑅𝑖 residue of component 𝑖

𝑅𝑗 residue of product 𝑅𝑗

𝜖𝑧 value of property 𝑧 of component 𝑖

𝑑𝑒𝑛𝑖 density of component 𝑖

𝑣𝑖 kinematic viscosity of component 𝑖

𝑇𝐹 flash point in kelvin

Continuous variables

𝑃𝑟𝑜𝑓𝑖𝑡 profit of a process

𝐹𝑖 feedstock of component 𝑖
75
𝐹𝐵𝑖,𝑗 amount of component 𝑖 blended into product 𝑗

𝑃𝑗 amount of product 𝑗

𝑃𝑟𝑗,𝑧 property 𝑧 of product 𝑗

𝑥𝑖,𝑗 volume/mass fraction of component 𝑖 in product 𝑗

𝑇𝑖 pour point in degrees Rankine of component 𝑖

𝑇𝑏 blend pour point in Rankine of product 𝑗

𝐶𝐹𝑃𝑃𝑏 cold filter plugging point of the blend in Rankine

𝑑𝑒𝑛𝑠𝑗 density of the mixture

𝑥𝑖 mass fraction of component 𝑖

𝑉𝐵𝑁𝑖 viscosity blending number of component 𝑖

𝑉𝐵𝑁𝑚𝑖𝑥𝑡𝑢𝑟𝑒 viscosity blending number of mixture

𝑉𝑚𝑖𝑥𝑡𝑢𝑟𝑒 viscosity of mixture

𝐵𝐼𝐹 flash point blending index of component 𝑖

𝐴𝑖 average boiling temperature (℃) of component 𝑖

𝐺𝑖 the components 𝑖 ASTM severity (T90-T10)

CI cetane index

76
 Chapter 4 Scheduling of refinery diesel blending

4.1 Introduction

Planning and scheduling approaches for overall modeling are linked for the best

combinatory solution solved for a suitable objective function (Lee et al, 1996), which

has been incorporated throughout the formulation of subsequent models compiled.

The overview for planning and scheduling hierarchy is related to the other

constituents involved across the network. This enables the successful function of the

procedure in order to propose a feasible optimal solution relevant to the refinery

process network being investigated by considering the associated limitations that

constrain the relationship values.

Optimization of a refinery indicates maximizing profit potential of the site. The

planning models are capable of making decisions that are fairly independent of time

such as long-term contracts. Otherwise, they are less applicable for short-term needs

where both the market and a plant are fluctuant. On the other hand, scheduling,

which aims to achieve planning targets and ensure stable operations while satisfying

the market requirements. For a scheduling plan, the optimal process variables, which

come from individual or several scheduled horizon, must lie within the overall

optimal solution space and within the defined constraints supplied at the beginning

of the model formulation.

Review of existing diesel blending scheduling problems shows that several

mathematical programming approaches are currently available for short-term

blending and scheduling problems. However, in order to reduce the problem

difficulty, most of the existing mathematical approaches are not ideal for the

optimisation of diesel blending scheduling problems due to the complexity and

77
accuracy requirement. As diesel takes a very important position in modern refineries

and even modern industries, it is necessary to develop a model for diesel blending

scheduling problem. In this Chapter, a new Mixed-Integer Non-Linear Programming

(MINLP) model for optimizing diesel blending scheduling which considers all the

properties that is in the product specifications and nonlinear prediction correlations.

In addition, due to the difficulty in solving an MINLP problem, a robust solving

algorithm is also presented

4.2 Problem definition

Scheduling is a sequence of jobs, with their start time and end time, that certain

ensures constraints are met. Scheduling is carried out for minimizing cost and/or

some measure of time like the overall project completion time. The diesel blending

scheduling system consists of three pieces of equipment i.e. component stock tanks,

blending tanks and product stock tanks as shown in Figure 4.1. These three pieces of

equipment are linked together through various piping segments, flow meters and

valves. The components from the component tanks are transferred to the blending

(mixing) tanks according to the recipes. Thus, different products can be produced

and stored in their suitable product stock tanks.

Figure 4.1 Illustration of a blending problem

78
The main features of the proposed method are summarized as follows:

1. A single period optimization model is developed that is able to deal with multiple
product demands with the same due date while satisfying the product
specifications.

2. Discrete-time representations are used in the proposed approach.

3. Binary variables are used to represent assignment decisions.

The key elements in a diesel blending planning and scheduling problem that requires

attention are as follows:

Decision variables:

 Amount and type of product being produced from blending tanks in each time
interval.

 Blending ratio of product blended in the blending tank in each time interval.

Parameters:

 Minimum and maximum inventory capacities for each blending tank and storage
tank

 Minimum and maximum flow rate capacities for the blending tank

 Standard specifications for different types of diesel products.

Constraints:

 Blending tank can store only one product during the scheduling horizon

 Quality limitation on each product must be satisfied.

79
  Demand of different grade of diesel must be satisfied.

 Mass balance.

Assumptions:

 The composition requirements of products are not considered in this research.

 The input bounds of each components stream to each blender are neglected.

 The change-over cost of blenders is not considered in this research.

Another preliminary major issue during the mathematical model formulation of a

scheduling problem for any process is the representation of time. The two main
methods to represent time have been introduced in Chapter 2. Discrete-time
representation provides a reference grid of time for all operations competing for
shared resources, such as equipment items. This renders the possibility of
formulating the various constraints in the scheduling problem in a relatively
straightforward way (Floudas and Lin 2004). In addition, due to the variable nature
of the timings of events, it becomes more challenging to model the scheduling
process and the continuous-time approach may lead to mathematical models with
more complicated structures compared to their discrete-time counterparts. As the
great number of variables is one of the biggest challenges in optimizing diesel
blending scheduling problem, to decrease model scale, discrete-time representation
is applied in this work.

4.3 Mathematical model

A new nonlinear diesel blending model is presented in this section. This model is
based on an assumption that the blenders have the same capacities that are available
for different kind of diesel products.

Objective function: to maximum the total profit for all the diesel products.

80
 𝑃𝑟𝑜𝑓𝑖𝑡 = ∑𝑁𝑃 𝑁𝐹
𝑗=1 𝑃𝑗 ∙ 𝑃𝑟𝑖𝑐𝑒𝑃,𝑗 − ∑𝑖=1 𝐹𝑖 ∙ 𝑃𝑟𝑖𝑐𝑒𝐹,𝑖 (4.1)

Subject to:

1) Operation constraint

∑𝑗 𝐴𝑗,𝑛,𝑡 ≤ 1 ∀ 𝑛, 𝑡 (4.2)

Binary variable 𝐴𝑗,𝑛,𝑡 denotes that product 𝑗 is blended in blender 𝑛 during time

interval 𝑡. Constraint 4.2 donates that only 1 product can be produced in 1 blender

during 1 time interval. 𝑁 is the number of available blenders.

2) Material balance for component tanks

𝐹𝐹𝑖,𝑡 + 𝑉𝐶𝑖,𝑡−1 = 𝑉𝐶𝑖,𝑡 + ∑𝑛 𝐹𝐵𝑖,𝑛,𝑡 ∀ 𝑖, 𝑛, 𝑡 (4.3)

Where 𝐹𝐹𝑖,𝑡 is the input to component 𝑖 , 𝑉𝐶𝑘,𝑡 is the original amount of

component in component 𝑖, 𝐹𝐵𝑖,𝑛,𝑡 is the flowrate of component 𝑖 to blender 𝑛

during time interval 𝑡.

3) Material balance for blending tank

∑𝑖 𝐹𝐵𝑖.𝑛,𝑡 = 𝐹𝑃𝑗,𝑛,𝑡 ∀𝑗, 𝑛, 𝑡 (4.4)

𝐹𝑃𝑗,𝑛,𝑡 is the flowrate or product 𝑗 from blender 𝑛 to product storage tank.

4) Blending tank capacity

𝑉𝐵𝑚𝑖𝑛 ∗ 𝐴𝑗,𝑛,𝑡 ≤ 𝐹𝑃𝑗,𝑛,𝑡 ≤ 𝑉𝐵𝑚𝑎𝑥 ∗ 𝐴𝑗,𝑛,𝑡 ∀ 𝑗, 𝑛, 𝑡 (4.5)

Constraint (4.5) specifies that minimum and maximum volumetric flowrates must be

satisfied when product 𝑗 is blended during time interval 𝑡.

81
5) Other constraints

𝐹𝐵𝑖,𝑛,𝑡 = 𝐹𝑃𝑗,𝑛,𝑡 ∗ 𝑥𝑖,𝑗,𝑛,𝑡 ∀ 𝑖, 𝑗, 𝑛, 𝑡 (4.6)

where 𝑉𝑜𝑙𝑢𝑚𝑒𝑖,𝑗 is the volume amount of component 𝑖 in product 𝑗.

𝐹𝐵𝑖,𝑛,𝑡 ∗ 𝑑𝑒𝑛𝑖 = 𝑥𝑥𝑖,𝑗,𝑛,𝑡 ∀ 𝑖, 𝑗, 𝑛, 𝑡 (4.7)

where 𝑥𝑥𝑖,𝑗 is the mass amount of component 𝑖 in product 𝑗.

