Data Stream Molecular Management

MOLECULAR MANAGEMENT FOR REFINING
OPERATIONS



A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy
in the Faculty of Engineering and Physical Sciences

2010

Yongwen Wu




Centre for Process Integration
School of Chemical Engineering and Analytical Science




2
Table of Contents
List of Figures.......................................................................................................... 8
List of Tables ......................................................................................................... 12
Abstract.................................................................................................................. 16
Declaration............................................................................................................. 18
Copyright Statement............................................................................................. 19
Acknowledgements................................................................................................ 21
Chapter 1 Introduction............................................................................... 22
1.1 Introduction............................................................................................. 23
1.2 A Refinery Scheme ................................................................................. 23
1.3 Current Status of Refining Industry........................................................ 24
1.3.1 Product Specifications............................................................................ 24
1.3.2 Changing Market Demands and Supply ................................................ 27
1.3.3 Refining Margin and Refinery Optimisation ......................................... 28
1.4 Molecular Management .......................................................................... 30
1.5 Present Research ..................................................................................... 30
1.6 Structure of Thesis .................................................................................. 31
Chapter 2 Molecular Characterisation of Petroleum Fractions............. 33
2.1 Introduction............................................................................................. 34
2.2 Complexity Nature of Petroleum Fractions ............................................ 34
2.3 Review of Previous Methods .................................................................. 35
2.3.1 Traditional Methods............................................................................... 35
2.3.2 Modern Analytical Laboratory Methods................................................ 36
2.3.3 Computer-aided Molecular Explicit Methods........................................ 38
2.3.3.1 Challenges of Molecular Characterisation Methods................... 38
2.3.3.2 Stochastic Methods ..................................................................... 39
2.3.3.3 Deterministic Methods................................................................ 41
2.3.4 Existing MTHS Methods ....................................................................... 43
2.3.5 Limitations of Existing MTHS Methods ............................................... 44
2.3.5.1 Limitation of Representation Matrix........................................... 44
3
2.3.5.2 Limitation of the Transformation Method .................................. 45
2.3.6 A Brief Case Showing the Shortcomings of the Existing Methods....... 45
2.4 A Modified MTHS Framework .............................................................. 48
2.5 Improved MTHS Matrix Representation Model..................................... 49
2.5.1 Improved MTHS Matrix Representation Model for Light Petroleum
Fractions.......................................................................................................... 49
2.5.2 Improved MTHS Matrix Representation Model for Middle Petroleum
Fractions.......................................................................................................... 50
2.6 Transformation Methodology ................................................................. 55
2.6.1 Assumptions........................................................................................... 55
2.6.1.1 Statistical Distribution Assumption ............................................ 55
2.6.1.2 Property Estimation Assumption ................................................ 57
2.6.2 Mathematical Model .............................................................................. 60
2.6.2.1 Objective Function...................................................................... 61
2.6.2.2 Constraints .................................................................................. 62
2.7 Optimisation Engines.............................................................................. 65
2.8 Case Studies ............................................................................................ 67
2.8.1 FCC Gasoline Stream Case.................................................................... 67
2.8.2 SRGO Feed ............................................................................................ 70
2.8.3 LCO Feed............................................................................................... 75
2.9 Summary................................................................................................. 77
Chapter 3 Molecular Modelling of Gasoline Blending ............................ 78
3.1 Introduction............................................................................................. 79
3.2 Gasoline Blending................................................................................... 79
3.2.1 A Brief Introduction of Gasoline Blending............................................ 79
3.2.1.1 Blending Process......................................................................... 80
3.2.1.2 Blending Type............................................................................. 80
3.2.1.3 Gasoline Blending Stocks ........................................................... 81
3.2.1.4 Gasoline Specifications............................................................... 82
3.2.2 Motivation of this Research on Gasoline Blending ............................... 85
3.3 A New Molecular Model for Property Prediction .................................. 86
3.3.1 Review of Previous Methodologies for ON........................................... 87
3.3.2 A New Methodology Correlating ON with Bulk Properties.................. 87
4
3.3.2.1 Assumptions................................................................................ 87
3.3.2.2 Methodology............................................................................... 91
3.3.3 Case Study.............................................................................................. 96
3.3.3.1 Result of the Regression Phase ................................................... 97
3.3.3.2 Result of the Prediction Phase .................................................. 100
3.4 Gasoline Blending Model ..................................................................... 101
3.4.1 Review of Gasoline Blending Models ................................................. 101
3.4.2 Existing Blending Models for ON and RVP Properties ...................... 102
3.4.2.1 Octane Number ......................................................................... 102
3.4.2.2 Reid Vapour Pressure................................................................ 105
3.4.3 A New Molecular Gasoline Blending Methodology ........................... 106
3.4.3.1 Diagram..................................................................................... 106
3.4.3.2 Mathematical Model ................................................................. 107
3.4.4 Gasoline Blending Optimisation Model .............................................. 108
3.4.5 Case Study............................................................................................ 109
3.4.5.1 Traditional Method ................................................................... 110
3.4.5.2 Molecular Blending Model ....................................................... 111
3.5 Summary............................................................................................... 112
3.6 Nomenclature........................................................................................ 112
Chapter 4 Molecular Modelling of Semiregenerative Catalytic
Reforming ............................................................................................... 114
4.1 Introduction........................................................................................... 116
4.1.1 Catalytic Reforming Process................................................................ 117
4.1.2 Feed Characteristics ............................................................................. 119
4.1.3 Operating Conditions ........................................................................... 120
4.1.4 Product ................................................................................................. 122
4.1.5 Review of Previous Work.................................................................... 123
4.1.6 Motivation of Molecular Modelling of Catalytic Reforming .............. 126
4.2 Chemical Reactions Network and Kinetics .......................................... 127
4.2.1 Dehydrogenation of Naphthenes to Aromatics.................................... 128
4.2.2 Isomerisation of Paraffins and Naphthenes ......................................... 129
4.2.3 Dehydrocyclisation of Paraffins........................................................... 129
4.2.4 Hydrocracking and Dealkylation ......................................................... 130
5
4.2.5 Kinetics ................................................................................................ 131
4.3 Process Model ....................................................................................... 131
4.4 Case Study............................................................................................. 134
4.4.1 Simulation of the Process..................................................................... 135
4.4.2 Sensitivity Analysis of Operating Conditions...................................... 139
4.5 Catalyst Deactivation ............................................................................ 142
4.5.1 Mathematical Model of Catalyst Deactivation .................................... 142
4.5.2 Multi-period Process Model................................................................. 144
4.6 Catalytic Reforming Process Optimisation........................................... 146
4.6.1 Mathematical Model ............................................................................ 147
4.6.2 Optimisation Approach........................................................................ 148
4.7 Case Study – Multi-period Process Simulation and Optimisation........ 148
4.7.1 Multi-period Process Simulation ......................................................... 148
4.7.2 Sensitivity Analysis of Operating Temperatures ................................. 150
4.7.3 Process Optimisation............................................................................ 151
4.8 Summary............................................................................................... 153
4.9 Nomenclature........................................................................................ 154
Chapter 5 Molecular Modelling of Diesel Hydrotreater ....................... 156
5.1 Introduction........................................................................................... 157
5.1.1 Diesel Hydrotreating Process............................................................... 157
5.1.2 Feed Characteristics ............................................................................. 159
5.1.3 Operating Conditions ........................................................................... 159
5.1.4 Product Specification........................................................................... 161
5.1.5 Motivation of a Molecular Model for Diesel Hydrotreater.................. 162
5.2 Reactions Network and Kinetics........................................................... 163
5.2.1 Hydrodesulphurisation (HDS) ............................................................. 164
5.2.1.1 Sulphur Compounds.................................................................. 164
5.2.1.2 Reactions Network and Kinetics............................................... 166
5.2.1.3 Obtaining Kinetic Parameters – Structure Contribution Approach
................................................................................................... 168
5.2.2 Hydrodearomatisation (HDA).............................................................. 171
5.2.2.1 Aromatic Compounds ............................................................... 171
5.2.2.2 Reactions Network and Kinetics............................................... 171
6
5.2.2.3 Obtaining Kinetic Parameters ................................................... 173
5.3 Modelling of a Trickle – bed Reactor ................................................... 174
5.3.1 Mathematical Equations....................................................................... 175
5.3.2 Estimation of Physical Properties ........................................................ 177
5.3.3 Mathematical Methodology and Solving Procedure............................ 179
5.4 Case Study – Modelling of Diesel Hydrotreater................................... 181
5.4.1 Simulation of a Diesel Hydrotreater .................................................... 181
5.4.2 Sensitivity Analysis of Operating Conditions...................................... 183
5.5 Catalyst Deactivation ............................................................................ 186
5.5.1 Mathematical Model of Catalyst Deactivation .................................... 186
5.5.2 Multi-period Model of Catalyst Deactivation...................................... 188
5.6 Diesel Hydrotreater Optimisation......................................................... 189
5.6.1 Mathematical Model ............................................................................ 190
5.7 Case Study – Optimisation of Diesel Hydrotreater............................... 191
5.8 Summary............................................................................................... 192
5.9 Nomenclature........................................................................................ 193
Chapter 6 Integrated Site and Process Optimisation with Molecular
Modelling ................................................................................................... 195
6.1 Introduction........................................................................................... 196
6.1.1 Challenges of Refinery Optimisation................................................... 196
6.1.2 Decomposition Strategy for Refinery Optimisation (Zhang, 2000) .... 198
6.2 Incorporating Molecular Management into Refinery Optimisation ..... 199
6.3 Application I: Exploitation of Interaction between Refinery Material
Processing Network and Processes ................................................................... 199
6.3.1 Introduction.......................................................................................... 199
6.3.2 Site Level Model .................................................................................. 200
6.3.3 Site Optimisation with Process Simulation.......................................... 202
6.3.4 Integrated Site and Process Optimisation ............................................ 204
6.3.5 Case Study............................................................................................ 205
6.3.5.1 Problem Definition.................................................................... 205
6.3.5.2 Modelling of Refining Streams and Processes ......................... 207
6.3.5.3 Strategy of Case Study.............................................................. 208
6.3.5.4 Optimisation Results................................................................. 209
7
6.4 Application II: Exploitation of Interactions between Hydrogen
Network and Hydroprocesses ........................................................................... 215
6.4.1 Introduction.......................................................................................... 215
6.4.1.1 Hydrogen Network in Refinery................................................. 215
6.4.1.2 Hydrogen Network Management.............................................. 216
6.4.2 Integrating Hydrogen Network and Hydroprocesses........................... 220
6.4.3 Site Level Model .................................................................................. 220
6.4.4 Site Optimisation with Process Simulation.......................................... 226
6.4.5 Integrated Site and Process Optimisation ............................................ 227
6.4.6 Case Study............................................................................................ 228
6.5 Summary............................................................................................... 232
6.6 Nomenclature........................................................................................ 233
6.6.1 Application I ........................................................................................ 233
6.6.2 Application II ....................................................................................... 233
Chapter 7 Conclusions and Future Work............................................... 236
7.1 Conclusions........................................................................................... 237
7.2 Future Work .......................................................................................... 239
References ............................................................................................................ 241
Appendix A Joback Group Contribution................................................... 258
Appendix B Parameters of Kinetic Model of Catalytic Reformer........... 259
Appendix C Parameters of Group Contribution Approach..................... 261
Appendix D Physical Properties Calculation............................................. 264
Appendix E Boundary Value Problem....................................................... 271
Appendix F RFCC Model............................................................................ 275

8
List of Figures
Figure 1.1 Flowsheet of a refinery (Gary and Handwerk, 1994)............................ 24
Figure 1.2 Oil demand growth by product, in North America, Europe, Asia and
Middle East, 2008-2014 (Oil Market Report, 2009)....................................... 27
Figure 2.1 Complexity of typical petroleum hydrocarbon type analysis
(www.epa.gov)................................................................................................ 35
Figure 2.2 Chemical complexity of higher boiling products (Read, 1976) ............ 35
Figure 2.3 Flow diagram of stochastic modelling of molecular structures and
compositions of a complex feedstock (Campbell, 1998) ................................ 40
Figure 2.4 Schematic representation of the methodology (Aye, 2003) .................. 43
Figure 2.5 Research octane number of isooctane isomers (Ghosh, 2006).............. 45
Figure 2.6 Predicted molecular composition with 40 sample matrices .................. 47
Figure 2.7 Predicted molecular composition with 80 sample matrices .................. 47
Figure 2.8 New MTHS framework for the characterisation of refining streams.... 48
Figure 2.9 MTHS Matrix representation of diesel fractions (Peng, 1999) ............. 50
Figure 2.10 C
15
H
12
isomer corresponding to Table 2.5 generated by SMOG........ 52
Figure 2.11 (C
17
, A) isomers distribution with boiling point.................................. 53
Figure 2.12 Gamma distribution fitted fractions within PONA homologous series
of a FCC gasoline stream (Chen, 1995) .......................................................... 56
Figure 2.13 Gamma distribution fitted fractions within homologous series of a
middle distillate (Fafet, 1995) ......................................................................... 56
Figure 2.14 Calculation procedure based on the second assumption ..................... 57
Figure 2.15 Simulated annealing algorithm (Kirkpatrick, 1983)............................ 66
Figure 2.16 Comparison of the detailed PIONA volume fraction between the
measured and those based on the existing and proposed methodologies........ 69
Figure 2.17 Distillation profiles of the SRGO from the measured and the predicted
......................................................................................................................... 74
Figure 3.1 Simplified petroleum refinery flowsheet (Gupta, 2008) ....................... 80
Figure 3.2 Research Octane Number of different families of hydrocarbons (Riazi,
2005) ............................................................................................................... 86
Figure 3.3 Nonlinear interactions between two molecules belonging to different
homologous series (Ghosh, 2006)................................................................... 88
Figure 3.4 Simplified diagram for predicting ON of blending streams .................. 89
9
Figure 3.5 Diagram for the methodology of predicting ON of gasoline streams
from one of refining process ........................................................................... 91
Figure 3.6 Series of procedures for achieving the optimal coefficients for
predicting ONs of PIONA lumps.................................................................... 93
Figure 3.7 Normalised distributions of the related properties for the proposed
methodology (Each dot stands for a different sample) ................................... 96
Figure 3.8 Comparison of PIONA volume fractions between the measured and
predicted in regression phase .......................................................................... 97
Figure 3.9 Comparison of RON between the measured and predicted in regression
phase................................................................................................................ 98
Figure 3.10 Comparison of MON between the measured and predicted in
regression phase .............................................................................................. 98
Figure 3.11 Comparison of RVP between the measured and predicted in regression
phase................................................................................................................ 99
Figure 3.12 Proposed molecular gasoline blending methodology........................ 106
Figure 4.1 Simplified semiregenerative process of catalytic reforming (Gary and
Handwerk, 2001)........................................................................................... 118
Figure 4.2 Pressure influence (Robert, 2003) ....................................................... 121
Figure 4.3 Generalised reaction network .............................................................. 127
Figure 4.4 Diagram of the simulation of catalytic reforming ............................... 134
Figure 4.5 Reactors configuration and operating conditions ................................ 135
Figure 4.6 Distillate profiles of feedstock and product from the measured and the
predicted........................................................................................................ 136
Figure 4.7 Comparison of the product molecular composition ............................ 137
Figure 4.8 Profiles of composition through the reactors....................................... 138
Figure 4.9 Composition profiles under the adiabatic operating mode.................. 138
Figure 4.10 Temperature and pressure profile under the adiabatic operating mode
....................................................................................................................... 139
Figure 4.11 Influence of temperature on quality of reformate and yield (Pressure of
150 psi).......................................................................................................... 140
Figure 4.12 Influence of temperature on product yields (Pressure of 150 psi)..... 140
Figure 4.13 Influence of pressure on reformate yield and quality (T: 783.15K).. 141
Figure 4.14 Influence of pressure on product distribution and yield (T: 783.15K)
....................................................................................................................... 141
10
Figure 4.15 Influence of WHSV on reformate yield and quality.......................... 142
Figure 4.16 Influence of WHSV on product distribution ..................................... 142
Figure 4.17 Simulation procedure of the proposed multi-period process model.. 145
Figure 4.18 Profit and reformate ON through running cycle................................ 149
Figure 4.19 Product distributions through running cycle ..................................... 149
Figure 4.20 Catalyst activities of three reactors through running cycle ............... 150
Figure 4.21 Influence of temperature on overall profit and RON ........................ 150
Figure 4.22 Influence of temperature on the overall hydrogen and reformate yields
....................................................................................................................... 151
Figure 4.23 Optimal operating temperature through the running periods targeting
the maximal profit ......................................................................................... 152
Figure 4.24 Product distribution through the running periods targeting the maximal
profit.............................................................................................................. 153
Figure 5.1 A simplified diesel hydrotreating process flowsheet (Gary, 2001) ..... 158
Figure 5.2 Difficulties of desulphurisation of different sulphur compounds
(Froment, 2007) ............................................................................................ 164
Figure 5.3 Reaction Network for the HDS of DBT.............................................. 166
Figure 5.4 HDA reactions in diesel hydrotreater (Neurock, 1990)....................... 171
Figure 5.5 Solving procedure for a diesel hydrotreater tickle-bed reactor ........... 179
Figure 5.6 simulated process integrated with H2S scrubber and flash ................. 180
Figure 5.7 Axial profiles of the sulphur compound content and the partial pressure
of H2S (625 K).............................................................................................. 182
Figure 5.8 Axial concentration of hydrogen in the liquid phase and partial pressure
of hydrogen in the vapour phase (625 K) ..................................................... 183
Figure 5.9 Influence of temperature on the product compositions ....................... 184
Figure 5.10 Influence of the LHSV on the product compositions........................ 184
Figure 5.11 Influence of the pressure on the product composition....................... 185
Figure 5.12 Influence of the H
2
/oil ratio on the product composition.................. 185
Figure 5.13 Influence of catalyst activity on the sulphur removal........................ 186
Figure 5.14 Multi-period of run length on the catalyst activity basis division..... 189
Figure 6.1 A general connection........................................................................... 200
Figure 6.2 Site level optimisation with process simulation .................................. 203
Figure 6.3 Integration of site level optimisation and process optimisation .......... 204
Figure 6.4 Flowsheet of a refinery........................................................................ 205
11
Figure 6.5 Composition of gasoline90 in different modes.................................... 212
Figure 6.6 Composition of gasoline93 in different modes.................................... 213
Figure 6.7 Composition of gasoline95 in different modes.................................... 213
Figure 6.8 Composition of gasoline97 in different modes.................................... 213
Figure 6.9 Composition of diesel in different modes............................................ 214
Figure 6.10 A typical hydrogen network .............................................................. 216
Figure 6.11 Simplified diagram of a hydrogen consumer (Alves, 1999) ............. 217
Figure 6.12 Composite curves (Liu, 2002) ........................................................... 218
Figure 6.13 A hydrogen surplus diagram (Liu, 2002) .......................................... 218
Figure 6.14 Balanced hydrogen surplus cascade diagram (Liu, 2002)................. 218
Figure 6.15 Representation change of a process for new method ........................ 221
Figure 6.16 Modified diagram of a hydrogen consuming process ....................... 221
Figure 6.17 Site optimisation with process simulation/optimisation.................... 227
Figure 6.18 Integration of hydrogen network and hydroprocesses....................... 228
Figure 6.19 The hydrogen network of the case (Sun, 2004)................................. 229
Figure 6.20 Hydrogen surplus diagram................................................................. 230
Figure 6.21 Hydrogen surplus diagrams of periods.............................................. 231
12
List of Tables
Table 1.1 European Union diesel specification (Official Journal of the European
Communities, 2009)........................................................................................ 25
Table 1.2 European Union petrol specification ...................................................... 26
Table 2.1 Typical Measured Isomer Distribution (wt %) for i-Octane (Ghosh,
2006) ............................................................................................................... 44
Table 2.2 Distillation profile of a FCC stream........................................................ 46
Table 2.3 Comparisons of properties between measured and two groups of
estimated ......................................................................................................... 46
Table 2.4 New MTHS representation matrix for light petroleum fractions............ 49
Table 2.5 One of C
15
H
12
isomers output from SMOG............................................ 52
Table 2.6 Isomers generation of each homologous series (* represent the property
of the entry is calculated by extrapolation or interpolation) ........................... 54
Table 2.7 Properties estimation methodology for pure compounds and mixtures,
mixing rules..................................................................................................... 58
Table 2.8 Properties comparison of a gasoline stream based on both correlations
and mixing rules.............................................................................................. 60
Table 2.9 Measured molecular composition of a FCC stream (vol %)................... 67
Table 2.10 Generated matrix for the FCC stream by the proposed methodology .. 68
Table 2.11 Comparison of properties...................................................................... 68
Table 2.12 Comparison of distillation profile between the measured and the
predicted from the developed method............................................................. 70
Table 2.13 Properties of SRGO Feed (Marafi, 2007) ............................................. 71
Table 2.14 MTHS matrix (wt %) generated for GO-LF SRGO by simulated
annealing algorithm......................................................................................... 72
Table 2.15 Parameters of homologous series predicted for the gamma distribution
and the distribution.......................................................................................... 73
Table 2.16 Comparison of the SRGO properties between the measured and the
predicted.......................................................................................................... 74
Table 2.17 Properties verification between calculated based on mixing rule and
correlations...................................................................................................... 75
Table 2.18 Measured properties of LCO ................................................................ 76
Table 2.19 Comparison of LCO properties between the predicted and measured . 76
13
Table 3.1 Clean Air Act and CARB specifications (USA) (Aye, 2003) ................ 82
Table 3.2 California (USA) Phase 2 specifications for gasoline (Simon, 2007) .... 84
Table 3.3 Coefficients of Equation 3.20 (Riazi, 2006) ........................................... 94
Table 3.4 Model performance in regression phase ................................................. 99
Table 3.5 Model performance of the direct correlated model (see section 3.3.3.1)99
Table 3.6 Model performance of interpolation prediction in the prediction phase
....................................................................................................................... 100
Table 3.7 Result of an example of extrapolation prediction................................. 100
Table 3.8 Coefficients in ethyl octane blending equations (Healy et al., 1959) ... 104
Table 3.9 Available feedstock properties and information about blending
components ................................................................................................... 109
Table 3.10 Product specifications for two grades of gasolines............................. 109
Table 3.11 Detailed product distribution (the conventional approach) ................ 110
Table 3.12 Blended product properties (the conventional approach) ................... 110
Table 3.13 Detailed product distribution (molecular modelling) ......................... 111
Table 3.14 Blended product properties (molecular modelling) ............................ 111
Table 4.1 Compositions of two typical feeds (Gary, 2001) .................................. 119
Table 4.2 Typical product distribution from paraffinic feed at 15 bar with RON of
98 (George, 2004) ......................................................................................... 122
Table 4.3 Typical composition (wt %) of reformates with low operating pressure
(George, 2004) .............................................................................................. 123
Table 4.4 Molecular composition of feedstock (mol %) (Ancheyta, 2000) ......... 135
Table 4.5 Comparison of the properties between the measured and predicted for
feedstock and product ................................................................................... 136
Table 4.6 Product distribution based on 100 mol feedstock................................. 137
Table 4.7 Objectives of base case ......................................................................... 152
Table 5.1 Typical characteristics of feed to diesel hydrotreaters (Heinrich et al,
2001) ............................................................................................................. 159
Table 5.2 EN 590 diesel fuel requirements – date introduced: 1/1/2005.............. 161
Table 5.3 Sulphur distribution in various LCO fractions (Depauw, 1997; Carcía,
2002; Nylén, 2004) ....................................................................................... 165
Table 5.4 kinetic parameters number needed for the kinetic model of HDS with
molecules represented by the MTHS matrix................................................. 169
Table 5.5 Physical property of the model ............................................................. 178
14
Table 5.6 Properties estimation methods .............................................................. 178
Table 5.7 Configuration of the reactor and operating conditions ......................... 181
Table 5.8 Composition and properties of the product of the measured and predicted
....................................................................................................................... 182
Table 5.9 Monoaromatics content and sulphur content of the products with three
different reactor temperatures ....................................................................... 182
Table 5.10 Activity division of catalyst for three stages....................................... 191
Table 5.11 Constraints of the optimisation case ................................................... 192
Table 5.12 Optimal operating conditions and results ........................................... 192
Table 6.1 Unit capacity......................................................................................... 205
Table 6.2 Properties of two crudes........................................................................ 206
Table 6.3 Availability of crudes............................................................................ 206
Table 6.4 Major market conditions of refining products ...................................... 207
Table 6.5 Investigation modes of case study ........................................................ 208
Table 6.6 Gasoline specification........................................................................... 208
Table 6.7 Diesel specification............................................................................... 208
Table 6.8 Total profit of the refinery in the different modes ................................ 209
Table 6.9 Crude oil selection in the different modes ............................................ 210
Table 6.10 Process utilisation in the different modes ........................................... 210
Table 6.11 Main product distribution in different modes ..................................... 211
Table 6.12 Gasoline90 product properties in different modes.............................. 211
Table 6.13 Gasoline97 product properties in different modes.............................. 212
Table 6.14 Diesel product properties in different modes...................................... 212
Table 6.15 Operating conditions of processes in different modes........................ 214
Table 6.16 Calibrated data of hydrogen sinks (Sun, 2004)................................... 229
Table 6.17 Calibrated data of hydrogen sources (Sun, 2004)............................... 229
Table 6.18 Operating conditions of DHT for base case........................................ 230
Table 6.19 Constraints of operating conditions for DHT ..................................... 231
Table 6.20 Optimal operating conditions of diesel hydrotreater in each period... 231
Table A.1 Joback group contribution for boiling point and Gibbs energy ........... 258
Table B.1 Factors for pressure effect (Ancheyta, 1994) ....................................... 259
Table B.2 Activation energies for each reforming reaction (Henningsen, 1970) . 259
Table B.3 Kinetic constants of the model (Ancheyta, 2000) ................................ 260
15
Table C.1 Numerical values for the structural contributions for (s)DBT at 573K
(Froment, 2004) ............................................................................................ 261
Table C.2 Rate and adsorption parameters related to HDS of DBT (Froment, 2008)
....................................................................................................................... 262
Table D.1 Constants for the simple and heavy reference fluid............................. 266
Table D.2 Constants used for the generalised viscosity correlation ..................... 267
Table D.3 Constants used for the generalised correlation for thermal conductivity
....................................................................................................................... 268
16
Abstract
Molecular management targets the right molecules to be at the right place, at the
right time and at the right price. It consists of molecular characterisation of refining
streams, molecular modelling and optimisation of refining processes, as well as
overall refinery optimisation integrating material processing system and utility
system on the molecular level. The need to increase modelling details to a
molecular level is not just a result of political regulations, which force refiners to
managing the molecule properly, but also seems to be a very promising to increase
the refining margin. In this work, four aspects of molecular management are
investigated respectively.
Molecular Type Homologous Series (MTHS) matrix framework is enhanced on
both representation construction and transformation methodology. To improve the
accuracy and adequacy of the representation model, different strategies are
formulated separately to consider isomers for light and middle distillates. By
introducing statistical distribution, which takes the composition distribution of
molecules into account, the transformation approach is revolutionised to increase
the usability, and tackle the challenge of possibly achieving significantly different
compositions from the same bulk properties by the existing approaches. The
methodology is also enhanced by applying extensive bulk properties. Case studies
demonstrate the effectiveness and accuracy of the methodology.
Based on the proposed characterisation method, refining processes are modelled on
a molecular level, and then process level optimisation is preformed to have an
insight view of economic performance. Three different processes, including
gasoline blending, catalytic reforming, and diesel hydrotreating, are investigated
respectively. Regarding gasoline blending, the property prediction of blending
components, and the blending nonlinearity are discussed. To tightly control on the
property giveaway, a molecular model of gasoline blending is developed, and then
integrated into the recipe optimisation. As for the conversion processes, catalytic
reforming and diesel hydrotreating, reactions and reactors are modelled separately,
and then followed by the consideration of catalyst deactivation. A homogeneous
rigorous molecular model of a semiregenerative catalytic reforming process,
17
considering pressure drop, has been developed. In addition, a multi-period process
optimisation model has been formulated. Regarding diesel hydrotreating, a
molecular model of reactions with a three-phase trickle-bed reactor has been
developed. The concept of reaction family is successfully applied. A structural
contribution approach is used to obtain kinetics and adsorption parameters. A
series of procedures are developed to solve the complex problem. Thereafter, a
process optimisation model has been developed with the consideration of catalyst
deactivation, with a new strategy on the division of catalyst life.
Finally, a two-level decomposition optimisation method is extended to incorporate
molecular modelling into the overall refinery optimisation, and then applied in two
aspects. Firstly, with the integration of the process and the site-level models, a
better perspective is obtained with regard to a material processing system. By
molecular modelling of refining streams and processes, the integrated approach not
only controls the molecules in products properly, but also increases the overall
performance. In the second application, a framework integrating a hydrogen
network with hydroprocesses is developed to target the maximum profit, rather
than saving hydrogen. It allocates hydrogen on the hydrogen network level and
utilise hydrogen efficiently on the process level by optimising operating
conditions. Consequently, the extent of achieving the maximum profit could be
fully exploited with optimal hydrogen utilisation.
18
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or
other institution of learning.
Yongwen Wu
19
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Property Rights and/or Reproductions.
[iv] 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.

20





To
My parents, Ximu Wu and Jumei Bao
&
Wife, Lu Chen

21
Acknowledgements
I would like to show my sincere gratitude towards my supervisor, Dr. Nan Zhang,
for his continuous source of guidance, support and advice throughout the period of
my research. I very much appreciate his encouraged independent research style
while providing feedback on both the theoretical and practical aspects of my work,
which enhances my independent work capability. Also, thanks to his zealous
guidance of badminton techniques.
Many thanks to the Centre of Process Integration, the School of Chemical
Engineering and Analytical Science, and the Overseas Research Scholarship
Scheme. Without their financial support, this research would never have been
started or completed.
Special thanks to all staffs of Centre for Process Integration for their direct and
indirect helps during my PhD study. I would like to express my special thanks to
Professor Robin Smith and Dr. Qiying Scarlet Yin for providing opportunities
during my application.
I have great pleasure in expressing my appreciations to all students of CPI for
providing a stimulating and friendly environment. Thanks to Imran, Nan Jia,
Xuesong, Yuhang, Yu Rong, Zixin, Yufei, Kok Siew, Muneeb, Ankur, Bostjan,
Sourabh, Sonia for their kind help and sharing experience of life in Manchester.
Last but not least, I would like to express my deepest gratitude towards my family.
Without the continuous unconditional support and love from my parents
throughout my life, I would not become who I am today. My warmest gratitude
goes to my wife, Lu, for her priceless love, support and understanding.


22
Chapter 1 Introduction
1.1 Introduction.............................................................................................23
1.2 A Typical Refinery Scheme....................................................................23
1.3 Current Status of Refining Industry........................................................24
1.3.1 Product Specifications............................................................................24
1.3.2 Changing Market Demands and Supply ................................................26
1.3.3 Refining Margin and Refinery Optimisation .........................................28
1.4 Molecular Management ..........................................................................30
1.5 Present Research .....................................................................................30
1.6 Structure of Thesis ..................................................................................31


23
1.1 Introduction
The refining industry has been experiencing tremendous changes, especially in the
past decades due to the ever volatising margins, tightening governmental
regulations and arrival of new and competitive fuels such as biofuels. On the other
hand, the significant amount of oil consumption, also rapidly increased, leads to
the great importance of refining economy. Refiners are running out of conventional
options to comply with higher product quality specifications and more stringent
environmental regulations as it targets molecular species, which hits the very heart
of the traditional refinery configurations. Therefore, a new refining strategy to help
satisfy the molecular specifications, and simultaneously maintain/improve the
profit margins is of importance for refiners to survive.
Molecular management is a promising technology to satisfy the restriction of the
contents of specific components or component classes in fuels. More importantly,
it helps refiners to yield significant economic benefits considering refining
optimisation of both individual processes and refinerywide models (Zhang, 2005;
Katzer, 2000; Briesen, 2004). In this chapter, a typical refinery scheme is
introduced firstly, followed by a brief review of challenges facing the refinery
industry. Then the strategy of molecular management is concluded to be very
necessary to a refinery, which leads to the objective of present research. Finally,
the structure of thesis is presented with a brief overview of each chapter.
1.2 A Refinery Scheme
Nowadays, oil refining is a joint production system with a very complex technical
structure and a vast number of outputs that are strongly correlated. A general
refinery consists of crude oil operations, conversion units, and product blending
among which involves many different and complicated connections as Figure 1.1
illustrates.
24

Figure 1.1 Flowsheet of a refinery (Gary and Handwerk, 1994)
Refining starts from Atmosphere Distillation Unit (ADU) which is fed with crude
oil to obtain gas, light/heavy naphtha, kerosene, and diesel. To remain competitive,
the bottom of ADU would be vacuum distilled to retrieve gas oil for upgrading to
lighter products, and even heavy end processes such as Delayed Coker,
Visbreaking and Residue Fluid Catalytic Cracking (RFCC) are adopted to handle
the residue from Vacuum Distillation Unit (VDU). Blend stocks of gasoline are
mainly from the products of Catalytic Reforming Unit (CCRU) and Fluid Catalytic
Cracking Unit (FCCU). CCRU fed by heavy naphtha is as octane number improver
while FCCU converts gas oil into more profitable gasoline. Straight run diesel and
streams from hydrocracker and FCCU compose of the major composition of diesel
products. To comply with the environmental regulations on products and improve
the performance of some particular processes, hydroprocessing helps to eliminate
and reduce sulphur and nitrogen contents. The schematic layout only depicts one
of hundreds of different refining configurations.
1.3 Current Status of Refining Industry
1.3.1 Product Specifications
The refining industry today has to comply with higher product quality
specifications and more stringent environmental regulations, with more emphasis
on the molecular composition of refining products. Composition concerns such as
25
benzene, total aromatics, total olefin and oxygenates are being phased in since
1992, in addition to the traditional qualities, and gradually tightened to a critical
level. For instance, in 1995, the U.S. Environmental Protection Agency fixed the
average benzene content has to be less than 1 volume percent in gasoline for
Federal Phase I, and retains the benzene limit for Phase II in 2000, followed by the
maximum level of benzene reduced to 0.8 volume percent for Phase III in 2004,
and even an annual average maximum benzene content of 0.62 liquid volume
percent becoming effective from 2011 (Bacon, 2009). Obviously, the increases in
the environmental awareness and concerns are demanding refining fuels to be
cleaner.
Table 1.1 European Union diesel specification (Official Journal of the European
Communities, 2009)
EN 590 Directive
98/70
Directive
98/70
Directive
98/70
Entry to force 1993/1996 2000 2005 2009
Polycyclic aromatic
hydrocarbons [% v/v] max
- 11 11 6
Sulphur [ppm] max 2000/500 350 50 10
Cetane number, min 46 - 49 51 51 51
Density at 15
o
C [kg/m
3
], max 860 845 845 845
Distillation T95 [
o
C] max 360 360 360 360
Fatty Acid Methyl Ester
(FAME) content [% v/v] max
- - - 7
Table 1.1 and Table 1.2 list European Union fuel specifications including gasoline
and diesel respectively. These specifications might be well above the restriction
imposed in many other countries but it is reasonable to postulate that these could
be adopted in more countries around the world. These tightening specifications
challenge the conventional refining technologies. For instance, sulphur contents in
both gasoline and diesel fuels see a dramatic reduction, from 500 ppm to 10 ppm,
almost free, which demands that refiners should have a clear understanding about
different sulphur compounds present in refining streams because different sulphur
compounds have very different kinetic properties, and then require quite different
26
operating conditions to eliminate. To implement it, a molecular level
understanding about refining streams and processes should be achieved.
Table 1.2 European Union petrol specification
EN 228
Directive
98/70
Directive
98/70
Directive 98/70
Entry to force 1993/1995 2000 2005 2009
Vehicle emission
Standard equivalent
Euro II Euro III Euro IV Euro V
Sulphur [ppm] max 500 150 50 10
Ried Vapour Pressure
(RVP) [kPa] summer
35 - 100 60/70 60/70 60/70
Distillation [% v/v] min
E100 (
o
C) - 46 46 46
E150 (
o
C) - 75 75 75
Hydrocarbon analysis:
Olefins [% v/v] max - 18 18 18
Aromatics [% v/v] max - 42 35 35
Benzene [% v/v] max 5.0 1.0 1.0 1.0
Oxygen [% m/m] max - 2.7 2.7 2.7
Oxygenates [% v/v] max
Methanol - 3 3 3
Ethanol - 5 5 10
Iso-propyl alcohol - 10 10 12
Tert-butyl alcohol - 7 7 15
Iso-butyl alcohol - 10 10 15
Ethers containing 5 or
more carbon atoms
- 15 15 22
Other oxygenates - 10 10 15
Use of additives
(MMT banned
from 2010
MMT: Methylcyclopentadienyl Manganese Tricarbonyl
27
1.3.2 Changing Market Demands and Supply
Basically, the oil consumption is expected to increase due to the rapidly growing
economy of the world, especially in China and India. In 2030, the world is
expected to consume nearly 27% more oil than in 2006, increased from 4029 Mtoe
to 5109 Mtoe (World Energy Outlook, 2009). As the price of crude oil increases,
the heavy fuel oil, as the feed for generating electricity, becomes less economic
attractive. At the same time, it is forecasted that the fastest growing petroleum
products will be distillate (including diesel, jet fuel, and kerosene), liquefied
petroleum gas (LPG), and gasoline as illustrated in Figure 1.2 (Oil Market Report,
2009).

Figure 1.2 Oil demand growth by product, in North America, Europe, Asia and
Middle East, 2008-2014 (Oil Market Report, 2009)
Many European countries have seen a rapid growth on the demand of diesel used
by private cars due to its high driving characteristics, and commercial diesel use is
also growing strongly in the Mediterranean and Eastern Europe. Much of the
current refining capacity in Europe was commissioned at a time when the demand
for diesel was relatively small and gasoline production was the key aim of refiners.
While the overall refining capacity is roughly in line with current demand, there is
a considerable imbalance in supply and demand between gasoline and diesel.
28
Since the late 1980s, crude oil slates have becomes heavier and sourer (Swain,
1998). Usually heavy crude oil would consume more utilities and capacities on the
thermal and/or catalytic conversion processes. Moreover, the more heteroatom
such as S, N, O, etc, contained in the heavy crude oil brings problems associated
with pollution, catalyst poisoning, etc. This has led to an economic incentive to
minimise invaluable heavier products and to maximise production of the more
valuable light products.
The ability and extent of a refiner to achieve swinging products from gasoline to
diesel and changing the selection of crude oil will largely depend on individual
refining configurations. For example, a simple refinery with no upgrading facilities
can only really influence product yields by processing alternative crudes. While
there is an opportunity to target crudes with high middle distillate content, these
are currently trading at a significant cost premium over heavier, more sour crudes.
In addition, it is unlikely that there will be significant spare capacity in the
downstream hydrotreater, which is essential to meet the current diesel sulphur
specifications. Therefore, the changing market demand and supply restrains the
achievable profit from the refinery.
1.3.3 Refining Margin and Refinery Optimisation
Refiners face difficulties in practically meeting the tight specifications with
existing blend stocks and limiting the cut range of blend stocks, and current market
demand. Hence, the product yield and the profit are reduced due to the increment
in the production of lower value products. Much of the profit comes from
processing a high throughput of crude oil in a refinery although it sees periods of
high profitability in recent years.
Low refining margin has been promoting extensive work on process modelling and
refinery optimisation, with the aim of pushing the operation of a refinery to give
optimal performance and hence, maximum profit. Considerable research effort has
been put into refinery optimisation since early 1950s, when linear programming
technology started to produce industrial applications, mainly for planning purpose.
Since 1970s, along with the rapid development of computer technology, more
interests have been attracted to nonlinear programming and its application to
29
rigorous process simulation and optimisation. It is, however, apparent that models
relating to process operations of different refinery units are highly non-linear. This
then led to further research on how to handle the non-linearities related to the
kinetics, thermodynamics, etc. of each process through non-linear programming
technologies. The challenge then was to develop a rigorous approach that can
account for both highly non-linear process models (containing detailed
descriptions of operating conditions e.g. temperatures, pressures, etc.) and at the
same time optimise the overall refinery performance.
On the other hand, as the basis of refinery optimisation, the industrial widely used
conventional modelling methodology based on bulk property characterisation of
feedstock has the inherent disadvantages. First of all, the specifications of
molecular requirement on the refining products are not easily targeted since the
conventional simulation model could not provide molecule information of
products. On the other hand, the developed process models are not practical any
more since the characteristics of feed stock and operating conditions are different.
For example, with the less demand on fuel oils in the market, the heavy oils and
residua may require deep processing in FCC. Thus modern FCC units are often
required to process multiple feed streams from various sources such as a vacuum
distillation column, delayed coker, hydrocracker, etc. In this case, bulk property
characterisation cannot properly describe the composition of feedstocks with
different processing history any more, because feedstocks with similar bulk
properties could have significantly different molecular compositions. Various
studies have indicated that reaction patterns differ between different molecule
structures, therefore possibly leading to quite different product distribution for
those different feed stocks. Therefore, the refiners are forced to deal with
molecules rather than boiling ranges to manage its molecules to ensure survival.
Molecules are the common foundation for feedstock composition, property
calculation, process chemistry, and reaction kinetics and thermodynamics.
Molecule-based models can incorporate multilevel information from the surface
and quantum chemical calculations to the process issues and can serve a common
fundamental form for both process and chemistry research and development.
Although detailed feed characterisation and chemistry insights on molecule level
30
are highly desirable in the refining processes modelling, it was unlikely to
distinguish petroleum mixtures in the level of individual molecules due to the
enormous complexities of petroleum fractions in the past few decades. Two
technological advancements have helped modelling at the molecular level becomes
achievable. One is recent developments in analytical chemistry that now permit the
direct, or at least indirect, measurement of molecules in complex feedstocks and
products. The other is advancements in information technology, especially the
explosion of computational power, provide the possibility to track molecules
during both reaction and separation processes. Collectively, these two enabling
advancements motivate the development of refinery optimisation on a molecular
level to help refineries conquer these external and internal challenges.
1.4 Molecular Management
Molecular management targets the right molecules to be at the right place, at the
right time and at the right price (Aye and Zhang, 2005). It consists of molecular
characterisation of refining streams, molecular modelling of refining processes,
process level optimisation, and overall refinery optimisation integrating material
processing system and utility system on the molecular level. As seen, the need to
increase modelling details is not just a result of political regulations. The increase
in the details of composition by means of molecular information also seems to be a
very promising. In a long-sighted article on the future development of refining,
Katzer et al. (2000) stated: “We believe the refinery will change more in the next
20–30 years than it has in the last 70 years.” One of the key issues they raised is
how to increase the level of composition detail. This will bring a paradigm shift
toward considering refinery processes “more and more like today’s chemical
plants.” With such a molecular level of modelling detail, it should be possible to
track the path of each individual molecule as it is processed. This should allow us
to get the most value out of any molecular species.
1.5 Present Research
It is obvious that molecular management is of importance to ensure refiners’
survival, but achieving it is facing lots of challenges, which will be addressed
separately in different chapters in terms of different aspects of molecular
31
management. In this work, four aspects relating to molecular management,
including molecular characterisation of refining streams, molecular modeling of
refining processes, process level optimisation on a molecular level, and overall
refinery optimisation considering utility system, will be explored related to two
most profitable products, which are gasoline and diesel.
1.6 Structure of Thesis
This thesis consists of seven chapters. A brief overview of each chapter is as
follows.
Chapter 2 Molecular characterisation of petroleum fractions
The complexity nature of petroleum fractions is introduced firstly, followed by a
brief review of existing methods including traditional methods, laboratory
analytical methods, as well as computer-aided molecularly explicit characterisation
methods which is the focus of this research. By illustrating the limitations of the
existing methods, finally a novel methodology is proposed to overcome these
disadvantages.
Chapter 3 Molecular modelling of gasoline blending
This chapter consists of three distinct aspects. Firstly, a brief introduction about
gasoline blending operation including blending streams, the type of blending, as
well as the gasoline specifications, is described. In the second section, a series of
procedures are developed to predict the properties and compositions of blending
feedstocks based on the easily obtained information with a high accuracy by
employing the molecular modelling technique. The last part will introduce a
molecular blending model to achieve an optimal recipe of gasoline blending with
the tighter control on the property giveaway for the maximum profit.
Chapter 4 Molecular modelling of catalytic reforming
This chapter, first, briefly introduces catalytic reforming process, along with a
short review of previous work on modelling of catalytic reforming. To build up a
molecular model of a catalytic reformer, chemical reactions and modelling of the
reactor are described respectively. Another important issue of catalyst deactivation,
32
which has a serious impact on the economic performance of a catalytic reforming,
is also considered in a reasonable way. Finally, a multi-period process level
optimisation model is developed with the consideration of catalyst deactivation.
Chapter 5 Molecular modelling of diesel hydrotreating
In the chapter, a detailed kinetic model for hydrotreating process with a three-
phase reactor based on feedstocks and products in terms of the MTHS matrix
representation is developed. Beyond the molecular modelling of a diesel
hydrotreater, a multi-period model of run cycle is proposed to take the catalyst
deactivation into account, and a process optimisation model is developed to help
the refiners increase margins as well.
Chapter 6 Integrated site and process optimisation with molecular modelling
This chapter, first, introduces the challenges of refinery optimisation, followed by
a brief review of optimisation techniques. Then, a decomposed strategy is
incorporated with molecular management. The integrated framework is applied in
an overall refinery optimisation, including site and process level optimisation
based on molecular management. Secondly, an exploitation of interactions
between hydroprocesses, with rigorous process models based on molecular
information, and a hydrogen network is investigated by applying the proposed
methodology.
Chapter 7 Conclusions and future work
Conclusions are drawn from this research, and some suggestions are made for
future work.

33
Chapter 2 Molecular Characterisation of
Petroleum Fractions
2.1 Introduction............................................................................................. 34
2.2 Complexity Nature of Petroleum Fractions ............................................ 34
2.3 Review of Previous Methods .................................................................. 35
2.3.1 Traditional Methods............................................................................... 35
2.3.2 Modern Analytical Laboratory Methods................................................ 36
2.3.3 Computer-aided Molecular Explicit Methods........................................ 38
2.3.4 Existing MTHS Methods ....................................................................... 43
2.3.5 Limitations of Existing MTHS Methods................................................ 44
2.3.6 A Brief Case Showing the Shortcomings of the Existing Methods....... 45
2.4 A Modified MTHS Framework .............................................................. 48
2.5 Improved MTHS Matrix Representation Model..................................... 49
2.5.1 Improved MTHS Matrix Representation Model for Light Petroleum
Fractions.......................................................................................................... 49
2.5.2 Improved MTHS Matrix Representation Model for Middle Petroleum
Fractions.......................................................................................................... 50
2.6 Transformation Methodology ................................................................. 55
2.6.1 Assumptions........................................................................................... 55
2.6.2 Mathematical Model .............................................................................. 60
2.7 Optimisation Engines.............................................................................. 65
2.8 Case Studies ............................................................................................ 67
2.8.1 FCC Gasoline Stream Case.................................................................... 67
2.8.2 SRGO Feed ............................................................................................ 70
2.8.3 LCO Feed............................................................................................... 75
2.9 Summary ................................................................................................. 77
34
2.1 Introduction
The characterisation of petroleum fractions has received significant attention in
recent decades because the understanding of refining feedstock and products is the
very fundamental step to the design and operation of almost every refining process,
which consequently has a significant impact on economic performance in refining
industry. Most of traditional characterisation methods are based on physical bulk
properties such as boiling point, specific gravity, etc., mostly due to the limitations
in the analytical chemistry and computer hardware and software capabilities.
Along with the state-of-art chemistry analytical technological advancements, and
the explosive growth of information technology, molecularly explicit
characterisation methods have been developed intensively to comply with higher
product quality specifications and more stringent environmental regulations, with
more emphasis on the molecular composition of refining products.
In this chapter, the complexity nature of petroleum fractions is introduced firstly,
followed by a brief review of existing methods including the traditional methods,
laboratory analytical methods, as well as computer-aided molecularly explicit
characterisation methods. By illustrating the limitations of the existing methods,
finally a novel methodology is proposed to overcome these disadvantages, which is
demonstrated in case studies.
2.2 Complexity Nature of Petroleum Fractions
Refining streams or petroleum fractions are the products or intermediate products
of crude oil through three major different refining processes of separation,
conversion and finishing, and each of them is a unique mixture of thousands of
different molecules. These molecules mainly fall into two categories: hydrocarbon
composing of hydrogen and carbon atoms only, and hydrocarbon with heteroatoms
such as sulphur, nitrogen, oxygen, etc. Crude oil composition schematic
(Environmental Protection Agency, USA) in Figure 2.1 shows the complexity of
typical petroleum hydrocarbon type analysis for Arabian heavy crude. In addition,
Figure 2.2 shows the numbers of isomers become literally astronomical in heavy
petroleum fractions. Besides dealing with the numerous isomers, the heteroatoms
35

such as sulphur, nitrogen and oxygen, etc. that involve a variety of functional
groups at various possible locations within a molecule impose further difficulties in
carrying out exact compositional analysis. Although such molecule by molecule
analysis might not be essential, but to comply with the environmental regulations
and further understand the nature of streams, molecular analysis to a certain extent
is necessary.

Figure 2.1 Complexity of typical petroleum hydrocarbon type analysis (www.epa.gov)

Figure 2.2 Chemical complexity of higher boiling products (Read, 1976)
2.3 Review of Previous Methods
2.3.1 Traditional Methods
Most traditional process models and even the current widely used commercial
software tools group the molecules mainly according to its bulk properties. Three
characterisation methods with the non-molecule basis are peseudocomponent
36

characterisation, compound class characterisation, and average structure
parameters characterisation.
The peseudocomponent concept (Katz and Brown, 1933) is to transpose ASTM
(American Society for Testing and Materials) curves into a representative set of
components. A petroleum fraction or crude oil TBP (True Boiling Point) curve is
divided into close-cut fractions, which are then handled as pure components.
Design procedures for crude oil distillation based on peseudocomponents have
been proposed and have found widespread industrial acceptance. Compound class
characterisation is based on chromatographic separation and describes oil mixtures,
in terms of operationally defined fractions. As the compound classes are defined by
their solubility characteristics, their molecular nature is not well defined. Average
structural parameter methods describe a petroleum mixture using structural
parameters, such as the number of aromatic rings, the carbon/hydrogen ratio, etc.,
from results obtained from laboratory methods such as nuclear magnetic resonance
spectrometry and elemental analysis. The pitfall of these methods is that the
functional groups fail to provide information about the actual components.
One of common disadvantages on the traditional characterisation methodology is
that they fail to represent detailed molecule information, which both increasing
technical and environmental concerns have focused on.
2.3.2 Modern Analytical Laboratory Methods
Along with the state-of-art chemistry analytical technological advancements,
laboratory methodology such as gas chromatography (GC), high performance
liquid chromatography (HPLC), mass spectroscopy (MS), nuclear magnetic
resonance spectroscopy (NMR) and many other newly developed methods could
identify and quantify most of several hundred molecules present in the petroleum
fractions. The basic principles and the typical applications of these analytical
methods would be briefly interpreted in the following sections since they are
fundamental to the molecularly explicit characterisation models.
Basically GC, mainly used in the analysis of light and middle distillates due to its
high resolution, separates molecules according to their boiling points. It is invented
by Martin and Synge, who suggested its possibility in a paper on liquid
37

chromatography published in 1941 (Martin and Synge, 1941). Johansen et al.
(1985) developed a gas chromatography method to analyse the hydrocarbons by
structural group type in gasoline and distillates. Matisová et al. (1985) claimed that
high resolution capillary gas chromatography (HRCGC) could provide complete
component analysis of refining streams and hence offer petrochemical engineers
with the information and knowledge required to convert crude petroleum into
profitable products. Teng (1994) developed a gas chromatography – mass
spectrometric (GC-MS) method equipped with special software and included the
analysis of oxygenated compounds in a single run. It is one of the few techniques
capable of distinguishing between paraffins and naphthenes, thus providing a true
PIONA (Paraffins, Isoparaffins, Olefins, Naphthenes, and Aromatics) analysis,
which is often required in the control of gasoline production.
HPLC utilises a column that holds chromatographic packing material (stationary
phase), a pump that moves the mobile phase(s) through the column, and a detector
that shows the retention times of the molecules. The mechanism of adsorption,
desorption and partition of those components between packing and solvent is used
in HPLC to separate components. It is widely used in the analysis of heavier
petroleum fractions. Separation of aromatic compounds based on the number of
aromatic rings is one of the features of HPLC analysis.
NMR is based on the principle that proton and
13
C nuclei in different chemical
groups have different electronic environments and hence different resonance
conditions. They can measure directly aromatic and aliphatic carbons; hydrogen
distributions and the concentration of various structural groups can be determined
when combined with elemental analysis.
1
H and
13
C are responsible for revealing
the complicated structures of petroleum fractions.
MS by far provides the most detailed information on the compositions of
petroleum fractions. It analyses compounds according to their molecular weight
and chemical formula C
n
H
2n+Z
X, where C is Carbon, H is hydrogen while X refers
to heteroatoms while n is the number of carbon and Z is the hydrogen deficiency.
Although it could provide important information about the molecular structure, its
application is limited to light petroleum fractions such as gasoline.
38

Compared with the traditional characterisation approaches, modern laboratory
analytical technology to some certain extent shows its advantage of retrieving the
detailed molecule information directly or indirectly. On the other hand, it is these
capabilities of chemistry analysis that enhances the possibility of bringing the
brand new characterisation methodology for refining streams. However, the main
two disadvantages of time and cost consumption preclude its wide use in the
refining industry, especially for the refinery online/offline optimisation. More
importantly, then analytical approach has reached its limitations due to the
complexity nature of heavy stream as reviewed in the previous section.
2.3.3 Computer-aided Molecular Explicit Methods
With the development of information technology, computer-aided molecular
explicit methods have seen a more rapid growth. Most endeavors on this contain
two basic problems. One is a representation model - what can be used to represent
petroleum streams with the astronomical number of hydrocarbons and
hydrocarbons with heteroatoms. The other is a transformation methodology - how
molecular information is obtained since streams with similar bulk properties could
have significantly different molecular compositions. To solve these problems,
several challenges need to be tackled properly.
2.3.3.1 Challenges of Molecular Characterisation Methods
As mentioned before, the complexity nature of petroleum fractions precludes
determining the complete molecular composition. Therefore, how to select the
representative molecules, as well as how to consider isomers in a reasonable way is
the first challenge to molecular characterisation of petroleum fractions.
Even the representative molecules have been determined, a large amount of
properties of the representative molecules are not easily obtained. Properties of a
mixture depend on the properties of its constituents. Generally, properties include
physical properties, thermodynamic properties, and transport properties. Physical
properties have density, boiling point, molecular weight, and refractive index, etc.,
and thermodynamic properties include enthalpy, heat capacity, heat of
vaporization, equilibrium ratios, and fugacity, etc. Transport properties include
viscosity, thermal conductivity, diffusion coefficient, and surface tension, etc.
39

There are also some properties which reflect the quality of fuels, such as cetane
number for diesel, octane number for gasoline, etc. Although not all of these
properties are necessary for the molecular characterisation, it would enhance the
accuracy of predicting the molecular composition if applying more properties,
because different characteristics of molecules could be captured.
Most of properties do not blend linearly, which means different mixing rules
should be built up to calculate the properties of the mixture based on the properties
of pure compounds. Sometimes, established mixing rules could only be applied in
a certain narrow range. Therefore, they should be used properly.
The common practice to characterise petroleum fractions on a molecular level is
transforming bulk properties into molecular composition by minimising the
difference of the bulk properties between the calculated and measured. However,
lots of different molecules could have similar properties, which make this method
hard to distinguish molecules with different structures but similar properties, while
the molecules with different structures have quite different reaction patterns.
Regarding to representation model for characterisation, two kinds of methods have
been developed: stochastic and deterministic methodology. The main difference
between these two methods is the way to decide the representative molecules.
2.3.3.2 Stochastic Methods
The idea behind the stochastic methodology is that any molecule in a petroleum
stream can be viewed as a collection of molecular attributes (number of aromatic
rings, number of naphthenic rings, number of side chains, length of side chains,
etc.), each of which is represented by a PDF (probability density function). The
PDF is a function that provides the probability of finding the value or less of a
given attribute. By sampling the attribute PDFs, the values of the structural
attributes for an individual molecule can be determined, which in turn specifies the
molecule.
Neurock et al. (1990, 1994) developed a Monte Carlo construction technique
whereby petroleum molecules are stochastically constructed by random sampling
of PDFs, one for each molecular attribute. Monte Carlo sampling of the set of
40

PDFs provides a large ensemble of “computer” molecules whose properties can be
compared to experimentally measured values. Campbell (1998) developed the
overall steps to transform indirect analytical information about the molecules in a
feedstock into a molecular representation. Both the identities and weight fractions
of the molecules are sought (see Figure 2.3). Recent work on the stochastic method
was done by Hudebine and his colleagues (2002, 2004).

Figure 2.3 Flow diagram of stochastic modelling of molecular structures and
compositions of a complex feedstock (Campbell, 1998)
It is worthy to note that the concept of using PDFs to describe complex mixtures
has existed for a long time. Flory (1936) developed a modified gamma distribution
to describe the molecular size distribution of condensation polymers. Libanati
(1992) studied the thermal degradation of an infinite polymer and indicated that the
molecular weights of the products followed a log-normal distribution. The
application of probability distribution functions was extended to petroleum
fractions when it was hypothesized and later confirmed that kerogen, which breaks
Monte Carlo Sampling
Global Optimisation
Analytical chemistry
(PIONA, H/C, NMR, VPO...)
Optimal Set of PDF
Parameters
Identities of Optimal Feedstock
Molecules, Near Optimal Wt
Fractions
Optimal Wt. Fractions of
Optimal (Quadrature)
Molecules
Initial Conditions for Detailed
Molecular-Based Method
“Quadrature” Analysis
Global Optimisation
41

down to form oil, could be modelled as an infinite polymer, and thus, the
molecular weight distribution of oil should be similar to that of polymer products.
Shibata et al. (1987) used mixed distributions to enhance phase equilibrium
calculations for a petroleum reservoir. Whitson (1990) used a gamma distribution
to fit the molar and weight distribution of the C
7+
fraction of crude oil, further
supporting the notion of representing crude oil components with PDFs. Riazi et al.
(1997) developed a versatile correlation based on an extensive analysis of more
than 100 mixtures. In addition, direct experimental evidences also provide the
same pattern. Pederson et al. (1992) showed that an exponential distribution could
be used to accurately predict the quantities of heavier components.
Although the stochastic method was fairly accurate in representing the composition
in heavy oil, the method is impractical for use in detailed kinetic modelling with
the computational power available today, especially for the refinery optimisation.
2.3.3.3 Deterministic Methods
The main reason of the time-consuming characteristic for the stochastic method is
that a new library of possible molecules is generated for each new simulation. A
deterministic methodology is significantly faster than stochastic methods by
predefining a molecular library which makes it more attractive for commercial
packages. Thus the predefined library is extremely important for the accuracy to
represent the petroleum fractions since if an important component is not included
in the library, the obtained composition can never be representative for the
mixture. The ways for constructing a molecular library range from experimental
methods (Wahl et al., 2002) to group contribution methods (Hudebine et al., 2002).
Jabr et al. (1992) attempted to characterise petroleum naphtha by dividing it into
five cuts with unified boiling ranges, the physical properties of which are
calculated using correlations from the literature. For each cut, representative
chemical components are assumed, the compositions of which are determined by
solving a system of linear equations to arrive at the properties of the blend.
However, the assumption that only five components or less can be used within
each cut, since only five independent properties were considered, led the authors to
42

use 9 true components and 16 pseudocomponents in a 25-component feed when
testing the method on a debutanizer feed.
Albahri (2005) recognised that a boiling point curve provides an infinite number of
experimental data which can be used to estimate the composition of any number of
pure components as desired. However, the number of components chosen to
represent a petroleum fraction, the key factor to determine the representation
accuracy, is hard to decide. Van et al. (2007) developed a methodology based on
Shannon’s entropy criterion and allows generating a molecular composition of a
naphtha fraction that meets all the boundary conditions set by the industrially
available commercial indices. It is attractively fast due to the transformation of a
nonlinear equation in the N mole fractions (N ~102) into a nonlinear equation in
with maximal 14 parameters. Similarly, the candidate feedstock molecules as the
crucial element for the success of representing petroleum fractions is not easy to
decide, as the paper showed that the simulation results from a library with 173
components is observed worse than that with the reduced library containing 37
molecules. As the author pointed out that the main reason for this behaviour is that
the entropy method is too insensitive to predict mole fractions of non-important
components accurately, because it differentiates between components based on the
difference in physical properties of these components.
García et al (2010) developed a method to characterise gas oil, and thereafter, the
achieved molecular composition is successfully applied in hydrotreating. By
representing composition of gas oil by 28 chemical families and 30 carbon
numbers (from 1 to 30), the method applies two standard distributions for the
families with and without polycyclic core for the length of the alkyl side chains to
calculate the distribution of molecules within each family, and the overall fraction
of each family is calculated based on three chemical analyses.
As reviewed above, one key to the accuracy of representing a petroleum streams is
a proper representative molecule model. Molecule Type Homologous Series
(MTHS) matrix representation, firstly presented by Peng (1999) followed by
continuous development, brings the possibility to overcome this problem.
43

2.3.4 Existing MTHS Methods
In an attempt to extend the molecular modelling into the refinery optimisation
framework, Peng (1999) introduced the concept where MTHS characterisation of a
petroleum mixture is visualised as a matrix where the rows represent carbon
number and the column representing the homologous series.
Molecules that belong to a homologous series have the same base structure with
varying carbon numbers. In the matrix, molecules belonging to a homologous
series with the same carbon number are lumped into a single entry. Apart from the
hydrocarbon molecules, different sulphur and nitrogen compounds are also present
in the matrix. The different base structures of each series are captured by
difference in molecular types such as benzene ring, naphthene. The element
defined in the matrix represents molar/weight percent of either a single molecule or
a lump of all possible molecular isomers.

Figure 2.4 Schematic representation of the methodology (Aye, 2003)
Based on MTHS matrix, Zhang (1999) developed an approach to transfer bulk
properties into molecular composition. Aye (2003) extended MTHS framework to
consider isomers, and enhanced the transformation method by generating sample
streams database to consider the processing history as shown in Figure 2.4.
44

2.3.5 Limitations of Existing MTHS Methods
The existing MTHS methodology to some extent improves the performance of
characterisation of light fractions. However, its inherent limitation prevents the
wide application. The limitations of the existing MTHS methodology would be
analysed on both representative model and transformation method.
2.3.5.1 Limitation of Representation Matrix
The representation MTHS matrix is different for light and middle petroleum
fractions because that molecular species existing in middle fractions are more
complex than those in the light fractions. So the limitations of representation
matrix of existing method will be discussed for two types of fractions separately.
Table 2.1 Typical Measured Isomer Distribution (wt %) for i-Octane (Ghosh, 2006)
Stream Type Monomethyls Dimethyls Trimethyls
Alkylates 0 18.5 81.5
Reformates 68.9 31.1 0
For light fractions, the assumption of the fixed internal distribution between
isomers for all refinery processes in the exiting MTHS matrix is not accurately
applicable in practice. The methodology assumes that the isomers are in
thermodynamic equilibrium then lumping isomers into one entry of matrix. This
assumption is true for some processes, but not for all processes. Table 2.1 shows
that the distribution of isooctane in reformates is inconsistent with that in alkylates.
Lumping all isomers together neglects the significant difference on both physical
and chemistry properties. The analysis results from the American Petroleum
Institute Research Project 45 demonstrate that the structural contributions lead to
dramatic changes of research octane number between isomers, well illustrated by
Figure 2.5. Similar difference could be observed in other properties such as Reid
Vapour Pressure (RVP), viscosity, etc. Meanwhile, chemistry patterns would differ
significantly for different isomers (Lappas, 1999).
45

Octane
0
20
40
60
80
100
120
140
2
-
M
3
-
M
4
-
M
3
-
E
2
,
2
-
D
M
2
,
3
-
D
M
2
,
4
-
D
M
2
,
5
-
D
M
3
,
3
-
D
M
3
,
4
-
D
M
2
-
M
,
3
-
E
3
-
M
,
3
-
E
2
,
2
,
3
-
T
M
2
,
2
,
4
-
T
M
2
,
3
,
3
-
T
M
2
,
3
,
4
-
T
M
2
,
2
,
3
,
3
-
t
e
t
r
a
m
R
O
N

Figure 2.5 Research octane number of isooctane isomers (Ghosh, 2006)
Regarding to the representation matrix for middle petroleum fractions, isomers of
each entry have not been taken into consideration, in which currently just straight
chain alkyl substitute is used as a representative for each entry.
2.3.5.2 Limitation of the Transformation Method
In terms of the transformation methodology, there exist several shortcomings. First
of all, the existing approach demands a large amount of sample matrices in the
database, which is extremely difficult, especially for heavy fractions. Secondly, if
the properties of sample streams do not cover the properties of the predicted
streams, molecular composition cannot be predicted accurately because it assumes
that the predicted stream is a blend of several well-characterised sample streams.
Thirdly, the problem that the fractions with similar properties could have
significantly different molecular compositions is not tackled at all. Last but not
least, from mathematical perspectives, the problem of existing lots of local
optimums, which present different molecular compositions, has not been
considered.
2.3.6 A Brief Case Showing the Shortcomings of the Existing Methods
To illustrate the shortcomings of the existing approach, a simple case is studied.
The stream is the gasoline product of a FCC process, with the distillation profile in
Table 2.2 and the measured properties.

46

Table 2.2 Distillation profile of a FCC stream
Cumulative (vol%) Temperature (
o
F)
5 74.85
10 87.71
30 149.58
50 204.91
70 281.51
90 328.09
95 347.15
Two groups of results were presented by applying two different sample matrix
numbers from a sample database containing 250 samples (Desai, 2008). Seed40 is
with 40 samples, while seed80 has 80. Table 2.3 compares the result of measured
properties between measured and two groups of estimated properties respectively.
Table 2.3 Comparisons of properties between measured and two groups of estimated
Properties Comparison
Msd Seed40 Diff (%) Seed80 Diff (%)
MW 97.49 97.49 0.00 97.49 0.00
SG 0.75 0.75 0.00 0.75 0.00
RVP(psi) 6.17 6.17 0.00 6.17 0.00
RON 90.89 91.68 0.86 92.07 1.29
MON 78.06 77.73 -0.43 78.20 0.18
P(vol%) 4.22 4.22 0.00 4.22 0.00
I 24.80 24.80 0.00 24.80 0.00
O 32.99 32.99 0.00 32.99 0.00
N 8.97 8.97 0.00 8.97 0.00
A 29.02 29.02 0.00 29.02 0.00
Msd: the Measured
47

Seed40
0
5
10
15
20
25
30
C4 C5 C6 C7 C8 C9 C10 C11
v
o
l
%
N
A
O
I
P

Figure 2.6 Predicted molecular composition with 40 sample matrices
Illustrated as Table 2.3, the existing MTHS method has an excellent performance
on minimising the difference between the measured and the estimated. Regarding
to molecular composition for the FCC gasoline, two totally different results are
observed as Figure 2.6 and Figure 2.7. The predicted molecular composition with
40 sample matrices has a small C
9
concentration of 0.11%, olefin fully occupied by
C
5
, and high aromatics of C
8
etc., which obviously fits badly with reality.
Seed80
0
5
10
15
20
25
30
C4 C5 C6 C7 C8 C9 C10 C11
N
A
O
I
P

Figure 2.7 Predicted molecular composition with 80 sample matrices
Another issue related to molecular characterisation of petroleum fractions is also
presented in this case, which is that streams with different molecular compositions
could have similar bulk properties as seen from the results with seed40 and seed80.
48

To summarise, the existing approach is needed to improve, and some aspects even
have not been considered at all. In this work, an improved MTHS framework is
developed in order to address the shortcomings of the existing approach.
2.4 A Modified MTHS Framework
The proposed modified MTHS framework as Figure 2.8 consists of two separated
steps, namely database setup and transformation step. The database setup starts
with collecting pure component properties from the property databanks of API-
TDB, AIChE-DIPPR, PGL and others, and estimating the properties using
correlations for those which are not available. The second step in database setup is
to calculate properties of each entry of the proposed MTHS representation matrix
introduced in section 2.5 by proper mixing rules.
Regarding to the transformation step, the emphasis of this step is the
transformation of bulk properties into molecular composition by integrating the
assumptions detailed in section 2.6.1. The first step is the laboratory analysis of
petroleum fractions, comprising the measurement of fundamental properties such
as distillation profile, specific gravity, etc. The other properties, if not available,
could be estimated by correlations. The second step in this scheme comprises using
an optimisation program that calculates the optimal molecular composition for the
predicted fraction. The mathematical model is discussed in section 2.6.2.