𝐹𝑃𝑗,𝑛,𝑡 ∗ 𝑑𝑒𝑛𝑠𝑗,𝑡 = 𝑦𝑦𝑗,𝑡 ∀ 𝑗, 𝑛, 𝑡 (4.8)

where 𝑦𝑦𝑗 is the mass amount of product 𝑗 and 𝑑𝑒𝑛𝑠𝑗 is density of product 𝑗

∑𝑖 𝑥𝑖,𝑗,𝑛,𝑡 ∗ 𝑑𝑒𝑛𝑖 = 𝑑𝑒𝑛𝑠𝑗,𝑡 ∀ 𝑗, 𝑛, 𝑡 (4.9)

6) Product specification requirement

For properties that can be predicted by different nonlinear correlations

𝑃𝑟𝑗,𝑧,𝑡 = 𝑓(𝑥𝑖,𝑗,𝑡 , 𝜖𝑧 ) ∀ 𝑖, 𝑗, 𝑧, 𝑡 (4.10)

For properties that can be predicted by linear correlations

𝑃𝑟𝑗,𝑧,𝑡 = ∑𝑖 𝑥𝑖,𝑗,𝑡 ∗ 𝜖𝑧 ∀ 𝑗, 𝑧, 𝑡 (4.11)

𝑃𝑟𝑗,𝑧,𝑡 = ∑𝑖 𝑤𝑖,𝑗,𝑡 ∗ 𝜖𝑧 ∀ 𝑗, 𝑧, 𝑡 (4.12)

7) Product demand

∑𝑡≤𝑑 𝐹𝑃𝑗,𝑛,𝑡 ≥ ∑𝑑𝑡≤𝑑 𝑑𝑑𝑗,𝑑𝑡 ∀ 𝑗, 𝑛 (4.13)

The constraint above defines all the products to be achieved the market demand at
82
the due date.

Diesel blending scheduling model is to optimise objective function (Equation 4.1)

subject to equations (4.2-4.13).

4.4 Solution algorithm

As we know, an MINLP model is difficult to solve. The existing MINLP solvers can

optimize some straightforward MINLP problems. However, scheduling of diesel

blending problem contains large number of binary variables and massive equations,

which exceeds the solving capacity of existing MINLP solvers. Therefore, a modest

growth in problem size can lead to a significant increase in the computational

requirements. For instance, in the case shown in section 4.4, there are more than 300

continuous variables and 24 binary variables. Besides, all existing algorithms scale

exponentially in the worst case (Floudas and Lin, 2004). If the case is solved by the

existing MINLP solvers (DICOPT etc.), an infeasible result will be obtained. The

optimal solution cannot be obtained directly from the optimisation software.

Therefore, in this work, a robust solution algorithm is developed as shown in Figure

4.2.

In a diesel blending scheduling case, the problem is divided into 2 sub-problems.

The first one is the Non-Linear Programming (NLP) diesel blending planning

problem. This problem is formulated and optimized using the method proposed in

Chapter 3. Nonlinear blending correlations are used to predict product properties in

the NLP model. Once the result is obtained, it provides the component volume

fractions blended in each diesel product, which is incorporated into the next

sub-problem, a Mixed-Integer Linear Programming (MILP) scheduling problem. The

MILP scheduling model is developed by the method proposed in Chapter3. The

blending recipe is fixed by the result from the first NLP blending model. By
83
optimizing the MILP problem, the scheduling result for blending operation is

obtained. In addition, by taking into account more operating conditions in the

scheduling model, the solution from the scheduling model will be more practical to

be used for daily operation. The next step is to validate the solution for the blending

scheduling problem using the NLP model. This is where the iteration starts. The

solution for the diesel scheduling problem is optimised in one iteration. This process

will be repeated until the solution of the MILP scheduling model is equal or close

enough to the solution in the previous iteration, which indicates the maximum profit

is achieved in the optimal solution

Figure 4.284
Solving Algorithm
4.5 Case study

4.5.1 Basic information

An assumed case study is presented to demonstrate the effectiveness and superiority

of the proposed diesel blending scheduling model. The data of the scheduling part

including inventory, requirements of product and so is referenced from Mendes and

Grossmann’s oil blending scheduling case (Mendes and Grossmann, 2006), while the

properties are modified to satisfying the requirements of the diesel streams.

The objective of this case study is to find an optimal schedule for the blending of

four components streams to produce three different grades of diesel products. The

number of blenders available is 3 and the capacity of each is 5.0 Mbbl. A certain

amount of feedstocks are placed in the storage tanks before the blending, The

products are transferred to storage tanks every day in a fixed daily production.

Properties, production and inventory limits are listed in Table 4.1 along with cost of

each component. During the blending process, the inventory varies depend on

production and blending recipe, but it need to be in line with the storage tank

capacity range.

85
 Table 4.1 Feedstock properties

F1 F2 F3 F4
Cetane Number 68 34 73 73
Sulphur Content(ppm) 12 8 2 8
Density(g*ml-1 ) 0.867 0.8559 0.8287 0.8162
CFPP(°C) -4 -2 -12 -10
2
Viscosity(mm /sec ) 3.8 1.5 4.4 2.7
Ash Content(% (m/m) ) 0.003 0.1 0.01 0.008
PAH(% (m/m) ) 9 13 4 2
Flash Point(°C) 50 70 60 55
Cost($/bbl) 24 20 36 34
Production Rate (Mbbl/day) 1.5 3.3 2 1.4
Initial Stock (Mbbl) 4.8 2 7.5 2.2
Minimum Stock (Mbbl) 0.5 0.5 0.5 0.5
Maximum Stock (Mbbl) 10 25 25 10

Product specifications are specified in Table 4.2. Three diesel products graded by

CFPP (cold filter plugging point) have different prices. This is the key variable in

this case.

Table 4.2 Product specifications

P1 P2 P3
Cetane Number ≥46 ≥46 ≥46
Sulphur Content(ppm) ≤10 ≤10 ≤10
Density(g*ml-1) 0.82-0.86 0.82-0.86 0.82-0.86
CFPP(°C) 0 -5 -10
Viscosity(mm2/sec ) 2-4.5 2-4.5 2-4.5
Ash Content(% (m/m) ) ≤0.01 ≤0.01 ≤0.01
PAH(% (m/m) ) ≤11 ≤11 ≤11
Flash Point(°C) ≥55 ≥55 ≥55
Price($/bbl) 31 33 34

Table 4.3 allocates the daily requirements or the three grades of products. The

inventory of products must be greater than the due day demand besides of the

minimum inventory. The production of each product is limited because of the

86
blender capacity and other operation limits.

Table 4.3 Inventory and daily requirements of products

P1 P2 P3
Requirements (Mbbl) MIN MAX LIFT MIN MAX LIFT MIN MAX LIFT
Day1 0.5 5 1 0.5 0.5 1.2 0.5 5 1
Day2
Day3 0.5 5 2.5
Day4 0.5 5 2.5 0.5 5 2.3
Day5
Day6
Day7 0.5 5 3
Day8 0.5 5 1 0.5 0.5 2.2
Inventory (Mbbl) 0.5 15 0.5 15 0.5 15
Rate(Mbbl/day) 0.5 5 0 5 0.5 5

In this case, the objective is to find an optimal scheduling to maximize the profit

with satisfying the product specifications and daily demand during an 8-day period.

The major constraints are the inventory limits for feedstocks and products, product

specifications, daily demand and other operation constraints.

4.5.2 Solving process

All the solving process is operated in GAMS 23.5.

The solving algorithm proposed in this chapter is applied to optimize the diesel

blending scheduling problem. Firstly, formulation as the model presented before.

Secondly, the model is decomposed into 2 sub models, an NLP model for blending

planning and an MILP model for scheduling. The problem is then solved by

optimising the planning model. The iterative method is applied to obtain an overall

optimal solution.

Firstly, the NLP blending planning model is solved by CONOPT, which contains 106

equations and 78 variables. The blending recipe is shown in Table 4.4.

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 Table 4.4 The First Blending Recipe from the NLP model

P1 P2 P3
F1 0.443 0.511 0.206
F2 0.537 0.372 0.099
F3 0 0.061 0.462
F4 0.021 0.057 0.233

In Table 4.5 when the volume fractions of the same product are added together, the

result of Product 1 is 1.001, same as Product 2. This is down to an approximation in

GAMS, and won’t affect the calculation and optimization.

Then, fix the recipe in the scheduling model as in Table 4.3. Solve the MILP problem

using CPLEX, with 1380 equations, 492 single variables and 72 binary variables.

Generation time is 0.032s. Through optimizing the MILP scheduling problem, new

productions scheme is as Table 4.5.

Table 4.5 New Productions by the MILP model

P1 P2 P3
Production (Mbbl) 7.5 54.0 43.7

The new productions are different from the first productions due to limitations of

blender capacity and operating constraints. The new productions are more in line

with the practical situation and operating conditions. Afterwards, the productions in

the NLP planning model are fixed and the iteration started as Figure 4.2 represents.

The optimal solution is achieved in iteration 2. The product properties are shown in

Table 4.6.

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 Table 4.6 Productions properties of the optimal solution

P1 P2 P3
Cetane Number 47.1 49 67.4
Sulphur Content(ppm) 9.2 8.7 6.9
Density(g*ml-1) 0.856 0.85 0.827
CFPP(°C) -0.2 -5.4 -10.6
Viscosity(mm2/sec ) 2.000 2.000 2.773
Ash Content(% (m/m) ) 0.008 0.008 0.008
PAH(% (m/m) ) 11.000 9.984 4.413
Flash Point(°C) 59.6 60.1 60.0
Price($/bbl) 31 33 34
Production 20.84 6.50 18.20

The feedstock and product inventory is a key variable of a diesel blending

scheduling problem. The inventory should be in the range of limits during the whole

time horizon.

A B

C D

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 Figure 4.3 Inventories of feedstocks during the blending process

A B

Figure 4.4 Inventory of products during the blending process

From Figures 4.3 and 4.4, the inventory of feedstock and product varies during the

process, but remains between the upper and lower bounds at all the times.

90
 Blender Product 1 2 3 4 5 6 7 8
P1 5
n1 P2
P3 2.627 5

P1 5
n2 P2 5 5 4.5 5
P3

P1 1.5 5 4.538 0.5 0.5

n3 P2 1.5
P3 5

Figure 4.5 Gantt Chart for the scheduling result

During the problem time period, the blender operations are as shown in Figure 4.5.

In summary, the diesel blending scheduling case has been modelled and optimized

by the methods proposed in this chapter. The optimal objective is $605 Million. The

market daily demand is achieved with all the product specifications satisfied.

This case is solved by CONOPT in GAMS 23.5 on Dell M14 (Intel® Core™

2.40GHz) running Windows 10. It contains 1380 equations, 492 single variables and

72 discrete variables. The execution time is 0.032s.

4.6 Summary

In this chapter, a new MINLP model has be developed for scheduling of refinery

diesel blending. This model applies nonlinear correlations for property prediction,

which will make the model more accurate and complex. All the specifications from

diesel product standards are included in the model, which will increase the model

scale. Existing MINLP solvers are not capable of solving a nonconvex diesel

blending scheduling problem which contains a large number of binary variables and

equations. In order to solve the MINLP model, a new solution algorithm has been

applied to decompose the MINLP problem into two parts: NLP and MILP and
91
combine them with iterations. A case study shows that the scheduling model is

feasible and this solution algorithm is effective in optimisation.

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 Nomenclature

Sets

𝑖 component index

𝑗 product index

𝑡 time interval index

𝑛 blender index

Parameters

𝑃𝑟𝑖𝑐𝑒𝑗 price of a product

𝐶𝑜𝑠𝑡𝑖 cost of a component

𝑉𝐶𝑘,𝑡 the original amount of component in component 𝑖

𝑉𝐵𝑚𝑖𝑛 , 𝑉𝐵𝑚𝑎𝑥 minimum and maximum volumetric flowrates

𝜖𝑧 value of property 𝑧 of component 𝑖

𝑑𝑑𝑗,𝑑𝑡 market demand at the due date of product 𝑗

Binary variables

𝐴𝑗,𝑛,𝑡 binary variable to denote that product j is blended in blender 𝑛

during time interval 𝑡

Continuous variables

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𝑃𝑟𝑜𝑓𝑖𝑡 profit of a process

𝐹𝐹𝑖,𝑡 input to component 𝑖

𝐹𝐵𝑖,𝑛,𝑡 the flowrate of component 𝑖 to blender 𝑛 during time interval

𝐹𝑃𝑗,𝑛,𝑡 flowrate or product 𝑗 from blender 𝑛 to product storage tank

𝑃𝑟𝑗,,𝑧,𝑡 property 𝑧 of product 𝑗

𝑥𝑖,𝑗,𝑡 volume/mass fraction of component 𝑖 in product 𝑗

94
 Chapter 5 Modelling and Optimisation of Gasoline

Blending Scheduling

5.1 Introduction

5.1.1 Gasoline

Gasoline, also called gas or petrol, is a mixture of volatile, and flammable liquid

hydrocarbons derived from petroleum, and used as fuel for internal-combustion

engines. It is also used as a solvent for oils and fats. Originally a by-product of the

petroleum industry (kerosene being the principal product), gasoline became the

preferred automobile fuel because of its high energy of combustion and capacity to

mix readily with air in a carburettor.

Gasoline is a complex mixture of hundreds of different hydrocarbons. Most are

saturated and contain 4 to 12 carbon atoms per molecule. Gasoline used in

automobiles boils mainly between 30°and 200° C, which is normally lower than

diesel (150°C-300°C).

5.1.2. Gasoline blending

Similar to diesel, gasoline can be produced in various processes in a modern oil

refinery. Due to the different sources of gasoline streams, they contain both superior

and inferior properties. Besides, different marketing locations served by a refinery

may have different requirement and regulatory specifications that may also vary

seasonally. Therefore, refiners need to select optimal combinations of various

intermediate gasoline intermediates in a particular blending ratio to produce

on-specification products. Figure 5.1 shows a simplified petroleum flowsheet. Only a

95
small portion of distillates from distillation unit can go directly to blending processes.

Most out-streams from the distillation unit are transported to upgrading processes.

The streams coming from these upgrading processes are much more valuable and are

sent to blending processes.

Major gasoline components come from: distillation unit, catalytic reforming unit,

fluid catalytic cracking unit, isomerisation unit, alkylation unit, and other units such

as coking, hydrotreating and hydrocracker.

Figure 5.1 A schematic of the gasoline blending operations

In addition, different additives such as oxygenates, antioxidants, anti-rust agents,

detergents, lubricants, etc. are used to further improve the gasoline products’ quality

to meet the product specifications.

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The objective of gasoline blending is to find the optimal blending recipe to achieve a

best overall profit while satisfying the environmental regulations and market

demand.

From the introduction above, gasoline and diesel blending operations share a lot of

similarities:

 Several feedstocks are blended into several grades of products with various

specifications.

 The objective is to generate an optimal blending recipe

 Accurate prediction of product properties is the key part of the optimization due

to product specifications.

 The nature of gasoline blending and diesel blending is nonlinear, but linear

models are widely used to simplify the problem.

In recent years, much work has been done for gasoline blending optimization in the

literature. Rigby, Lasdon, and Waren (1995) discussed successful implementation of

decision support systems for off-line multi-period blending problems at Texaco.

Kelly (2004) analyzed the underlying mathematical modelling of complex non-linear

formulations for planning models of semi-continuous facilities where the optimal

operation of petroleum refineries and petrochemical plants was mainly addressed.

Numerous reformulation results and decomposition methods (e.g. column generation,

Lagrangian relaxation/decomposition) have been proposed to improve the solution of

lot-sizing-based production planning problems (Miller, Nemhauser, and Savelsbergh,

2003). To obtain more accurate production targets, the above formulations have also

been extended to include overtime, product substitutes, productivity and capacity

utilization. These extensions form the basis of many production planning systems
97
(Pochet and Wolsey, 2006). In addition, in industries, commercial applications such

as Aspen Blend™ and Aspen PIMS-MBO™ from AspenTech are also available for

dealing with online and offline blending optimization problems

However, when it comes to gasoline blending scheduling, only linear blending

models have been adopted so far. Some researchers tried to apply nonlinear blending

models in optimizing gasoline blending scheduling problem with many restrictions.

Glismann and Gruhn (2001) proposed a two-level optimization approach where a

non-linear model is used for the recipe optimization whereas a Mixed-Integer Linear

Programming (MILP) is utilized for the scheduling problem. But products

specifications are not considered in this model as constraints.

It is widely recognized that it is necessary to use Non-Linear Programming (NLP)

models for the property prediction for gasoline blending. Therefore, it would be

relevant to see whether the developed methodology for nonlinear diesel scheduling

could be extended to nonlinear gasoline blending scheduling.

In this Chapter, the model is modified by using gasoline blending models to replace

the diesel blending models. The scheduling part remains the same since both are

product blending problem. The solving algorithm for Mixed-Integer Non-linear

Programming (MINLP) problem is also employed to optimize gasoline blending

scheduling problems.

5.2 Existing gasoline property correlations

There are several properties that are important in characterizing automotive gasoline

such as octane number (ON), Reid vapor pressure (RVP), ASTM distillation points,

viscosity, flash point, and aniline point. Ideal mixing refers to quality blending as its

volumetric average (Barrow, 1961). However, most gasoline properties blend in a

98
non-ideal and nonlinear fashion, necessitating the use of more complex blending

models to predict these properties (Rusin, 1975). In this section, blending models for

key properties – octane number, RVP, and ASTM distillation points - are presented

and discussed.

5.2.1 Octane number

Octane numbers indicate the antiknock characteristics of gasoline or the ability of the

gasoline to resist detonation during combustion in the combustion chamber. There

are two types of octane number: research octane number (RON) is measured by

ASTM D 908 under city condition, and, motor octane number is measured by ASTM

D 357 under road conditions. RON is normally greater than MON by 6-12. Since

RON and MON both are not linear properties, complex blending models are needed

for accurate prediction of blended octane numbers.

Early research on the octane number of hydrocarbons showed that octane numbers of

aromatics and branched iso-paraffins are higher than those of the corresponding

paraffins (Lovell, 1931). The American Petroleum Institute (API) analyzed octane

numbers of more than 300 hydrocarbon molecules and developed several gasoline

composition based correlations (ASTM, 1958; API, 1986; Scott, E, J, 1958).

Anderson (1972) developed a linear octane number prediction method for different

gasoline using 31 molecular lumps based on the gas chromatographic (GC) analysis.

However, a high average error around 2.8 is shown when predicting catalytically

cracked naphthas due to the shortcoming of linear ON model. Since then,

Researchers have been considering the nonlinear interactions between different

chemical compounds of gasoline and putting emphasis on the enhancement of

reliability of octane number correlations (Rusin, 1981; Habib, 1989; Cotterman,

1989). Leeuwen (1994) correlates the GC analysed gasoline composition with

99
octane number by neural networks; Meusinger (1999) and Moros (2000) used

genetic algorithms and neural networks to identify partial ONs of gasoline

components based on the structural elements of the molecule. Other researches on

chemical composition based ON methods include Twu and Coon (1997), and Albahri

(2000). Ghosh (2006) developed a detailed composition based octane number

prediction model covering variety of gasoline process streams based on the analysis

of 1471 gasoline fuels with 57 hydrocarbon lumps from GC analysis. The model

provides an acceptable accuracy within a standard error of 1 number for both RON

and MON.

For blending index method, the simplest form of their tabulated blending indexes has

be converted into the relations (Riazi, 2005):

𝐵𝐼𝑅𝑂𝑁
36.01 + 38.33𝑋 − 99.8𝑋 2 + 341.3𝑋 3 − 507.2𝑋 4 + 268.64𝑋 5 11 ≤ 𝑅𝑂𝑁 ≤ 76
={ −299.5 + 1272𝑋 − 1552.9𝑋 2 + 651𝑋 3 76 ≤ 𝑅𝑂𝑁 ≤ 103
2206.3 − 4313.64𝑋 + 2178.57𝑋 2 103 ≤ 𝑅𝑂𝑁

X=RON/100 (5.1)

5.2.2 RVP

The RVP (Reid vapour pressure) of a gasoline blend affects the gasoline performance

in terms of ease of starting, engine warm-up, and rate of acceleration. Two

fundamental methods for predicting blended RVP are given in Stewart et al. (1959)

and Vazques-Esparragoza et al. (1992). Stewart et al. (1959) presented one of the

first theoretical approaches for predicting blended RVP. The method uses component

data (such as feedstock composition and component volatility), thermodynamic

relationships, and a set of simplified assumptions (i.e. presence of air and water

vapour are ignored, absolute pressure is taken as the RVP, volatile components are

100
assumed to have the density of butanes, and the non-volatile components are

assumed to have the thermal expansion characteristics of n-octane) to predict the

blended RVP of a mixture. Vazques-Esparragoza et al. presented an iterative

procedure that extended Stewart's method. In this approach, the additivity of liquid

and gas volumes is assumed and a different equation of state is used. Furthermore,

Vazques-Esparragoza et al. approach requires that the molar composition of

feedstocks to be known. The computations required in both of these methods are

complex in comparison to those required in other approaches.