Figure 2.8 New MTHS framework for the characterisation of refining streams

49

2.5 Improved MTHS Matrix Representation Model
2.5.1 Improved MTHS Matrix Representation Model for Light
Petroleum Fractions
Table 2.4 New MTHS representation matrix for light petroleum fractions
Sulphur Content (wt %) = Nitrogen Content (wt %) = Oxygenates content (wt %) =
NP MP DP TP NO BO N A
C4
C5
C6
C7
C8
C9
C10
C11
C12
Table 2.4 illustrates the new MTHS representation matrix for light petroleum
fractions, where the rows stand for carbon numbers and the columns for
homologous series, with sulphur, nitrogen and oxygenate contents. The molecules
with the same homologous series and carbon number are lumped into one entry of
the matrix as they have similar properties. The elements defined in the matrix
represent the molar/weight/volume percent of either a single molecule or a lump of
all possible structural molecular isomers.
The limitations of the analytical techniques and the knowledge on refinery process
chemistry determine which molecular types and homologous series are
incorporated in the matrix. Aye (2005) tried to catch the structural contribution on
properties by assuming thermodynamic equilibrium for calculating the internal
distribution between isomers. Instead of lumping all isomers into one entry, the
new MTHS matrix lumps isoparaffins into three homologous series: monomethyls
(MP), dimethyls (DP), and trimethyls (TP) isoparaffins, and lumps olefins into two
series: normal (NO) and branched olefins (BO). The main reason for constructing
50

the new homologous series is based on the observations that the two key properties
of gasoline streams – ON and RVP (Reid Vapour Pressure) are similar for isomers
within each new homologous series, and molecules belonging to MP, DP and TP
take the majority of the isoparaffins concentration. Although the physical
properties for olefin isomers do not differ significantly, chemistry patterns are
different (Lappas, 1999). Regarding naphthenes and aromatics, there are small
variations in the physical properties of isomers and the detailed information on
isomers might not be available. In summary, each entry is a lump of isomers with
the same homologous series and carbon number.
2.5.2 Improved MTHS Matrix Representation Model for Middle
Petroleum Fractions

Figure 2.9 MTHS Matrix representation of diesel fractions (Peng, 1999)
Figure 2.9 shows the MTHS representation matrix for diesel streams, which is
different from the matrix for gasoline stream. Generally, gasoline streams cover C
4

to C
12
, and diesel streams cover C
9
to C
26
. Due to astronomical number of isomers
for heavier hydrocarbons, isoparaffins are lumped into one homologous series
rather than three as for gasoline. More homologous series are incorporated into the
matrix for diesel streams. Hydrocarbons are divided into 13 homologous series: nP,
iP for normal and iso-paraffins, O for olefins, 1N, 2N, 3N for naphthenic
compounds, 1A, 2A, 3A for one-ring to three-ring aromatic compounds, 1A1N,
2A1N, 1A2N for compounds containing both naphthenic and aromatic rings.
Regarding hydrocarbons with heteroatoms, sulphur compounds are lumped into
five homologous series, SI, SII, SIII, SIV and SV, according to different kinetic
51

characteristics, which is critical to the refining processes modelling, especially
hydroprocessing. The same strategy is applied for nitrogen compounds, as lumping
it into NI and NII.
One of the most challenging problems for petroleum fraction analysis is the rapid
growing number of isomers with increasing boiling point of petroleum fractions,
especially in middle and heavy petroleum fractions. Read (1976) demonstrated that
the number of paraffin isomers reaches the order of 10
7
or 10
8
when the carbon
number comes to 25. To consider isomers for middle petroleum fractions properly,
a set of rules is set up.
• Enumerating isomers of each entry in the MTHS matrix using the software
(SMOG, Institute of Organic Chemistry, Russian Academy of Sciences), up to
a carbon number as high as possible;
• For those entries for which not all isomers can be enumerated, parts of
molecules with a certain characteristics (low Gibbs Energy) are enumerated;
• Apply the group contribution method (Prausnitz, 2001) to calculate the
properties of each isomer;
• Assume that isomers are in the thermodynamic equilibrium, and calculate the
internal distribution of isomers;
• These isomers are lumped into each entry, and the properties of each entry are
calculated based on mixing rules.
Structural Molecular Generation (SMOG) is a program for exhaustive, irredundant,
and efficient generation of chemical isomers by their gross formula and a set of
structural constraints (Institute of Organic Chemistry, Russian Academy of
Sciences). In our case, the structural constraint is the basic structure of each
homologous series. The output of SMOG is a matrix, which represents the
connection between elements as Table 2.5 and Figure 2.10 show.
The entry which connects carbon and carbon in the matrix represents the bond
number, such as C2 and C3 connected by double bonds. The entry connecting
carbon and hydrogen represents hydrogen number. The matrices from SMOG are
transformed to basic structures that the Joback group contribution method needs.
52


Figure 2.10 C
15
H
12
isomer corresponding to Table 2.5 generated by SMOG
Table 2.5 One of C
15
H
12
isomers output from SMOG
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15
C1 -
C2 1 -
C3 0 2 -
C4 0 0 1 -
C5 0 0 0 2 -
C6 2 0 0 0 1 -
C7 0 0 1 0 0 0 -
C8 0 0 0 0 0 0 2 -
C9 0 0 0 0 0 0 0 1 -
C10 0 1 0 0 0 0 0 0 2 -
C11 0 0 0 0 0 0 0 1 0 0 -
C12 0 0 0 0 0 0 0 0 0 0 2 -
C13 0 0 0 0 0 0 0 0 0 0 0 1 -
C14 0 0 0 0 0 0 1 0 0 0 0 0 2 -
C15 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -
H 1 0 0 1 0 1 0 0 1 1 1 1 1 1 3
To set up and simplify isomers generation rules, some entries of each homologous
series are investigated to get the property of boiling point and distribution between
isomers based on the assumption that isomers are in the state of thermodynamic
equilibrium. Figure 2.11 shows the result of molecules (C
17
, A).
Some observations for the entry of (C
17
, A) are outlined as follows:
• The entry of (C17, A) has 26071 isomers;
53

• Joback group contribution method can distinguish 56 different isomers without
the capability to consider the position of basic structures;
• Boiling points of isomers have a big difference between each other, which can
be as high as 605 – 640 K;
• The majority of the isomer composition is occupied by a small part of isomers,
which have branches on an aromatics ring as many as possible.
(C17, 1A) Isomers distribution
0
0.2
0.4
0.6
0.8
1
605 610 615 620 625 630 635 640
Boiling Point (K)
C
u
m
u
l
a
t
i
v
e

F
r
a
c
t
i
o
n

Figure 2.11 (C
17
, A) isomers distribution with boiling point
The analysis is carried out on some entries to find out the particular characteristics
for each homologous series. Based on these observations and characteristics
analysis, a structure fragments list is generated to reduce isomer generation for
those entries with an astronomical number of isomers. The molecules constructed
by those fragments would have lower Gibbs energy, which then take the majority
of the isomer composition. Table 2.6 gives the isomer number of each entry from
SMOG.
Group contribution methods are based on the principle that the properties of a
compound are the function of the atoms and structural groups combining to form
the compound. Group contribution methods estimate the physical properties of a
species by using the contributions that have been assigned to different atoms and
atomic groups for each type of physical constant (Prausnitz et al., 2001). The
method of Joback and Reid (1987) is adapted in this work as it covers a broad
range of compounds and functional groups and is simple in application.

54
Table 2.6 Isomers generation of each homologous series (* represent the property of the entry is calculated by extrapolation or interpolation)
IP 1O 1N 2N 3N 1A 1A1N 1A2N 2A 2A1N 3A
9 34 153 12 11
10 74 377 40 1 32 1 1
11 158 914 106 3 79 4 2
12 354 2281 317 20 218 22 12
13 801 5690 868 81 555 80 32
14 1857 14397 2462 349 1 1471 290 1 110 1 1
15 4346 36564 6778 1292 4 3812 936 6 310 5 5
16 10358 93650 18801 4660 35 9998 2952 45 920 32 30
17 24893 240916 51561 15786 184 26071 8896 224 2558 135 115
18 60522 623338 141583 51994 966 68388 26336 1026 7177 543 425
19 148283 1619346 386865 165708 4330 179250 76310 4116 19660 1930 1396
20 * 4224993 1056815 517297 18291 471504 218570 15508 53864 6568 4440
21 910724 1741717 543896 466763 71728 271958 618978 54912 146180 21200 13470
22 2278657 1870473 7082742 1579860 268529 3541321 * 186792 396296 66497 *
23 1056131 2515449 729632 6953378 962461 314316 * 613477 1070296 202919 116140
24 793372 1706630 894989 5894661 594828 442424 249889 285324 1035075 608019 332827
25 3687776 * 6372846 * 5977592 3131423 * 1834149 * 167909 860608
26 * * * * 1596391 * * 655868 * 1585695 *
55
2.6 Transformation Methodology
2.6.1 Assumptions
The proposed methodology is based on two assumptions. One is that the molecular
composition within each homologous series follows a statistical distribution
against a certain property such as molecular weight or boiling point. The other
assumption follows a general belief that the global properties of a petroleum
fraction are close to the calculated from pure compounds based on mixing rules
(Albahri, 2005).
2.6.1.1 Statistical Distribution Assumption
As reviewed in section 2.3.3.2, statistic distribution has been used to describe
complex mixtures. Klein et al. (2005) recommends gamma distribution (eq. 2.1)
because of its flexibility that it ranges from an exponential distribution to a delta
function and can also approximate a normal distribution.
) (
e ) x (
) x ( p
/ ) x ( 1
α Γ β
η
α
β η α − − −
−
= (2.1)
where α, β, and η are three parameters of gamma distribution. x denotes the
property, and p is the probability density function.
∫
∞
−
=
0
t 1 x
dt e t ) x (
-
Γ (2.2)
To verify this assumption, gamma distribution is applied to fit the fractions of
hydrocarbons with different carbon number within each homologous series for a
FCC gasoline stream (Figure 2.12) and a middle distillate (Figure 2.13). The
results show a good agreement between the predicted data from gamma
distribution and the measured data. The data is from the literature (Chen, 1995;
Fafet, 1995).
56

0
2
4
6
8
10
12
14
50 70 90 110 130 150 170
Molecular weight
F
r
a
c
t
i
o
n

(
m
o
l
%
)
Gamma -Olefin
Measured - Olefin
Gamma - Isoparaffins
Measured - isoparaffins
Gamma - Napthene
Measued - Napthene
Gamma - aromatics
Measured - aromatics

Figure 2.12 Gamma distribution fitted fractions within PONA homologous series of a
FCC gasoline stream (Chen, 1995)
0
1
2
3
4
5
6
7
C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26
C
o
m
p
o
s
i
t
i
o
n
(
%
)
0
0.5
1
1.5
2
2.5
C
o
m
p
o
s
i
t
i
o
n
(
%
)
2A-Predicted
P-Measured
P-Predicted
2A-Measured
3A-Measured
3A-Predicted
1A-Measured
1A-Predicted
2A1N-Measured
2A1N-Predicted

Figure 2.13 Gamma distribution fitted fractions within homologous series of a middle
distillate (Fafet, 1995)
By assuming that compositions of the entries within each homologous series
follow a gamma distribution with a certain property, some benefits are obtained.
First of all, the need of the extremely-hard achievable sample matrices database
has been removed, together with the limitation of the extrapolation capability. The
most important benefit from this assumption is that the new methodology is
capable of handling the challenge that the fractions with similar properties could
have significantly different molecular compositions, because the distribution
between molecules is taken into consideration. Furthermore, the shape of the
distribution curve is easily controlled as integrated in mathematical model (section
2.6.2). Last but not least, the degrees of freedom to represent molecular
57

composition are reduced dramatically, such as from 18 to 4 for each homologous
series regarding diesel fractions, including three parameters for the gamma
distribution, and one fraction of each homologous series.
2.6.1.2 Property Estimation Assumption
The other assumption follows a general belief that the bulk properties of a
petroleum fraction are close to the calculated from pure compounds based on
mixing rules. The bulk properties could be measured in a laboratory or estimated
by correlations based on the fundamental measured properties. In terms of
characteristics of molecules, molecular energy and size are two important
parameters, which in our case are used as the fundamental properties, represented
by boiling point and density respectively.

Figure 2.14 Calculation procedure based on the second assumption
Besides the measured properties such as distillation profile, specific gravity, etc.,
other derived bulk properties from correlations are also applied to capture the
characteristics of each molecule in a petroleum fraction. Those properties are listed
Collect fundamental properties
of molecules, or estimate them
by group contribution methods
Estimate other properties of
molecules by correlations
Molecular
composition
of mixture
Calculate global properties
of mixture by mixing rules
Measure the fundamental
properties of mixture (SG, TBP)
Estimate other bulk properties
of mixture by correlations
Procedure to calculate
properties from mixing rules
Procedure to calculate
properties based on correlations
58

in Table 2.7. The calculation procedure (Figure 2.14) following the assumption
involves computing the properties of pure compounds and mixtures based on the
fundamental properties, and those of mixtures based on mixing rules with
molecular composition. Intensive correlations for mixture and pure compounds and
mixing rules for these properties are developed in the past, and most are available
from API TDB (1970) and Riazi (2005) as listed in Table 2.7, together with the
deviations of the correlations.
Table 2.7 Properties estimation methodology for pure compounds and mixtures,
mixing rules
Properties Pure compounds Correlations Mixing
Rules
Volume/weight/molar
average boiling point (
o
C)
Experimental/Group
contribution method
API 2B1.1 Eq 3.45
Molecular weight (g/mol) Eq 2.40 API 2B2.1 Eq 3.45
Specific gravity Experimental/Group
contribution method
Experimental Eq 5.126
Research octane number Experimental Experimental (Ghosh,
2006)
Motor octane number Experimental Experimental (Ghosh,
2006)
Reid vapour pressure
(kPa)
Eq 3.102 Eq 3.103 API 5B 1.3
Refractive index Eq 2.116 API 2B5.1 Eq 3.45
Aniline point (
o
C) Eq 3.125 API 2B9.1 API 2-
1.8/2-1.9
Kinematic viscosity(100
F) (cSt)
Eq. 2.128 (Wauquier,1995) Eq. 3.45
Kinematic viscosity(210
F) (cSt)
Eq. 2.129 (Wauquier,1995) Eq. 3.45
Critical pressure (kPa) Eq. 2.40 API 4D4.1 API 4B2.1
Critical temperature (°C) Eq. 2.40 API 4D3.1 API 4B1.1
Critical volume (m
3
/kg) Eq. 2.40 Eq. 2.40 API 4B3.1
59

Properties Pure compounds Correlations Mixing
Rules
CH weight ratio (wt/wt) Calculated Eq. 2.120 Calculated
Watson K Eq. 2.13 Eq. 2.13 API 2-0.9
Acentric factor Eq. 2.105 API 2B3.1 Eq. 5.115
Heat of vaporisation at
NBP (kJ/kg)
API 7C1.1 Eq. 7.54/7.56 API 7C2.1
Heat of combustion,77 F
(kJ/kg)
API 14A1.1/1.2 API 14A 1.3 Eq. 3.45
Liq heat capacity,60
F,1atm (kJ/kg·
o
C)
Eq 7.40 Eq. 7.43 Eq. 6.74
IG heat capacity,60 F,1atm
(kJ/kg·
o
C)
Eq. 6.72 Eq. 6.72 Eq. 6.74
Critical compressibility
Factor
Calculated Calculated Eq. 3.45
Liquid Thermal
conductivity at 25
o
C
Eq. 8.42/8.43 Eq. 8.46 API 12A
2.1
Cloud Point (
o
C) API 2B12.1 API 2B12.1 Eq
3.117/3.121
Surface tension at 25
o
C
(dyne/cm)
Eq 8.85 API 10A3.2 Eq. 8.87
Eq: equations in the reference (Riazi, 2005), API: (API TDB, 1997)
To verify the assumption, the properties of a gasoline stream with the detailed
molecular composition are calculated based on both correlations and mixing rules.
The small deviations show a good agreement between them. This assumption is
also verified in the literature (Albahri, 2005).



60

Table 2.8 Properties comparison of a gasoline stream based on both correlations and
mixing rules
Properties Mixing rules Correlation Error%
Volume average boiling point (°C) 112.48 113.23 0.67
Mole average boiling point (°C) 106.07 102.83 -3.06
Weight average boiling point (°C) 114.87 115.82 0.83
Molecular weight (g/mol) 102.01 103.99 1.94
Specific gravity 0.76 0.76 0.00
Reid vapour pressure (kPa) 13.31 13.17 -1.04
Refractive index 1.43 1.42 -0.70
Aniline point (°C) 37.24 37.26 0.06
Kinematic viscosity(100 °F) (cSt) 0.42 0.40 -4.76
Kinematic viscosity(210 °F) (cSt) 0.18 0.19 5.56
Critical pressure (kPa) 3312.10 3197.23 -3.47
Critical temperature (°C) 292.47 294.93 0.84
Critical volume (m
3
/kg) 0.0037 0.0037 0.0000
CH weight ratio (wt/wt) 6.66 6.31 -5.26
Watson K 11.58 11.55 -0.26
Acentric factor 0.30 0.29 -2.77
Heat of vaporisation at NBP (kJ/kg) 320.66 313.92 -2.10
Heat of combustion,77 °F (kJ/kg) 42961.64 43548.42 1.37
Liq heat capacity,60 °F,1atm (kJ/kg·°C) 1.97 2.01 2.13
IG heat capacity,60 °F,1atm (kJ/kg·°C) 1.38 1.42 3.03
Critical compressibility Factor 0.28 0.27 -3.57
Liquid Thermal conductivity at 25 °C 0.12 0.12 0.00
Cloud Point (°C) -104.41 -102.66 -1.68
Surface tension at 25 °C (dyne/cm) 22.68 23.33 2.87
2.6.2 Mathematical Model
The mathematical model for the transformation methodology is as follows.
61

2.6.2.1 Objective Function
The objective function:
2
, 3
2
, 2
2
, 1
) ( ) ( ) (
∑ ∑ ∑
∈
−
× +
−
× +
−
× =
PIONA f
msd
f
pred
f
msd
f
j
P
msd
P
pred
p
msd
P
P
T
msd
T
pred
T
msd
T
T
C
C C
w
p
p p
w
V
V V
w Obj
∑ ∑
−
× +
−
× +
E
2
msd
E
pred
E
msd
E
E , 5
2
C
msd
C
pred
C
msd
C
C , 4
)
C
C C
w ( )
C
C C
w ( (2.3)
where subscripts of T, P, f, C, E stands for measured temperature of a distillation
profile, properties listed in Table 2.7, the measurably-distinguished homologous
series, carbon number, and atoms of sulphur, nitrogen, and oxygen respectively.
Superscripts of msd and pred denote the measured and the predicted respectively.
w
1
-w
5
are weighting factors, determined as the inverse of the standard deviation of
the experimentally determined value for the measured properties or the correlation
calculated value for the derived properties respectively.
The chi-square statistic is a typical objective function used to optimise a
representative feed to an actual feed by minimizing the objective function. The
objective function is taken as the sum of the square of the percentage error between
the observed and calculated properties. It consists of different kinds of differences.
The first difference is between the measured distillation profiles and the calculated
ones from the predicted molecular composition. An interpolation method is
integrated into the optimisation program to determine the standard distillation
profile. The second part of the objective function compares all the other properties
excluding the distillation profile and the homologous series composition between
the measured/estimated by correlations and the predicted from molecular
composition. Homologous series composition difference is the third part of the
objective function. Although several developed correlations could be employed to
calculate homologous series composition, in the new methodology, homologous
series composition would be determined experimentally. The fourth part of the
objective function is the difference of molecular type composition between the
measured if available and the predicted. The final term is the difference of
composition for atoms such as sulphur, nitrogen, and this term is particularly
62

useful for diesel streams. If other data are available, other terms can easily be
added into this flexible objective function as needed.
2.6.2.2 Constraints
The assumption that molecular compositions within each homologous series follow
a gamma distribution against boiling point is as follows:
j , i
j
j
j
b
j , 1 i
j
j
j
j
b
j , i
j
b
j , 1 i
b
j , i
y
) (
) T (
,
) (
) T (
,
) T ( F ) T ( F =







 −
−







 −
= −
−
−
α Γ
β
η
α γ
α Γ
β
η
α γ
for 1 > i
(2.4)
j
j
j
j
b
j
j
b
j
y
T
T F
, 1
, 1
, 1
) (
) (
,
) ( =
Γ







 −
=
α
β
η
α γ
, for 1 = i (2.5)
∫
− −
=
x
0
t 1 s
dt e t ) x , s ( γ (2.6)
where subscript i and j denote carbon number and homologous series of the MTHS
matrix respectively. γ(x,y) is incomplete gamma function as Equation 2.6, and
) T ( F
b
j , i
denotes cumulative distribution function of gamma distribution at
b
j , i
T .
b
j , i
T
is normal boiling point of the entry(i,j) of the MTHS matrix. y
i,j
stands for the
fraction of the entry(i,j) within j homologous series of the MTHS matrix.
Therefore, the weight fraction of the entry(i,j) can be calculated according to the
weight fraction
w
j
x of homologous series j.
w
j
x will be optimised. ε is the tolerance
that allows small deviation of molecular composition between the optimal and the
calculated based on a gamma distribution.










+ × =
∑
ε
ii
j , ii
j , i w
j
w
j , i
y
y
x x (2.7)
∑
=
i
w
j i
w
j
x x
,
(2.8)
63

∑
=
j
w
j
x 1 (2.9)
The inter-conversion of weight, volume and molar fractions is as follows:
∑∑
=
ii jj
jj ii
w
jj ii
j i
w
j i v
j i
SG x
SG x
x
, ,
, ,
,
/
/
(2.10)
where
m
j , i
v
j , i
w
j , i
x , x , x denote the weight/volume/molar fraction of the entry(i,j) in the
MTHS matrix.
j , i j , i
MW , SG stand for specific gravity and molecular weight of the
entry (i,j) of the MTHS matrix respectively.
The cumulative volume against the boiling point of each molecule is as follows:
∑∑
=
jj ii
v
jj , ii
cv
j , i
x x , for { }
b
j , i
b
jj , ii
T T ; jj , ii jj , ii ≤ ∈ (2.11)
The cumulative volume against some particular temperature { }
TBP
T is calculated
through the linear interpolation as follows:
) T T (
T T
x x
x V
b
' j , ' i b
' j , ' i
b
'' j , '' i
cv
' j , ' i
cv
'' j , '' i cv
' j , ' i
pred
T
−
−
−
+ = for { }
b
' ' j , ' ' i
b
' j , ' i
T T T ' ' j , ' ' i , ' j , ' i ≤ ≤ ∈ (2.12)
The properties are calculated based on the fundamental properties by correlations
are as follows:
) SG , T ( f p
b P
msd
P
= (2.13)
The properties are calculated based on mixing rule with the volume, weight or
molar molecular composition as follows:
) p , x ( f p
P , j , i
v
j , i P
pred
P
= (2.14)
) p , x ( f p
P , j , i
w
j , i P
pred
P
= (2.15)
) p , x ( f p
P , j , i
m
j , i P
pred
P
= (2.16)
64

The molecular fractions in terms of the measurably-distinguished homologous
series are as follows:
∑
∈
=
f ) j , i ( e
v
j , i
pred
f
x C (2.17)
The molecular fractions in terms of carbon number are as follows:
∑
∈
=
C i
v
j , i
pred
C
x C (2.18)
The weight contents of atoms excluding hydrogen and carbon such as sulphur,
nitrogen and oxygen are as follows:
∑
∈
=
E ) j , i ( e
w
j , i
pred
E
x C (2.19)
The application of gamma distribution to control the fraction distribution within
each homologous series enables that some information could be utilised. For
instance, in most circumstances, the fraction of C
8
or C
9
for gasoline streams is the
maximum within aromatic homologous series, and that of C
16
or C
17
for diesel
streams is the maximum within some homologous series. That information could
be written as eq. 2.20 for gasoline, and eq. 2.21 for diesel respectively:
b
A C A A A
b
A C
T T
, 9 , 8
) 1 ( ≤ + − ≤ η β α (2.20)
b
j , 17 C j j j
b
j , 16 C
T ) 1 ( T ≤ + − ≤ η β α (2.21)
The listed equations and terms above are not necessarily the same for different
cases, and could be changed depending on the available information. For example,
regarding diesel streams, the fractions of different sulphur compound types lumped
as SI, SII, SIII, SIV, SV, SVI are important if the predicted molecular composition
is for kinetic models of processes. The distribution between different sulphur
compound lumps sometimes is available in the literature or could be measured, and
could be treated as constraints as well.
65

2.7 Optimisation Engines
The non-linear high dimensional problems with a complex search space can be
solved by two classes of search methods: deterministic and stochastic ones. The
deterministic methods, such as successive quadratic programming (SQP), are very
efficient to solve the convex/concave problems, while require the computation of
first and/or second order derivatives of the objective function and/or constraints,
which makes these methods not applicable to a non-differentiable or discontinuous
problem. Deterministic methods largely depend on the chosen initial solution in the
search for the optimal solution.
Stochastic optimisation techniques have higher probability of escaping local
optima and finding solutions in the vicinity of the global optimum for complex
non-linear and non-convex problems compared to the deterministic methods
(Arora, 2004). In the stochastic techniques, the problem is treated as a black-box.
A black-box may be defined as a system that provides output for a given input and
the information about internal calculations is not required. The optimisation
algorithm makes use of the values of the objective function at randomly chosen
points in the search space. The black-box treatment decouples the simulation and
optimisation of the design problem and improves the performance of optimisation
algorithm for complex problems.
Simulated annealing (SA) is a widely applied stochastic optimisation algorithm
due to its robustness and simplicity to be implemented (Athier et al., 1997).
Simulated annealing algorithm has been developed using the analogy to the
physical annealing of metals where a metal in a molten state at a very high
temperature is cooled down very slowly. In a molten state the metal atoms are
distributed randomly. When the system, i.e. the metal, is cooled it reaches the state
of minimum energy. If the annealing process is carried out slowly such that at any
point in time the system is close to thermodynamic equilibrium then the system
may reach stable crystalline structure with minimum energy. However, if the metal
is not cooled sufficiently slowly or the initial temperature of the system is not high
enough, then a glassy meta-stable structure, with energy higher than the desired
minimum level, is formed.
66


Figure 2.15 Simulated annealing algorithm (Kirkpatrick, 1983)
The simulated annealing algorithm (Kirkpatrick, 1983) represented in Figure 2.15
starts with an initial trial solution at an appropriate high value of the annealing
temperature. The annealing temperature serves as a control parameter for the
optimisation. The initial trial solution is modified by a random change, known as a
random move; the objective function for this new prospective solution is evaluated
against that of previous trial solution. The modification made to the current trial
solution may be accepted or rejected based on the acceptance criterion employed.
This process of modification, simulation and evaluation is repeated a number of
times (N) determined by the parameter known as the Markov chain length (Nmax),
to obtain a decent set of sample solutions. Once several candidate solutions have
been obtained, the annealing temperature is reduced. This cycle is continued until
67

the termination criterion is satisfied. The annealing temperature, acceptance
criterion, Markov chain length and termination criterion constitute the simulated
annealing parameters.
2.8 Case Studies
Three cases are studied, including one FCC gasoline fraction previously used to
demonstrate the shortcomings of the existing MTHS method, and two middle
petroleum fractions: straight run gas oil (SRGO) and light cycle oil (LCO) stream.
2.8.1 FCC Gasoline Stream Case
To compare the existing and proposed methodology, the case in section 2.3.6
would be employed to get the molecular composition. Table 2.9 gives the
measured molecular composition in terms of PIONA fraction.
Table 2.9 Measured molecular composition of a FCC stream (vol %)
vol% nP iP O N A
C4 0.10 0.00 0.50 0.00 0.00
C5 1.00 5.52 9.84 0.89 0.00
C6 1.71 6.23 9.54 2.21 1.20
C7 0.40 5.22 6.33 1.31 4.02
C8 0.30 3.51 3.27 3.11 7.23
C9 0.20 2.21 1.81 0.56 11.15
C10 0.20 1.41 1.00 0.87 5.42
C11 0.30 0.70 0.70 0.02 0.00
C12 0.00 0.00 0.00 0.00 0.00
The input information such as distillation profile, specific gravity etc is given in
the section 2.3.6. The generated new matrix for the FCC stream is as Table 2.10,
while Table 2.11 compares the property difference between the measured and
those calculated from both the existing and the proposed methodologies.

68

Table 2.10 Generated matrix for the FCC stream by the proposed methodology
Iso-paraffin Olefin vol%
NP MP DP TP NO BO A N sum
C4 0.00 0.07 0.18 0.17 0.43
C5 0.02 4.70 0.91 8.13 1.85 2.03 17.63
C6 0.35 5.49 1.49 7.96 2.89 0.61 2.15 20.94
C7 0.96 2.89 1.68 0.04 3.97 2.80 3.60 1.79 17.72
C8 1.25 0.89 1.64 0.11 1.36 1.76 8.35 1.43 16.80
C9 0.90 0.21 1.61 0.20 0.30 0.93 9.91 0.85 14.91
C10 0.51 0.04 1.24 0.28 0.06 0.42 4.42 0.48 7.44
C11 0.23 0.01 0.96 0.32 0.01 0.16 2.18 0.25 4.12
C12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
sum 4.22 14.30 9.53 0.95 21.97 10.99 29.07 8.97 100.00
Table 2.11 Comparison of properties
Properties Comparison
Measured New App. Error (%) Existing Error (%)
MW (g/mol) 97.49 97.41 -0.08 97.49 0.00
Specific Gravity 0.75 0.75 -0.07 0.75 0.00
RVP (psi) 6.17 6.16 -0.12 6.17 0.00
RON 90.89 90.86 -0.03 91.68 0.86
MON 78.06 78.23 0.22 77.73 -0.43
P (vol%) 4.22 4.22 -0.02 4.22 0.00
I (vol%) 24.80 24.77 -0.13 24.80 0.00
O (vol%) 32.99 32.94 -0.16 32.99 0.00
N (vol%) 8.97 8.97 0.00 8.97 0.00
A (vol%) 29.02 29.10 0.29 29.02 0.00
69

n-paraffin content
0.0
0.5
1.0
1.5
2.0
2.5
C4 C5 C6 C7 C8 C9 C10 C11 C12
v
o
l
u
m
e

f
r
a
c
t
i
o
n

(
%
)
Measued
New
Existing

isoparaffin
0
1
2
3
4
5
6
7
8
C4 C5 C6 C7 C8 C9 C10 C11 C12
v
o
l
u
m
e

f
r
a
c
t
i
o
n
(
%
)
Measued
New
Existing

(a) paraffin content comparison (b) isoparaffin content comparison
Olefin content
0
2
4
6
8
10
12
14
C4 C5 C6 C7 C8 C9 C10 C11 C12
v
o
l
u
m
e

f
r
a
c
t
i
o
n
(
%
)
Measued
New
Existing

Aromatics content
0
2
4
6
8
10
12
14
C6 C7 C8 C9 C10 C11 C12
v
o
l
u
m
e

f
r
a
c
t
i
o
n
(
%
)
Measued
New
Existing

( c ) olefin content comparison (d) aromatics content comparison
Naphthene content
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
C5 C6 C7 C8 C9 C10 C11 C12
v
o
l
u
m
e

f
r
a
c
t
i
o
n
(
%
)
Measued
New
Existing

(e) naphthene content comparison
Figure 2.16 Comparison of the detailed PIONA volume fraction between the
measured and those based on the existing and proposed methodologies
Figure 2.16 exhibits the comparison of the detailed molecular composition between
the measured and calculated by the existing and proposed methodologies. As seen
in Figure 2.16 (a), the molecular composition from the proposed methodology has
a little gap with the measured. The reasons may come from two points. One is the
70

normal paraffin content is relatively small with the total volume fraction of 4.22%,
and the other is the measured composition dose not follows with statistic
distribution exactly possibly due to the inherent equipment and human errors. The
consistency between the measured and the predicted distillation profile is shown in
Table 2.12.
Table 2.12 Comparison of distillation profile between the measured and the predicted
from the developed method
vol% Measured (°F) Predicted (°F) Error(%)
5 74.85 74.84 -0.01
10 87.71 87.71 0.00
30 149.58 149.58 0.00
50 204.91 204.79 -0.06
70 281.51 281.31 -0.07
90 328.09 328.88 -0.24
95 347.15 347.38 0.01
2.8.2 SRGO Feed
In this section, two examples are present to illustrate the proposed methodology,
for generating MTHS matrices of middle petroleum fractions. In the first example,
a straight run gas oil from one of Kuwait crudes (Marafi, 2007) is applied to
generate a MTHS matrix. The information available for the SRGO fraction
regarding the physical properties and composition is shown in Table 2.13.
To follow the first assumption, it is supposed that the weight fractions of the
MTHS matrix entries within each homologous series follow a gamma distribution
against boiling point. The reason using boiling point rather than molecular weight
is that the difference between two consecutive molecular weights within each
homologous series is always the same, and not for boiling point. More importantly,
boiling point is more common to be used. Since most of compounds locate
between C12 and C21 (Bacon, 2009), the following constraints are applied.
( )
b
j , 21 C j j j
b
j , 12 C
T 1 T ≤ + − ≤ η β α (2.22)
71

To avoid the distribution between molecules within each homologous series too
narrow or too wide, the scale parameter β and the shape parameter α of gamma
distribution has its individual limits.
20 1
j
≤ ≤ α
(2.23)
100 19
j
≤ ≤ β
(2.24)
As known, there are no olefins in straight run gas oil, therefore, olefin homologous
series is eliminated. Diesel streams are more complex than gasoline in terms of
molecular species. To simplify the problem, in this case, the derived properties, if
not measured, are excluded for the transformation methodology. Sulphur
compound types are crucial to the hydrotreating process. Therefore, a distribution
between different sulphur compound types – lumped as SII, SIII, SIV, SV in the
MTHS matrix is applied from the literature (Depauw, 1997; Nylén, 2004). The
applied weight distribution in this case is SII : SIII : SIV : SV = 7.5 : 2 : 1 : 0.4.
Table 2.13 Properties of SRGO Feed (Marafi, 2007)
Feed Properties GO-LF
Density @ 15
o
C (g/cc) 0.8962
Sulphur (%wt) 3.22
Total aromatics (%wt) 45.68
Monoaromatics (%wt) 19.47
Polyaromatics (%wt) 26.21
Cetane index 38.2
ASTM D86 (°C)
IBP 236
10 vol % 261
30 vol % 288
50 vol % 314
70 vol % 340
90 vol % 366
95 vol % 375
72
Table 2.14 MTHS matrix (wt %) generated for GO-LF SRGO by simulated annealing algorithm
P IP N A AA AN NN AAA AAN ANN NNN SII SIII SIV SV
C9 0.00 0.00 0.00 0.00 0.00
C10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01
C11 0.02 0.00 0.10 0.00 0.00 0.00 0.00 0.39
C12 0.08 0.01 0.68 0.02 0.12 0.04 0.02 1.99 0.04
C13 0.22 0.12 1.88 0.04 1.07 0.24 0.09 3.67 0.37 0.03
C14 0.44 0.54 2.48 0.09 2.65 0.58 0.23 0.04 0.03 0.00 0.00 3.73 1.62 0.21 0.03
C15 0.69 1.47 2.26 0.11 3.05 0.69 0.44 0.61 1.48 0.14 0.05 2.56 1.20 0.29 0.11
C16 0.91 2.73 1.47 0.09 2.16 0.60 0.60 0.49 2.22 0.79 0.29 1.34 0.47 0.29 0.13
C17 1.06 3.83 0.76 0.06 1.05 0.37 0.67 0.25 1.04 1.01 0.67 0.57 0.13 0.26 0.12
C18 1.11 4.31 0.32 0.04 0.43 0.20 0.61 0.10 0.32 0.69 0.89 0.21 0.03 0.22 0.10
C19 1.09 4.06 0.12 0.02 0.12 0.09 0.49 0.04 0.08 0.31 0.88 0.07 0.01 0.17 0.08
C20 1.00 2.98 0.04 0.01 0.05 0.03 0.33 0.02 0.02 0.12 0.69 0.02 0.00 0.14 0.06
C21 0.90 2.72 0.01 0.00 0.01 0.01 0.21 0.01 0.00 0.04 0.47 0.01 0.00 0.10 0.05
C22 0.77 1.55 0.00 0.00 0.00 0.00 0.11 0.00 0.00 0.01 0.29 0.00 0.00 0.08 0.03
C23 0.64 0.76 0.00 0.00 0.00 0.00 0.06 0.00 0.00 0.00 0.16 0.00 0.00 0.06 0.03
C24 0.53 0.54 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.08 0.00 0.00 0.04 0.02
C25 0.43 0.35 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.04 0.00 0.00 0.03 0.01
C26 0.35 0.12 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.02 0.00 0.00 0.02 0.01
73

The optimal parameters of the gamma distribution and fractions of homologous
series are given in Table 2.15. As seen, normal paraffins and iso-paraffins have
very close values of two parameters α and β, which means they have very similar
distribution of molecules. Similarly, homologous series of N, A, 2A and AN have
similar distributions. The molecular composition is shown in Table 2.14.
Table 2.15 Parameters of homologous series predicted for the gamma distribution
and the distribution
α β η X
P 17.32 25.91 190.00 10.21
I 16.87 24.56 230.00 26.12
O 11.08 19.00 271.00 10.14
N 15.29 19.01 314.88 0.47
A 13.18 19.00 373.18 10.72
AA 12.18 19.00 376.12 2.85
AN 14.89 22.80 277.27 3.90
NN 2.01 42.37 590.25 1.56
AAA 4.89 19.01 583.93 5.20
AAN 7.17 19.02 552.30 3.11
ANN 6.09 30.55 520.00 4.53
NNN 10.72 19.00 414.50 14.56
SII 4.49 19.01 608.50 3.88
SIII 2.04 100.00 627.83 1.94
SIV 1.86 99.99 673.11 0.78
SV 17.32 25.91 190.00 10.21
Figure 2.17 shows the comparison of distillation profile between the measured and
the predicted with some deviation of IBP, and also a comparison of the SRGO
properties and compositions is given in Table 2.16 and shows a reasonable
accuracy. Molecular weight, which value is calculated based on a correlation, is
applied to ensure mass balance. Furthermore, to illustrate the accuracy of the
achievable molecular composition, other properties, which are not applied in the
74

prediction, are predicted based on the optimal molecular composition and
correlations respectively, and compared. The results are given as Table 2.17.
200
240
280
320
360
400
0 10 20 30 40 50 60 70 80 90 100
cumulative volume (%)
T
e
m
p
e
r
a
t
u
r
e

(
o
C
)
Measured
Predicted

Figure 2.17 Distillation profiles of the SRGO from the measured and the predicted
Table 2.16 Comparison of the SRGO properties between the measured and the
predicted
Feed Properties Measured Predicted Error (%)
Density @ 15 °C (g/cc) 0.8962 0.8910 -0.58
Sulphur (%wt) 3.22 3.20 -0.62
Total aromatics (%wt) 45.68 45.08 -1.31
Monoaromatics (%wt) 19.47 21.00 7.86
Polyaromatics (%wt) 26.21 24.08 -8.13
Cetane index 38.2 37.8 -1.05
molecular weight (g/mol) 245.722* 243.460 -0.92



75

Table 2.17 Properties verification between calculated based on mixing rule and
correlations
mixing
rule
correlation Deviation (%)
Volume average Boiling point (°C) 322.65 317.84 -1.51
Mole average Boiling Point (°C) 313.57 308.66 -1.59
Weight Average Boiling Point (
o
C) 325.58 319.44 -1.92
Refractive Index 1.49 1.50 0.67
Aniline point (
o
C) 97.1 107.4 9.59
critical pressure (kPa) 1732.5 1742.7 0.59
critical temperature (
o
C) 539.2 512.5 -5.21
critical volume(m
3
/kg) 0.0038 0.0039 2.56
CH weight ratio (wt/wt) 7.09 6.97 -1.72
Watson K 11.54 11.37 -1.50
Acentric factor 0.723 0.733 1.36
heat of vaporisation at NBP(kJ/kg) 227.01 214.89 -5.64
heat of combustion,77 F(kJ/kg) 42015.5 42492.2 1.12
Liquid Thermal Conductivity at 25
o
C 0.152 0.148 -2.70
Surface Tension at 25
o
C (dyne/cm) 32.00 32.92 2.79
2.8.3 LCO Feed
In the second example of middle petroleum fractions, a light cycle oil (Ancheyta,
1999) is applied for the generation of a molecular composition used in chapter 6.
The properties of the LCO are shown in Table 2.18.
Table 2.19 shows the comparison of the properties and composition between the
predicted and the measured. API gravity has the biggest deviation of 2.5%, while
others are within 0.5%.


76

Table 2.18 Measured properties of LCO
Feed Properties GO-LF
API gravity 12.8
Sulphur (%wt) 3.50
Total aromatics (%wt) 72.0
Cetane index 26.2
Distillation (
o
C)
IBP 182
10 vol % 257
30 vol % 276
50 vol % 295
70 vol % 327
90 vol % 368
EBP 399
Table 2.19 Comparison of LCO properties between the predicted and measured
Feed Properties Measured Simulated
Annealing
Dif (%)
API gravity 12.8 13.12 2.500
Cetane index 26.2 26.20 -0.009
Sulphur (wt%) 3.5 3.50 0.001
Aromatics (wt%) 72 72.00 0.000
Distillation (
o
C)
IBP 182 182.00 0.000
10 vol % 257 256.06 -0.365
30 vol % 276 276.14 0.049
50 vol % 295 295.03 0.011
70 vol % 327 327.17 0.053
90 vol % 368 368.36 0.098
95 vol % 399 398.96 -0.01
77

It can be concluded from the results of the two examples on the matrix generation
that the proposed MTHS framework for the characterisation of diesel fractions can
provide a reasonable approximation for the composition, by taking the
consideration of isomers properly, integrating statistic distribution to set up the
distribution between entries within each homologous series, and solving the
problem with the simulated annealing methodology.
2.9 Summary
The conventional characterisation methods that are widely used in refinery process
modelling cannot provide detailed information at the molecular level. Such
information is needed for modelling of refinery processes to satisfy cleaner fuel
specifications. The MTHS matrix characterisation approach is a systematic
representation of detailed molecular information. In order to avoid expensive and
time consuming chemical analysis of petroleum fractions, previous researchers
developed methods for generation of MTHS matrices by minimising the difference
between the calculated and the measured bulk properties of streams. However, the
existing method has shortcomings, which prevent it from wide application.
A new methodology has been developed for molecular modeling of light and
middle petroleum fractions. Composition of light and middle distillates can be
characterised quickly without too much experimental effort. The method
revolutionised the MTHS framework on both the representation matrix by
considering isomers, and the transformation approach by introducing statistical
distribution and extensive properties. One of the main advantages of this method
over others is that the method not only focuses on minimising the difference of
properties between the measured and the calculated, but also takes the distribution
between molecules into account, which efficiently deals with the problem that
different molecular compositions could be achieved based on the same bulk
properties.
78
Chapter 3 Molecular Modelling of Gasoline
Blending
3.1 Introduction............................................................................................. 79
3.2 Gasoline Blending................................................................................... 79
3.2.1 A Brief Introduction of Gasoline Blending............................................ 79
3.2.2 Motivation of this Research on Gasoline Blending ............................... 85
3.3 A New Molecular Model for Property Prediction................................... 86
3.3.1 Review of Previous Methodologies for ON........................................... 87
3.3.2 A New Methodology Correlating ON with Bulk Properties.................. 87
3.3.3 Case Study.............................................................................................. 96
3.4 Gasoline Blending Model ..................................................................... 101
3.4.1 Review of Gasoline Blending Models ................................................. 101
3.4.2 Existing Blending Models for ON and RVP Properties ...................... 102
3.4.3 A New Molecular Gasoline Blending Methodology ........................... 106
3.4.4 Gasoline Blending Optimisation Model............................................... 108
3.4.5 Case Study............................................................................................ 109
3.5 Summary ............................................................................................... 112
3.6 Nomenclature ........................................................................................ 112

79
3.1 Introduction
Product blending targets allocating available components in a way to meet product
demands and specifications at the least cost and to produce incremental products
which maximise the overall profit. The major refining products from blending are
gasoline, diesel, jet fuels, lubricating oils, and heating fuels. The volume of
products sold even by a medium-sized refiner, are so huge that savings of a
fraction of a cent per unit will result in a substantial increase in profit over a period
of one year. For example, if a refiner sells about one billion gallons of gasoline per
year (about 65,000 BPCD; several refiners sell more than that in the United States),
a saving of one one-hundredth of a cent per gallon results in an additional profit of
$100,000 per year. Moreover, the demand of refining products is increasing
gradually, and will remain the increasing trend in the foreseeable future. On the
other hand, the refining industry today has to comply with higher product quality
specifications and more stringent environmental regulations, with more emphasis
on the molecular composition of refining products, under the increased number of
tighter environmental regulations from different agencies. These situations make
product blending crucial in the competitive industry to increase or maintain the
refining margin. However, many refiners used to treat product blending as a linear
problem, combined with a trial-and-error procedure, which increases property
giveaway with a huge profit loss (Gupta, 2008). Furthermore, the specifications
concerning molecular composition and properties of refining products result in a
large cost of instrument and maintenance. These scenarios lead to an aspiration for
investigating the nonlinear blending nature of most specifications, as well as
developing a methodology to predict properties based on easily obtained
properties, which both ultimately increase refining profit.
3.2 Gasoline Blending
3.2.1 A Brief Introduction of Gasoline Blending
Gasoline blending is a process of mixing/blending various refinery streams
produced by different refinery units along with additives to produce different
grades of products. The blending ratio depends upon the amount and the cost of the
80

production of each stream, specifications, demand and the price of the final
product. Selection of the blending components and their proportions in the product
blend is a complex problem. Figure 3.1 shows a simplified refinery flowsheet
related to gasoline blending.

Figure 3.1 Simplified petroleum refinery flowsheet (Gupta, 2008)
3.2.1.1 Blending Process
3.2.1.2 Blending Type
Regarding operation types, in-line blending and batch blending are two general
ways. In-line blending, also termed as continuous blending, involves mixing of
various component streams in a blender continuously, and at the same time
supplying products to a product storage tank. The in-line blender periodically
samples the blend and automatically tests the properties of samples online. This
information is used to adjust the feedstock flow rate so that the blend meets the
quality specifications in spite of unanticipated fluctuation in the properties of
feedstocks. This type of blending is very useful because of the fact that blending,
quality analysis, loading and unloading can be done in a single run. However,
techniques on on-line measurements, process control, as well as on-line
optimisation are the keys to the success of this type of blending.
81

In batch blending, various component streams are fed to the blender one after
another and converted to the product. Batch blending is a time consuming process
and requires storage tanks for both pre-blended and final products. Batch blending
is very cost effective when demand for a product is small. In batch blending the
feed quality is fairly constant over the time as compared to in-line blending. In oil
refineries, the batch blending is traditionally preferred but due to economic
pressures for reducing on-site tankage and low inventory requirement for safety
purposes, in-line blending is preferred (Singh et al., 2000).
3.2.1.3 Gasoline Blending Stocks
The incoming crude oil contains a wide range of materials, from light ones, such as
gasoline, to the heaviest ones, such as industrial fuel oil and asphalt. The crude oil
is split into various component streams by distillation according to their boiling
point ranges. Only a small portion of the distillate can go directly to gasoline
blending. Most of the output streams from the distillation unit are sent to other
processing units where the molecules are reformed to improve their quality or are
cracked and recombined into lighter, more valuable ones. These resulting products,
of widely different qualities, are then sent to intermediate storage tanks from which
they are blended into gasoline. A large refinery can have more than 20 blending
feedstocks that are blended into several grades of gasoline. The refinery processes
for producing gasoline blending streams are as follows:
Catalytic reforming: converts saturated, low octane hydrocarbons into higher-
octane products rich in aromatics.
Fluidised catalytic cracking: breaks large hydrocarbon molecules into gasoline
range products containing around 30% aromatics and 20-30% olefins.
Isomerisation: raises gasoline fraction octane by converting straight chain
hydrocarbons into branched isomers.
Alkylation: reacts gaseous olefin streams with iso-butane to produce liquid
high octane iso-alkanes, and only available in limited quantities in refinery.
Others: other naphtha streams in a refinery can be from hydrocracking,
visbreaking, coking and hydrotreating steps.
In addition to these streams, additives are blended to meet with the product
specifications. The different types of additives are: oxygenates (used as octane
82

enhancers), anti-oxidants (to reduce gum formation), anti-rust agents (to inhibit
rusting and protect the engine fuel system), detergents (to prevent deposits in the
engine fuel system), lubricants (to lubricate piston rings and cylinders), dyes (to
distinguish grades and brands), anti-icing agents (to retard icing and fuel line
freezing), etc.
3.2.1.4 Gasoline Specifications
Table 3.1 Clean Air Act and CARB specifications (USA) (Aye, 2003)

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. Table 3.1 gives the most stringent current specifications for
gasoline under Clean Air Act and in California (U.S.A). New compositional
measurements such as oxygenates, total aromatics, benzene and total olefins are
being phased in since 1992 in addition to the traditional gasoline quality
measurement. The increases in the environmental awareness and concerns are
demanding refinery fuels to be cleaner.These specifications might be well above
the restrictions imposed in many other countries but it is reasonable to postulate
that the specifications in more countries around the world will be close or even
stricter, as the reasons behind the strict regulations become apparent. As
specifications tightened, the conventional refining technologies are challenged.
83

A number of properties are used to characterise automotive gasoline and the
components that are blended to produce them, including octane number, Reid
vapour pressure (RVP), ASTM distillation points, viscosity, flash point, and
aniline point, as well as various properties from the concerns of environmental
consideration.
The octane number of a fuel is defined as the percentage of iso-octane (with octane
number 100) in a blend with n-heptane (having octane number of 0) that exhibits
the same resistance to knocking as the test fuel under standard conditions in a
standard engine. Antiknock properties of fuels for spark engines are characterised
by two standard test procedures. Research Octane Number (RON) could be
obtained from ASTM D-908, while ASTM D-357 gives the motor octane number
(MON). RON represents antiknock properties under conditions of low speed and
frequent accelerations while the MON represents engine performance under more
severe high speed conditions. The main difference between automotive gasoline
grades is their antiknock properties. For example, nowadays, in many parts of
Europe, regular and premium gasolines are specified to have posted octane
numbers of 95 and 97, respectively. Required octane number of gasolines vary
with parameters such as air temperature, altitude, humidity, and engine speed.
Improving the octane number of fuel would result in reducing power loss of the
engine, improving fuel economy, and a reduction in environmental pollutants and
engine damage (Bacon et al., 2009). For these reasons, octane number is one of the
important properties related to the quality of gasolines. Usually the control of ON
giveaway, having a great impact on the refining profitability, is one of the most
challenging tasks in gasoline blending. The model with high accuracy for
predicting ON of blending components, and ON of blends will be discussed in the
late sections.
Reid vapour pressure is the absolute pressure exerted by a mixture at 37.8
o
C at a
vapour-to-liquid volume ratio of 4. RVP is one of most important gasoline
properties, and it is used as a criterion for blending. For the specifications on
vapour pressure of gasoline, there are six different classes according to locations
and/or seasons. Vapour pressure limits for each class (54, 62, 69, 79, 93, 103 kPa)
are also specified.
84

As gasoline is distilled, the temperatures at which various fractions are evaporated
are calculated. Specifications define the temperatures at which various percentages
of the fuel are evaporated. Distillation limits include maximum temperatures that
10% is evaporated (50-70 °C), 50% is evaporated (110-121 °C), 90% is evaporated
(185-190 °C), and the final boiling point (225 °C). A minimum temperature for
50% evaporated is approximately (77 °C), and a maximum amount of residue after
distillation is about 2%.
Benzene is carcinogenic, and it is required to be below a certain level in gasoline.
Aromatics produce more smoke and smog, and produce benzene as a by-product
on incomplete combustion. There are specifications for benzene content
(maximum) and aromatics content (maximum). This restricts a refiner from using
too much of reformate, one of the major octane provider blend stocks, in which
benzene and aromatics are abundant. Benzene, overall aromatic and olefin contents
in finished motor and aviation gasoline are determined by gas chromatography.
Table 3.2 California (USA) Phase 2 specifications for gasoline (Simon, 2007)
Sulphur (wt.% max) 0.004
RVP (kPa, max) 48.3
Benzene (vol% max) 1
Aromatics (vol% max) 25
Olefins (vol% max) 6
ASTM 90% (°C, max) 149
Sulphur compounds are corrosive, foul smelling, and increase sulphur
dioxide/trioxide emissions. There are specifications for maximum sulphur in order
to minimise air toxics and corrosive components. The 2007 specification of
maximum sulphur content is 0.004 wt% in California (USA).
Oxygenates reduction is due to the recent findings that oxygenates such as methyl
tertiary butyl ether (MTBE) are water soluble and contaminate water sources, and
could also seriously harm the handler. Thus phasing out of water soluble
oxygenates, which are very high in octane number, are on the way. This not only
causes octane loss, it also reduces the amount of gasoline produced by 3-4% and
85

refiners loose the non-aromatic, non-olefinic, and low-sulphur blend stock (UOP
2000). Moreover, according to the studies done by various researches shows that
the cost of production of gasoline would increase by about 30% with the oxygenate
ban. Their future is uncertain from political standpoint.
Other properties include viscosity (maximum), API gravity, density, olefins
(maximum vol%) and specific gravity. Table 3.2 shows the specification for
gasoline in California (USA).
3.2.2 Motivation of this Research on Gasoline Blending
To achieve a successful operation in most petroleum refineries, gasoline blending
is considered as a key process. This indicates the need to employ tight controls of
blending operations on property giveaway as it can provide a crucial edge to the
profitability of a refinery. As reviewed before, many refiners used to treat gasoline
blending as a linear problem, sometimes as a non-linear one but still with a big
giveaway due to the model accuracy, which leads to a significant profit loss. On
the other hand, the compositional specifications such as benzene, aromatic and
olefin contents, and other properties specifications need a demanding investment
on the expensive instruments, constant maintenance, frequent standardisation, as
well as consuming feedstock/product for analysis. Moreover, it is not suitable on-
line monitoring. In the petroleum industry, measurement of the physical properties
of hydrocarbons forms the basis of commodity pricing and the assessment of
process parameters. The key measurement performed on gasoline is the calculation
of octane number. The ASTM standard for reporting this measurement is an
internal combustion engine in which octane is measured by interpolating between
the nearest standards above and below the unknown sample. The procedure is time
consuming, involves expensive (over $100,000) and maintenance– intensive
equipment, requires skilled labour and is not well suited to on–line monitoring.
Although modern analytical technology is able to measure molecular information
both online and offline, it cannot be used in a virtual environment, and will
increase a large maintenance cost.
86

3.3 A New Molecular Model for Property Prediction

Figure 3.2 Research Octane Number of different families of hydrocarbons (Riazi,
2005)
As reviewed in chapter 2, numerous efforts have been put into developing
correlations for predicting properties based on easily measured distillation profile
and density in the past (see Table 2.7). However, some properties such as ON
cannot be directly estimated from the boiling point and density, since ON very
much depends on the chemical structure of components of the mixture. Figure 3.2
shows variation of RON with boiling point of pure hydrocarbons from different
families. Knock results from the premature combustion of gasoline due to
compression in the engine. As the fuel/air mixture is compressed in the internal
combustion engine, certain molecules in gasoline tend to self-ignite even before
they reach the ignition spark, thereby creating a resistive expansive motion in the
compression stroke of the engine and hence the knock. Depending on the thermal
stability of molecules and the ensuing radicals, certain molecules tend to combust
sooner than others. Consequently, ON is a direct function of the molecular
composition of gasoline fuel, and any modelling effort should explicitly
acknowledge it.
87

3.3.1 Review of Previous Methodologies for ON
Previous studies have attempted to mathematically describe the ON as a function
of gasoline composition. Anderson et al. (1972) developed a useful and simple
method – an ideal model - for predicting the RON of different types of naphtha
based on the gas chromatographic analysis of a sample by characterising a stream
using 31 molecular lumps, and computing ON of the fuel as a linear addition of the
contribution from each lump. Later on, more and more researchers (Rusin, 1981;
Habib, 1989; Cotterman, 1989) found that the octane number is not generally a
linear mixing property due to the interactions existing between the compounds of
different chemical natures (olefins, paraffins, naphthenes, and aromatics). This can
generate effects of synergy or inhibition and give the mixture a higher/lower
octane number than its individual components. Lugo (1999) developed correlations
between catalytic cracking naphtha ON and composition using a non-ideal model
based on Anderson’s lumps. Other relevant work in this includes the work by Twu
and Coon (1997), and Albahri (2003). More recently, a detailed gasoline
composition-based octane model (Ghosh, 2006) was presented with a total of 57
hydrocarbon lumps to predict ON of any type of gasoline fuels based on the
analysis of 1471 gasoline fuels from different process streams. The model predicts
the octane number within a standard error of 1 number for RON and MON for a
broad range of ONs from 30 to 120.
All of these methods predict ON by correlating molecular composition, which
obviously demand the molecular composition measured by different chemistry
analytical methods.
3.3.2 A New Methodology Correlating ON with Bulk Properties
3.3.2.1 Assumptions
Published studies (API, 1997; Scott, 1958; Ghosh, 2006) reveal that hydrocarbons
belonging to the same homologous series blend linearly on ON. That is to say that
paraffins blend linearly with other paraffins, olefins blend linearly with other
olefins, and so on. However, a blend of olefins and aromatics may exhibit
88

significant deviation from linearity. Such nonlinear interaction in a binary blend is
qualitatively described in Figure 3.3.

Figure 3.3 Nonlinear interactions between two molecules belonging to different
homologous series (Ghosh, 2006)
According to this behaviour, an assumption is made that gasoline blending streams
could be lumped as P, I, O, N, A, and the interaction between each lump is
considered. Then, the proposed model could be expressed as Equation 3.1.
) , (
i i
ON x f ON = PIONA i ∈ ∀ (3.1)
where x
i
represents the fraction of i lump, and ON
i
for ON of lump i.
The detailed gasoline composition-based octane model (Ghosh, 2006) will be
applied to PIONA-lump model as Equation 3.2.
( )
∑ ∑ ∑
∑ ∑
∈ ∈ ∈
∈ ∈
− +
+
= =
PIONA i PI i
v
i
PI i
i
v
i PI i
v
i
PIONA i PI i
i i
v
i PI i i
v
i
i i
) x x ( I x
ON x I ON x
ON , x f ON
β β
β β
(3.2)
where β
i
is the fixed coefficient.
v
O
b
PO
v
N
b
PN
v
O
a
PO
v
N
a
PN
PI
x k x k 1
x k x k
I
+ +
+
= (3.3)
In this model, the nonlinear interactions between paraffins and naphthenes and
between paraffins and olefins are considered.
89

Based on the assumption made and the available molecular blending model, the
problem switches to correlating PIONA volume fractions and PIONA ONs with
easily obtained bulk properties through Equations 3.4 and 3.5 as Figure 3.4 shows.
) , ( d TBP f x
i
= PIONA i ∈ ∀ (3.4)
) , ( d TBP f ON
i
= PIONA i ∈ ∀ (3.5)

Figure 3.4 Simplified diagram for predicting ON of blending streams
The second assumption is made that fractions and ONs of PIONA lumps could be
correlated with TBP curve and density of gasoline streams. Moreover, the
correlations will depend on refining process type. As reviewed, straight run
naphtha from atmospheric distillation unit, gasoline streams from FCC and CCR
units, etc. are potential gasoline blending components, therefore the correlations of
Equations 3.4 – 3.5 will be developed for each process. This assumption excludes
the possibility that the streams from the same refining process with similar TBP
and density could have quite different ONs.
The assumption of correlating fractions and ONs of PIONA lumps with bulk
properties is aspired from the mostly commonly used correlation of ASTM D4737
for cetane number of diesel fuels illustrated as Equation 3.6.
( ) ( )
N 90 N N 50 N N 10
T B 42 . 0 0523 . 0 T B 901 . 0 131 . 0 T 0892 . 0 2 . 45 CN − + + + + =
( ) [ ]+ − +
2
N 90
2
N 10
T T 00049 . 0
2
N N
B 60 B 107 +
(3.6)
Distillation profile,
density of gasoline
streams
PIONA prediction based
on regressed model
ON of PIONA
prediction based on
regressed model
Molecular gasoline
blending model for
ON prediction
90

where d is specific gravity at 60
o
F, and T
x
is the TBP temperature (in
o
C) at which
x vol% of the sample has distilled.
1 e B
) 85 . 0 d ( 5 . 3
N
− =
− −
(3.7)
215 T T
10 N 10
− = (3.8)
260 T T
50 N 50
− = (3.9)
310 T T
90 N 90
− = (3.10)
Despite its empirical nature, this simplified quadratic correlation has enjoyed
enviable success in describing CN of various diesel fuels and their blends. It is
used extensively within the petroleum industry. Therefore, the quadratic equations
are proposed to correlate the fractions and ONs of PIONA lumps with bulk
properties as Equations 3.11 and 3.12.
N 90 N
f
i , 7 N 50 N
f
i , 6 N 10 N
f
i , 5
2
N 90
f
i , 4
2
N 50
f
i , 3
2
N 10
f
i , 2
2
N
f
i , 1
pred
i
T B a T B a T B a T a T a T a B a x + + + + + + =
+ + + +
N 90
f
i , 10 N 50
f
i , 9 N 10
f
i , 8
T a T a T a
f
i , 12 N
f
i , 11
a B a + PIONA i ∈ ∀
(3.11)
ON
i , 7 N 50 N
ON
i , 6 N 10 N
ON
i , 5
2
N 90
ON
i , 4
2
N 50
ON
i , 3
2
N 10
ON
i , 2
2
N
ON
i , 1
pred
i
B a T B a T B a T a T a T a B a ON + + + + + + =
+ + + +
N 90
ON
i , 10 N 50
ON
i , 9 N 10
ON
i , 8
T a T a T a
ON
i , 12 N
ON
i , 11
a B a + PIONA i ∈ ∀
(3.12)
where
1 e B
) d d ( 5 . 3
N
− =
− −
(3.13)
100 / T T
10 N 10
= (3.14)
100 / T T
50 N 50
= (3.15)
100 / T T
90 N 90
= (3.16)
The coefficients in the correlations will be regressed by the proposed methodology.
91

3.3.2.2 Methodology

Figure 3.5 Diagram for the methodology of predicting ON of gasoline streams from
one of refining process
The diagram for the proposed methodology used to predict ON based on easily
obtained bulk properties is depicted in Figure 3.5. The whole procedure involves
two phases, namely regression and prediction phases. The regression phase, as the
START
Measurement: Distillation
Profile, Density and
Octane Number
Measurement:
PIONA fractions
PIONA fraction regression
Optimisation Model
Optimal Coefficients for
PIONA fractions prediction
Predicted
PIONA fractions
ONs of PIONA regression
Optimisation Model
Optimal Coefficients for
ONs of PIONA prediction
Regression Phase
Prediction Phase
Fractions and ONs of
PIONA prediction
Molecular
Blending Model
Predicted
ON
END
92

name implies, targets on achieving the optimal coefficients of the correlations for
the prediction of the fractions and ONs of PIONA lumps, while the prediction
phase will apply the optimal coefficients to predict the fractions and ONs of
PIONA lumps, which are used to predict ON as Equation 3.2.
The first step in this scheme consists of information gathering about gasoline
streams from the investigated refining process, including distillation profile,
density, and ON, as well as compositional fractions of PIONA lumps. This
experimental information provides the basic input for the regression models.
The second step is to use a regression optimisation model based on least square
method for correlating the fractions of PIONA lumps by Equation 3.11. The
mathematical model for this step is as follows.
Objective function is to minimise the difference of fractions between predicted and
measured, in which the measured data is from the first step.
∑
×
−
=
j
2
msd
j , i
pred
j , i
msd
j , i
i
) 100
x
x x
( obj (3.17)
Subject to
+ + + + + + =
j , N 50 j , N
f
i , 6 j , N 10 j , N
f
i , 5
2
j , N 90
f
i , 4
2
j , N 50
f
i , 3
2
j , N 10
f
i , 2
2
j , N
f
i , 1
pred
j , i
T B a T B a T a T a T a B a x
f
i , 12 j , N
f
i , 11 j , N 90
f
i , 10 j , N 50
f
i , 9 j , N 10
f
i , 8 j , N 90 j , N
f
i , 7
a B a T a T a T a T B a + + + + +
PIONA i ∈ ∀ , J j ∈ ∀
(3.18)
0 x
pred
j , i
≥ (3.19)
where J stands for the all sample streams of the investigated refining process
collected from the first step. The optimal coefficients of a
f
will be used in the
prediction phase.
The third step comprises of a regression optimisation model to correlate ONs of
PIONA lumps with bulk properties. It cannot be implemented in the same way as
the fractions regression model in the second step because ONs of PIONA lumps
93

are unknown. Therefore, an iterative procedure is proposed to implement it as
Figure 3.6 shows.

Figure 3.6 Series of procedures for achieving the optimal coefficients for predicting
ONs of PIONA lumps
The first part of the step is to estimate ONs of PIONA lumps according to a
correlation from the literature (Riazi, 2005) as Equations 3.20 and 3.21. These
values are treated as the initial guess of
1 pred
j , i
ON .
4
j , 50 i
3
j , 50 i
2
j , 50 i j , 50 i i
Init
j , i
T e T d T c T b a RON + + + + = (3.20)
) O (% 12 . 0 d 0 . 20 RON 83 . 0 5 . 22 MON
Init
j , i
Init
j , i
− − + = (3.21)
The coefficients are given in Table 3.3. For isoparaffins, there are four sub-classes,
and the ON of isoparaffins would be the average of these four.
Correlations (3.20) to
get the initial guess of
ONs of PIONA
Minimising Equation 3.22
by changing the coefficients
of correlations (3.23)
Minimising Equation 3.24 by
changing ONs of PIONA lumps
1 pred
j , i
ON for each stream
tol dif ≤ ∆
Stop
Update
1 pred
j , i
ON
94

Table 3.3 Coefficients of Equation 3.20 (Riazi, 2006)
RON a b c D e
P 1514.964439 -3893.446054 1211.056162 3649.119954 -2507.33327
I 95.927 -157.53 561 -600 200
92.069 57.63 -65 0 0
109.38 -38.83 -26 0 0
97.652 -20.8 58 -200 100
O 517.8532645 -1064.055902 181.0178314 1237.306636 -777.6732827
N 3.704079298 390.917866 -493.279582 98.66492226 82.24068859
A 145.668 -54.336 16.276 0 0
The following parts are within the iteration. The second part minimises the
differences of ONs of PIONA lumps between the predicted based on Equation 3.23
and the predicted result from the first step for the first iteration or the updated
result from the late iteration. The optimisation model is as follows.
The objective function:
∑
×
−
=
j
2
1 pred
j , i
1 pred
j , i
pred
j , i
i
) 100
ON
ON ON
( obj (3.22)
where
1 pred
j , i
ON is the result from the first step or the update result from the
iteration.
Subject to
+ + + + + =
j , N 10 j , N
ON
i , 5
2
j , N 90
ON
i , 4
2
j , N 50
ON
i , 3
2
j , N 10
ON
i , 2
2
j , N
ON
i , 1
pred
j , i
T B a T a T a T a B a ON
+ + + + +
j , N 90
ON
i , 10 j , N 50
ON
i , 9 j , N 10
ON
i , 8 j , N 90 j , N
ON
i , 7 j , N 50 j , N
ON
i , 6
T a T a T a T B a T B a
ON
i , 12 j , N
ON
i , 11
a B a +
PIONA i ∈ ∀ , J j ∈ ∀ (3.23)
The third part of the step consists of minimising the difference of ON of the stream
between the measured and the predicted from the molecular model as Equation 3.2
by changing the ONs of PIONA lumps of
1 pred
j , i
ON , and simultaneously remaining
the optimal ONs of PIONA lumps close to the result from the second part of the
step (
pred
j , i
ON ) as much as possible. The optimisation model is as follow.
95

Objective function
∑
∈
− + − =
PIONA i
2 pred
j , i
1 pred
j , i
2 msd
j
pred
j j
) ON ON ( w ) ON ON ( Obj J j ∈ ∀ (3.24)
Subject to
∑ ∑ ∑
∑ ∑
∈ ∈ ∈
∈ ∈
− +
+
=
PIONA i PI i
pred
j , i
PI i
i
pred
j , i j , PI i
pred
j , i
PIONA i PI i
1 pred
j , i i
pred
j , i j , PI
1 pred
j , i i
pred
j , i
pred
j
) x x ( I x
ON x I ON x
ON
β β
β β
(3.25)
1 pred
j , I
1 pred
j , P
RON RON ≤ (3.26)
1 pred
j , N
1 pred
j , O
RON RON ≥ (3.27)
100 RON
1 pred
j , A
≥ (3.28)
25 . 0 ) 100
ON
ON ON
(
2
msd
j
msd
j
pred
j
≤ ×
−
(3.29)
where w is the weighting factor, and the current value is 100. The first constraint in
this optimisation model is the molecular model for predicting ON of the stream
based on PIONA lumps. Equations 3.26 – 3.29 are applied to RON, and will be
changed accordingly for MON. The last constraint is for the accuracy requirement
of ON prediction, as the default of 0.5% deviation.
The iteration will be stopped until the change of the objective function is less than
tolerance. From this step, the optimal coefficients for predicting ONs of PIONA
based on bulk properties are achieved, which will be used in the prediction phase.
After achieving the optimal coefficients of correlations, ON of the stream could be
predicted based on Equation 3.2 after calculating the fractions of PIONA from
Equation 3.11 and ONs of PIONA lumps from Equation 3.12, which is termed as
the prediction phase in Figure 3.5.
The proposed methodology can be applied to predict other properties as well, such
as RVP. The difference in the methodology for different properties is that different
molecular blending models instead of Equation 3.2 should be introduced. As for
RVP, Equation 3.30 is introduced as the molecular blending model.
96

∑ ∑ ∑
∑ ∑
∈ ∈ ∈
∈ ∈
− +
+
=
PIONA i A i
v
i
A i
i
v
i A i
v
i
PIONA i A i
i i
v
i A i i
v
i
) x x ( I x
RVP x I RVP x
RVP
β β
β β
(3.30)
where
v
N
b
AN
v
O
b
AO
v
I
v
P
b
AP
v
N
a
AN
v
O
a
AO
v
I
v
P
a
AP
A
x k x k ) x x ( k 1
x k x k ) x x ( k
I
+ + + +
+ + +
= (3.31)
The nonlinear interactions between aromatics and other homologous series (PION)
are taken into account due to the well-known non-ideal blending behaviour of non-
aromatics with aromatics (API, 1997). As for the initial value (Equation 3.20) of
RVP, RVP of each entry of MTHS matrix is applied.
3.3.3 Case Study
0
0.2
0.4
0.6
0.8
1
N
o
r
m
a
i
l
i
s
e
d

d
i
s
t
r
i
b
u
t
i
o
n
SG T10 T50 T90 P I O N A RON MON RVP

Figure 3.7 Normalised distributions of the related properties for the proposed
methodology (Each dot stands for a different sample)
The proposed methodology will be applied to ON and RVP properties for the
gasoline stream from a FCC unit in a plant. Historical data are obtained from the
97

report of the FCC units. Normalised distributions of properties including specific
gravity, T
10
, T
50
, T
90
, PIONA fractions, RON, MON and RVP are illustrated in
Figure 3.7. 80% of the obtained dataset is used for the regression phase, and the
rest to verify the accuracy of the proposed methodology. The proposed
methodology is applied to ON/RVP properties. Many different initial guesses were
assumed, and the parameters were re-optimised to ensure that the optimisation
problem was not trapped in an inferior local solution.
3.3.3.1 Result of the Regression Phase
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35 40
Measured
P
r
e
d
i
c
t
e
d
P
I
O
N
A

Figure 3.8 Comparison of PIONA volume fractions between the measured and
predicted in regression phase
In the regression phase, the coefficients of the correlations will be optimised based
on the proposed methodology. Figure 3.8 – 3.11 illustrate the results of the
regression model for PIONA fractions, RON, MON and RVP respectively. Table
3.4 summarises the model performance. The overall standard error is defined as
( )
∑
− n / pred meas
2
, and the average represents the average of absolute errors
between the measured and the predicted. The overall standard errors for RON,
MON and RVP are 0.38, 0.51 number, and 0.24 psi. To have a comparison, direct
quadratic correlations between properties including RON, MON and RVP and the
easily obtained properties are applied, and the results are shown in Table 3.5. 0.25,
0.33 number of RON and MON, 0.16psi of RVP are improved in terms of the
overall standard errors. This improvement may seem marginal, but even a 0.1
98

number improvement in the prediction error has a significant economic
consequence (Ghosh, 2006).
90
91
92
93
94
95
90 91 92 93 94 95
Measured RON
P
r
e
d
i
c
t
e
d

R
O
N

Figure 3.9 Comparison of RON between the measured and predicted in regression
phase
78
79
80
81
82
83
84
78 79 80 81 82 83 84
Measured MON
P
r
e
d
i
c
t
e
d

M
O
N

Figure 3.10 Comparison of MON between the measured and predicted in regression
phase