The easiest blending index method for RVP prediction is developed by Chevron.

𝑅𝑉𝑃𝐼𝑖 = (𝑅𝑉𝑃𝑖 )1.25 (5.2)

0.8
𝑅𝑉𝑃𝑏 = (∑ 𝑉𝑖 𝑅𝑉𝑃𝐼𝑖 ) (5.3)

5.2.3 Boiling range

For gasoline boiling range, Ethyl Corporation model mentioned in Chapter 3 can

also be used here to predict D86 distillation.

𝐷86𝑋𝐵 = ∑𝑛𝑖=1 𝑣𝑖 𝐵𝑉𝑥𝑖 (5.4)

𝐺𝑖
BV𝑥𝑖 = 𝐶0𝑥 + 𝐶1𝑥 𝐴𝑖 + 𝐶2𝑥 𝐴2𝑖 + 𝐶3𝑥 𝐴3𝑖 + 𝐶4𝑥 𝐴𝑖 𝐺𝑖 + 𝐶5𝑥 +
𝐴𝑖
𝐺𝑖
𝐶6𝑥 + 𝐶7𝑥 𝐺𝑖 (5.5)
𝐴2𝑖

5.3 Mathematical model

Gasoline blending planning and scheduling are interactive. Planning operation deals

with recipe generation according to market demand and product specifications. The

101
result of planning model, which is the recipe, is sent to the scheduling level.

Scheduling works in a more specific way. It allocates what is going to be done in

each time interval, including conducting the process in terms of, where streams go

and when an assignment ends. On the other hand, the feedback from the scheduling

level can help the planning operationists make better decision at the planning level.

Specific to gasoline blending problem, planning level decides a blending recipe to

achieve an optimal overall profit while the product specifications and market

demands are satisfied. After obtaining the blending recipe, the scheduling level deals

with how to achieve an optimal profit according to the recipe and market demand

with specifications in restricted time and process capacity under operating

constraints.

5.3.1 Planning model

Assumptions:

 The composition requirements of products are not considered in this research.

 The input bounds of each components stream to each blender are neglected.

 The change-over cost of blenders is not considered in this research.

 Flowrate limits are not considered in this research.

The objective of planning model is to maximize the profit through the process, which

is equal to total sale subtracting the cost of feedstocks:

𝑃𝑟𝑜𝑓𝑖𝑡 = ∑𝑁𝑃 𝑁𝐹
𝑗=1 𝑃𝑗 ∙ 𝑃𝑟𝑖𝑐𝑒𝑗 − ∑𝑖=1 𝐹𝑖 𝐶𝑜𝑠𝑡𝑖 (5.6)

Subject to:

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4) Material balance for component tanks

𝐹𝑖 = 𝑅𝑖 + ∑𝑗 𝐹𝐵𝑖,𝑗 ∀𝑖 (5.7)

5) Material balance for product tanks

𝑃𝑗 = 𝑅𝑗 + ∑𝑖 𝐹𝐵𝑖,𝑗 ∀𝑗 (5.8)

6) Market demand of each products must be satisfied

𝑃𝑗 ≥ 𝑃𝑗𝑚𝑖𝑛 ∀𝑗 (5.9)

7) Composition concentration

In order to satisfy product qualities and market conditions, upper and lower
bounds can be forced on the component concentration for different grades of
gasolines

𝐶𝐶𝑖,𝑗,𝑚𝑖𝑛 ≤ 𝐹𝐵𝑖,𝑗 ≤ 𝐶𝐶𝑖,𝑗,𝑚𝑎𝑥 ∀𝑖, 𝑗 (5.10)

𝐶𝐶𝑖,𝑗,𝑚𝑖𝑛 and 𝐶𝐶𝑖,𝑗,𝑚𝑎𝑥 are the minimum/maximum concentration of

component 𝑖 in product 𝑗.

8) Product specification requirement

For properties that can be predicted by linear correlations

𝑃𝑟𝑗,𝑧 = ∑𝑖 𝑥𝑖,𝑗 ∗ 𝜖𝑧 ∀ 𝑗, 𝑧 (5.11)

𝑃𝑟𝑗,𝑧 = ∑𝑖 𝑤𝑖,𝑗 ∗ 𝜖𝑧 ∀ 𝑗, 𝑧 (5.12)

For properties that can be predicted by different nonlinear correlations

103
 𝑃𝑟𝑗,𝑧 = 𝑓(𝑥𝑖,𝑗 , 𝜖𝑧 ) ∀ 𝑖, 𝑗, 𝑧 (5.13)

To improve its applicability, this model gives priorities to the blending index

methods for nonlinear properties. This is because these methods require less data

or other properties. The applied models are listed in Table 5.1

Table 5.1 Applied models for nonlinear properties

Method Property
Riazi Octane Number
Chevron RVP
Ethyl Corporation Boiling Range

For planning model, the objective is to maximize Equation 5.6

subject to Equations 5.7-5.13.

5.3.2 Model validation

A verification case from an Asian refinery is presented to show the accuracy of

properties prediction of blending products. Three blending components are

mixed together to produce the gasoline product. Feedstock 1 is an alkylate

stream, Feedstock 2 is an H/S LCN stream, and Feedstock 3 is a raffinate stream.

Measured properties of blending components and gasoline product, including

RON, RVP, D86 and blending ratio, are shown in Table 5.2. The linear result

comes from volume based property indices and the nonlinear result comes from

the correlations mentioned before. The calculated properties are compared with

the measured properties of blending product to show the performance and

difference between linear and nonlinear models.

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 Table 5.2 Gasoline blending model validation

F1 F2 F3 Product Linear Nonlinear

RON 95.6 92.6 75 93.7 92.3 92.6
RVP 32 63 70 59 59.3 59.5
10%℃ 82.6 51.6 51.6 53 55.6 53.07
50%℃ 106.8 93.3 64 93.9 93.9 93.5
90%℃ 136.6 161.6 78.5 169.9 155.1 159.5
Final℃ 215.6 189.5 95.5 196.8 189.2 199.07
ratio 12.85 83.25 3.9

Comparing the results, nonlinear model delivered better results on RON and D86.

For RVP, the results are similar. In order to reduce the prediction error, it is necessary

to apply nonlinear correlations in gasoline blending scheduling.

5.3.3 Scheduling model

Objective function: to maximum the total profit for all the diesel products while

subtracting the .feedstock costs.

𝑃𝑟𝑜𝑓𝑖𝑡 = ∑𝑁𝑃 𝑁𝐹
𝑗=1 𝑃𝑗 ∙ 𝑃𝑟𝑖𝑐𝑒𝑃,𝑗 − ∑𝑖=1 𝐹𝑖 ∙ 𝑃𝑟𝑖𝑐𝑒𝐹,𝑖 (5.13)

Subject to:

1) Operation constraint

∑𝑗 𝐴𝑗,𝑛,𝑡 ≤ 1 ∀ 𝑛, 𝑡 (5.14)

Binary variable 𝐴𝑗,𝑛,𝑡 is introduced in the model to denote whether product 𝑗 is

being blended in blender 𝑛 during time interval 𝑡.

2) Material balance for component tanks

𝐹𝐹𝑖,𝑡 + 𝑉𝐶𝑖,𝑡−1 = 𝑉𝐶𝑖,𝑡 + ∑𝑛 𝐹𝐵𝑖,𝑛,𝑡 ∀ 𝑖, 𝑡 (5.15)

105
3) Material balance for blending tanks

∑𝑖 𝐹𝐵𝑖.𝑛,𝑡 = 𝐹𝑃𝑗,𝑛,𝑡 ∀ 𝑗, 𝑛, 𝑡 (5.16)

4) Component concentration

𝐴𝑗,𝑛,𝑡 ∙ 𝐶𝐶𝑖,𝑗,𝑡,𝑚𝑖𝑛 ≤ 𝐹𝐵𝑖.𝑗,𝑛,𝑡 ≤ 𝐴𝑗,𝑛,𝑡 ∙ 𝐶𝐶𝑖,𝑗,𝑡,𝑚𝑎𝑥 ∀ 𝑗, 𝑛, 𝑡 (5.17)

𝐶𝐶𝑖,𝑗,𝑡,𝑚𝑖𝑛 and 𝐶𝐶𝑖,𝑗,𝑡,𝑚𝑎𝑥 are the minimum and maximum concentration of

component 𝑖 in product 𝑗 during time interval 𝑡. If product 𝑗 is not processing

in blender 𝑛 during time interval 𝑡 (𝐴𝑗,𝑛,𝑡 = 0), the flowrate of component 𝑖 to

blender 𝑛 to produce product 𝑗 during time interval 𝑡 will be zero.