99

7
7.5
8
8.5
9
7 7.5 8 8.5 9
Measured RVP
P
r
e
d
i
c
t
e
d

R
V
P

Figure 3.11 Comparison of RVP between the measured and predicted in regression
phase
Table 3.4 Model performance in regression phase
standard deviation average overall standard errors
P (vol%) 0.46 0.56 0.75
I (vol%) 1.19 3.94 1.99
O (vol%) 1.44 6.79 2.61
N (vol%) 0.38 0.41 0.64
A (vol%) 0.94 2.14 1.46
RON 0.18 0.34 0.38
MON 0.28 0.44 0.51
RVP (psi) 0.12 0.21 0.24
Table 3.5 Model performance of the direct correlated model (see section 3.3.3.1)
standard deviation average overall standard errors
RON 0.43 0.47 0.63
MON 0.42 0.73 0.84
RVP (psi) 0.26 0.32 0.40
100

3.3.3.2 Result of the Prediction Phase
To investigate the performances of interpolation and extrapolation predictions, the
prediction dataset includes the data both inside the range of properties and outside.
To define the prediction type, if the dataset of the basic input information including
density, T
10
, T
50
, and T
90
all locate within the ranges of these properties for the
regression phase, it’s defined as interpolation prediction. Otherwise, if any of these
properties of the dataset violates the ranges, it becomes extrapolation prediction.
Table 3.6 illustrates the good performance of the interpolation prediction, while
Table 3.7 gives the result of an example of the extrapolation prediction, which sees
bigger deviations of RON, MON and RVP properties. More investigation found
that more gaps of the properties from the ranges of regression dataset, higher
deviation will be generated, which is the common disadvantage of the regression
based models. To enhance the accuracy of the prediction, the dataset outside of the
regression range could be added for the regression to ensure the high accuracy of
predicted results.
Table 3.6 Model performance of interpolation prediction in the prediction phase
standard deviation average overall standard errors
RON 0.18 0.25 0.30
MON 0.17 0.36 0.39
RVP 0.24 0.42 0.46
Table 3.7 Result of an example of extrapolation prediction
Measured Prediction Error
RON 91.80 92.88 1.08
MON 81.20 82.71 1.51
RVP 8.27 7.34 0.93
101

3.4 Gasoline Blending Model
3.4.1 Review of Gasoline Blending Models
In the previous section (section 3.3), a new methodology is proposed to predict the
properties, which provides a fundamental information for gasoline blending. Since
the process control objectives for the product blending are often framed in terms of
meeting specifications on the properties of gasoline such as ON, RVP, viscosity,
etc., process models in the form of component property mixing rules are required
for effective process control.
The most simple and practical mixing rule (Riazi, 2005) that is applicable to most
physical properties is as follows:
∑
=
=
N
1 k
k k p
x θ θ (3.32)
where x
k
is the volume/weight/molar fraction of the blending component k, θ
k
is a
property for the blending component k, and θ
p
is property of the product with N
blending components. Equation 3.32 could be applied to any property, and has
various modified versions when it is applied to different properties. The type of
fraction used for x
k
depends on the type of property. For example, to calculate
molecular weight of a product, the most appropriate type of fraction is mole
fraction. However, when it is applied to density, specific gravity, or refractive
index, volume fraction should be used, or the modified version as Equation 3.33
with weight fraction can also be applied (Riazi, 2005).
∑
=
=
N
1 k
k wk p
/ x / 1 θ θ (3.33)
Equation 3.32 can be applied to predict the properties blend linearly such as
Aromatics, Benzene, Olefins, Oxygenates and sulphur contents. However, it has
been widely recognised that some gasoline properties blend in a non-ideal and
nonlinear fashion such as octane number, RVP, Aniline point, and viscosity, as
well as distillation profile etc., necessitating the use of more complex blending
models to predict these properties. Some of these properties can be converted to a
102

blending number or index to allow them to be blended linearly as Equation 3.34
shows.
∑
=
=
N
1 k
k k p
BI x BI (3.34)
where BI
k
is the blending index/number of the property of blending component k
which is the function of the property as Equation 3.35, and BI
p
is the blending
index/number of the property of the product, which can be inversely converted to
the property of the product as Equation 3.36. x
k
is the volume/weight/molar
fraction of blending component k.
) P ( f BI = (3.35)
) BI ( f P
1 −
= (3.36)
The properties blended according to Equation 3.34 include RVP, viscosity, Aniline
point, pour point and flash point (Riazi, 2005). However, one of serious
disadvantages is that these blending indices/values only can be applied in a narrow
property range, and will generate a big deviation for blending of streams with wide
different properties. RVP and octane number are two most important properties of
gasoline products with high non-linear blending nature. Several key factors are
very important for the blending models: (1) predictive accuracy; (2) complexity;
and (3) ease of implementation. The following section will firstly review the
models specific for ON and RVP blending, followed by a new proposed
methodology based on the molecular model, compared in these three key factors.
3.4.2 Existing Blending Models for ON and RVP Properties
3.4.2.1 Octane Number
Several blending models are available in the literature for the calculation of the
blend octane rating and all these models recognise the nonlinear dependence of the
blend octane number by modelling it with functions containing a linear part and a
nonlinear correction term. A number of empirical blending models are available in
the literature for predicting blended octane numbers given component properties
which include the blending octane number method (Gary and Handwerk, 2001),
103

the transformation method (Rusin et al., 1981), the Ethyl RT-70 models (Healy et
al., 1959), an olefins content based method from Stewart (1959), the interaction
method (Morris, 1975) and the excess method (Muller, 1992).
Both the blending octane number approach and the transformation method attempt
to convert the nonlinear blending problem to a linear problem by transforming
RON and MON into quantities that blend ideally on a volumetric basis. The results
of the blend calculations are then transformed back to an appropriate octane
number. Although the blending octane number method requires fewer and simpler
calculations than the far more complex transformation method, the blending octane
numbers must be computed from experimental data.
The interaction method and the excess method are essentially regression analysis
based approaches. In the interaction method, blending nonlinearity is accounted for
via two-factor interaction (or bilinear) terms, whereas in the excess method, the
deviation is accounted for using an excess (or bias) term. Both of these approaches
require a considerable amount of data from laboratory blending studies to estimate
the large number of parameters in the models.
For the transformation method, Rusin et al. (1981) have reported higher prediction
accuracy for extrapolation than for interpolation. The excess method, being linear,
is valid only within the vicinity of the nominal blend. Due to the fact that the
transformation models and the interaction models require more feedstock quality
data and contain more parameters, it is not very favourable though they seem to
provide slightly better predictive accuracy than the Ethyl RT-70 models.
Moreover, the Ethyl RT-70 models are much simpler and easier to use than the
transformation models.
Despite the age, the Ethyl RT-70 blending models are widely used and have
become a standard against which many of the newer models are compared. The
Ethyl RT-70 approach consists of a linear blending part, and the blending
nonlinearity is expressed in terms of the component sensitivity (RON-MON),
olefins content, and the aromatic content of the blend components expressed as
follow (Healy et al., 1959).
104

( ) ( ) [ ] ( ) ( ) [ ]
2
a a
2
2 a a a 1 a b
O O a S RON S RON a RON RON − + × − × + =
( ) ( ) [ ]
2
a a
2
3
A A a − + (3.37)
( ) ( ) [ ] ( ) ( ) [ ]
2
a a
2
2 a a a 1 a b
O O b S MON S MON b RON MON − + × − × + =
( ) ( ) [ ] { }
2
2
a a
2
3
100 / A A b − + (3.38)
where, a
i
and b
i
are standard coefficients and their values are given in Table 3.8,
and S is the component sensitivity. The subscript a stands for the average.
Table 3.8 Coefficients in ethyl octane blending equations (Healy et al., 1959)
Coefficients for RON Coefficients for RON
0.0 cc
TEL/ gal
1.5 cc
TEL/ gal
3.0
TEL/ gal
0.0 cc
TEL/ gal
1.5 cc
TEL/ gal
3.0 TEL/
gal
a
1
0.03224 0.04600 0.05411 0.03224 0.04563 0.05242
a
2
0.00101 0.00070 0.00098 0.00085 0.00066 0.00084
a
3
0.00000 -0.00035 -0.00074 0.00000 -0.00042 0.00080
b
1
0.0445 0.05122 0.03908 0.04285 0.04422 0.03532
b
2
0.00081 0.00000 0.00000 0.00066 0.00000 0.00000
b
3
-0.00645 -0.00539 -0.00703 0.00632 -0.00752 -0.00849
Although the Ethyl models are simple and easy to use, there are some
disadvantages. Firstly, the predictive accuracy will reach 0.82 ON of standard
deviation for the interpolation prediction with a narrow range of blending streams
(Rusin et al., 1981). Secondly, the model is a regression based model with a
limitation on the extrapolation prediction. Lastly, the model needs the
measurement of RON, MON, olefin and aromatic contents of each blending
streams.
More recently, molecular composition based octane blending models have been
receiving significant attention to maintain/increase the refining margins with the
serious forces from the environmental regulations. The main difference between
the molecular blending models and traditional models is that the interactions
between molecules/lumps are taken into account to achieve a high accuracy on ON
prediction. The methods have been reviewed in section 3.31.
105

3.4.2.2 Reid Vapour Pressure
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's. The method uses
component data (such as feedstock composition and component volatility),
thermodynamic relationships, and a set of simplified assumptions to predict the
blended RVP of a mixture. Vazques Esparragoza et al. (1992) 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, the Vazques-Esparragoza et al. (1992) approach requires that the
molar composition of the feedstocks to be known. The computations required in
both of these methods are complex in comparison to those required in other
approaches such as empirical approaches (Morris et al., 1975; Gary, J. H., 1994).
Comparisons of predictive accuracy of some of the methods can be found in
Stewart (1959) who looked at the standard deviation of prediction error for 67
blends using different blended RVP prediction approaches. The latest method
based on fundamental principles provides more accurate predictions. However,
these theoretical methods are rather tedious due to their computational
requirements. The interaction method requires numerous parameters to be updated.
Although not as accurate as the theoretical methods, the simplicity of the blending
index method makes it attractive for use in gasoline blending models. The equation
used to calculate the RVP index for each blending component developed by
Chevron Research Company is (Chevron, 1971):
( )
25 . 1
RVP RVPI = (3.39)
( ) [ ]
8 . 0
i i b
RVPI V RVP
∑
= (3.40)
However, the RVP blending values of pressurising agents increase with the
aromatic content of the gasoline. The results of a comprehensive blending study
(Morris, 2008) showed a considerable difference in RVP blending values of
normal butane with different gasoline components (aromatics & non-aromatics),
which cannot be handled by Chevron’s model leading to a big RVP giveaway.
106

3.4.3 A New Molecular Gasoline Blending Methodology
3.4.3.1 Diagram

Figure 3.12 Proposed molecular gasoline blending methodology
The proposed new molecular gasoline blending methodology is illustrated in
Figure 3.12, starting from the basic bulk properties information including
distillation profile and density. If the regression based model described in section
3.3.2 is set up, the fractions and ONs/RVPs of PIONA lumps can be predicted
according to the distillation profile and density. Otherwise, RVP/ON properties
START
Measurement: Distillation
Profile, Density of each
blending component

Having regressed model
as section 3.3.2?
PIONA fractions and
ONs/RVPs prediction
based on the proposed
prediction model
RVP/ON
measurement
Transformation method
in Chapter 2 to get
molecular composition
Fractions and ONs/RVPs of
PIONA lumps
For each
blending
component
Molecular blending
models for ON and RVP
prediction of product
Yes
No
END
107

should be measured for the transformation methodology investigated in Chapter 2
to achieve molecular composition of the blending stream in terms of MTHS
matrix, which will be used to calculate the fractions and ONs/RVPs of PIONA
lumps based on the assumption that the properties blend linearly within
homologous series. These steps should be applied to each blending component,
followed by the proposed molecular blending model for ON/RVP property
prediction of gasoline products.
3.4.3.2 Mathematical Model
The volume fractions and ONs/RVPs of PIONA lumps of blending streams are
predicted based on Equations 3.18 and 3.23, simplified as follows:
) d , T ( f x
j j j , i
= PIONA i ∈ ∀ , J j ∈ ∀ (3.41)
) d , T ( f ON
j j j , i
= PIONA i ∈ ∀ , J j ∈ ∀ (3.42)
) d , T ( f RVP
j j j , i
= PIONA i ∈ ∀ , J j ∈ ∀ (3.43)
The volume fractions and ONs/RVPs of PIONA lumps of blending products are
calculated based on linear mixing rules in Equations 3.44 – 3.46.
( )
∑
× =
j
j , i j i , p
x y x PIONA i ∈ ∀ , J j ∈ ∀ , P p ∈ ∀ (3.44)
( )
∑
∑
×
× ×
=
j
i , j j
j
i , j i , j j
i , p
x y
ON x y
ON PIONA i ∈ ∀ , J j ∈ ∀ , P p ∈ ∀ (3.45)
( )
∑
∑
×
× ×
=
j
i , j j
j
j , i i , j j
i , p
x y
RVP x y
RVP PIONA i ∈ ∀ , J j ∈ ∀ , P p ∈ ∀ (3.46)
where y
j
represents the blending ratio of component j.
The molecular models for ON/RVP prediction of products are defined as Equations
3.47 – 3.48, exactly the same as Equations 3.2 and 3.30.
108

∑ ∑ ∑
∑ ∑
∈ ∈ ∈
∈ ∈
− +
+
=
PIONA i PI i
i
PI i
i i PI i i
PIONA i PI i
i i i PI i i i
) x x ( I x
ON x I ON x
ON
β β
β β
(3.47)
∑ ∑ ∑
∑ ∑
∈ ∈ ∈
∈ ∈
− +
+
=
PIONA i A i
i
A i
i i A i i
PIONA i A i
i i i A i i i
) x x ( I x
RVP x I RVP x
RVP
β β
β β
(3.48)
3.4.4 Gasoline Blending Optimisation Model
The key component consideration introduces the nonlinearity in the blending
problem and makes it an NLP formulation with constraints. The main constraints
include: 1) product specifications, 2) the availability of blending stocks; 3) upper
and lower bounds of market demand, 4) commodity prices, and 5) mass balance.
The objective function is to maximise the profit as Equation 3.49.
( ) ( )
∑ ∑
∈ ∈
× − × =
P p J j
j j p p
C F C F ofit Pr (3.49)
where F is the amount of stream, either product or blending component. C is the
price of product/stock.
Subject to:
1) Product specifications
( )
j , i k , j k , p
x , f θ θ = PIONA i ∈ ∀ , J j ∈ ∀ , P p ∈ ∀ , θ ∈ ∀k (3.50)
max
k , p k , p
min
k , p
θ θ θ ≤ ≤ P p ∈ ∀ , θ ∈ ∀k (3.51)
2) Availability of blending stocks
max
j j
min
j
F F F ≤ ≤ J j ∈ ∀ (3.52)
3) Market demands
max
p p
min
p
F F F ≤ ≤ P p ∈ ∀ (3.53)
4) Mass balance
109

∑
∈
=
J j
p , j p
F F P p ∈ ∀ (3.54)
∑
∈
=
P p
p , j j
F F J j ∈ ∀ (3.55)
3.4.5 Case Study
Table 3.9 Available feedstock properties and information about blending components
RON MON RVP
(psi)
A
(%)
Olefin Benzene Availability
(kbbl)
Price
Stream 1 91.3 78.8 4.02 32.1 26.6 0.18 150 -
Stream 2 99.2 88.0 4.41 63.2 0.00 1.52 150 -
Stream 3 110.2 97.2 1.75 89.1 0.00 2.01 250 -
Stream 4 78.3 71.9 5.67 11.7 0.205 0.49 230 -
Stream 5 72.9 67.6 3.42 15.2 0.00 0.64 200 -
isopentane 85.5 80 35.9 - - - 55 -
Ethanol 107.0 89.0 9.6 - - - - $4.50/Gallon
Alkylate 93.7 83.9 9.40 - 20.14 0 150 $2.95/Gallon
Table 3.10 Product specifications for two grades of gasolines
RON MON RVP
(psi)
Aromatics
(%)
Olefin Benzene
(vol%)
Oxygenates
(O wt%)
Price
Product1 98 86 6.9 33 5.5 0.8 4 $4.11/Gallon
Product2 93 81 7.0 33 5.5 0.8 4 $3.85/Gallon
The problem consists of five component streams along with iso-pentane stream to
produce two different grades of gasoline. To meet with the product specifications,
The additive of ethanol and alkylate can be blended with the component streams.
Properties of blends are given in Table 3.9, and product specifications in Table
3.10. For ethanol, an additional constraint is considered that its concentration
should not exceed 10% in the final gasoline product. Ethanol and alkylate can be
purchased from the market at the price of 4.50$/Gallon and 2.95$/Gallon
respectively. Final products product1 and product2 can be sold in the market at
price of 4.11$/Gallon and 3.85$/Gallon respectively. The objective of the problem
110

is to maximise the profitability along with meeting the product specifications. Five
blending components and iso-pentane should be used up.
3.4.5.1 Traditional Method
Optimisation is carried out based on the conventional approaches: Ethyl RT-70
and Chevron’s correlations. The optimisation results are shown in Table 3.11 and
Table 3.12. Table 3.11 shows detailed product distribution and Table 3.12 gives
the blended product properties. Net revenue using the conventional approach is
172.0 MM$..
Table 3.11 Detailed product distribution (the conventional approach)
Product1 (kbbl) Product2 (kbbl)
Stream 1 0.00 150.00
Stream 2 0.00 150.00
Stream 3 98.34 151.66
Stream 4 74.78 155.22
Stream 5 0.09 199.91
isopentane 6.19 48.81
Ethanol 33.67 120.73
Alkylate 79.00 71.00
Total 292.06 1047.34
Table 3.12 Blended product properties (the conventional approach)
RON MON RVP
(psi)
Aromatics
(vol%)
Olefin
(vol%)
Benzene
(vol%)
Oxygenates
(O wt%)
Product1 98.00 87.05 6.90 33.00 5.50 0.80 4.0
Product2
93.00 82.62 6.99 31.19 5.21 0.73
4.0

111

3.4.5.2 Molecular Blending Model
Table 3.13 Detailed product distribution (molecular modelling)
Product1 (kbbl) Product2 (kbbl)
Stream 1 - 150.00
Stream 2 - 150.00
Stream 3 137.50 112.50
Stream 4 111.43 118.57
Stream 5 - 200.00
iso-pentane 9.19 45.81
Ethanol 42.36 89.99
Alkylate 111.31 38.69
Total 411.78 905.56
Optimisation is carried out using the molecular information of the available
feedstocks. Molecular models are implemented for ON/RVP using the proposed
molecular blending model. Table 3.13 shows detailed product distribution while
Table 3.14 illustrates the blend properties. Net revenue using the molecular models
is 173.9 MM$, a little higher profit.
Table 3.14 Blended product properties (molecular modelling)
RON MON RVP (psi) Aromatics
(vol%)
Olefin
(vol%)
Benzene
(vol%)
Oxygenates
(O wt%)
Product1 98.46 86.00 6.90 32.92 5.50 0.80 3.57
Product2
93.00 81.00 6.93 31.72 5.29 0.73 3.45
To summarise, molecular modelling of gasoline blending is capable of targeting
molecules within the constraints of the regulations, and controls giveaway tightly
to make more profit.

112

3.5 Summary
Firstly, to decrease the huge amount of cost for the instruments used to measure the
properties, a new methodology is proposed to predict ON/RVP properties based on
the easily obtained properties including distillation profile and density. The
developed method is on the basis of regression models, and shows a good
performance of interpolation prediction, illustrated by a case study that the overall
standard errors for RON, MON and RVP are 0.38, 0.51 number, and 0.24 psi.
However, the inherent disadvantage of the regression based model shows a bad
performance of the extrapolation prediction, which could be improved by adding
the extrapolated dataset in the regression process.
To tightly control on the property giveaway of gasoline blending, particularly with
nonlinear blending nature such as RON, MON and RVP, a novel molecular model
of gasoline blending on PIONA lumps is developed based on a detailed gasoline
composition-based octane model (Ghosh, 2006). The previously proposed property
prediction methodology is successfully applied to obtain the basic information for
the molecular blending model. Thereafter, the molecular blending model is
integrated into the recipe optimisation, demonstrated by a case study showing the
economic improvement from the tighter control on property giveaway compared
with the conventional approaches. The significance of this work is that the detailed
property consideration during optimisation helps to find better solutions and meet
with the product specifications more closely, and the proposed methodology can be
integrated into more complex overall site-level optimisation.
3.6 Nomenclature
List of sets
i PIONA
j sample stream
p product
k properties
ON RON and MON
List of symbols
113

ON
i
MON/RON of i
x
i
fraction of i
β
i
coefficient of i in the model
I
p
interaction term of paraffins with olefins and aromatics
b
PO
a
PO
b
PN
a
PN
k , k , k , k coefficients in the developed model
d density
TBP boiling point
T
10
, T
50
, T
90
temperature of distillation profile at volume of 10%, 50%, and 90%
respectively
CN cetane number
a
i,j
coefficients of the developed correlation
y
j
blending fraction of stream j
RVP Reid vapour pressure
F amount of a stream

114
Chapter 4 Molecular Modelling of
Semiregenerative Catalytic Reforming
4.1 Introduction...........................................................................................116
4.1.1 Catalytic Reforming Process................................................................117
4.1.2 Feed Characteristics .............................................................................119
4.1.3 Operating Conditions ...........................................................................120
4.1.4 Product Specifications..........................................................................122
4.1.5 Review of Previous Work....................................................................123
4.1.6 Motivation of Molecular Modelling of Catalytic Reforming ..............126
4.2 Chemical Reactions Network and Kinetics...........................................127
4.2.1 Dehydrogenation of Naphthenes to Aromatics ....................................128
4.2.2 Isomerisation of Paraffins and Naphthenes .........................................129
4.2.3 Dehydrocyclisation of Paraffins...........................................................129
4.2.4 Hydrocracking and Dealkylation .........................................................130
4.2.5 Kinetics ................................................................................................131
4.3 Process Model .......................................................................................131
4.4 Case Study.............................................................................................134
4.4.1 Simulation of the Process.....................................................................135
4.4.2 Sensitivity Analysis of Operating Conditions......................................139
4.5 Catalyst Deactivation ............................................................................142
4.5.1 Mathematical Model of Catalyst Deactivation ....................................142
4.5.2 Multi-period Process Model.................................................................144
4.6 Catalytic Reforming Process Optimisation...........................................146
4.6.1 Mathematical Model ............................................................................147
4.6.2 Optimisation Approach........................................................................148
4.7 Case Study – Multi-period Process Simulation and Optimisation........148
115
4.7.1 Multi-period Process Simulation .........................................................148
4.7.2 Sensitivity Analysis of Operating Temperatures .................................150
4.7.3 Process Optimisation............................................................................151
4.8 Summary ...............................................................................................153
4.9 Nomenclature ........................................................................................154

116
4.1 Introduction
Traditionally, catalytic reforming is a very important process for octane
improvement with 50 vol% contribution to the gasoline pool, and the production of
aromatic feedstock for the petrochemical industry, while a modern catalytic
reforming process is gradually treated as one of important sources of precious
hydrogen. The process converts gasoline-boiling-range low-octane hydrocarbons
consisting of C
5
-C
12
with a research octane number of 50-60, into high-octane
gasoline compounds of 90-105 for use as high-performance gasoline fuel. This is
achieved by transforming n-paraffins and naphthenes into the corresponding
isoparaffins and aromatics, which means high content of aromatics in the
reforming product. Recent environmental legislations established by different
agencies such as the Clean Air Act demand the reduction in emissions of volatile,
toxic, and polluting components in gasoline, such as benzene and aromatics.
Coupled with these stricter environmental regulations, there has been a consistent
increase in the demand for higher fuel efficiency standards of engines, and
therefore motor fuel with an even greater octane number. Higher-octane-number
products can be achieved under more severe conditions, but this will also cause the
violation of environmental regulations, and the reduction of cycle lengths of
catalyst, resulting in the higher operating cost. This scenario has continuously
forced the improvement of different aspects, such as reactor configurations,
catalyst, etc. One of most important strategies is to explore the trade-offs between
high-octane-number and the specification of aromatics limit. A proper selection of
operating conditions within plant constraints is essential to maximise the
profitability of a reformer. Advanced optimisation of such a complex process
requires a detailed mathematical model capable of accurately predicting the
reformat composition, the product quality, and the catalyst life cycle over a wide
range of operating conditions.
This chapter firstly briefly introduces catalytic reforming process, along with a
short review of previous works on modelling of catalytic reforming. To build up a
molecular model of a catalytic reformer, chemical reactions and modelling of the
reactor are described respectively. A case study demonstrates the accuracy of the
proposed model, together with the sensitivity analysis of the operating conditions.
117
Another important issue of catalyst deactivation, which has a serious impact on the
economic performance, is also considered. Finally, a multi-period process level
optimisation model is developed with the consideration of catalyst deactivation,
well illustrated in the case study.
4.1.1 Catalytic Reforming Process
Reforming processes are classified as continuous, cyclic, or semiregenerative
depending upon the frequency of catalyst regeneration. The continuous type is able
to maintain high catalyst activity and selectivity by continuous catalyst
regeneration as increased coke laydown and thermodynamic equilibrium yields of
reformate are both favoured by low pressure operation. This advantage has to be
evaluated with respect to higher capital cost and possible lower operating cost due
to lower hydrogen recycle rates and pressures needed to keep coke laydown at an
acceptable level.
The semiregenerative unit is at the other end of the spectrum and has the advantage
of lower capital cost. Regeneration requires the unit to be taken off-stream.
Depending upon severity of operation, regeneration is required at intervals of 3 to
24 months. High hydrogen recycle rates and operating pressures are utilised to
minimise coke laydown and consequent loss of catalyst activity.
The cyclic process is a compromise between these extremes and is characterised by
having a swing reactor in addition to those on-stream in which catalyst can be
regenerated without shutting the unit down. When the activity of catalyst in one of
the on-stream reactors drops below the desired level, this reactor is isolated from
the system and replaced by a swing reactor. The catalyst in the replaced reactor is
then regenerated by admitting hot air into the reactor to burn the carbon off the
catalyst. After regeneration it is used to replace the next reactor needing
regeneration.
118

Figure 4.1 Simplified semiregenerative process of catalytic reforming (Gary and
Handwerk, 2001)
The semiregenerative reforming process is typical of fixed-bed reactor reforming
operations and will be discussed in this work. Figure 4.1 shows a simplified
semiregenerative process diagram. The mixture of the feed and recycle hydrogen is
heated first by reactor effluent for energy saving. Then the mixture is further
heated up to a reactor inlet temperature before fed to the fixed-bed adiabatically
operated reactors in series, in which quantities of reactions take place in the
presence of catalyst. The major reactions in the first reactor are strongly
endothermic and very fast, causing a sharp temperature drop. To maintain the
reaction rate, the gases are reheated before being passed over the catalyst in the
second reactor. As the total reactor charge proceeds through the sequence of
heating and reacting, the reactions become less and less endothermic and the
temperature differential across the reactors decreases. Usually three or four
reactors are sufficient to provide the desired degree of reaction and heaters are
needed before each reactor to bring the mixture up to reaction temperature. In
practice, either separate heaters can be used or one heater can contain several
separate coils. The reaction mixture from the last reactor is cooled and the liquid
products condensed. The hydrogen-rich gases are separated from the liquid phase
in a drum separator, and the liquid from the separator is sent to a fractionator to be
stabilised, and finally sent to storage for gasoline blending. The hydrogen-rich gas
119
stream is split into a hydrogen recycle stream, passed to a compressor and then
circulated to join the naphtha charge, and a net hydrogen by-product which is used
in hydrotreating or hydrocracking operations or as a fuel.
There are numerous issues to be addressed for the performance of a reformer,
including feed characteristics, catalyst formulation, process configuration, reactor
design, operating conditions, and product specifications etc. The study of some of
these depends totally or partially on experimental work, such as catalyst
formulation, reactor design. However others can be undertaken theoretically via
modelling and simulation. These factors (feed characteristics, operating conditions,
and product specifications) would be briefly investigated in the following section.
4.1.2 Feed Characteristics
The typical feed to catalytic reforming process is heavy straight run gasoline or
naphtha (90 to 160 °C). The reason for the use of heavy naphtha as a feed is that
the ease of cyclisation and isomerisation reactions in the process increases with the
increase of carbon atoms. Light naphtha tends to crack forming butane and light
gases causing the lost in yield, hence it is not economical. Heavier feeds cause
formation of carbon deposits on the catalyst and partially deactivate it.
Table 4.1 Compositions of two typical feeds (Gary, 2001)
Paraffinic (Arabian Light) Naphthenic (Nigeria)
RON 50 66
Average MW 114 119
Sulphur (wtppm) 500 350
Paraffins (vol%) 66.8 29.3
Naphthenes (vol%) 21.8 61.85
Aromatics (vol%) 11.4 8.85
Table 4.1 gives the composition of two typical feeds: paraffinic and naphthenic.
RON is low with 50 for the paraffinic feed with very high paraffin content of more
than 60 vol%, and 66 for the naphthenic with naphthene content of more than 60
vol%. The average molecular weight is about 115, around C
8
. Sulphur is present in
the feed in the range of 500 and 350 wtppm, which are representative of straight
120
run gasolines coming from atmospheric distillation of crude. But values lower than
100 wtppm are found in a few particular crudes. These SR feeds contain limited
amounts of nitrogen in the form of amines, or oxygenated compounds in the form
of phenol or carboxylic acid. In some cases, traces (<1 ppm) of metals or
metalloids can be found, depending on the origin of the crudes. Feed pretreating, in
the form of hydrotreating, is usually employed to remove these materials.
Other feeds rather than SR naphtha can be sent to reforming as well. These are cuts
distilled in the same range of SR naphtha which is produced from conversion units
and have low octane numbers. For instance, visbreaking or coking gasolines can be
sent to reforming which are characterised by, in comparison with SR feeds, a high
olefin and acid sulphur content and larger amounts of nitrogen compounds.
Hydrocracking gasoline is another feed free of sulphur and nitrogen compounds
because the use of hydrogen in the hydrocracking process works as a hydrotreating
process, but such a feed is mainly made up of cyclopentane-structure naphthenes
and isoparaffins. FCC gasoline is another possible feed, characterised by
significant olefins and aromatics concentrations as well as the presence of
molecules containing heteroatoms such as S or N.
4.1.3 Operating Conditions
The key operating conditions, which affect the performance of reforming, are
reactor temperatures, reactor pressures, space velocity (SV), and
hydrogen/hydrocarbon ratio.
The operating temperature is the principal parameter of reactors that operators need
to watch carefully and adjust frequently through the entire run cycle. The typical
range of operating temperature is from 490 to 520
o
C. In practice, temperatures can
be chosen to balance the advantage of increased reformate quality (octane number)
and disadvantage of increased deactivation rate as well as aromatics content as
temperature increased. The operating temperature will impact yield of reforming
depending on the catalyst type: monometallic catalysts show a drop in yield as
soon as the temperature rises, while bimetallic catalysts remain same until the end
of a run.
121
The operating pressure is one of the key operating parameters, which will affect on
product yield and cycle length. Low pressure shows a trend of catalytic reforming
since it favours the increase of yield with high quality although with increase of
coke content as illustrated in Figure 4.2 (Meyers, 2004). To compensate the loss of
catalyst activity because of coke content, the operation type depending on catalyst
regeneration evolves from semiregenerative to continuous including cyclic. In the
beginning, the pressure used was greater than 50 bar, and pressure drop had little
influence in comparison with total pressure drop. The evolution allows operation at
pressure lower than 25 bar, therefore pressure drop in reactors became significant
in relation to the total pressure drop. In addition, the cost of recycle hydrogen
compression became a non-negligible item.

Figure 4.2 Pressure influence (Robert, 2003)
Space velocity is a measure of the contact time between reactants and catalyst, and
expressed as liquid hourly space velocity (LHSV) or weight hourly space velocity
(WHSV). The choice represents a compromise between allowable hydrocracking
and desired dehydrocyclisation. Aromatisation and isomersation are not affected
by changes in space velocity because these reaction approach equilibrium even at
high space velocity. Modern reformers usually operate between 1.0 and 2.0 h
-
1
(LHSV). As below 1.0 h
-1
undesired side reactions hydrocracking are increased,
and therefore reduce reformate yield.
H
2
/HC ratio is one of crucial operating parameters having impact on catalyst
deactivation. The advantage of increasing H
2
/HC ratio is that hydrogen will react
with coke precursors, removing them from catalyst before they form significant
122
amount of polycyclic aromatics, therefore, leading to a longer catalyst life. On the
other hand, increasing H
2
/HC ratio will affect aromatization, and increase
hydrocracking resulting in the decrease of reformate yield. A lower hydrogen
partial pressure favours dehydrogenation of naphthenes and dehydrocyclisation of
paraffins. The typical H
2
/HC ranges from 3 to 8 on molar basis.
4.1.4 Product
Table 4.2 Typical product distribution from paraffinic feed at 15 bar with RON of 98
(George, 2004)
Product Yield (wt%/feed)
H
2
2.5
CH
4
1.7
C
2
H
6
3.1
C
3
H
8
4.2
(n+i) C
4
H
10
6.0
C
5
+
82.5
As mentioned before, catalytic reforming produces C
5
+
reformate, hydrogen, also a
little amount of methane, ethane, propane and butanes. In the last few decades the
importance of the production of hydrogen, besides C
5
+
, has risen gradually with
pressures going down to 10 bar and less as a result of catalyst improvement. Table
4.2 gives an average product distribution from a paraffinic feed on a bimetallic at
15 bar. The desired products account for 85% weight and the ones with lower
added value represent less than 5% weight (methane and ethane).
Olefins and naphthenes concentrations are lower than 1% wt except for low
pressure which approach 1%. Table 4.3 shows a typical analysis for a low pressure
reformate. It should be noted that to achieve RON of 98, the aromatic content is
close to 70% wt. The octane rating in a reformate is generally provided by C
7
to
C
10
aromatics and by light iso-paraffins, especially C
5
. This is because C
6
, C
7
and
C
8
isoparaffins are not very branched and so they have a low RON.

123
Table 4.3 Typical composition (wt %) of reformates with low operating pressure
(George, 2004)
nP iP O N A sum
4 0.57 0.57
5 1.51 2.37 0.1 3.98
6 1.69 3.97 0.16 0.19 2.34 8.35
7 2.5 8.42 0.35 0.4 14.16 25.83
8 1.16 4.91 0.44 0.34 26.28 33.13
9 0.26 1.04 0.08 0 21.08 22.46
10 0.07 0.28 0 0 4.76 5.11
11 0 0.02 0 0 0.55 0.57
sum 7.76 21.01 1.13 0.93 69.17 100
Reformate is basically made up of C
7
to C
10
aromatics, directly related to the
desired research octane number. It is also important to note that reformates do not
contain any sulphur (S ≤ 0.1 ppm). High pressure reformates contain few olefins.
However, in modern units running at low hydrogen partial pressure, there are more
and more olefins. These olefins lower MON of gasoline and often make hydrogen
purification more complicated.
4.1.5 Review of Previous Work
The effects on investigating catalytic reforming have three aspects: kinetic models,
catalyst deactivation, as well as process optimisation. The main issue related to
kinetic models is the representation of reactants and corresponding products, which
falls in three ways: lumped model, pathways level and mechanistic level models.
Various kinetic models to represent catalytic reforming have been reported in the
literature, which have different levels of sophistication. The first significant effort
was made by Smith (1959), where the complex naphtha mixture is idealised so that
each of three hydrocarbon classes: paraffins, naphthenes, and aromatics, is
represented by a single compound having the average properties of that class. With
this simplified model, a kinetic analysis was developed which described the
reforming operation with satisfactory accuracy. However, the fact remains that it
oversimplifies the nature of the process, which cannot handle the operation over a
124
wide range of operating conditions. However, all the models up to that time were
pseudohomogeneous in nature.
Kmak (1972) presented the first endeavour to incorporate catalytic nature. By
deriving a reaction scheme with Hougen-Waston Langmuir-Hinshelwood (HWLH)
type of kinetics, the model explicitly accounts for the interaction of chemical
species with the catalyst. The developed model was limited to the representation of
isothermal operation at some points within the experimental temperature range in
which they fitted the parameters.
Marin et al. (1983) refined the Kmak (1972) model, developed the reaction
network covering the whole naphtha in the carbon number from C
5
to C
10
. The
network included 23 pseudocomponents and used HWLH rate equations. Marin
and Forment (1982), and Van Trimpont et al. (1988) also conducted separate
studies on C
6
and C
7
carbon number fractions respectively, and developed the
corresponding HWLH rate equations. Various possible reaction paths and
mechanisms were systematically evaluated before choosing the one that best fits
the experimental data on a laboratory-scale reactor. Taskar et al. (1997) applied the
kinetic scheme, and extended carbon number fractions from C
8
to C
10
based on
using rate expressions that have the same form as the C
6
and C
7
rate expression
from Marin and Froment (1988). Finally, it contains 35 pseudocomponents
connected together by a network of 36 reactions. Moreover, isoparaffins had been
further broken down into singe-branched paraffins and multi-branched paraffins
because the physical properties of two paraffins are different.
Padmavathi et al. (1997) developed a simulation model to monitor commercial
plant performance, given as the lumping details of the feed and reacting scheme,
parameter estimation and model validation details. The results of the model were
validated for 4 different commercial reactor performances with a good accuracy.
Ancheyta et al. (2000) proposed a model that utilises lumped mathematical
representation of the reactions that take place, which are written in terms of
isomers of the same nature. These groups range from 1 to 11 atoms of carbon for
paraffins, and from 6 to 11 carbon atoms for naphthenes and aromatics. The
cyclohexane formation via methylcyclopentane isomerisation and paraffins
isomerisation reactions were considered in the model. Additionally, an Arrhenius-
125
type variation was added to the model in order to include the effect of pressure and
temperature on the rate constants. The kinetic parameters were estimated using
experimental information obtained in a fix-bed pilot plant in which three reforming
reactors were loaded with different amounts of catalyst.
Mechanistic level models are also developed. Quann and Jaffe (1996) developed a
structure oriented lumping model, with a large number of key molecules generated
by assembling 22 structural groups in various ways. This synthetic feed has to
satisfy the observable characteristics, both chemical and physical. Klein and co-
workers (Wei and Klein, 2008) reduced the complexity of the feed by introducing
a number of representative pseudocomponents by Monte-Carlo simulation and
generated the reaction network of this synthetic feed by computers using graph
theory. Forment and his colleagues (Sotelo-Boyas and Froment, 2009) developed a
kinetic model based on a detailed description of the fundamental chemistry of the
transformation of each hydrocarbon, and applied singe event concept for rate
expressions. The results showed excellent agreement between the experimental and
estimated yield.
Catalyst deactivation has been investigated intensively. De Paulw and Froment
(1974) developed a methodology of characterising the deactivation of a catalyst by
coke deposition in the isomerisation reaction of n-pentane. The approach proposed
that the deactivation functions are related to the real cause of deactivation, which is
the actual amount of coke formed on the surface of the catalyst and not the process
on-stream time as is usually done. Marin and Froment (1982) and Van Trimpont et
al. (1988) applied the same methodology for C
6
and C
7
.
Because of the new legislation of benzene and aromatics content in commercial
gasoline, refiners have to investigate the operating condition properly by process
optimisation recently. Taskar and Riggs (1997) investigated different operating
strategies of time-invariant and time-optimal modes by optimising a
semiregenerative catalytic naphtha reformer with catalyst deactivation. The time-
optimal mode demonstrated significant economic improvement over the time-
invariant mode. Hu (2004) integrated catalytic reforming into an overall refinery
optimisation problem, and investigated the economic performance with the
optimisation of catalytic reforming process.
126
4.1.6 Motivation of Molecular Modelling of Catalytic Reforming
As mentioned previously, recently there has been a renewed interest in reforming
processes. Because reformate is a major source of aromatics due to the new
regulations on the commercial gasolines. In this sense, the operating severity has to
be reduced to decrease the amount of aromatics, which however adversely affects
the reformate octane number. Besides this, catalyst deactivation also plays a very
important role on economic performance. Olefinic intermediates are the main
cause of forming carbonaceous deposits on catalyst, which is suppressed by high
hydrogen partial pressure (De Pauw and Froment, 1974). However, high pressure
reduces the selectivity to aromatics in the desired product. Overall, high
temperature and low pressures would seem most desirable for the main reforming
reactions, but the same conditions favour deactivation of catalyst. For this reason,
the process operating conditions have to be a compromise.
To achieve this, optimisation plays a key role, which demands an appropriate
kinetic model combined with a suitable reactor model capable of predicting the
detailed reformate composition. Besides, the kinetic model should include the
impact of changing operating conditions on the process performance. A Lumped
model has its inherent disadvantages of rate coefficients depending on the feed
composition, while a mechanistic level model has too many details and takes a
very long computation time, which is not suitable for optimisation. A pathway
level model contains most of the observed species explicitly, and describes the
molecule-to-molecule transitions in a reaction network. The corresponding
mathematical model is numerically friendly and can be solved quickly. The model
developed by Ancheyta et al. (2000, 2001) considered the whole range of naphtha,
and the cyclohexane formation via methylcyclopentane isomeration, as well as
paraffins isomerisation. Additionally, the pressure effect on rate constants was also
included, which enhances the prediction accuracy. To include the cost of power
consumption due to the pressure drop of recycle hydrogen, the Ergun equation
(Fogler, 1992) for computing the differential pressure drop in a fixed bed is applied
in this work, which is not considered in Ancheyta’s work (2000; 2001). The
previous investigation on the optimisation of catalytic reforming (Taskar, 1997)
limited three periods for run cycle due to the enormously increased computational
127
burden if more periods were included at that time. However, along with the
development of computation capacity, it is possible to implement the investigation
on a monthly or even smaller period, which possibly achieves better economic
performance.
4.2 Chemical Reactions Network and Kinetics

Figure 4.3 Generalised reaction network
Reactions mainly involve four categories: dehydrogenation, isomerisation,
dehydrocyclisation, and hydrocracking. Every reaction produces an increase in
octane number, and except isomerisation of paraffins, results in a decrease in
reformate yield. The fastest reaction is dehydrogenation, and isomerisation is
moderately fast, while dehydrocyclisation and hydrocracking are the slowest. The
reactions are promoted by two kinds of active sites on catalyst, acidic and metallic.
The generalised reaction network is illustrated in Figure 4.3.
As in any series of complex chemical reactions, reactions occur which produce
undesirable products in addition to those desired. Reaction conditions have to be
chosen those favour the desired and inhibit the undesired reactions. Desirable
reactions lead to the formation of aromatics and isoparaffins as follows:
• Paraffins are isomerised and to some extent converted to naphthenes,
subsequently converted to aromatics,
• Olefins are saturated to form paraffins which then react as the first,
• Naphthenes are converted to aromatics,
• Aromatics are left essentially unchanged.
n-paraffins
Cracked
products

Cyclopentane
i-paraffins

Cyclohexane

Aromatics
Lighter
Aromatics

Lighter
Naphthenes

Hydrocracking

Hydrocracking

128
Reactions leading to the formation of undesirable products include:
• Dealkylation of side chains on naphthenes and aromatics to form butane and
lighter paraffins,
• Cracking of paraffins and naphthenes to form butane and lighter paraffins.
4.2.1 Dehydrogenation of Naphthenes to Aromatics
The principle reforming reaction in producing aromatics from naphthenes is
dehydrogenation of alkylcyclohexanes. The pathways of reactants and products in
terms of the MTHS matrix elements are as follows.
( ) ( ) ) P , C ( 3 A , C N , C
0 n n
+ → (4.1)
where n ranges from 6 to 12.
The dehydrogenation reactions are highly endothermic and cause a decrease in
temperature as the reaction progresses, which necessitates the use of inter-heaters
between catalyst beds to keep the mixture at sufficiently high temperatures for the
reactions to proceed at practical rates. Because this reaction proceeds rapidly and
produces hydrogen as well as aromatics, naphthenes are the most desirable
components in the feedstock.
Aromatics have a higher liquid density than paraffins or naphthenes, so volume of
the produced aromatics will be reduced. In addition, the conversion to aromatics
increases the gasoline end point because the boiling points of aromatics are higher
than those of paraffins and naphthenes. The yield of aromatics is increased by:
• High temperature (increases reaction rate but adversely affects chemical
equilibrium),
• Low pressure (shifts chemical equilibrium “to the right”),
• Low space velocity (promotes approach to equilibrium),
• Low hydrogen-to-hydrocarbon mole ratios (shifts chemical equilibrium “to the
right”, however, a sufficient hydrogen partial pressure must be maintained to
avoid excessive coke formation).
129
4.2.2 Isomerisation of Paraffins and Naphthenes
The isomerisation reactions occur moderately fast catalysed by acid sites at
commercial operating temperatures with small heat effects. Thermodynamic
equilibrium, however, slightly favours the isomers that are more highly branched.
Isomerisation of paraffins and cyclopentanes usually results in a lower octane
product than does conversion to aromatics. However, there is a substantial increase
over that of the un-isomerised materials. For isomerisation of paraffins, it is
common to assume that the isomerisation reactions are rapid enough to closely
approach thermodynamic equilibrium at normal reforming conditions (Gates,
1979). Therefore, the distribution of paraffins in the MTHS matrix classified as
NP, MP, DP, and TP will be calculated by known equilibrium in this work. The
isomerisation of methylcyclopentane (MCP) to cyclohexane, which is further
dehydrogenated to benzene, is considered for the naphthenes isomerisation.
Isomerisation yield is increased by high temperature (which increases reaction
rate), low space velocity, and low pressure.
4.2.3 Dehydrocyclisation of Paraffins
The most difficult reaction to promote is the dehydrocyclisation of paraffins,
consisting of molecular rearrangement of paraffins to naphthenes as shown in
Equation 4.2 in terms of MTHS matrix elements.
( ) ( ) ) P , C ( N , C P , C
0 n n
+ ↔ (4.2)
where n ranges from 6 to 12.
For cyclisation to occur, a paraffin with at least a six-carbon straight chain is
needed. The reaction becomes easier with increasing molecular weight of paraffins
because the probability of ring formation increases, however partially offset by
hydrocracking to lighter paraffins. The produced naphthenes are easily further
converted to aromatics by dehydrogenation. Dehydrocyclisation is favoured by low
pressure and high temperature, and requires both the metal and acid functions of
catalyst.
130
4.2.4 Hydrocracking and Dealkylation
The reactions of paraffins hydrocracking are given as Equation 4.3 in terms of
MTHS matrix elements.
( ) ( ) ( ) ) P , C ( P , C P , C P , C
i i n 0 n
+ ↔ +
−
(4.3)
where 5 1 ≤ ≤ i , and n≥5.
The hydrocracking reactions are exothermic and result in the production of lighter
liquid and gas products. They are relatively slow reactions and therefore most of
hydrocracking occurs in the last section of the reactor. The major hydrocracking
reactions involve the cracking and saturation of paraffins. In order to obtain high
product quality and yield, it is necessary to carefully control the hydrocracking
reactions. As paraffins crack into lighter paraffins, the reactions consume the
specious hydrogen and reduce the net liquid yield, although the remaining
aromatics become concentrated, thereby, increasing octane number. The
concentration of paraffins in the charge stock determines the extent of the
hydrocracking reaction, but the relative fraction of isomers produced in any
molecular weight group is independent of the charge stock, relaying on the
thermodynamic equilibrium as mentioned previously.
Dealkylation of aromatics and naphthenes includes both making the alkyl group –
a side chain on the aromatic or naphthene ring – smaller and removing the alkyl
group completely. Equations 4.4 and 4.5 show the dealkylation of aromatics and
naphthenes respectively in the form of MTHS matrix elements.
( ) ( ) ( ) ) P , C ( A , C P , C A , C
i i n 0 n
+ → +
−
(4.4)
( ) ( ) ( ) ) P , C ( N , C P , C N , C
i i n 0 n
+ → +
−
(4.5)
where n≥7, and i≤3.
Hydrocracking and dealkylation yields are increased by high temperature, high
pressure and low space velocity.
131
4.2.5 Kinetics
All reactions are presumed to be pseudo-first order with respect to the
hydrocarbon, given as Equation 4.6.
kC
dt
dC
= (4.6)
To consider the effects of pressure and temperature on kinetic constants, Ancheyta
(1994) integrated an Arrhenius-type variation for temperature consideration and a
factor for pressure into Krane’s model (1960). More improvements were made
thereafter (Ancheyta, 2000). The reaction rate constant is as Equation 4.7.
k
P
P
T T R
E
k k
Aj
i i
α
|
|
¹
|


\
|
×
(
¸
(

¸

− × × =
0 0
0
)
1 1
( exp
(4.7)
where k
0
is the rate constant with the 300 psig of pressure, and 766 K of
temperature. E
Aj
is the activation energy, R is ideal gas constant, and α
k
is the factor
for pressure effect. The activation energy for each reforming reaction and the
factor for pressure effect are given in Appendix B, as well as the kinetic constants
of the model.
4.3 Process Model
The mathematical equations are developed based on the following assumptions:
• Gas velocity is constant across the reactor section;
• The reactor is operated with an adiabatic and steady-state condition;
• No radial deviation of concentrations exists within the reactor.
The kinetic model described in the previous section was incorporated in a fixed-
bed one-dimensional pseudohomogeneous adiabatic reactor model. Under the
general reactor operating conditions, radial and axial dispersion effects were found
to be negligible. Therefore, a perfect plug-flow behaviour assumption is reasonable
(Taskar, 1997). The ordinary differential Equations 4.8 and 4.9, which describe the
reformate composition and temperature profiles at the steady state (Froment,
1990), are integrated through each reactor bed.
132
∑
∈
=
J j
j i , j
i
r
dw
dF
γ I i ∈ ∀ (4.8)
( )
∑
∑
∈
∈
−
=
I i
pi i
J j
j j
C F
H r
dw
dT
∆
(4.9)
where F
i
stands for molar flow rate of component i, and w is catalyst weight. γ
j,i
is
stoichiometric coefficient of component i in reaction j. r
j
is reaction rate of reaction
j. T is reactor temperature along with catalyst weight, and ∆H
j
represents reaction
heat of reaction j. C
pi
is specific heat capacity of component i.
Because reactor pressure is being reduced gradually due to the improvement of
catalyst, the cost for compressing recycle hydrogen to the reactor pressure is not
negligible any more. The equation describing the pressure drop as Equation 4.10,
the Ergun equation (Fogler, 1992), is integrated into the process model.
( )
c c p
3
p
A
1
G 75 . 1
d
1 150
d
G
dw
dP
ρ
µ ε
ε ρ
(
(
¸
(


¸

+
−
− = (4.10)
where P stands for pressure along with the catalyst weight, and G is superficial
mass velocity of gas mixture. d
p
is diameter of catalyst particle, while ρ describes
density of gas mixture. ε is for void fraction of catalyst bed, and µ for viscosity of
the gas mixture. A
c
is cross sectional area of the bed, and ρ
c
is density of catalyst.
The power consumption of compressor was estimated on the basis of calculated
adiabatic head and flow rate of recycle gases as Equation 4.11.
(
(
(
¸
(



¸

−
|
|
¹
|


\
|
−
=
−
1
P
P
1 k
k
FZRT H
k
1 k
in
out
adiabatic
∆ (4.11)
where F is molar flow rate of recycle gas, and Z is compressibility factor, which
value is 1 for ideal gas. T stands for temperature of recycle gas, and k is specific
heat ratio. P
out
, P
in
are pressures after compressor and before respectively.
∆H
adiabatic
is power consumption for recycle gas with molar flow rate F.
133
Besides, the cost for heating up feed to the inlet temperature of reactors between
beds is also needed to be considered. The energy balance of the system can be
described as Equation 4.12.
∑
∈
− =
R r
effluent r heating
H H H ∆ ∆ ∆ (4.12)
where r stands reactors, and ∆H
r
is the energy consumption to heat up feed from
the outlet temperature of previous reactor or the ambient temperature for the first
reactor to the inlet temperature of the next reactor. ∆H
effluent
is the energy of cooling
effluent from the outlet temperature of the last reactor to the ambient temperature.
Since fuel cost is of the interest, the rigorous modelling of heat exchanging is not
necessary, and macroscopic energy balance is used.
Another issue is that usually the analysis of feed naphtha is reported in terms of
bulk properties such as distillation profile and density, rather than molecular
composition. Therefore, the developed methodology in Chapter 2 will be employed
to transform bulk properties into molecular information. Moreover, the developed
methodology for the prediction of properties such as octane number in Chapter 3 is
also integrated to improve the accuracy of the prediction as Equation 4.13 which
appears as Equation 3.47 in Chapter 3.
∑ ∑ ∑
∑ ∑
∈ ∈ ∈
∈ ∈
− +
+
=
PIONA i PI i
i
PI i
i i PI i i
PIONA i PI i
i i i PI i i i
) x x ( I x
ON x I ON x
ON
β β
β β
(4.13)
134

Figure 4.4 Diagram of the simulation of catalytic reforming

The 4
th
Runge-Kutta integration method with adaptive step size is applied for the
integration. The whole simulation procedure is illustrated in Figure 4.4.
4.4 Case Study
The studied case (Ancheyta, 2000) is used to investigate the proposed model. The
semiregenerative catalytic reforming process consists of three fixed bed reactors.
Each reactor is operated in isothermal mode by independent temperature control.
The detailed operating condition is listed in Figure 4.5 with the flowsheet.
Start
Feed characterisation by the proposed
MTHS methodology (Chapter 2)

For each reactor, integration of
mass, energy balance equations as
well as pressure
Flash calculation
Product properties calculation
Compressor cost and
fuel cost calculation
End
135

Figure 4.5 Reactors configuration and operating conditions
Table 4.4 Molecular composition of feedstock (mol %) (Ancheyta, 2000)
P I N A sum
C4 0 0 0.00
C5 3.8 3.4 0.42 7.62
C6 4.4 6.7 3.21 0.8 15.11
C7 3.2 6.2 5.8 3.22 18.42
C8 6.36 6.52 4.71 4.71 22.30
C9 5.09 8.32 3.56 4.21 21.18
C10 2.97 6.22 0.6 2.7 12.49
C11 2.2 0 0.4 0.3 2.90
sum 28.02 37.36 18.70 15.94 100.02
Table 4.4 gives the detail molecular composition of feedstock. Reformate samples
were collected in a high-pressure product receiver. The remaining C
4
-
cracking
products are removed by distillation afterward.
4.4.1 Simulation of the Process
To illustrate the capability and accuracy of the proposed methodology, the
measured molecular composition of the feedstock is converted to bulk properties
firstly. Then based on the predicted properties, a new molecular composition for
the feedstock is predicted. By applying the kinetic models, the stabilised product
molecular composition and its corresponding bulk properties are determined
sequentially, which are compared with those results from the experimental data.
reactor 1 reactor 2 reactor 3 Feed stock
matrix
Product
matrix

T=490 °C
P=149.49 psi
WHSV=17.72 h
-1

T=500 °C
P=149.49 psi
WHSV=7.09 h
-1

T=510 °C
P=149.49 psi
WHSV=3.54 h
-1

H
2
/hydrocarbon = 6.5
136
Table 4.5 Comparison of the properties between the measured and predicted for
feedstock and product
Feedstock Product
Properties Measured
*
Predicted Measured
*
Predicted
SG 0.74 0.74 0.79 0.79
RVP(psi) 3.11 3.10 4.32 4.61
RON 62.98 63.15 97.38 97.45
MON 58.95 58.63 86.84 87.00
Benzene (vol%) 0.48 0.64 4.59 4.82
P (vol%) 69.24 69.27 39.21 38.83
N (vol%) 17.11 17.09 1.71 2.45
A (vol%) 13.65 13.63 59.08 58.72
70
120
170
220
270
320
370
0 20 40 60 80 100
Cumulative vol %
T
e
m
p
e
r
a
t
u
r
e

(
F
)

-

F
e
e
d
s
t
o
c
k
70
120
170
220
270
320
370
T
e
m
p
e
r
a
t
u
r
e

(
F
)

-

P
r
o
d
u
c
t
Measured - Feedstock
Predicted - Feedstock
Measured - Product
Predicted - product

Figure 4.6 Distillate profiles of feedstock and product from the measured and the
predicted
Table 4.5 compares the properties of the feedstock and product between the
measured and predicted, while Figure 4.6 gives distillation profile. Figure 4.7 gives
a view of the agreement of molecular composition of product between the
measured and the predicted. For the feedstock, the most deviations between the
measured and the predicted are less than 1% except for benzene with a small
fraction. Regarding the product, it sees a bigger deviation, especially 10 vol% of
distillate profile, while as the two key properties, ON and RVP see small gaps. It is
137
also safely concluded that A
7
-A
9
are the major molecules produced, which
contribute the majority of ON.
Product composition
0
4
8
12
16
20
P11 P10 P9 P8 P7 P6 P5 N11 N10 N9 N8 N7 N6 N5 A11 A10 A9 A8 A7 A6 MCP
Molecule
c
o
n

(
m
o
l
%
)
Measured
Predict ed

Figure 4.7 Comparison of the product molecular composition
Table 4.6 shows a good consistence of product distribution between the predicted
and the measured.
Table 4.6 Product distribution based on 100 mol feedstock
Measured Predicted
Product 96.12 mol 96.32 mol
P
4
8.18 mol 8.42 mol
P
3
9.57 mol 9.20 mol
P
2
6.63 mol 6.81 mol
P
1
4.22 mol 4.18 mol
H
2
128.93 mol 129.33 mol
H
2
purity (mol %) 81.84 81.88
Reformate composition profiles are presented in Figure 4.8. The reaction of
dehydrogenation of naphthenes to aromatics mostly takes place in the first reactor,
leading to the big increase of aromatics. Paraffin content is gradually reduced
because of dehydrocyclisation and cracking reactions. Cracked products including
C
1
to C
4
see an increase. Due to the isothermal operating mode, the composition
between continuous reactors changes smoothly.
138
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1
Fractional catalyst weight
o
v
e
r
a
l
l

c
o
m
p
o
s
i
t
i
o
n

(
m
o
l
%
)
C5+ Paraffins
Aromatics
Cracked
Product
Naphthenes
R1
R2
R3

Figure 4.8 Profiles of composition through the reactors
In this case, the temperature and pressure profile are not taken into account,
therefore, it is changed to operate in the adiabatic mode with the consideration of
pressure drop in the following section.
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1
Fractional catalyst weight
o
v
e
r
a
l
l

c
o
m
p
o
s
i
t
i
o
n

(
m
o
l

%
)
C5+ Paraffins
Aromatics
Cracked
Product
Naphthenes
R3
R2 R1

Figure 4.9 Composition profiles under the adiabatic operating mode

139
680
700
720
740
760
0 0.2 0.4 0.6 0.8 1
Fractional catalyst weight
T
e
m
p
e
r
a
t
u
r
e

(
K
)
138
140
142
144
146
148
150
152
P
r
e
s
s
u
r
e

(
p
s
i
)
Temperature
Pressure
R3 R2 R1

Figure 4.10 Temperature and pressure profile under the adiabatic operating mode
On the overall, the reactions taken place in catalytic reforming are endothermic,
which is illustrated in Figure 4.10 as the temperature will drop across the reactors.
The reactions of dehydrogenation of naphthenes to aromatics are very fast (as
Figure 4.9), and endothermic, causing the temperature drop by around 60 K in the
first reactor. In the second reactor, mostly the isomerisation takes place, and the
remaining naphthenes are dehydrogenated, which makes a moderate temperature
drop by around 30K. The temperature drop across the third reactor is relatively low
due to the exothermic hydrocracking of paraffins and dealkylation of naphthenes
and aromatics. Due to the temperature drop across reactors, the aromatic yield is
less than that with the isothermal operating model, as well as the cracked product.
The pressure drop across three reactors is 10.8 psi, by 7.2% of the reactor pressure.
4.4.2 Sensitivity Analysis of Operating Conditions
Effects of the operating conditions such as temperature, WHSV, and pressure are
analysed as well. Figure 4.11 gives the influence of the operating temperature on
the reformate yield and quality, and product distribution in Figure 4.12. It is
assumed that all three reactors are operated in the same inlet temperature. High
temperature will improve octane number of reformate, with the increase of
aromatics content, together with the reformate yield reduction due to the
hydrocracking reactions also favoured by high temperature. Therefore, to balance
the reformate yield and its quality, the temperature should be properly controlled.
140
80
85
90
95
100
105
760 770 780 790 800 810
Temperature (K)
O
N
80
85
90
95
R
e
f
o
r
m
a
t
e

y
i
e
l
d

(
w
t

%
)
Reformate yield
RON
MON

Figure 4.11 Influence of temperature on quality of reformate and yield (Pressure of
150 psi)
1
3
5
7
9
11
13
760 770 780 790 800
Temperature(K)
Y
i
e
l
d

(
w
t
%
)
LPG
GAS
H2

Figure 4.12 Influence of temperature on product yields (Pressure of 150 psi)
Figure 4.13 presents the influence of reactor pressure on the reformate yield and its
quality, as well as product distribution and yield in Figure 4.14. With the increase
of pressure, both reformate yield and quality decrease. High pressure favours
hydrocracking reactions, which reduces the reformate and hydrogen yield, and
slows down the other reactions such as dehydrogenation, dehydrocyclisation
reactions, which reduces reformate octane number.
141
86
88
90
92
94
96
130 140 150 160 170 180 190
Pressure (psi)
O
N
85
90
95
R
e
f
o
r
m
a
t
e

y
i
e
l
d

(
w
t

%
)
Reformate yield
RON
MON

Figure 4.13 Influence of pressure on reformate yield and quality (T: 783.15K)
1
3
5
7
9
11
110 120 130 140 150 160 170 180 190
Pressure (psi)
Y
i
e
l
d

(
w
t
%
)
LPG
GAS
H2

Figure 4.14 Influence of pressure on product distribution and yield (T: 783.15K)
The influence of WHSV on product distribution and quality, considering the fixed
catalyst weight and varying feed throughput, is also investigated as shown in
Figure 4.15 and Figure 4.16. Along with the increase of the throughput, the
reformate octane number is reduced, and the reformate yield is increased, while the
yields for other product such as hydrogen and cracked products are reduced.

142
80
85
90
95
100
105
0.5 1 1.5 2
WHSV/WHSV0
O
N
85
90
95
R
e
f
o
r
m
a
t
e

y
i
e
l
d

(
w
t

%
)
Reformate yield
RON
MON
T: 783.15K
P: 150 psi

Figure 4.15 Influence of WHSV on reformate yield and quality
1
3
5
7
9
0.5 1 1.5 2 WHSV/WHSV0
Y
i
e
l
d

(
w
t
%
)
LPG
GAS
H2
T: 783.15K
P: 150 psi

Figure 4.16 Influence of WHSV on product distribution
4.5 Catalyst Deactivation
4.5.1 Mathematical Model of Catalyst Deactivation
In refinery, the deactivation of catalyst by carbonaceous deposits is an important
technological problem. Deactivation in a reforming process is attributed to coke
formation and deposition. In reforming reactions of naphtha, the thermodynamics
are such that it would be desirable to work at high temperature and low pressure.
Such operating conditions favour coke formation, and many reforming units
operate under high pressure in order to increase the life time of catalyst.
143
The coke amount increases with the increasing temperature, and this evolution can
be explained by the effect of high temperature on the unsaturated products which
are coke precursors. Generally, heavier feedstock of catalytic reforming produces
more coke, but the cut with the lowest boiling range having a high content of
cyclopentanic compounds are great coke producers as well.
The model developed by De Pauw and Froment (1974) is applied in this work
because the model is related to the real cause of catalyst deactivation which is the
amount of coke formed on the catalyst surface. A deactivation function
c
φ also
termed as the catalyst activity, is given as Equation 4.14.
0
c
r
r
= φ (4.14)
where r
0
is the reaction rate without deactivation, and r is the reaction rate affected
by deactivation.
c
φ ranges from 0 to 1.
The catalyst activity is related to the coke content by an exponential function as
follows.
C
C
c
e
α
φ
−
= (4.15)
where α is the deactivation constant, and C
c
stands for the coke content described
as the weight of coke per unit catalyst weight calculated as Equation 4.16.
∫
= dt r C
c c
(4.16)
where r
c
describes the rates of coking reactions.
To simplify the problem, it is assumed that the coke generation is related to the
content of coke precursor including aromatics and cyclopentanic compounds, and
follows a pseudo-first-order equation with respect to the content of the coke
precursor as Equation 4.17.
pr c
kC r = (4.17)
144
where k is the rate constant, and related to temperature by the Arrhenius equation.
C
pr
stands for the concentration of coke precursor.
RT / E
0
a
e k k
−
= (4.18)
where k
0
and E
a
are regressed based on the experimental data.
4.5.2 Multi-period Process Model
The semiregenerative unit of catalytic reforming requires plant to be shut down for
catalyst regeneration every 3 to 24 months. The period between catalyst
regenerations is called cycle life of catalyst. During the run of the period, the
operating conditions, normally reactor inlet temperature will be changed to
compensate the catalyst activity loss caused by coke deposition. The operating
action can be described as changing temperature along with a series of running
periods of the process. In each running period, operators make a decision on how
many degrees of temperature should be changed, which will enhance the quality of
reformate for further gasoline blending, and simultaneously balance the quality and
deactivation of the catalyst to maximise the refining margins. Generally, the
running length of a reformer will meet the schedule of the refinery. Therefore, the
principle of changing temperature is to maximise the refining profit while meeting
the schedule.
145

Figure 4.17 Simulation procedure of the proposed multi-period process model
Based on this acknowledgement, a new multi-period process model of catalytic
reforming is proposed as Figure 4.17. The running length, which is fixed in
advance to meet the schedule, is divided into multiple periods as the length of each
period t
p
is known. The catalyst activity of the very first period of the running
starts from 1 (
s
p , c
φ ) for every reactor, assumed as totally activated by regeneration.
To find the end activity (
e
p , c
φ ) of catalyst of the period for individual reactor, a sub-
optimisation problem is applied respectively, which targets minimising the
Start
Multi-periods division to
decide t
p

First period
Start activity as 1
End activity of previous
stage (p-1) as the start
activity of stage p
Find the end activity of period p by
optimisation for each reactor
Last period
Profit, average properties
calculation
End
Yes

No

Yes

No

Process simulation based on
the average catalyst activity
146
difference of the time length from the prefixed (t
p
) and that based on the varying
end activity
e
p , c
φ . An average catalyst activity ( ( ) 2 /
e
p , c
s
p , c
φ φ + ) is assumed for the
simulation of the process in the period p as Equation 4.14, to calculate the content
of coke precursor in the product. The average content of coke precursor, taking the
contents at the inlet of reactor and outlet, is used in Equation 4.17 for the reaction
rate of coke formation. The bisection method is used to find the end activity, which
is the start activity of the next period. The calculation continues until the last
period. Finally, the economic performance or the overall product quality can be
calculated for the whole run length.
4.6 Catalytic Reforming Process Optimisation
The performance of catalytic reforming largely depends on the operating
conditions. Based on the results of sensitivity analysis, operating temperature plays
a key role determining the product yield and quality, as well as the life cycle of
catalyst. Therefore, a new optimisation model is proposed to target four different
objectives by optimising the operating temperature in each period. Four objectives
include maximum profit, gasoline yield, octane number, and hydrogen yield.
The rigorous process model is with the non-linearity and high dimensionality,
which makes optimisation even more complicated. In order to simplify the
problem regarding the degrees of freedom, it is assumed that the temperatures of
different periods are functions of the time as Equation 4.19.
4
p r
3
p r
2
p r p r r p , r
t e t d t c t b a T + + + + = (4.19)
where T
r,p
is the inlet temperature of reactor r in period p, and t
p
is the time of
period p. a
r
, b
r
, c
r
, d
r
, e
r
are the coefficients of reactor r of the function.
The advantage of the assumption, first of all, is that the degrees of freedom are
reduced to 15 for three reactors, and any number of periods. Secondly, the
temperatures would change smoothly, which is more reasonable in practice.
147
4.6.1 Mathematical Model
The objectives are listed as follows. The max profit (Equation 4.20) consists of the
income of selling products including reformate, hydrogen, gas and etc, the cost for
heating fuel, and power consumption for the compressor. Only the terms that could
be influenced by changing the operating temperatures are included, which means
the cost for the feedstock will be excluded because it is fixed.
( )
∑ ∑
∈
|
|
¹
|


\
|
− − =
P p
adibatic power heating fuel
product
product , p product
H C H C F C profit max ∆ ∆ (4.20)
where C
p,product
stands for the price of product (reformate, hydrogen, gas and etc.)
in period p, which is related to the quality of product as Equation 4.21 for the
reformate. F
p,product
is the product quantity in period p. C
fuel
is the price of fuel, and
C
power
is the price of every unit of power for compressor. ∆H
heating
, ∆H
adiabatic
are
defined previously.
( )
coef 0 p 0 reformate , p
C ON ON C C − + = (4.21)
where C
0
is the reference price of reformate with ON
0
. C
coef
is the coefficient for
the substantial price because of the increased ON.
∑
=
p
2 H , p
p
F
N
1
hydrogen max (4.22)
∑
=
p
p
p
ON
N
1
ON max (4.23)
∑
=
p
reformate , p
p
yield
N
1
eld gasolineyi max (4.24)
Equation 4.22, 4.23, and 4.24 describe the other three objectives. N
p
is the interval
number.
In this work, the only constraints are taken into account are the lower and upper
bounds of the operating temperature.
148
U
p , r
L
T T T ≤ ≤ (4.25)
4.6.2 Optimisation Approach
Since there is no explicit expression between the objectives and the coefficients of
the operating temperature functions, the optimisation is the simulation-based
methodology, which normally requires a large number of simulations. Therefore, it
is necessary to choose an optimiser that, in general requires fewer functional
evaluations for convergence. Sequential quadratic programming (SQP), which
typically needs a smaller number of iterations than other comparable methods, is
used to solve this nonlinear programming problem by introducing NAG MATLAB
library subroutine e04ue.
4.7 Case Study – Multi-period Process Simulation and
Optimisation
4.7.1 Multi-period Process Simulation
A multi-period process simulation is investigated on the case in section 4.4, which
does not consider the catalyst deactivation, based on the proposed multi-period
process model. The cycle length is scheduled as 1 year (12 months), and each
period as 1 month. Therefore, there are 12 periods. All three reactors are operated
at the inlet temperature of 783.15 K and the pressure of 150 psi. These would be
used as base case.
As Figure 4.18 and Figure 4.19 illustrate, along with the time progressing, the
profit and reformate quality octane number in each period will decrease, since the
inlet temperatures remain same. Although the reformate yield will increase shown
in Figure 4.19, reformate RON is decreased from around 95 to 80, which has a
significant negative effect on the economic performance, decreased by almost half
of the profit. The cracked products, hydrogen and C
4
-
hydrocarbon are gradually
reduced.
149
70
75
80
85
90
95
100
1 2 3 4 5 6 7 8 9 10 11 12
Time (months)
O
N
0
10
20
30
40
50
60
70
T
h
o
u
s
a
n
d
s
P
r
o
f
i
t
RON
MON
Profit
T: 783.15 K
P:150 psi

Figure 4.18 Profit and reformate ON through running cycle
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7 8 9 10 11 12
Time (months)
Y
i
e
l
d

(
w
t

%
)
88
89
90
91
92
93
94
95
R
e
f
o
r
m
a
t
e

y
i
e
l
d

(
w
t

%
)
H2
Gas
LPG
Reformate
T: 783.15 K
P:150 psi

Figure 4.19 Product distributions through running cycle
All the impacts come from the loss of catalyst activity, illustrated in Figure 4.20,
with final activity of 0.26, 0.18, and 0.12 for three reactors respectively. The
reason that the activity of the last reactor is least is that the content of coke
precursor (olefin and aromatic compounds) will increase across the reactors.