5) Product specification requirement

For properties that can be predicted by different nonlinear correlations

𝑃𝑟𝑗,𝑧,𝑚𝑖𝑛 ≤ 𝑃𝑟𝑗,𝑧,𝑡 = 𝑓(𝑥𝑖,𝑗,𝑡 , 𝜖𝑧 ) ≤ 𝑃𝑟𝑗,𝑧,𝑚𝑎𝑥 ∀ 𝑗, 𝑧, 𝑡 (5.18)

For properties that can be predicted by linear correlations

𝑃𝑟𝑗,𝑧,𝑚𝑖𝑛 ≤ 𝑃𝑟𝑗,𝑧,𝑡 = 𝑥𝑖,𝑗,𝑡 ∗ 𝜖𝑧 𝑃𝑟𝑗,𝑧,𝑚𝑎𝑥 ∀ 𝑗, 𝑧, 𝑡 (5.19)

6) Product demand

∑𝑡≤𝑑 𝐹𝑃𝑗,𝑛,𝑡 ≥ ∑𝑑𝑡 𝑑𝑑𝑗,𝑑𝑡 ∀ 𝑗, 𝑛 (5.20)

For scheduling problem, the objective is to maximize Equation 5.13 subject to

Equation 5.14-5.20.

5.4 Case study

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This case study was curled from the work by Mendez (2006) and Gupta (2008). The

data is modified to compose a gasoline blending scheduling problem. Five

components and n-butane are blended into two grades of gasoline. Component

streams are available in storage tanks with an available initial inventory, and will be

produced and transferred to storage tanks daily. From the component storage tanks,

the component streams can be sent to blending tanks for mixing and from blending

tanks the product streams can be transferred to different product storage tanks. In

addition, two kinds of additives, ethanol and alkylate, can be blended into the blends

in order to improve the product quality to meet the specifications. Properties of the

five component streams, n-butane stream and additives are specified in Table 5.3.

For ethanol, an additional constraint is considered i.e. the volume composition

should not exceed 10% in the two grades of products. Ethanol and alkylate can be

purchased from the market at the price of $189/bbl and $123.9/bbl respectively.

Table 5.3 Properties of streams and additives

Stream 1 Stream 2 Stream 3 Stream 4 Stream 5 n-butane Ethanol Alkylate

RON 97.2 93.8 100.7 97.6 89.3 93 107 93
MON 86.6 84.4 89.01 86.6 81.9 92 89 90
RVP(psi) 1.1 1.4 0.9 1.3 2.7 52.0 9.6 5.0
Aromatics(%) 78.1 64.3 89.9 85.5 15.2 0 0 0
Availability (bbl) 400 222 400 100 600 125
Cost ($/bbl) 105.0 95.0 110.0 107.0 108.0 114.0 189.0 123.9
Production Rate (Mbbl/day) 1.50 3.30 2.00 1.40 4.00 1.50
Initial Stock (Mbbl) 4.00 2.22 4.00 1.00 6.00 1.25
Minimum Stock (Mbbl) 0.50 0.50 0.50 0.50 0.50 0.50
Maximum Stock (Mbbl) 35.00 35.00 35.00 35.00 45.00 35.00

The two final gasoline products can be sold at the price of $115/bbl for Gasoline 89

and $126.8/bbl for gasoline 91. The product specifications are listed in Table 5.4.

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 Table 5.4 Product specifications and prices

Gasoline 89 Gasoline 91
AKI 89 91
RON 94 96
MON 84 86
RVP(psi) 6.9 6.9
Aromatics(%) 35 35
Price ($/bbl) 115 126.8

Table 5.5 allocates the daily requirements or the two grades of products. The

inventory of products must be greater than the due day demand besides of the

minimum inventory.

Table 5.5 Inventory and daily requirements of products

P1 P2
Requirements (Mbbl) MIN MAX LIFT MIN MAX LIFT
Day1 0.5 5.0 1.0 0.5 5.0 1.2
Day2
Day3 0.5 5.0 2.5
Day4 0.5 5.0 2.5 0.5 5.0 2.3
Day5 0.5 5.0 5.0
Day6 0.5 5.0 5.0
Day7 0.5 5.0 3.0 0.5 5.0 5.0
Day8 0.5 5.0 1.0
Inventory (Mbbl) 0.5 60.0 0.5 60.0
Rate(Mbbl/day) 0.5 5.0 0.0 5.0

The objective of this case study is to find an optimised schedule in an 8-day period

while the product specifications are satisfied.

Before optimizing the problem, several assumptions are made.

• The number of blenders is assumed to be 2.

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• The blending index method proposed by Riazi (2005) is applied to calculate

RON for blends. Meanwhile MON can be calculated using the method proposed

by Jenkins (1980)

MON=22.5+0.83RON-20*SG-0.12(%O)+0.5(TML)+0.2(TEL) (5.21)

SG is specific gravity and TML and TEL are the concentration of tetra methyl

lead and tetra ethyl lead in mL/UK gallon. And %O is the volume fraction of

olefins in the gasoline. In this case, since the densities are not provided, SG is

assumed to be 0.72, a very normal SG for gasoline stream. And TEL, TML

and %O are all assumed to be zero.

As nonlinear correlations are applied to predict ROM, MON, RVP of the blends, this

problem has become an MINLP problem. The algorithm proposed in Chapter 4 is

used to optimize this MINLP scheduling problem. It is firstly decomposed into an

NLP blending planning model and MILP scheduling model. The NLP model deals

with the nonlinear blending optimization. The result, which is gasoline blending

recipe in this case, is transferred to the next MILP scheduling problem as a fixed

recipe. After optimizing, the scheduling model returns a new production, in which

blending operation constraints are considered, to the NLP planning model. By fixing

the production, the NLP planning model starts the next iteration. As the MILP

scheduling model deals with specific blending operations, the result from it is more

realistic and practical than the planning result. After getting the feedback, the NLP

model can optimize the planning problem in a higher horizon. The process continues

until the result from scheduling model is the same or very close to that in last

iteration. This is the optimal point of the gasoline blending scheduling problem.

The problem is solved by CONOPT in GAMS 23.5 to maximize objective function

(Equation 5.6) subject to constraints (Equation 5.7-5.20). The solving process ends at

109
iteration 2.

The optimization results are shown in Table 5.6 to Table 5.7

Table 5.6 Detailed product composition and production

Compostion Gasoline 89 (bbl) Gasoline 91 (mbbl)

Stream 1 0 0
Stream 2 0.443 0.358
Stream 3 0.428 0.093
Stream 4 0 0
Stream 5 0.056 0.239
n-butane 0.072 0.049
Ethanol 0 0.1
Alkylate 0 0.161
Production(Mbbl) 8 68

Table 5.7 Blended product properties (nonlinear blending)

AKI RON MON RVP(psi) Aromatics(%)

Gasoline 89 90.1 94.0 86.1 6.9 35
Gasoline 91 91.9 96.0 87.8 6.9 35

110
 Invetory of Products
70
60

Invetory (Mbbl) 50
40
30
20
10
0
1 2 3 4 5 6 7 8
P1 2 2 7 4.5 4.5 4.5 1.5 0.5
P2 3.8 13.8 16.3 24 32.6 42.6 52.6 62.6

Figure 5.2 Inventory of products

Figure 5.3 Inventory of feedstocks

From Table 5.5, since the price of Gasoline 89 is very low compared with the

component cost, the local optimal solution only produces minimum amount of this

product that can meet the market demand and inventory requirement.

111
 Blender 1 2 3 4 5 6 7 8
P1
n1 P2 5 5 5 5 5 3.604 5 5

P1 5 3
n2 P2 5 5 5 5 5 5

Figure 5.4 Gantt Chart for the scheduling result

During the problem time period, the blender operations are as shown in Figure 5.4.

This case is solved by CONOPT in GAMS 23.5 on Dell M14 (Intel® Core™

2.40GHz) running Windows 10. It contains 1171 equations, 403 single variables and

32 discrete variables. The execution time is 0.032s. The local optimal profit of this

case is $ 897 Million.

5.5 Summary

In this Chapter, a new application of the proposed model is introduced. Although

there have been many research on gasoline blending scheduling, nonlinear

correlations and property prediction accuracy haven’t receive enough attention. After

modification, the model can deal with gasoline blending successfully. Due to

nonlinear gasoline property prediction models, the blending scheduling model

becomes an MINLP problem, which cannot be solved by existing MINLP solvers

because of the complexity of the equations and the large number of variables and

equations. The solving algorithm proposed in Chapter 4 is also introduced to solve

MINLP gasoline blending scheduling problem. This MINLP is decomposed into a

two-level optimisation problem. NLP part generates a blending recipe and fixes the

nonlinear variables in the MINLP formulation, which makes it an MILP to optimise

the scheduling problem. The iteration between the two-level models provides a

near-optimal solution for the gasoline blending scheduling problem. to A case study

is presented to prove the reliability, efficiency and superiority of the proposed model
112
and solving algorithm.

113
 Nomenclature

Sets

𝑖 component index

𝑗 product index

𝑡 time interval index

𝑛 blender index

Parameters

𝑅𝑉𝑃𝑖 RVP of component 𝑖

𝑅𝑉𝑃𝐼𝑖 blending index of RVP of component 𝑖

𝐴𝑖 average boiling temperature (℃) of component i

𝐺𝑖 the components i ASTM severity (T90-T10)

𝐶𝑜𝑠𝑡𝑖 cost of a component

𝑉𝐶𝑘,𝑡 the original amount of component in component 𝑖

𝑉𝐵𝑚𝑖𝑛 , 𝑉𝐵𝑚𝑎𝑥 minimum and maximum volumetric flowrates

𝑑𝑑𝑗,𝑑𝑡 market demand at the due date of product 𝑗

𝜖𝑧 value of property 𝑧 of component 𝑖

Binary variables
114
𝐴𝑗,𝑛,𝑡 binary variable to denote that product j is blended in blender 𝑛

during time interval 𝑡

Continuous variables

RON research octane number

MON motor octane number

RVP Reid vapour pressure

𝑅𝑉𝑃𝑏 RVP of mixture

𝑃𝑟𝑜𝑓𝑖𝑡 profit of a process

𝑃𝑟𝑖𝑐𝑒𝑗 price of a product

𝐹𝐹𝑖,𝑡 input to component 𝑖

𝐹𝐵𝑖,𝑛,𝑡 the flowrate of component 𝑖 to blender 𝑛 during time interval 𝑡

𝐹𝑃𝑗,𝑛,𝑡 flowrate or product 𝑗 from blender 𝑛 to product storage tank

𝑃𝑟𝑗,,𝑧,𝑡 property 𝑧 of product 𝑗

𝑥𝑖,𝑗,𝑡 volume/mass fraction of component 𝑖 in product 𝑗

115
 Chapter 6 Conclusions and future work

6.1 Conclusions

Due to decreased oil prices and degrading qualities of crude oil, stiff market

competition and stringent fuel specifications, refinery need to have smarter strategies

to meet product demands and generate profit. However, diesel production blending

problem has not received sufficient attention from academic researchers. Refineries

widely apply Linear Programming (LP) models, which could lead to big properties

and profit loss due to inaccuracy, to operate diesel blending process. More accurate

property prediction methods should be adopted in diesel blending operation.