150
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12
Time (months)
E
n
d

a
c
t
i
v
i
t
y
Reactor 1
Reactor 2
Reactor 3
T: 783.15 K
P:150 psi

Figure 4.20 Catalyst activities of three reactors through running cycle
4.7.2 Sensitivity Analysis of Operating Temperatures
520
540
560
580
600
773.15 783.15 793.15 803.15 813.15
Temperature (K)
O
v
e
r
a
l
l

P
r
o
f
i
t
(
M
$
)
84
86
88
90
92
94
R
O
N
Profit
RON

Figure 4.21 Influence of temperature on overall profit and RON
The impacts of operating temperature on process performances, including overall
profit, octane number, hydrogen and reformate yields, are analysed as Figure 4.21
and Figure 4.22. The operating temperatures of three reactors are the same in any
of period for the simplification of sensitivity analysis. The overall profit shows a
similar trend with temperature as RON as Figure 4.21 shows because of the major
contribution of profit from the reformate related to its quality. The overall profit
and average RON are increased rapidly with the temperature increase at the
151
beginning, and then the substantial increase decreases along with high temperature
because of reformate yield decreases. Due to the fixed run cycle length, the
optimiser would choose the low temperatures in the later periods leading to low
reformate quality, if high temperatures are selected in the first periods. Therefore,
how to determine the operating temperature profile through the periods is not
obvious without the process optimisation.
1.5
1.55
1.6
1.65
1.7
1.75
770 780 790 800 810 820
Temperature (K)
A
v
e
r
a
g
e

H
2

y
i
e
l
d

(
w
t

%
)
86
88
90
92
94
A
v
e
r
a
g
e

r
e
f
o
r
m
a
t
e

y
i
e
l
d

H2
Reformate

Figure 4.22 Influence of temperature on the overall hydrogen and reformate yields
Figure 4.22 presents the influence of temperature on the overall reformate and
hydrogen yields. As known, the reformate yield will increase with the decrease of
operating temperatures, along with the deteriorating of reformate quality. But for
hydrogen yield, high temperature favour both hydrocracking reactions, which
consumes hydrogen, and dehydrogenation, which produces hydrogen. As Figure
4.22 shows that the hydrogen yield would be maximised if operated at the
temperature of 790 – 800K with all same inlet temperatures for reactors.
4.7.3 Process Optimisation
The proposed process optimisation methodology is applied for the base case in the
section 4.4 for the optimal operating temperature of each period. Different
objectives including maximising profit, reformate yield, and hydrogen yields are
employed. The major impact on the profit is the reformate quality, therefore, the
optimal operating temperatures for maximising profit and RON is similar. The
lower and upper bounds for temperature are 760K and 803.15K respectively.
152
Table 4.7 presents the results of different process performances by adapting
different objectives. The mode of maximising reformate yield has the lowest profit
because of the low reformate quality of octane number with the average 75.7.
Table 4.7 Objectives of base case
Base case Max profit Max hydrogen Max reformate
Profit(M$) 427963 600441 596602 253467
RON 82.26 89.45 89.18 75.70
MON 76.26 82.19 81.98 70.81
Hydrogen (wt%) 1.52 1.80 1.81 1.18
Reformate (wt %) 94.68 90.47 90.86 97.34
755
765
775
785
795
805
1 2 3 4 5 6 7 8 9 10 11 12
Time (months)
T
e
m
p
e
r
a
t
u
r
e

(
K
)
Reactor 1
Reactor 2
Reactor 3

Figure 4.23 Optimal operating temperature through the running periods targeting
the maximal profit
Figure 4.23 gives the temperature profiles of three reactors, in which the objective
function is maximising the profit. The first reactor is operated at the lowest
temperature compared with the other two, and gradually increased, finally to the
upper bound. The operating temperature of the second reactor shows the similar
trend, while it is close to the upper bound for the third reactor. The characteristics
of the temperature profiles possibly is determined by that dehydrogenation, mainly
in the first reactor, is very fast, and the rate of reactions taken place in the
following reactors is relatively slow.
153
Figure 4.24 presents the product distribution through the running periods for the
maximal profit operating mode. Although the operating temperatures are always
increased gradually, the reformate yield is reduced first because of the high
operating temperature, followed with the gradual growth because of catalyst
deactivation.
0
1
2
3
4
5
6
7
8
9
1 2 3 4 5 6 7 8 9 10 11 12
Time(months)
y
i
e
l
d

(
w
t
%
)
86
88
90
92
94
96
98
100
R
e
f
o
r
m
a
t
e

y
i
e
l
d

(
w
t
%
)
H2
Gas
LPG
Reformate

Figure 4.24 Product distribution through the running periods targeting the maximal
profit
4.8 Summary
A rigorous molecular model of a semiregenerative catalytic reforming process has
been developed based on the developed MTHS matrix for feedstock and product
streams. The process model includes a kinetic model which takes into account the
most important reactions of the catalytic reforming process. Pressure drop has been
taken into account due to the non-negligible cost for the power consumption of
compressing the recycle hydrogen gas. Composition, temperature and pressure
have been obtained to provide information about the extent of conversion in the
reactors. The case study has compared the results from the proposed molecular
model with the measured data. The results not only demonstrate that the developed
model is capable of simulating the reactions in a catalytic reformer and being
applied in the process optimisation, but also illustrates the accuracy of the
proposed characterisation methodology on naphtha streams. Furthermore,
154
sensitivity analysis of operating conditions exhibits different characteristics impact
on the process performance.
A process level optimisation model has been developed with the consideration of
catalyst deactivation. Firstly, the model of catalyst deactivation correlating coke
amount on catalyst with reaction rate is performed. Secondly, a multi-period
process model of catalytic reforming has been developed based on time-division
intervals of the running cycle. Lastly, the optimisation model targeting different
objectives by varying the operating temperatures of the reactors in the periods is
successfully implemented assuming the temperature profile follows a smooth
function with respect to time. The case study shows the capability of the proposed
optimisation model, which will be integrated into the site-level optimisation in the
later chapter.
4.9 Nomenclature
List of sets
i component index
j reaction index
r reactor index
p period index of multi-period model

List of symbols
t time
k, k
0
rate constant with temperature T and pressure P, rate constant with
temperature of 766 K and 300 psi
EA
j
activation energy
R ideal gas constant
α
k
factor for pressure effect
T operating temperature
P operating pressure
F
i
molar flow of the component i
w catalyst weight
γj,i stoichiometric coefficient of component i in reaction j
155
r
j
reaction rate of reaction j
∆H
j
reaction heat of reaction j
Cp
i
specific heat capacity of component i
G superficial mass velocity
d
p
diameter of catalyst particle
ρ, ρ
c
density of gas mixture, density of catalyst
ε void fraction of catalyst
µ viscosity of the gas mixture
Ac cross section area of the bed
Z compressibility factor
P
in
, P
out
inlet and outlet pressure of compressor
∆H
adiabatic
power consumption of the compressor

156
Chapter 5 Molecular Modelling of Diesel
Hydrotreater
5.1 Introduction...........................................................................................157
5.1.1 Diesel Hydrotreating Process...............................................................157
5.1.2 Feed Characteristics .............................................................................159
5.1.3 Operating Conditions ...........................................................................159
5.1.4 Product Specification ...........................................................................161
5.1.5 Motivation of a Molecular Model for Diesel Hydrotreater..................162
5.2 Reactions Network and Kinetics...........................................................163
5.2.1 Hydrodesulphurisation (HDS) .............................................................164
5.2.2 Hydrodearomatisation (HDA)..............................................................171
5.3 Modelling of a Trickle – bed Reactor ...................................................174
5.3.1 Mathematical Equations.......................................................................175
5.3.2 Estimation of Physical Properties ........................................................177
5.3.3 Mathematical Methodology and Solving Procedure............................179
5.4 Case Study – Modelling of Diesel Hydrotreater ...................................181
5.4.1 Simulation of a Diesel Hydrotreater ....................................................181
5.4.2 Sensitivity Analysis of Operating Conditions......................................183
5.5 Catalyst Deactivation ............................................................................186
5.5.1 Mathematical Model of Catalyst Deactivation ....................................186
5.5.2 Multi-period Model of Catalyst Deactivation......................................188
5.6 Diesel Hydrotreater Optimisation .........................................................189
5.6.1 Mathematical Model ............................................................................190
5.7 Case Study – Optimisation of Diesel Hydrotreater...............................191
5.8 Summary ...............................................................................................192
5.9 Nomenclature ........................................................................................193

157
5.1 Introduction
Current trend of dieselisation is because of the higher efficiency in diesel fuel
consumption and lower CO
2
emissions. However, increasing concerns about the
environmental issues have led to the stricter legislation on the quality of diesel,
such as ultra-low sulphur diesel (ULSD), even sulphur free diesel. Therefore,
refiners must increase their hydrotreating capability by revamping existing
processes or building new processes to meet the future scenarios. As the margins
decrease, refiners also want to enhance it through process optimisation. However,
the traditional lumped process model is not capable of predicting the behaviors of
deep hydrotreating because different sulphur compounds have quite different
reaction characteristics. These scenarios lead to an aspiration for a detailed kinetic
model of diesel hydrotreating processes on a molecular level.
In this chapter, firstly, diesel hydrotreating process is briefly introduced, along
with the issues to the performance of a hydrotreater. To build up a molecular
model of a diesel hydrotreater, chemical reactions and the modelling of a reactor
are described respectively. In the chemical reactions part, hydrodesulphurisation
(HDS) and hydrodearomatisation (HDA) are included, and investigated with three
aspects: compounds taking reactions, reactions network and kinetic models, as well
as the method to obtain kinetic parameters. Regarding the reactor modelling,
mathematical equations are given firstly, followed by the estimation of the required
physical properties, and the mathematical solving procedure. A case is simulated
with the proposed model, together with the sensitivity analysis of the operating
conditions. Catalyst deactivation, which has a serious impact on the economic
performance, is also considered in this research. Finally, a multi-period process
level optimisation model is developed, and applied in a case study.
5.1.1 Diesel Hydrotreating Process
Diesel hydrotreating process (DHT) is usually used to remove sulphur in diesel oil
to produce the qualified products. In addition to sulphur reduction, diesel
hydrotreating can also help to improve other qualities such as cetane number,
oxidation stability, polynuclear aromatic content and color.
158

Figure 5.1 A simplified diesel hydrotreating process flowsheet (Gary, 2001)
Figure 5.1 shows a simplified diesel hydrotreating process flowsheet (Gary, 2001).
The mixture of a feed and hydrogen gas is heated first by reactor effluent, because
usually hydrotreating reactions are exothermic and release a huge amount of heat,
which can be integrated for the energy saving. Then the mixture is further heated
up to the reactor inlet temperature before fed to a reactor, in which quantities of
reactions take place in the presence of catalysts. Sulphur in the form of hydrogen
sulphide, and nitrogen as ammonia accumulates through the reactor in the vapour
phase. Hydrogen is separated first from the streams out of the reactor, and then
recycled or purified to remove the light hydrocarbon accumulated in the streams.
To decrease the inhibition of hydrogen sulphide and ammonia on the hydrotreating
reactions, hydrogen sulphide and ammonia usually are removed from the vapour
phase. Makeup hydrogen stream must be present to maintain the partial pressure of
hydrogen, which has a great impact on the hydrotreating reactions.
There are numerous issues to be addressed for the performance of a hydrotreater,
including feed characteristics, catalysts formulation, process configuration, reactor
design, operating conditions, and product specifications etc.
159
5.1.2 Feed Characteristics
Sulphur, nitrogen and aromatic contents are the most important feed
characteristics. Usually, the aromatic content of a feed will govern the chemical
hydrogen consumption at low space velocities and high hydrogen partial pressures
required for a very low sulphur diesel production.
Generally, cracked stocks can be included in the feed up to the level limited by the
product cetane or gravity without a significant impact on hydrotreater performance.
There is a small increase in API gravity and cetane index after the hydrotreating
reactions. If a significant improvement in cetane or gravity is required, a multi-
stage design using aromatics saturation catalysts in the second stage may be the
more economical option. Table 5.1 gives typical characteristics for potential diesel
blending stocks, including yields, sulphur contents and cetane etc.
Table 5.1 Typical characteristics of feed to diesel hydrotreaters (Heinrich et al, 2001)

5.1.3 Operating Conditions
The key operating conditions of a diesel hydrotreating unit are liquid hourly space
velocity (LHSV), hydrogen partial pressure, make-up hydrogen purity,
hydrogen/oil ratio, cycle length, and reactor temperature.
For a given cycle length and treating severity, reactor space velocity, and hydrogen
gas quantity as well as hydrogen partial pressure are the variables optimised along
160
with reactor temperature. As the hydrogen partial pressure is increased, the catalyst
deactivation rate is reduced. Thus, space velocity can be increased accordingly for
a constant cycle length. However, this is at the expense of higher hydrogen
consumption. Another important variable is the ratio of total hydrogen supplied to
a reactor bed to the chemical hydrogen consumption for that bed.
For the revamp designs, the achievable hydrogen partial pressure is restricted by
the existing equipment and piping mechanical design, and hydraulics in the reactor
loop. A higher treat gas rate can be used to increase the hydrogen partial pressure,
but this is usually limited because of the associated increase in the reactor loop
pressure drop and the corresponding maximum operating pressure of the various
system components. Make-up hydrogen purity impacts the hydrogen partial
pressure for a fixed reactor operating pressure. Lower purity make-up hydrogen
requires higher hydrogen circulation rates to maintain the target hydrogen partial
pressure and may even require a purge stream from the cold separator. If the make-
up hydrogen purity is too low, there is no combination of recycle rate and purge
that can be used to achieve the target reactor outlet partial pressure. For a revamp
design, increased make-up hydrogen purity is the most effective means of
increasing the hydrogen partial pressure.
For new designs, cycle lengths have typically been set at 24–36 months. This has
been based on the logic that, at some point, the cycle will be limited by factors
other than catalyst activity: namely, reactor pressure drop (Korsten, 1996).
Hydrogen partial pressure has a major impact on cycle length from a catalyst
activity standpoint. For a fixed space velocity, the cycle length increases with
hydrogen partial pressure. Maximum reactor outlet temperature at end-of-cycle
catalyst conditions is generally set at 725–750 °F to avoid aromatics saturation
equilibrium constraints. This is also influenced by the quantity of cracked stocks in
the feed and the crude source. Hydrotreating catalyst performance correlations for
reactor temperature are usually based on the weighted average bed temperature
(WABT). The temperature rise is usually limited to 40–50 °F per bed by
quenching. Thus, for a 50°F temperature rise and a 725 °F maximum reactor outlet
temperature, the end-of-run WABT would be (725-50) + 2/3(50) = 708 °F. The
start-of-run WABT has to be sufficient to obtain the required removal of sulphur
161
and nitrogen. Cycle length is determined by the catalyst deactivation rate at the
design space velocity and hydrogen partial pressure. During the cycle, the increase
in WABT will be 30– 50 °F, with lower deactivation rates occurring at higher
hydrogen partial pressures.
5.1.4 Product Specification
Table 5.2 EN 590 diesel fuel requirements – date introduced: 1/1/2005
Diesel specification parameter Units Limits
Cetane Number 51.0 minimum
Cetane Index 46.0 minimum
Density at 15
o
C kg/m
3
820 – 845
Polycyclic Aromatic Hydrocarbons % (m/m) 11 maximum
Sulphur Content mg/kg 10 maximum
Flash Point °C >55
Carbon Residue (on 10% Dist. Residue) % (m/m) 0.3 maximum
Ash Content % (m/m) 0.01 maximum
Total Contamination mg/kg 24 maximum
Copper Strip Corrosion (3 Hours at 50
o
C)
Oxidation Stability g/m
3
25 maximum
Lubricity, WSD at 60
o
C 460 maximum
Viscosity at 40
o
C mm
2
/sec 2 – 4.5
Distillation Vol. Recovered at:
250
o
C % (v/v) <65
350
o
C % (v/v) 85 minimum
95 % Point °C 360 maximum
Fatty Acid Methyl Esters (FAME) Content % (v/v) 5 maximum
Sulphur content is one of the most important specifications of diesel fuel. Recently,
the constraint on the aromatic content has become a legal issue in some areas. The
higher the cetane number, the shorter is the delay interval of an engine. Generally,
diesel engines will operate well on fuels with cetane numbers above 50. The flash
point temperature of diesel fuel is the minimum temperature at which the fuel will
ignite on application of an ignition source under specified conditions. Minimum
162
flash point temperatures are required for proper safety and handling of diesel fuel.
Table 5.2 gives diesel fuel specifications in the European Union.
5.1.5 Motivation of a Molecular Model for Diesel Hydrotreater
To fulfil the stringent environmental requirements on diesel fuel, it is necessary to
have a deep understanding on the behaviour of DHT process from different points
of view as reviewed in the last section: feed characteristics, operating conditions
and product specifications etc. Conventional models usually lump sulphur
compounds as one or two pseudo compounds, and the pseudo order of reaction rate
could vary from first order to second according to different feedstocks and
operating conditions (Landau et al., 1998; Beuttner and Schmid, 1963; Cotta et al.,
2000). As the parameters are derived from the specific hydrodesulphurisation
conditions, the models have a restricted application for deep desulphurisation.
Another important factor is that the well-known inhibitory effect of H
2
S and
nitrogen compounds on the hydrodesulphurisation rate is not accounted for in the
conventional models (Korsten, 1996). Therefore, in order to have a deep
understanding of diesel hydrotreater behaviour, a detailed kinetic model on the
basis of molecular information is required.
For light feeds, the reactions are frequently performed in two-phase (gas –solid)
fixed-bed reactors. However, when the installation range of the feed increases,
hydrogen, a liquid–gas mixture of the partially vaporised feed, and solid catalyst
are commonly found. This latter system is called a trickle-bed reactor (TBR),
which is referenced in the literature as a reactor in which a liquid phase and a gas
phase flow concurrently downward through a fixed-bed of catalyst particles while
reactions occur (Rodrguez, 2004). Therefore, in nature, diesel hydrotreating
reactions take place in a three-phase reactor. Moreover, the investigation of the
hydrodesulphurisation especially shows a large inhibiting effect of hydrogen
sulphide on conversion (Gates et al., 1979; Vrinat, 1983). Since the concentration
of H
2
S increases along with the reactor, the pseudohomogeneous plug-flow model
cannot yield satisfying results, because a change of the gas-phase concentrations
and the mass transfer between the phases are neglected. For a reliable result
achievement, a three-phase reactor should be considered.
163
This research tries to develop a detailed kinetic model for hydrotreating process
with a three-phase reactor based on feedstocks and products in terms of the MTHS
matrix representation. Beyond the molecular modelling of a diesel hydrotreater, a
multi-period model of run cycle is proposed to take the catalyst deactivation into
account, and a process optimisation model is developed to help the refiners
increase margins as well. Furthermore, the developed model will be integrated into
hydrogen network management detailed in chapter 6.
The work consists of four aspects: reactions network and kinetics, modelling of a
trickle-bed reactor, modelling of catalyst deactivation, and the optimisation model.
5.2 Reactions Network and Kinetics
Reactions in diesel hydrotreating processes are complex, generally involving tens
of thousands of reaction steps and species. Girgis and Gates (1991) have provided
a detailed literature review of the early studies on the hydrotreating chemistry,
including thermodynamics, reactivities, reaction networks, and reaction kinetics.
These studies provide molecular information and mechanism of the hydrotreating
reactions of various species in middle distillates. The reactions are classified as
hydrodearomatisation (HDA), hydrodesulphurisation (HDS), hydrodenitrogenation
(HDN), and hydrodeoxygenation (HDO). Based on the classification, Sun (2004)
successfully introduced reaction family to build up molecular modelling of a diesel
hydrotreater based on the MTHS framework, with a pseudohomogeneous reactor
model. Each group includes the reaction families that show similar reactions. The
molecular level pathways of these reaction families can be expressed as the inter-
conversions of the matrix elements. However, kinetic parameters obtaining is not
solved properly. In this work, HDN and HDO are not considered due to two
reasons. One is that the fractions of nitrogen compounds and oxygen compounds
are very low, while sulphur content in products is ultra low. HDA is the main
hydrogen consumption reaction which would impact the hydrogen partial pressure
in the vapor phase and the hydrogen concentration in the liquid phase. The other is
that the research on HDO and HDN is not as mature as that on HDS and HDA.
Obtaining kinetic parameters is a crucial step for a kinetic model. As mentioned
before, hydrotreating process involves tens of thousands of reactions, in which a
164
set of kinetic parameters are corresponded. For instance, Froment (1994)
concluded that 1133 parameters are needed to be determined for HDS of DBT and
methyl-DBT, not including other reactions. Therefore, it is a big challenge of how
to obtain kinetic parameters properly.
5.2.1 Hydrodesulphurisation (HDS)
Sulphur atoms tend to be bound in the oil as “sulphur bridges” between two carbon
atoms or to be contained in a saturated ring structure. Removal of these sulphur
atoms usually requires only the breaking of the two sulphur-carbon bonds per
sulphur atom and the subsequent addition of four atoms of hydrogen to cap the
ends of the bonds that were broken. When the part of a molecule that contains
sulphur can access catalyst surface, sulphur removal is relatively easy.
5.2.1.1 Sulphur Compounds

Figure 5.2 Difficulties of desulphurisation of different sulphur compounds (Froment,
2007)
The types of sulphur compounds present in different fractions of petroleum
distillates may be different with each type, exhibiting different relative reactivities.
The operating severity needed for different types of sulphur compounds are
considerably different as Figure 5.2 shows. A clear understanding of the nature of
sulphur compounds present in different petroleum fractions as well as the kinetics
165
and mechanism of their desulphurisation processes under hydrotreating conditions
is of interest to refiners for proper choice of feedstocks for the production of low
sulphur diesel fuels cost effectively. In addition, the understanding of sulphur
compounds in petroleum fractions also helps the optimisation of operating
conditions for deep desulphurisation.
Table 5.3 Sulphur distribution in various LCO fractions (Depauw, 1997; Carcía,
2002; Nylén, 2004)
Sulphur compound Sulphur distribution (%)
Depauw Carcía Nylén
BT 1.9 0.4 1.5
C1-BT 9.5 4.3 10.2
C2-BT 15.1 12.7 19.1
C3-BT + 22.1 19.9 29.3
DBT 2.2 3.8 3.3
C1-DBT 11.8 16.5 12.5
C2-DBT 15.9 22.2 11.8
4,6 – DMDBT 1.1 - 1.3
C3 – DBT + 20.6 20.2 12.4
Total sulphur (ppm) 7809 11911 ~ 11750
C1-: substitute with one carbon, C2- substitute with two carbons, C3+- substitute
with three and more than three carbons
Efforts have been made to monitor and identify traces of sulphur compounds in
various petroleum fractions, using methods mainly based on capillary gas
chromatography equipped with various types of detectors such as GC-AED
(Atomic Emission Detector), GC-MS, GC-FPD (Flame Photometric Detector), and
GC-SCD (Sulphur Chemiluminescence Detection). Andari (1996) quantitatively
estimated sulphur compounds in different cuts from Kuwait crude oil, and found
that thiophene and its alkyl derivatives constituted about 60% of the total sulphur
compounds in the naphtha fraction, while the remaining 40% was composed of
mercaptanes and alkyl sulphides. Regarding the gas oil boiling point range (210 –
340 °C), the alkyl benzothiophenes (BT) account for the major portion in the
fraction boiling in the narrow range 235 – 257 °C, and alkyl dibenzothiophenes
166
(DBT) are highly concentrated in a fraction boiling between 280 – 325 °C, and
both are absent in the fraction boiling above 330 oC. Detailed characterisation of
sulphur components present in light cycle oils were also performed (Depauw and
Froment, 1997; Carcía, 2002; Nylén, 2004) as Table 5.3 illustrates. According to
the difficulty of desulphurisation, sulphur compounds are classified into five
categories in the MTHS matrix for middle distillate: SI, SII, SIII, SIV, and SV.
5.2.1.2 Reactions Network and Kinetics
The fundamental transformations in HDS for sulphur compounds are similar and
summarised as follows:
1. Adsorption (coordination) of the sulphur compound to the active site
2. Hydrogenation of unsaturated C=C bonds
3. Cleavage of two carbon-sulphur bonds (sequential or simultaneous)
4. Addition of hydrogen to the broken bonds of both sulphur and carbon
5. Release of the hydrocarbon product from the catalytic site
6. Release of H
2
S from the site
S
S
Hydrogenation Hydrogenolysis
S
Dibenzothiophene(DBT)
1,2,3,4-Tetrahydro
dibenzothiophene
1,2,3,4,10,11-Hexa-
hydrodibenzothiophene
+H
2
(B)
+H
2
(A)
-H
2
S
+H
2
+H
2
-H
2
S
+H
2
-H
2
Cyclohexylbenzene(CHB)
Slow
Bicyclohexane

Figure 5.3 Reaction Network for the HDS of DBT
For HDS reactions of thiophenic species, it is suggested that two reaction pathways
take place on two different types of sites on the catalyst, denoted σ for
hydrogenolysis and τ for hydrogenation (Van Parijs et al., 1986; Duayne et al.,
167
2001). As Figure 5.3 shows the proposed reaction mechanism for
dibenzothiophene HDS, it involves two parallel pathways: hydrogenation and
hydrogenolysis, inferred to occur on two different kinds of sites (Houalla et al.,
1978; Vanrysselberghe and Froment, 1996).
Froment et al had investigated the reaction network and kinetics of
hydrodesulphurisation for different sulphur compounds, including thiophene (Van
Parijs and Froment 1986), benzothiophene (Van Parijs and Froment 1986),
dibenzothiophene (Vanrysselberghe and Froment, 1996) and 4-
methyldibenzothiophenen and 4,6-dimenthyldibenzothiophene (Vanrysselberghe
and Froment, 1998), and concluded that the surface reaction between absorbed
reactants and two competitively absorbed hydrogen atoms was the rate-
determining step for hydrogenation and hydrogenolysis reactions. Therefore, a
uniform kinetic model of HDS for various sulphur compounds was suggested as
follows (Vanrysselberghe and Froment, 1998).
Hougen-Waston rate equation:
τ
τ τ τ
σ
σ σ σ
DEN
C C K K k
DEN
C C K K k
r
H s s H s H s s H s
s
2 , , , 2 , , ,
+ = (5.1)
with
3
2 , ,
1 





+ + =
∑ H H
i
i i
C K C K DEN
σ σ σ
(5.2)
3
2 , ,
1 





+ + =
∑ H H
i
i i
C K C K DEN
τ τ τ
(5.3)
where r
s
is the reaction rate of sulphur compound s, k
s,σ
k
s,τ
are the rate coefficients
for the reactions of sulphur compound s on σ and τ sites respectively, K
i,σ
K
i,τ
are
the adsorption coefficient of component i on σ and τ sites, C
i
is the liquid
concentration of component i.
168
The HDS pathways of various sulphur compounds in terms of the MTHS matrix
elements implemented by Sun (2004) are applied in this research outlined as
follows.
( ) ( ) ) , ( , ) , ( ,
0 0
SI C P C P C SI C
n n
+ → +
(5.4)
( ) ( ) ) , ( , ) , ( 3 ,
0 0
SI C A C P C SII C
n n
+ → +
(5.5)
( ) ( ) ) , ( , ) , ( 5 ,
0 0
SI C N C P C SII C
n n
+ → +
(5.6)
( ) ( ) ) , ( , ) , ( 2 ,
0 0
SI C AA C P C SIII C
n n
+ → +
(5.7)
( ) ( ) ) , ( _ , ) , ( 5 ,
0 0
SI C N A C P C SIII C
n n
+ → +
(5.8)
( ) ( ) ) , ( , ) , ( 2 ,
0 0
SI C AA C P C SIV C
n n
+ → +
(5.9)
( ) ( ) ) , ( _ , ) , ( 5 ,
0 0
SI C N A C P C SIV C
n n
+ → +
(5.10)
( ) ( ) ) , ( , ) , ( 2 ,
0 0
SI C AA C P C SV C
n n
+ → +
(5.11)
( ) ( ) ) , ( _ , ) , ( 5 ,
0 0
SI C N A C P C SV C
n n
+ → +
(5.12)
5.2.1.3 Obtaining Kinetic Parameters – Structure Contribution Approach
Table 5.4 gives the information about the kinetic parameters number to build up
the kinetic model of HDS with the stream representation of the MTHS matrix.
Take SIII reaction family as an example, in a diesel fraction, SIII class of carbon
number ranges from 12 to 26 which means 15 sulphur lumps of SIII exist in diesel
fraction. For each sulphur lump of SIII, both hydrogenation and hydrogenolysis
take place on different sites, therefore leading to two sets of reaction parameters
(rate coefficient and activation energy) and adsorption parameters. SI class could
be eliminated for diesel fractions because SI is negligible as in the 5.2.1.1 section.
169
Table 5.4 kinetic parameters number needed for the kinetic model of HDS with
molecules represented by the MTHS matrix

σ
k
τ
k
σ
K
τ
K
SI 18×2 18×2 18×2
SII 18×2 18×2 18×2 18×2
SIII 15×2 15×2 15×2 15×2
SIV 14×2 14×2 14×2 14×2
SV 13×2 13×2 13×2 13×2
P 18×2 18×2
A 18×2 18×2
N 18×2 18×2
AA 15×2 15×2
AN 15×2 15×2
H
2
S 1×2 1×2
H
2
1×2 1×2
Sum 156 120 328 328
Total number of 932 prohibits the way of parameter estimation based on the
experimental data. Some simplifications and different strategies to achieve these
parameters are needed. Structural contributions approach was firstly introduced to
handle this particular problem by Froment (1994). Based on the observation of the
hydrogenolysis rate coefficients of thiophene, benzothiphene and selected methyl-
substituted dibenzothiophenens, Froment concluded that the position of the methyl
substituent is more important than their number. The hydrogenolysis reactions
involve vertical adsorption of the molecules through the S-atom on the σ-sites
(Houalla et al., 1978). Then several assumptions are made (Froment, 1994):
1. In the adsorption electronic and steric effects are to be considered separately;
2. Methyl groups at a distance from the sulphur atom beyond the α-position
only exert electronic effects on the adsorption;
3. Only methyl groups on the aromatic ring exert an electronic influence;
4. Methyl groups in the 4- and 6- positions also sterically hinder the adsorption;
5. Once a molecule is adsorbed, only the electronic effects of the methyl groups
are of importance.
170
Based upon these assumptions, the equilibrium constant for the adsorption of the
various substituted DBT on the σ-sites is related to that of the parent molecule
through the following expression (Froment, 1994):
) ; ; ( ) ; ; (
, , , ,
p n m K p n m K K K
sDBT
ST
sDBT
EL DBT sDBT σ σ σ σ
= (5.13)
m, n and p indicate the position of the methyl group in mono-, di-, and tri-
substituted DBT. Only three structural contributions are required to account for the
electronic effect of the substituents and two for the setric hindrance effect when
there are substituents in α-position with respect to the S-atom. If there is one
substituent in 4- or 6- position, ) p ; n ; m ( K
sDBT
, ST σ
is written ) 0 ; 0 ; 4 ( K
sDBT
, ST σ
or
) 0 ; 0 ; 6 ( K
sDBT
, ST σ
. For substituents in both 4- and 6-positions, it is ) 0 ; 6 ; 4 ( K
sDBT
, ST σ
.
The simplification of the rate coefficients for the hydrogenolysis reactions of the
substituted DBT follows the same pattern:
) ; ; ( ) ; ; (
, , , ,
p n m k p n m k k k
sDBT
ST
sDBT
EL DBT sDBT σ σ σ σ
= (5.14)
For the adsorption of species on τ-sites, which is considered to be flat, only the
number of substituents and not their position has to be taken into account, so that
the electronic and steric hindrance effects may be lumped. In this case, the
adsorption equilibrium constant is simplified as follows:
) ; ; (
, , ,
p n m K K K
sDBT
EL ST DBT sDBT τ τ τ +
= (5.15)
Regarding to the hydrogenation reaction rate coefficients, the expression is
described:
) ; ; (
, , ,
p n m k k k
sDBT
EL ST DBT sDBT τ τ τ +
= (5.16)
The final result regarding HDS of (s)DBT is given in Appendix C, as well as the
way to apply structural contribution approach for (s)BT.
171
5.2.2 Hydrodearomatisation (HDA)
HDA reactions consist of the addition reactions of hydrogen with aromatic species
existing in a petroleum feedstock, and are reversible and exothermic with
equilibrium conversions of hydrocarbons under practical processing conditions
(Girgis and Gates, 1991). The extent of these reactions at equilibrium decreases
with the increase of temperature. HDA is different from HDS and HDN owing to
thermodynamic equilibrium limitations, so a clear understanding of the effects of
catalyst type, and process variables on the chemistry and thermodynamic
equilibrium of different types of aromatic compounds present in petroleum
feedstock is necessary for determination of optimum operating strategies.
5.2.2.1 Aromatic Compounds
Analysis of petroleum fractions shows that the aromatic compounds in petroleum
mixtures mainly fall into four groups, namely monoaromatics, diaromatics,
triaromatics and polycyclic aromatics (Stanislaus and Cooper, 1994). The
polycyclic aromatics with four or more condensed benzene rings are usually
present in high-boiling fractions (Boiling range > 350°C), while the first three
types are present in middle distillates. It is seen that diaromatics constitute a major
portion of the total aromatic content in straight run gas oil. Therefore the MTHS
matrix representation, of middle distillate fractions, excludes polycyclic aromatic
compounds in this work, represented by A, AA, AAA, AN, AAN, and ANN.
5.2.2.2 Reactions Network and Kinetics
(C14,AAA) (C14,AAN) (C14,NAN) (C14,NNN)
(C8,1N) (C8,1A)
(C10,AN) (C10,NN) (C10,AA)

Figure 5.4 HDA reactions in diesel hydrotreater (Neurock, 1990)