A model is developed to optimize diesel blending planning problem. Instead of linear

correlations for property estimation, which is mostly used in the refining industry,

nonlinear correlations for property prediction of diesel blending are applied to

improve the model accuracy. The properties in the diesel product specifications are

taken into account in this model. With the application of nonlinear correlations in the

model, the accuracy and complexity of the problem both increase. To avoid

infeasible solutions, a solution algorithm is proposed. By decomposing the model

into several sub-models, the problem is solved layer by layer. The initial point of

each layer comes from the upper level layer, until to a simply NLP model that can be

easily worked out by the solvers. A diesel blending production case is optimized by

this model. The NLP model with complex Non-Linear correlations is solved using

the solution algorithm.

On the basis of the NLP model, an MINLP model for diesel blending scheduling is

developed. For diesel production blending, the nature of nonlinear blending makes

scheduling an MINLP problem. Existing MINLP solvers fail to solve this problem

due to large number of equations and variables. To overcome the difficulties in

116
solving an MINLP problem, a robust algorithm is successfully developed. The model

is decomposed into two sub-models: NLP model for planning part and MILP model

for scheduling part. The NLP model deals with the diesel blending planning

optimization, which generates a blending recipe. Then, the blending recipe is

delivered to the next level, MILP scheduling model as a fixed recipe. After the

scheduling optimisation is performed, the new production is transferred to the NLP

planning mode to modify the blending optimization. After several iterations, the

overall optimal solution can be achieved. Through this algorithm, the MINLP

problem which cannot be solved by existing solvers can be solved.

In addition, the model is developed for diesel production blending scheduling

problem, but it can be expanded to other refinery processes, such as gasoline

blending. Considering the difference between the blending model of gasoline and

diesel, the proposed model needs to be modified before modelling the gasoline

blending problem. However, due to the same nature of nonlinear blending, the

gasoline MINLP blending scheduling problem can be optimised through the

proposed solution algorithm.

In this work, NLP models are developed in diesel blending planning and scheduling.

The proposed model and solution algorithm can improve the model accuracy,

increase the profit and reduce the computation effort. This provides a significant

improvement to the decision making procedure for refinery diesel blending

operation..

6.2 Future work

As this work introduces a model for diesel product blending, it is just the first step

for refining optimization. Therefore, there is a large scope of the future research.

117
Nonlinear blending models have been researched for years. They are more accurate

than LP models in refinery optimization. But there still are potential in improving

model accuracy. More industrial case studies can be applied to validate and improve

the developed methodology.

Only off line blending is considered in this work, however, in line blending is also a

widely used blending method in refineries. More research can be developed in

refinery in line diesel blending and optimization.

To achieve an overall optimization, the methodology for diesel blending can be

expanded to consider detailed upstream processes for producing more cost effective

diesel blending stocks.

As a more specific process level, more research can be addressed in advanced

process control for refinery diesel blending operation.

118
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126
 Appendix A Diesel blending optimization in GAMS

sets i diesel feedstock / F1, F2, F3, F4/

j products / P1, P2, P3, P4/

parameters

amount(i) amount of diesel i (t)

/ F1 1500

F2 1200

F3 1300

F4 800

CN(i) Cetane number of diesel i

/ F1 68

F2 34

F3 73

F4 73

/
127
SC(i) Sulphur content of diesel i (ppm)

/ F1 12

F2 8

F3 2

F4 8

Den(i) Density of diesel i (g*ml-1)

/ F1 0.8670

F2 0.8559

F3 0.8287

F4 0.8162

PPt(i) Pour point of diesel i

/ F1 -20

F2 -14

F3 -37

F4 -5

128
 /

CFPP(i) Could filter plugging point of diesel i

/ F1 -15

F2 -9

F3 -16

F4 3

v(i) viscosity of diesel i

/F1 3.8

F2 1.5

F3 4.4

F4 2.7

CR(i) Carbon residue of diesel i

/F1 0.2

F2 0.1

129
 F3 0.3

F4 0.4

AC(i) Ash content of diesel i

/F1 0.003

F2 0.01

F3 0.01

F4 0.008

PAH(i) polycyclic aromatic hydrocarbons in diesel i

/F1 9

F2 13

F3 4

F4 2

FP(i) flash point of diesel i

/F1 50

130
 F2 70

F3 60

F4 55

price(j) price of product j

/ P1 1270

P2 1290

P3 1320

P4 1330/

CNsta(j) standard Cetane number of product j

/ P1 46

P2 46

P3 46

P4 46/

SCsta(j) standard sulphur content of product j (ppm)

/ P1 10

P2 10

131
 P3 10

P4 10/

PPtsta(j) standard Pour Point of product j

/ P1 0

P2 -10

P3 -20

P4 -35/

CFPPsta(j) standard Cold filter plugging point of product j

/ P1 0

P2 -5

P3 -10

P4 -15/

Densitylower(j) lower limit of density (g*ml-1)

/ P1 0.82

P2 0.82

P3 0.82

P4 0.82/

132
 Densityupper(j) upper limit of density (g*ml-1)

/ P1 0.86

P2 0.86

P3 0.86

P4 0.86/

viscositylower(j) lower limit of viscosity

/P1 2

P2 2

P3 2

P4 2/

viscosityupper(j) upper limit of viscosity

/P1 4.5

P2 4.5

P3 4.5

P4 4.5 /

FPtsta(j) standard Flash Point of product j

/ P1 55

133
 P2 55

P3 55

P4 55/

BPI(i) Initial boiling point

/F1 131.5

F2 140.7

F3 205

F4 151.7

BP10(i) 10% boiling point

/F1 137.2

F2 165.4

F3 262.6

F4 256.9

BP30(i) 30% boiling point

/F1 139.9

134
 F2 173.4

F3 275.6

F4 272.2

BP50(i) 50% boiling point

/F1 143.8

F2 199.2

F3 301.8

F4 307.9

BP90(i) 90% boiling point

/F1 158.5

F2 246.9

F3 349.9

F4 367.6

135
BP95(i) 95% boiling point

/F1 166.2

F2 254.8

F3 361.6

F4 387.6

BPF(i) Final boiling point

/F1 185.6

F2 266.8

F3 372.3

F4 396.7

POSITIVE VARIABLES

x(i,j) volume fraction of feed i in product j

136
variables

yy(j) amount of product j (ton)

xx(i,j) mass of feed i in product j

dens(j) density of product j

CarbonP(j)

CNP(j)

PAHP(j)

ashP(j)

volume(i,j) volume of feed i in product j

SulphurP(j)

VBNi(i) Viscosity Blending Index of feed i

137
 VBNj(j) Viscosity Blending Index of product j

vis(j) viscosity of product j

y(j) volume amount of product j(L)

FB(i)

PourP(j)

CFPPp(j)

BIF(i) blending index of flash point of feed i

BIfp(j) blending index of flash point of product j

flashp(j) flash point of product j

BVXi(i)

BVX10(i)

138
 BVX30(i)

BVX50(i)

BVX90(i)

BVX95(i)

BVXf(i)

Ai(i)

Gi(i)

BPFI(j) Initial boiling point

BPF10(j) 10% boiling point

BPF30(j) 30% boiling point

BPF50(j) 50% boiling point

BPF90(j) 90% boiling point

BPF95(j) 95% boiling point

BPFF(j) Final boiling point

equations

density(j)

139
densityl(j)

densityu(j)

profit

Cetanenumber1(j)

Cetanenumber2(j)

Sulphurcontent1(j)

Sulphurcontent2(j)

Cfpp1(j)

VBN1(i)

VBN2(j)

140
Viscosity(j)

viscositystand1(j)

viscositystand2(j)

ashcontent1(j)

ashcontent2(j)

pahydro1(j)

pahydro2(j)

BI1(i)

BI2(j)

BI3(j)

BI4(j)

A(i)

C(j)

D(i,j)

E(i,j)

141
G(j)

Boilingpoint2(i)

Boilingpoint4(i)

Boilingpoint5(i)

Boilingpoint9(j)

Boilingpoint11(j)

Boilingpoint12(j)

Aieq(i)

Gieq(i)

142
;

density(j).. dens(j)=e= sum(i,den(i)*x(i,j);

densityu(j).. dens(j)=l=densityupper(j);

densityl(j).. dens(j)=g=densitylower(j);

profit.. s=e=sum(j, y(j)*price(j));

Cetanenumber1(j).. sum(i,x(i,j)*CN(i))=g=CNsta(j);

Cetanenumber2(j).. sum(i,x(i,j)*CN(i))=e=CNP(j);

Sulphurcontent1(j).. sum(i,xx(i,j)*SC(i)/((yy(j)+0.000001)))=l=SCsta(j);

Sulphurcontent2(j).. sum(i,xx(i,j)*SC(i)/((yy(j)+0.000001)))=e=SulphurP(j);

Aieq(i).. Ai(i)=e=(BP10(i)+BP50(i)*2+BP90(i))/4;

Gieq(i).. Gi(i)=e=BP90(i)-BP10(i);

Boilingpoint2(i)..

BVX10(i)=e=-1120+Ai(i)*(17.77218623)+Ai(i)*Ai(i)*(-0.05949307)+Ai(i)*Ai(i)*

Ai(i)*(0.00006561)+Ai(i)*Gi(i)*(-0.04940709)+(-11600)*Gi(i)/(Ai(i)+0.000000001
143
)+(1030000)*Gi(i)/(Ai(i)*Ai(i)+0.0000001)+(37.7815769)*Gi(i);

Boilingpoint4(i)..

BVX50(i)=e=-6.77060E+3+Ai(i)*(42.62167742)+Ai(i)*Ai(i)*(-0.05126593)+Ai(i)*

Ai(i)*Ai(i)*

(-0.00002842)+Ai(i)*Gi(i)*( -0.30859948)+( -5.55642E+4)*Gi(i)/(Ai(i)+0.0000000

01)+(5.055108E+6)*Gi(i)/(Ai(i)*Ai(i)+0.0000001)+( 2.202761E+2)*Gi(i);

Boilingpoint5(i)..

BVX90(i)=e=-3170+Ai(i)*(58.53687623)+Ai(i)*Ai(i)*(-0.25951042)+Ai(i)*Ai(i)*

Ai(i)*

(0.00034356)+Ai(i)*Gi(i)*( -0.0512486)+(-204000)*Gi(i)/(Ai(i)+0.000000001)+(16

80000)*Gi(i)/(Ai(i)*Ai(i)+0.0000001)+(64.70628018)*Gi(i);

Boilingpoint9(j).. BPF10(j)=e=sum(i,x(i,j)*BVX10(i));

Boilingpoint11(j).. BPF50(j)=e=sum(i,x(i,j)*BVX50(i));

Boilingpoint12(j).. BPF90(j)=e=sum(i,x(i,j)*BVX90(i));

Cfpp1(j)..

144
13.45*log(cfppsta(j)+459.67)=g=log(sum(i,(((x(i,j))**1.03)*((cfpp(i)+459.67)**13.

45)+0.00000001)));

ashcontent1(j).. sum(i,xx(i,j)*AC(i)/(yy(j)+0.00000001))=l=0.01;

ashcontent2(j).. sum(i,xx(i,j)*AC(i)/(yy(j)+0.00000001))=e=AshP(j);

pahydro1(j).. sum(i,xx(i,j)*pah(i)/(yy(j)+0.00000001))=l=11;

pahydro2(j).. sum(i,xx(i,j)*pah(i)/(yy(j)+0.00000001))=e=PAHP(j);

VBN1(i).. VBNi(i)=e=14.534*log(log(v(i)+0.8))+10.975;

VBN2(j).. VBNj(j)=e=sum(i,(xx(i,j)/(yy(j)+0.0000001)*VBNi(i)));

viscosity(j).. vis(j)=e=exp(exp((VBNj(j)-10.975)/14.534))-0.8;

viscositystand1(j).. vis(j)=l=viscosityupper(j);

viscositystand2(j).. vis(j)=g=viscositylower(j);

BI1(i).. log10(BIF(i)+0.00001)=e=-6.1188+(2414/(FP(i)+273.15-42.6));

BI2(j).. BIfp(j)=e=sum(i,x(i,j)*BIF(i));

BI3(j).. log10(BIfp(j)+0.00001)=e=-6.1188+(2414/(flashp(j)+273.15-42.6));

145
BI4(j).. flashp(j)=g=FPtsta(j);

A(i).. sum(j,xx(i,j))=l=amount(i);

C(j).. yy(j)=e=sum(i,xx(i,j));

D(i,j).. volume(i,j)=e=y(j)*x(i,j);

E(i,j).. volume(i,j)*den(i)=e=xx(i,j);

G(j).. dens(j)*y(j)=e=yy(j);

yy.lo('P1')=500;

yy.lo('P2')=800;

yy.lo('P3')=700;

yy.lo('P4')=300;

146
option NLP= conOPT ;

Model diesel2 /density

densityl

densityu

profit

147
/;

solve diesel2 using nlp maximazing s;

Model diesel1 /density

densityl

densityu

profit

Cetanenumber1

Cetanenumber2

Sulphurcontent1

Sulphurcontent2

Cfpp1

148
VBN1

VBN2

Viscosity

viscositystand1

viscositystand2

ashcontent1

ashcontent2

pahydro1

pahydro2

BI1

BI2

BI3

149
BI4

/;

solve diesel1 using nlp maximazing s;

Model blending /all/;

solve blending using nlp maximizing s ;

150
display yy.l,yy.m, x.l,x.m, XX.L,s.l,s.m;

151
 Appendix B Diesel blending scheduling optimization in

GAMS

sets i diesel feedstock / F1, F2, F3, F4/

j products / P1, P2, P3/

t time interval /1,2,3,4,5,6,7,8/

n blender /n1,n2,N3/

parameters

AVA(I)

/F1 39.9

F2 28.4

F3 23.5

F4 13.4/

iniinventory(i) initial inventory of diesel i (Mbbl)

/ F1 4.8

F2 2.0

F3 2.6

152
 F4 2.3

Production(I) daily production of i (mbbl)

/ F1 1.5

F2 3.3

F3 2.0

F4 1.4

minstock(i) minimum stock

/ F1 0.5

F2 0.5

F3 0.5

F4 0.5

maxstock(i) maximum stock

/ F1 10

153
 F2 25

F3 25

F4 10

minstockJ(J) minimum stock

/ P1 0.5

P2 0.5

P3 0.5

maxstockJ(J) maximum stock

/ P1 15

P2 15

P3 15

154
CN(i) Cetane number of diesel i

/ F1 68

F2 34

F3 73

F4 73

SC(i) Sulphur content of diesel i (ppm)

/ F1 12

F2 8

F3 2

F4 8

Den(i) Density of diesel i (g*ml-1)

/ F1 0.8670

F2 0.8559

F3 0.8287

F4 0.8162

155
 /

PPt(i) Pour point of diesel i

/ F1 -20

F2 -14

F3 -37

F4 -5

CFPP(i) Could filter plugging point of diesel i

/ F1 -4

F2 -2

F3 -12

F4 -10

v(i) viscosity of diesel i

/F1 3.8

F2 1.5

F3 4.4

156
 F4 2.7

CR(i) Carbon residue of diesel i

/F1 0.2

F2 0.1

F3 0.3

F4 0.4

AC(i) Ash content of diesel i

/F1 0.003

F2 0.01

F3 0.01

F4 0.008

PAH(i) polycyclic aromatic hydrocarbons in diesel i

/F1 9

F2 13

157
 F3 4

F4 2

FP(i) flash point of diesel i

/F1 50

F2 70

F3 60

F4 55

price(j) price of product j $ per bbl

/ P1 31

P2 33

P3 35

cost(i)

/F1 22

F2 20

158
 F3 26

F4 24

CNsta(j) standard Cetane number of product j

/ P1 46

P2 46

P3 46

SCsta(j) standard sulphur content of product j (ppm)

/ P1 10

P2 10

P3 10

PPtsta(j) standard Pour Point of product j

/ P1 0

P2 -10

159
 P3 -20

CFPPsta(j) standard Cold filter plugging point of product j

/ P1 0

P2 -5

P3 -10

Densitylower(j) lower limit of density (g*ml-1)

/ P1 0.82

P2 0.82

P3 0.82

Densityupper(j) upper limit of density (g*ml-1)

/ P1 0.86

P2 0.86

P3 0.86

160
 viscositylower(j) lower limit of viscosity

/P1 2

P2 2

P3 2

viscosityupper(j) upper limit of viscosity

/P1 4.5

P2 4.5

P3 4.5

FPtsta(j) standard Flash Point of product j

/ P1 55

P2 55

P3 55

Table LIFT(j,t)

161
 1 2 3 4 5 6 7

P1 1.0 2.5 3.0

1.0

P2 1.2 2.5 2.3

P3 1.0

2.2

Table xmilp(i,j)

P1 P2 P3

F1

F2

F3

F4

positive variables

x(i,j) volume fraction of feed i in product j

162
 yy(j) amount of product j (MASS)

xx(i,j) mass of feed i in product j

dens(j) density of product j

y(j)

volume(i,j)

FlowrateP(j,n,t) volume of product j being blended in blender n during time slot t

FlowrateB(i,j,n,t) volume of component i being transfered to blender n during

time slot t

ymilp(j)

BIfp(j) blending index of flash point of product j

SCALARS PPPPP/ 0 /

number /1/ ;

variable

163
totalpro

PourP(j)

CFPPp(j)

BIF(i) blending index of flash point of feed i

flashp(j) flash point of product j

AVAdaily(i,t)

AVARES (i,t) daily residue in inventory tank

AVARESj(j,t)

bias(j)

yy(j) amount of product j (MASS)

xx(i,j) mass of feed i in product j

dens(j) density of product j

164
 CarbonP(j)

CNP(j)

PAHP(j)

ashP(j)

volume(i,j) volume of feed i in product j

SulphurP(j)

VBNi(i) Viscosity Blending Index of feed i

VBNj(j) Viscosity Blending Index of product j

vis(j) viscosity of product j

y(j) volume amount of product j(L)

FB(i)

binary variable

A(j,n,t) denote if product j is processed in blender during time slot t

equations

165
density(j)

densityl(j)

densityu(j)

profit

Cetanenumber1(j)

Cetanenumber2(j)

Sulphurcontent1(j)

Sulphurcontent2(j)

Cfpp1(j)

VBN1(i)

VBN2(j)

Viscosity(j)

viscositystand1(j)

viscositystand2(j)

ashcontent1(j)

ashcontent2(j)

pahydro1(j)

166
pahydro2(j)

BI1(i)

BI2(j)

BI3(j)

BI4(j)

AA(i)

B(J)

C(j)

D(i,j)

E(i,j)

F(j)

GG(j)

profitMILP

blendingbalance2(j,n,t)

blendingbalance3(i,j,n,t)

blendingbalance4(j)

167
blendingbalance5(j,n,t)

blendingbalance6(j,n,t)

blendoperation3(n,t)

D2(i,j,n,t)

*D3(i)

AVA1(i,t)

AVA2(i,t)

AVA21(i,t)

AVA22(i,t)

AVA23(i,t)

AVA24(i,t)

AVA25(i,t)

AVA26(i,t)

AVA31(j,t)

AVA32(j,t)

AVA33(j,t)

168
AVA34(j,t)

AVA35(j,t)

AVA36(j,t)

AVA3(j,t)

AVA4(j,t)

AVA5(i,t)

AVA6(i,t)

AVA7(j,t)

AVA8(j,t)

density(j).. dens(j)=e=(sum(i,x(i,j)*den(i)));

densityu(j).. dens(j)=l=densityupper(j);

densityl(j).. dens(j)=g=densitylower(j);

profit.. s=e=sum(j, y(j)*price(j))-sum((i,j),volume(i,j)*cost(i));

Cetanenumber1(j).. sum(i,x(i,j)*CN(i))=g=CNsta(j);

Cetanenumber2(j).. sum(i,x(i,j)*CN(i))=e=CNP(j);

Sulphurcontent1(j).. sum(i,xx(i,j)*SC(i)/((yy(j)+0.000001)))=l=SCsta(j);

169
Sulphurcontent2(j).. sum(i,xx(i,j)*SC(i)/((yy(j)+0.000001)))=e=SulphurP(j);

Cfpp1(j)..

13.45*log(cfppsta(j)+459.67)=g=log(sum(i,(((x(i,j))**1.03)*((cfpp(i)+459.67)**13.

45)+0.00000001)));

ashcontent1(j).. sum(i,xx(i,j)*AC(i)/(yy(j)+0.00000001))=l=0.01;

ashcontent2(j).. sum(i,xx(i,j)*AC(i)/(yy(j)+0.00000001))=e=AshP(j);

pahydro1(j).. sum(i,xx(i,j)*pah(i)/(yy(j)+0.00000001))=l=11;

pahydro2(j).. sum(i,xx(i,j)*pah(i)/(yy(j)+0.00000001))=e=PAHP(j);

VBN1(i).. VBNi(i)=e=14.534*log(log(v(i)+0.8))+10.975;

VBN2(j).. VBNj(j)=e=sum(i,(xx(i,j)/(yy(j)+0.0000001)*VBNi(i)));

viscosity(j).. vis(j)=e=exp(exp((VBNj(j)-10.975)/14.534))-0.8;

viscositystand1(j).. vis(j)=l=viscosityupper(j);

viscositystand2(j).. vis(j)=g=viscositylower(j);

BI1(i).. log10(BIF(i)+0.00001)=e=-6.1188+(2414/(FP(i)+273.15-42.6));

BI2(j).. BIfp(j)=e=sum(i,x(i,j)*BIF(i));
170
BI3(j).. log10(BIfp(j)+0.00001)=e=-6.1188+(2414/(flashp(j)+273.15-42.6));

BI4(j).. flashp(j)=g=FPtsta(j);

AA(i).. sum(j,volume (i,j))=l=AVA(i);

B(J).. sum(i,x(i,j))=e=1;

C(j).. yy(j)=e=sum(i,xx(i,j));

D(i,j).. volume(i,j)=e=y(j)*x(i,j);

E(i,j).. volume(i,j)*den(i)=e=xx(i,j);

F(j).. sum(i,volume(i,j))=e=y(j);

GG(j).. dens(j)*y(j)=e=yy(j);

h.. sum(j,y(j))=l=120;

profitMILP..

sum((j,n,t),

FlowrateP(j,n,t)*price(j))-sum((i,j,n,t),FlowrateB(i,j,n,t)*cost(i))=e=totalpro;

blendingbalance2(j,n,t)..

sum(i,FlowrateB(i,j,n,t))=e=FlowrateP(j,n,t) ;

171
blendingbalance3(i,j,n,t)..

FlowrateB(i,j,n,t)=e=FlowrateP(j,n,t)*xmilp(i,j); ;

blendingbalance5(j,n,t)..

FlowrateP(j,n,t)=l=5*A(j,n,t);

blendingbalance6(j,n,t)..

FlowrateP(j,n,t)=g=0.5*A(j,n,t);

blendingbalance4(j)..

yMILP(j)=e=sum((n,t),FlowrateP(j,n,t));

blendoperation3(n,t).. sum((j), A(j,n,t))=l=1;

172
D2(i,j,n,t)..

FlowrateP(j,n,t)*xMILP(i,j)=e=FlowrateB(i,j,n,t);

*D3(i)..

Volumeres(i)=e=AVA(i)-sum((j,t),FlowrateB(i,j,t))+INIINVENTORY(I);

AVA1(i,t).. AVAres(i,'1')=e=

iniinventory(i)+production(i)-sum((j,n),FlowrateB(i,j,n,'1'));

AVA2(i,t).. AVAres(i,'2')=e= AVAres(i,'1')+production

(i)-sum((j,n),FlowrateB(i,j,n,'2'));

AVA21(i,t).. AVAres(i,'3')=e= AVAres(i,'2')+production

(i)-sum((j,n),FlowrateB(i,j,n,'3'));

AVA22(i,t).. AVAres(i,'4')=e= AVAres(i,'3')+production

(i)-sum((j,n),FlowrateB(i,j,n,'4'));

AVA23(i,t).. AVAres(i,'5')=e= AVAres(i,'4')+production

(i)-sum((j,n),FlowrateB(i,j,n,'5'));

AVA24(i,t).. AVAres(i,'6')=e= AVAres(i,'5')+production

173
(i)-sum((j,n),FlowrateB(i,j,n,'6'));

AVA25(i,t).. AVAres(i,'7')=e= AVAres(i,'6')+production

(i)-sum((j,n),FlowrateB(i,j,n,'7'));

AVA26(i,t).. AVAres(i,'8')=e= AVAres(i,'7')+production

(i)-sum((j,n),FlowrateB(i,j,n,'8'));

AVA3(j,t).. AVAresj(j,'2')=e=

AVAresj(j,'1')+sum(n,FlowrateP(j,n,'2'))-LIFT(j,'2');

AVA31(j,t).. AVAresj(j,'3')=e=

AVAresj(j,'2')+sum(n,FlowrateP(j,n,'3'))-LIFT(j,'3');

AVA32(j,t).. AVAresj(j,'4')=e=

AVAresj(j,'3')+sum(n,FlowrateP(j,n,'4'))-LIFT(j,'4');

AVA33(j,t).. AVAresj(j,'5')=e=

AVAresj(j,'4')+sum(n,FlowrateP(j,n,'5'))-LIFT(j,'5');

AVA34(j,t).. AVAresj(j,'6')=e=

AVAresj(j,'5')+sum(n,FlowrateP(j,n,'6'))-LIFT(j,'6');

AVA35(j,t).. AVAresj(j,'7')=e=

AVAresj(j,'6')+sum(n,FlowrateP(j,n,'7'))-LIFT(j,'7');

174
AVA36(j,t).. AVAresj(j,'8')=e=

AVAresj(j,'7')+sum(n,FlowrateP(j,n,'8'))-LIFT(j,'8');

AVA4(j,t).. AVAresj(j,'1')=e=

sum(n,flowrateP(j,n,'1'))-LIFT(j,'1');

AVA5(i,t).. AVAres(i,t)=g=minstock(i);

AVA6(i,t).. AVAres(i,t)=l=maxstock(i);

AVA7(j,t).. AVAresj(j,t)=g=minstockj(j);

AVA8(j,t).. AVAresj(j,t)=l=maxstockj(j);

y.lo('p1')= 7.5;

y.lo('p2')= 6.0;

y.lo('p3')=3.2;

Model diesel2 /density

175
densityl

densityu

profit

*avalable

AA

GG

h/

solve diesel2 using nlp maximizing s;

Model diesel1 /density

densityl

densityu

profit

176
Cetanenumber1

Cetanenumber2

Sulphurcontent1

Sulphurcontent2

*avalable

Cfpp1

VBN1

VBN2

Viscosity

viscositystand1

viscositystand2

177
ashcontent1

ashcontent2

pahydro1

pahydro2

BI1

BI2

BI3

BI4

AA

GG

/;

178
solve diesel1 using nlp maximazing s;

display y.l,y.m, x.l,x.m, XX.L,s.l,s.m,volume.l;

xmilp(i,j)=x.L(i,j);

MODEL SCHEDULING /profitMILP, blendingbalance2,blendingbalance4,

blendingbalance3

blendingbalance5,

blendingbalance6,

blendoperation3,

D2,

*D3,

*avalable

AVA1,AVA2,AVA3

AVA4

AVA21

AVA22

AVA23

AVA24

179
AVA25

AVA26

AVA31

AVA32

AVA33

AVA34

AVA35

AVA36

AVA5

AVA6

AVA7

AVA8

/;

solve Scheduling using MIP maximizing totalpro;

display totalpro.l,totalpro.m,y.l,y.m,flowrateB.l,flowratep.l,A.l,ymilp.l,XMILP;

WHILE (((PPPPP < totalpro.l)),

PPPPP = totalpro.l;

180
* Pj(j)= ymIlp.l(j);

number= number+1;

y.lo(j)=ymilp.l(j);

y.up(j)=ymilp.l(j);

solve diesel2 using nlp maximazing s;

solve diesel1 using nlp maximazing s;

*solve blending using nlp maximizing s ;

xmilp(i,j)=x.L(i,j);

display x.l,xmilp, TOTALPRO.L;

solve Scheduling using MIP maximizing totalpro;

DISPLAY TOTALPRO.L,FLOWRATEP.L,PPPPP,

y.l,x.l,number,flowratep.l,A.L,avares.l, AVARESJ.L; )

display totalpro.l,y.l,x.l,number,flowratep.l,A.L,avares.l, AVARESJ.L;

181