172
The reaction networks for the above mentioned aromatic compounds of diesel
hydrotreating feedstocks are obtained from the literature (Girgis and Gates, 1991;
Korre et al., 1995) and presented as Figure 5.4. The hydrogenation of aromatic
compounds shows several qualitative trends:
1. Polynuclear aromatics hydrogenation proceeds in a ring-by-ring manner;
2. Hydrogenation reactivity increases with the number of aromatic rings;
3. For groups with the same number of fused aromatic rings, hydrogenation
reactivity increases with the presence of alkyl branches and naphthenic rings;
4. For multi-ring aromatics, polynuclear aromatics proceed in a ring-by-ring
manner. Hydrogenation of the ring located at the end of the molecule is faster
than hydrogenation of the ring in the middle.
The pathways for HDA of these aromatic compounds in terms of the conversion
between the elements of the MTHS matrix are shown as follows.
( ) ( ) ( ) N C P C A C
n n
, , 3 ,
0
↔ + (5.17)
( ) ( ) ( ) AN C P C AA C
n n
, , 2 ,
0
↔ + (5.18)
( ) ( ) ( ) NN C P C AN C
n n
, , 3 ,
0
↔ + (5.19)
( ) ( ) ( ) AAN C P C AAA C
n n
, , 2 ,
0
↔ + (5.20)
( ) ( ) ( ) ANN C P C AAN C
n n
, , 2 ,
0
↔ + (5.21)
( ) ( ) ( ) NNN C P C ANN C
n n
, , 3 ,
0
↔ + (5.22)
Various kinetic models were developed for different class of aromatic compounds.
The Langmuir-Hinshewood-Hougen-Waston (LHHW) (Froment and Bischoff,
1990) rate expression (eq 2.23) was widely used and simplified.
( )
∑
+
−
=
m
m m
ij
eq j i
n
H i
ij
sr
ij
C K
K C C P K k
r
1
/
2
(5.23)
173
where
ij
r is the rate of conversion of compound i to compound j, C
i
is the
concentration of compound i, K
m
is the adsorption parameters of compound m,
ij
sr
k
is the surface reaction rate parameter,
ij
eq
K is the overall hydrogenation equilibrium
constant,
2 H
P is the hydrogen partial pressure in the reactor, n is the reaction
stoichiometry with respect to hydrogen. Korre (1994) lumped some parameters and
simplified the equation as follows.
( )
∑
+
−
=
m
m m
ij j i ij
ij
C K
K C C k
r
1
/
(5.24)
where k
ij
is the combined numerator rate parameter, including surface reaction and
adsorption parameter contributions, and hydrogen pressure. K
ij
is the equilibrium
ratio.
5.2.2.3 Obtaining Kinetic Parameters
The quantitative structure-reactivity correlations concept is applied to account for
the effect of substituent carbon atoms on reactivity using representative model
compounds as base structures. In order to reflect the effect of molecular structure
on reactivity of a species quantitative structure-reactivity correlations (QS/RC) can
be explored to relate the reactivity of components with their molecular properties
for a homologous series of reactions (Klein et al., 2006).
Based on the experimental data of reaction pathways, kinetics, and mechanisms for
catalytic hydrogenation of one-, two-, three-, and four-fused aromatic ring
compounds, Korre (1994) used 7 parameters for QS/RC that characterised the
associated set of series of homologous reactions to represent the rate law
parameters for hydrogenation and dehydrogenation. LHHW adsorption constants is
correlated with the number of aromatic rings and the number of saturated carbons,
surface reaction rate constants correlates with the enthalpy of hydrogenation and
the highest bond order (HBO) in the aromatic ring being saturated. Semiempirical
molecular orbital calculations provided acceptable estimates of the enthalpy of
reaction, which, via compensation, provided estimates of the entropy of reaction,
174
and thus equilibrium constant. A combination of three correlations is
recommended (eq 5.25 – 5.27).
SC AR i
N N K 0964 . 0 654 . 0 04 . 1 ln + + = (5.25)
HBO H n k
R sr
22 . 8 133 . 0 91 . 7 0 . 15 ln
0
+ ∆ + − − = (5.26)
0
289 . 0 63 . 6 91 . 3 ln
R eq
H n K ∆ + − − = (5.27)
where NAR is the number of aromatic rings in a PNA molecule, NSC is the
number of saturated carbons in a PNA molecule, HBO is the highest bond order in
an aromatic ring. The bond order (as calculated in MOPAC/AMI, Dewar, 1985) is
the scaled sum of squares of the electronic density matrix overlap between two
atoms. n is reaction stoichiometry with respect to hydrogen,
0
R
H ∆ is the difference
between gas-phase heats of formation of products and reactants under the standard
condition.
An alternative way is that Sun (2004) regressed the data available for benzene,
some alkylbenzenes, and the products of their hydrogenation based on the data
(Stull et al. 1969), and obtained a set of correlations particularly for equilibrium
constants of aromatic compound in terms of the MTHS matrix.
5.3 Modelling of a Trickle – bed Reactor
Recently, the research on modelling a hydrotreater with three-phase trickle-bed
reactor is intensive. An adiabatic multiphase reactor was simulated with a one-
dimensional heterogeneous model (Froment, 1994), the calculation of the
concentration profile within the catalyst particle, and the consideration of pressure
drop. Korsten (1996) developed a simplified three-phase reactor model by
assuming a constant catalyst effectiveness factor down through the reactor, and
only hydrogen and hydrogen sulphide existing in vapor phase with the fixed
temperature and pressure. Mederos (2007) compared the behaviors of tricked-bed
reactors with cocurrent and countercurrent operation modes by developing a
dynamic plug-flow heterogeneous one-dimensional reactor model.
175
In commercial applications, trickle and pulse flow are the most likely flow
regimes. Trickle flow features are a continuous gas phase and a dispersed liquid
phase flowing as a laminar film or as rivulets over the particles. The pulse flow
regime is obtained at higher liquid and gas throughputs (Froment, 1994).
According to Wammes et al. (1990), the pulse flow regime is not attained at high
pressures and realistic liquid flow rates, if the molecular weight of the gas phase is
of the order of that of nitrogen. In a hydroprocessing unit operating, for example,
at 310
o
C and 50 bar, the molecular weight of the gas phase is approximately 20
g/mol. Therefore, strong indications exist that trickle flow is the dominating flow
regime. Besides, it is commonly accepted that in commercial hydroprocessing
reactors, all the particles are completely wetted when the gas and liquid are
adequately distributed (Shah, 1979). Deviations from tickle flow can be neglected
for both phased, which is confirmed by Korsten (1996). Therefore, the developed
reactor model is a one-dimensional heterogeneous model with both the gas and
liquid phase in plug flow.
Regarding the modelling of a diesel hydrotreater, there are three issues:
mathematical equations, the estimation of physical properties, and the
mathematical methodology for solving the complex model.
5.3.1 Mathematical Equations
The mathematical equations are developed based on the following assumptions:
1. Reactions only take place on the catalyst;
2. Gas and liquid velocities are constant across the reactor section;
3. The reactor is operated isothermally under isobaric and steady-state condition;
4. No radial deviation of concentration exists within the reactor;
5. The catalyst particles are completely wetted.
Although the model by Korsten (1996) is simpler, and easier to be solved, the
assumption that the catalyst effectiveness factor is constant down through the
reactor prevents the application in this research. Because the reactor configuration
would impact the catalyst effectiveness factor and it is different for different
reactors and operating conditions. Therefore, the model developed by Froment
(1994) is applied in this research.
176
The steady state continuity equation for component i of the gas phase is written as








− − =
iL
i
ig
L L
ig
G
C
H
p
a K
dz
dp
RT
u
N i ,..., 1 = (5.28)
at 0 = z ,
0
ig ig
p p =
where
G
u is the superficial velocity of the gas, R is the gas constant, T represents
the reactor temperature,
ig
p is the partial pressure of compound i,
L L
a K describes
the mass transfer between the gas and the liquid phases, and the liquid-phase
concentration of compound i in equilibrium with the bulk partial pressure is
represented by the term
i ig
H p .
iL
C represents the concentration in the liquid
phase of compound i. The partial pressure of component i in the gas phase can only
change by transfer to or from the liquid phase. The interphase mass transfer rate is
described as follows.








− =
iL
i
ig
L i
C
H
p
K N (5.29)
The liquid phase contacts the gas phase and the solid phase, which is reflected in
the continuity equations for the reacting species by two terms, accounting
respectively for the liquid-solid and the gas-liquid interphase mass transfer:
( )








− + − =
iL
i
ig
L L iL
S
iS s s
iL
L
C
H
p
a K C C a K
dz
dC
u (5.30)
at 0 = z ,
0
iL iL
C C =
where
L
u is the superficial velocity of the liquid, and
s s
a K describes the mass
transfer between the liquid and the solid phases,
S
iS
C represents the concentration
of component i on the catalyst surface.
The concentration gradients inside the catalyst particles where the reactions take
place are accounted to calculate the effectiveness factor. The pores are considered
177
to be completely filled with liquid. The continuity equation for component i inside
a spherical catalyst is written:
[ ]
∑
=
=








r
N
j
s iS j S
iS ie
T C r i j S
d
dC
d
d D
1
2
2
) ,..., ( , ρ
ξ
ξ
ξ ξ
(5.31)
with boundary conditions:
at 0 = ξ , 0 =
ξ d
dC
iS

at
2
p
d
= ξ ( ) [ ]
∑
=
= −
Nr
j
s
S
iS j j B iL
S
iS s s
T C r i j S C C a K
1
) ,..., ( , η ρ (5.32)
where
iS
C represents the concentration of component i inside the solid, ξ is radial
coordinate,
ie
D is the effective diffusivity of component i for transport in a
pseudocontinuum, d
p
is the equivalent particle diameter, ρ
s
, ρ
B
are the catalyst
density and bulk density, Nr represents the number of reactions, η
s
is the
effectiveness factor of reaction j for solid particle, Ts is the temperature of the
catalyst solid, r
j
is the reaction rate of reaction j per unit catalyst mass for
heterogeneous reaction,
[ ] i j S ,
represents the stoichiometric coefficient of
component i in reaction j.
The effectiveness factor for a general nonlinear reaction rate is defined as
∫
∫
=
dV r
rdV
0
η (5.33)
As for the spherical catalyst, eq 5.33 could be written as
∫
=
R
d C r
R C r
0
2
3 0
) (
) (
3
ξ ξ η (5.34)
5.3.2 Estimation of Physical Properties
The mathematical model needs quantities of physical properties of pure
compounds and the gas and liquid mixtures as Table 5.5 shows. Regarding pure
178
compounds/lumps in terms of the MTHS matrix elements, physical property could
be separated into temperature-independent properties and temperature-dependent
properties. The physical properties for both gas and liquid phases obviously
depend on the composition of streams and operating conditions.
Table 5.5 Physical property of the model
Type Property
Temperature-
independent
properties
MW, T
b
, T
C
, P
C
, V
C
, Z
C
, ω,
0
p
C ,
0
f
H ,
0
f
G ∆ , SG

Pure
compounds/lumps
Dependent properties
V
m
, µ , k , D, H ,
p
C ,
L L
a K ,
s s
a K ,
H ∆
Gas
ρ ,
p
C , µ , k ,
L L
a K , D, Vm,
Phase
Liquid
ρ ,
p
C , µ , k ,
S S
a K , D, Vm
Table 5.6 Properties estimation methods
Properties Estimation method
Basic properties(TC, PC, TB, etc) Joback group contribution
Heat of reaction
Heat of vaporization
Heat capacity of both phases
Density of both phases
Henry coefficients

Peng Robinson Equation of
state
Viscosity of both phases
Thermal conductivity of both phases
Chung et al (1988)
Diffusion coefficients Reid et al. (1987)
Mass transfer coefficients for gas-liquid phase Goto and Smith (1975)
Mass transfer coefficients for liquid-solid phase Froment and Bischoff (1990)
Table 5.6 gives the estimation methods. Basic properties including critical
temperature (T
C
), critical pressure (P
C
), critical compressibility factor (Z
C
), boiling
point (T
b
), heat of formation (
0
f
H ), Gibbs free energy of formation (
0
f
G ∆ ), and
179
ideal gas heat capacity (
0
p
C ), etc are estimated by Joback group contribution
method, which has been introduced in the previous chapter. These properties
would be used to calculate some of other properties based on correlations such as
acentric factor. Then Peng Robinson equation of state is applied to estimate some
properties including enthalpy of all compounds, heat of reactions, heat of
vaporisation, densities of both phases, Henry coefficients (
iL ig i
C p H = ). Detailed
calculation of some physical properties could be found in Appendix D.
5.3.3 Mathematical Methodology and Solving Procedure

Figure 5.5 Solving procedure for a diesel hydrotreater tickle-bed reactor


Collocation orthogonal
method to get effectiveness
factor
Use Newton-Raphson method to
update the concentration of molecules
on the catalyst surface
Estimate/Update the
concentration of molecules
on the catalyst surface
STOP
Runge-Kutta integration method
to get the concentration of
molecules in liquid and vapour
phases
Effectiveness factor and
concentration of molecules on the
catalyst surface is steady?

All the concentration in
vapour and liquid phases are
steady?
180
The mathematical model involves ordinary differential equations with the initial
value type, in which conditions are specified at only one position such as eq. 5.28,
eq. 5.30 and eq. 5.32 etc., and with boundary value type as well, in which
conditions are specified at two different points in domain such as eq. 5.31.
Different mathematical techniques are needed to handle these two different types
of differential equations. Usually, for the first type – ordinary differential equations
with initial value, a fourth order Runge-Kutta method is widely used. To solve
boundary value problem, detailed information could be found in Appendix E.
The surface concentration is unknown, since resistance of mass transfer is
accounted for at the catalyst surface. Therefore, an initial guess of the surface
concentration has to be made first, which is used in the orthogonal collocation
method to perform the intraparticle integration to get the effectiveness factor. The
effectiveness factor is used to update the concentration in the liquid. Iterations are
performed between these two steps until the change of the concentrations in the
liquid and on the catalyst surface are in the tolerance. Those values provide the
basis of the fourth-order Runge-Kutta integration method with variable step size.

Figure 5.6 simulated process integrated with H2S scrubber and flash
A flash (Figure 5.6) is also integrated into the process in order to get the molecular
composition of vapour phase, which considers the impact of the recycle hydrogen
stream. An initial guess of the molecular composition of the recycle hydrogen
stream is made, and iterations are performed to update the molecular composition
of the recycle stream until the criteria is satisfied. The developed framework for
the modelling of a diesel hydrotreater is implemented in FORTRAN.
3-phase Diesel
Hydrotreater

Makeup H2
H
2
S/NH
3

removal
Unit
Vapor
Liquid
181
5.4 Case Study – Modelling of Diesel Hydrotreater
5.4.1 Simulation of a Diesel Hydrotreater
To verify the developed model and the solving methodology, sets of the
experimental data (Marafi, 2007) on hydrotreating diesel streams are applied.
Table 5.7 gives the configuration of the reactor and its operating conditions. The
properties and the MTHS matrix of straight run gas oil are listed in the section 3.5
of chapter 3. Thermodynamic equilibrium was assumed between the gas and liquid
phases at the reactor inlet.
Table 5.7 Configuration of the reactor and operating conditions
Reactor configuration
Diameter (m) 1
Length (m) 20
Density of bed (
3
r cat
m kg )
710
Catalyst characteristics
Equivalent diameter (m)
3
10 3 . 1
−
×
Density(
3
/ m kg )
1420
Porosity(
3 3
/
p f
m m )
0.6
Operating condition
Temperature(K) 610, 625, 640
Pressure(bar) 40
LHSV( ( ) h m m
cat l
3 3
/ )
1.30
H2/oil 200
Flash temperature(K) 298.15
Hydrogen purity(mol/mol) 0.91
Table 5.8 compares the composition and the properties of the hydrotreated product
between the measured and the predicted at the reactor temperature of 625K, which
shows a good agreement. Table 5.9 compares sulphur contents and monoaromatics
contents of the products with three different operating temperatures, which also
shows a good consistence.
182
Table 5.8 Composition and properties of the product of the measured and predicted
Measured Predicted
Total aromatics (wt%) 37.91 37.62
Monoaromatics (wt%) 29.45 29.67
Polyaromatics (wt%) 8.45 7.95
Density @ 15
o
C (g/cc) 0.8609 0.86
Sulphur content (wtppm) 689.00 695.83
Table 5.9 Monoaromatics content and sulphur content of the products with three
different reactor temperatures
Monoaromatics (wt%) Sulphur (wtppm)
Temperature Measured Predicted Measured Predicted
610K 30.70 31.06 1380.00 1302.54
625K 29.45 29.67 689.00 695.83
640K 28.80 28.82 490.00 482.79
0
50
100
150
200
250
300
350
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial position
C
o
n
c
e
n
t
r
a
t
i
o
n

(
m
o
l
/
m
3
)
0
0.5
1
1.5
2
2.5
3
H
2
S

p
a
r
t
i
a
l

p
r
e
s
s
u
r
e

(
b
a
r
)
H2S
SII
SIII
SIV
SV
PH2S

Figure 5.7 Axial profiles of the sulphur compound content and the partial pressure of
H2S (625 K)
The evolution of sulphur contents of SII, SIII, SIV, and SV through the reactor is
shown in Figure 5.7. As seen, the major fraction of the sulphur removal is taken
place in the initial part of the reactor – 0.2 length comparable ratio of the reactor,
and in the left part of the reactor, sulphur is removed slowly. That is because
183
benzothiophene (SII) reacts fastest. The slowest reaction is the removal of 4,6-
dimenthyldibenzothiphene and its substituted 4,6-diDBT (SV), which comprise the
major components of sulphur compound in hydrotreated products. The sulphur
removal rate order follows: SII > SIII >SIV >SV.
The partial pressure of H
2
S in the gas phase increases dramatically at the beginning
of the reactor due to the fast removal of sulphur from SII. The fast consumption of
hydrogen in the initial part of the reactor is also reflected in Figure 5.8. The
concentration of hydrogen in the liquid phase at the initial part of the reactor is far
from the saturation, which makes the hydrogen concentration in the liquid phase at
the initial part of the reactor become the key of the reaction rate.
0
20
40
60
80
100
120
140
160
180
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Axial position
C
o
n
c
e
n
t
r
a
t
i
o
n

(
m
o
l
/
m
3
)
0
5
10
15
20
25
30
35
40
H
2

p
a
r
t
i
a
l

p
r
e
s
s
u
r
e

(
b
a
r
)
C(H2)
PH2

Figure 5.8 Axial concentration of hydrogen in the liquid phase and partial pressure
of hydrogen in the vapour phase (625 K)
5.4.2 Sensitivity Analysis of Operating Conditions
Effects of operating conditions such as temperature, LHSV, pressure, and H
2
/oil
are analysed as well. The operating condition with the temperature of 625K is used
as the basis for the sensitivity analysis.
184
0
5
10
15
20
25
30
35
40
45
50
600 620 640 660 680 700
Temperature (K)
A
r
o
m
a
t
i
c
s

c
o
n
t
e
n
t

(
w
t
%
)
0
500
1000
1500
2000
2500
3000
S
u
l
p
h
u
r

c
o
n
t
e
n
t

(
w
t
p
p
m
)
Total Aromatics(wt%)
MonoAromatics(wt%)
PolyAromatics(wt%)
Sulphur Content(wtppm)

Figure 5.9 Influence of temperature on the product compositions
Figure 5.9 illustrates the influence of the operating temperature on the product
composition. High temperature favours the reactions of both HDS and HDA.
However, HDA reaction is controlled by thermodynamic equilibrium, and too high
temperature will prevent it. As for HDS, the increased efficiency of sulphur
removal is decreased with the increase of the operating temperature, which means
that only increasing operating temperature may be not efficient to meet the sulphur
conversion requirement.
0
5
10
15
20
25
30
35
40
0.95 1.05 1.15 1.25 1.35 1.45
LHSV (hr-1)
A
r
o
m
a
t
i
c
s

c
o
n
t
e
n
t

(
w
t
%
)
0
100
200
300
400
500
600
700
800
S
u
l
p
h
u
r

c
o
n
t
e
n
t

(
w
t
p
p
m
)
Total Aromatics(wt%)
MonoAromatics(wt%)
PolyAromatics(wt%)
Sulphur Content(wtppm)

Figure 5.10 Influence of the LHSV on the product compositions
Figure 5.10 shows the influence of LHSV on the product compositions. As feed
flow rate is increased, sulphur and aromatics contents in the product are increased
185
as well. To balance between the ultra low sulphur requirement and profit margins,
LHSV is necessarily an important parameter to be optimised for the design.
Figure 5.11 shows the influence of the reactor pressure on the product
composition. As the reactor pressure increases, the concentration of hydrogen in
the liquid would be increased as well, which impacts the reactions seriously. As for
HDS, the increased efficiency of sulphur removal is decreased with the increase of
the reactor pressure. Reactor pressure is one of important design parameters.
6
11
16
21
26
31
36
41
40 45 50 55 60 65 70 75 80
Operating pressure (bar)
A
r
o
m
a
t
i
c
s

c
o
n
t
e
n
t

(
w
t
%
)
0
100
200
300
400
500
600
700
800
S
u
l
p
h
u
r

c
o
n
t
e
n
t

(
w
t
p
p
m
)
Total Aromatics(wt%)
MonoAromatics(wt%)
PolyAromatics(wt%)
Sulphur Content(wtppm)

Figure 5.11 Influence of the pressure on the product composition
7
12
17
22
27
32
37
42
160 170 180 190 200 210 220 230 240 250
H2/oil
A
r
o
m
a
t
i
c
s

c
o
n
t
e
n
t

(
w
t
%
)
0
200
400
600
800
1000
1200
S
u
l
p
h
u
r

C
o
n
t
e
n
t

(
w
t
p
p
m
)
Total Aromatics(wt%)
MonoAromatics(wt%)
PolyAromatics(wt%)
Sulphur Content(wtppm)

Figure 5.12 Influence of the H
2
/oil ratio on the product composition

186
Figure 5.12 presents the influence of H
2
/oil ratio on the product composition. As
the ratio increases, the partial pressure of hydrogen and the concentration of
hydrogen in the liquid are increased as well, which favors all the reactions. As for
HDS, the increased efficiency of sulphur removal is decreased with the increase of
H
2
/oil, therefore H
2
/oil should only be increased to a certain extent considering the
balance between the efficiency and cost.
The impact of catalyst activity on sulphur reactions is also performed. As Figure
5.13 shows, sulphur content in the liquid product is increased dramatically with the
loss of catalyst activity. Therefore changing operating condition such as increasing
operating temperature or hydrogen flow rate to compensate catalyst deactivation is
necessary.
100
1000
10000
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Catalyst relative activity
S
u
l
p
h
u
r

c
o
n
t
e
n
t

(
w
t
p
p
m
)

Figure 5.13 Influence of catalyst activity on the sulphur removal
To summarise, the trend of changing operating condition is obvious, but the extent
of these changes should be optimised properly.
5.5 Catalyst Deactivation
5.5.1 Mathematical Model of Catalyst Deactivation
Catalyst deactivation has a strong effect on the run length of a hydrotreating
reactor, and consequently the margins. Therefore, a deep understanding on the
mechanism of catalyst deactivation could help increase the profitability.
187
The mechanism for catalyst deactivation has three different stages (Tamm and
Harnsberger, 1981):
Stage 1 – rapid formation of initial coke with significant loss in catalyst activity;
Stage 2 – gradual build-up in pore by continuous accumulation of coke, causing
further loss in the intrinsic activity of the catalyst;
Stage 3 – constriction or blockage of pores by coke with complete loss of
catalytic activity due to diffusion limitation.
The model developed by Sun (2004) is applied in this work. Equation 5.35 is a
quantitative description of catalyst activity.
0
r
r
= α (5.35)
where r
0
is the reaction rate of catalyst at the start of the run, r is the rate of
reaction after a determined time-on-stream.
De Jong et al. (1997) correlated the activity of catalyst with the coke content on the
catalyst as equation 5.36.
( )
b
c
W a − =1 α (5.36)
where a, b are the coefficients regressed by the experimental data, and W
c
is the
weight content of coke on catalyst calculated as equation 5.37.
∫
=
T
coke
dt r Wc
0
(5.37)
The reaction includes a coke formation model and a reactivity-coke content
relationship (De Jong, 1994): (i) thermal condensation reactions of aromatic
moieties and (ii) catalytic dehydrogenation reactions. Equation 5.38 describes the
total rate of coke deposition that includes thermal and catalytic coke.
t c coke
r r r + = (5.38)
where r
c
is the catalytic coking rate, and r
t
is the thermal coking rate.
188
The mathematical models for thermal and catalytic coking are shown as follows.
p adsp
p adsp c
c
C K
C K k
r
+
=
1
(5.39)
2 H
p t
t
P
C k
r = (5.40)
where k
t
is the rate constant for thermal coking, P
H2
is the hydrogen partial
pressure, K
adsp
is the adsorption constant of coke precursor, C
p
is the concentration
of coke precursor, can be set as the aromatic content in the feedstock.
5.5.2 Multi-period Model of Catalyst Deactivation
During the run of a diesel hydrotreater, operating conditions are needed to be
changed to compensate the activity loss caused by coke to satisfy the product
specification. Under industrial operating conditions, catalytic conversion activity
of a diesel hydrotreater is maintained by constantly raising the temperature (Tamm
and Harnsberger, 1981). Sun (2004) developed a model for the operation involving
making multi-stage decisions, and these decisions are inter-related by dividing the
whole run length into multiple periods in terms of time. In each period, the
minimum increase of reactor temperature that can meet the sulphur specification
would be raised.
However, as reviewed previously, not only reactor temperature is the important
parameter that can help meet the product specification, but also other parameters
such as pressure, LHSV, and hydrogen/oil ratio. As known, the increase of
temperature would help the removal of sulphur content, but also prevent HDA
reactions, and shorten catalyst life leading to the increase of operating cost. Low
LHSV is preferred to remove sulphur content, but consequently leads to the loss of
the income. As for hydrogen/oil ratio, high value favours the removal of sulphur
content, but also increases the operating cost. How to compensate the loss of the
catalyst activity is not obvious considering the economic performance.
189

Figure 5.14 Multi-period of run length on the catalyst activity basis division
Another shortcoming of the model (Sun, 2004) is that the decision of each period,
the minimal increased temperature, depends on the history of operations, which
makes the problem quite complex and being solved sequentially. Moreover, multi-
stage on the time-basis division cannot accurately present the physical meaning of
catalyst activity. A multi-period model on the catalyst activity basis division of run
length is proposed as Figure 5.14 shows.
The activity of catalyst starts from α
0
, which is 1 for catalyst without any deposit
of carbon, or a certain value for the regenerated catalyst with a certain deposit of
carbon on catalyst. The end activity is that catalyst with it cannot satisfy the
product specification with any compensation by changing operating conditions.
Since the reaction rate of each period would depend on the start and end activities
of catalyst, and its operating conditions in the stage, the simulation with catalyst
deactivation in each period will no longer depends on the history of operations.
Therefore, the simulation in each period could be performed simultaneously.
The length of each period is calculated using the model of catalyst deactivation.
The coke deposit on catalyst can be calculated according to the activity of catalyst
based on Equation 5.36. Then according to Equation 5.37, the time length of each
period could be calculated. The run length of a diesel hydrotreater is the sum of all
these intervals.
5.6 Diesel Hydrotreater Optimisation
Due to the non-linearity and high dimensionality of a rigorous diesel hydrotreater
model, little information about the process level optimisation is published. A
decision support tool for process optimisation of sulphur free diesel production is
developed with a simplified model for a hydrotreater on the site-wide level in
industry, which targets the maximal of the margin by adapting the process
operation to changes in the specification requirements without capital investments,
i
α
1 + i
α
N
α
0
α
0
L

i
L

1 − N
L

190
taking account of blend values, deactivation costs of the catalyst, shutdown margin
losses, product specifications and quality margins (Lukszo, 2006). The model is a
site-wide level model, which cannot handle the change of feedstock. Abbasi (2009)
employed genetic algorithm (GA) to handle the no-linearity and high
dimensionality of a complex model of a three-phase trickle-bed reactor, which
leads to the convergence problem through conventional algorithms as the author
reported. The variables to be optimised are gas and liquid superficial velocity, the
reactor temperature and pressure, and the length of reactor. The optimisation
objective of the work is to find out the appropriate operational conditions at steady
state that lead to the highest amount of sulphur removal in presence of conditions
that will minimise the gas make. However, the model has not considered the
catalyst deactivation, which has a serious impact on the economic data. Moreover,
stochastic optimisation usually takes a huge amount of CPU resources.
The proposed optimisation model would integrate the developed multi-period
hydrotreater model, targeting the minimal operating cost by changing the operating
temperature, hydrogen stream quantity, with the constraints of product
specification and practices.
5.6.1 Mathematical Model
The annualised operating cost is shown as equation 5.41.






+ +
+
=
∑
∑
=
=
shutdown loss cat
N
k
k
H
k H
N
k
shutdown k
L C C L F c
L L
obj
1
2
2
1
365
(5.41)
The operating cost includes hydrogen utility cost, catalyst cost, and the economic
lost because of shutdown.
The molecular composition of product from a diesel hydrotreater is calculated
through the simulation expressed as Equation 5.42.
( ) ,... , L , r , P , T , C f C
c r r
F
j
p
iV
α = (5.42)
191
The constraints include the product specification such as sulphur content limit,
temperature/hydrogen allowable change range, and run length illustrated as
Equations 5.43 – 5.46.
spec
prod
k
S S ≤ (5.43)
Max k Min
T T T ≤ ≤ (5.44)
Max
H
k Min
F F F ≤ ≤
2
(5.45)
∑
=
≤ ≤
N
k
Max k Min
L L L
1
(5.46)
Deterministic algorithm rather than stochastic algorithm is employed because of
large amount of simulations demanded by stochastic algorithm leading to the huge
CPU time. Successive quadratic programming (SQP) algorithm is successfully
applied in the optimisation by introducing NAG FORTRAN library function
E04UCF without any difficulty of convergence problem.
5.7 Case Study – Optimisation of Diesel Hydrotreater
Diesel product of the simulation case in section 5.4 never reaches the specification
with the maximum sulphur content of 50 wtppm. The proposed optimisation model
is applied to upgrade the straight run gas oil with the satisfaction of the sulphur
specification, and remaining the throughput. Due to the consideration of catalyst
deactivation and high sulphur content, only increasing operating temperature and
hydrogen flow rate would not meet the product specification, therefore, the reactor
pressure is increased to 60 bar, and fixed. The whole run length is split into three
stages shown as Table 5.10 with the constraint given in Table 5.11.
Table 5.10 Activity division of catalyst for three stages
Stage Start activity End activity
S 1 0.75
M 0.75 0.6
E 0.6 0.4
192
Table 5.11 Constraints of the optimisation case
Property Bound
Sulphur content (wtppm) ≤50
Temperature(K) ≤700
Hydrogen (t/day) ≤15
Catalyst life (days) ≥300
Table 5.12 presents the optimal operating conditions, the sulphur content of
product, the time length of each period and aromatic conversion as well. Both the
reactor temperature and the hydrogen flow rate are increased to compensate the
loss of catalyst activity along with the time. The sulphur content of product is
satisfied at the bound. The run length of the diesel hydrotreater is 350 days.
Aromatics conversion decreases significantly through stages because of the
increase of the operating temperature and the loss of activity.
Table 5.12 Optimal operating conditions and results
S M E
Temperature (K) 685.01 689.77 700.00
Hydrogen (t/day) 11.93 12.47 12.40
Sulphur (wtppm) 50.00 50.00 49.80
Duration(days) 39.40 127.01 184.22
Aromatic conversion (wt%) 17.20 13.28 5.51
5.8 Summary
A molecular model of hydrotreating reactions with a three-phase trickle-bed
reactor has been developed based on the developed MTHS matrix for feedstock
and product streams. First of all, structural contribution approach is applied for
kinetics and adsorption parameters, which is tailored for the MTHS matrix.
Secondly, correlations and models are employed to calculate a big number of the
properties for pure compounds and the phases of gas and liquid. Lastly, a
simulation method is proposed to solve the model, combining a fourth order
Runge-Kutta integration method for integration in the axial direction and an
orthogonal collocation method for the intraparticle integration within catalyst
193
sphere. The result under the different operating conditions between the calculated
and the measured is compared in a case study, and shows that the developed model
is capable of simulating a diesel hydrotreater.
A process level optimisation model has been developed with the consideration of
catalyst deactivation. Firstly, the model of catalyst deactivation correlates coke
amount on catalyst with reaction rate. Secondly, a new division of catalyst life is
proposed to make stages independent with each other. Lastly, the optimisation
model targeting minimising the operating cost with the satisfactions of product
specifications is successfully implemented. This step also provides the possibility
to explore the interactions between hydrotreaters and hydrogen network.
5.9 Nomenclature
List of symbols
r reaction rate
k reaction rate constant
K adsorption constant
Keq equilibrium constant
N
AR
number of aromatic rings in a PNA molecule
N
SC
number of saturated carbons in a PNA molecule
HBO highest bond order in an aromatic ring
0
R
H ∆ difference between gas-phase heats of formation of products and
reactants under the standard condition
n reaction stoichiometry with respect to hydrogen
u
g
superficial velocity of the gas
u
L
superficial velocity of the liquid
R gas constant
T represents the reactor temperature
P represents the reactor pressure
p
ig
partial pressure of compound i
K
LaL
the mass transfer between the gas and the liquid phases
K
SaS
mass transfer between the liquid and the solid phases
H
i
Henry coefficient of the entry i in the MTHS matrix
194
C
iL
concentration in the liquid phase of compound i
S
iS
C concentration of component i on the catalyst surface
C
iS
concentration of component i inside the catalyst
D
ie
effective diffusivity of component i for transport in a pseudo
continuum
d
p
equivalent particle diameter
ρ
s
catalyst density
ρ
B
catalyst bulk density
Nr number of reactions
ηj effectiveness factor of reaction j for solid particle
S[j,i] stoichiometric coefficient of component i in reaction j
R
c
radius of spherical catalyst
a, b coefficients
W
c
weight content of coke on the catalyst
L
k
the time length of the interval k of catalyst life length
Lshutdown time length for the shutdown because of catalyst replacement
C
H2
price of hydrogen
C
cat
catalyst cost of one life cycle
2 H
k
F vapour flow rate fed to DHT
S sulphur content

Subscripts
s hydrodesulphurisation
τ hydrogenation site
σ hydrogenolysis site
i, j entries of the MTHS matrix
k interval of catalyst life cycle
m reactions taking place in hydrotreater, including HDS, HDA
ST steric effect for structure group contribution method
EL electronic effect for structure group contribution method
m, n, p the position of substitents on DBT
ξ radial coordinate of spherical catalyst
195
Chapter 6 Integrated Site and Process
Optimisation with Molecular Modelling
6.1 Introduction...........................................................................................196
6.1.1 Challenges of Refinery Optimisation................................................... 196
6.1.2 Decomposition Strategy for Refinery Optimisation (Zhang, 2000)..... 198
6.2 Incorporating Molecular Management into Refinery Optimisation......199
6.3 Application I: Exploitation of Interaction between Refinery Material
Processing Network and Processes ...................................................................199
6.3.1 Introduction.......................................................................................... 199
6.3.2 Site Level Model .................................................................................. 200
6.3.3 Site Optimisation with Process Simulation.......................................... 202
6.3.4 Integrated Site and Process Optimisation ............................................ 204
6.3.5 Case Study............................................................................................ 205
6.4 Application II: Exploitation of Interactions between Hydrogen Network
and Hydroprocesses ..........................................................................................215
6.4.1 Introduction.......................................................................................... 215
6.4.2 Integrating Hydrogen Network and Hydroprocesses........................... 220
6.4.3 Site Level Model .................................................................................. 220
6.4.4 Site Optimisation with Process Simulation.......................................... 226
6.4.5 Integrated Site and Process Optimisation ............................................ 227
6.4.6 Case Study............................................................................................ 228
6.5 Summary ...............................................................................................232
6.6 Nomenclature ........................................................................................233
6.6.1 Application I......................................................................................... 233
6.6.2 Application II ....................................................................................... 233

196
6.1 Introduction
A typical refinery involves a wide spectrum of activities, starting from crude oil
operations, refining operations, and final product blending. The nature of value
chain is such that its economics are extremely complex and heavily linked,
consisting of so many decisions making in different levels. From the managerial
level, managers need to decide which crudes to buy, which products to produce,
which operating route to follow, etc. From the process level, operators have to
determine the detailed operating conditions for equipments. All decisions are
highly inter-related and the interactions have large impact on the overall profit.
Besides the internal complex nature of refining operations, the current external
picture of refining industry is characterised by fluctuating markets, heavier, sourer,
costly crude oils, higher product quality specifications, and more stringent
environmental regulations with more emphasis on the molecules of products.
Therefore, smarter operation strategies based on molecular management are very
necessary to maintain margin while simultaneously following the regulations.
Refinery optimisation targets on making right decisions of the highly interacted
operations on different levels to achieve the maximal profit or the minimal cost.
This chapter firstly introduces the challenges of refinery optimisation, followed by
a brief review of the optimisation techniques. Then, a decomposed strategy
(Zhang, 2000), which effectively and efficiently handles the complexity of refinery
optimisation on both site and process levels, is incorporated with molecular
management. The integrated framework firstly is applied in an overall refinery
optimisation focusing on the material processing system. Secondly, an exploitation
of interaction between hydroprocesses and hydrogen network is investigated. The
goodness of both applications is well illustrated in the case studies respectively.
6.1.1 Challenges of Refinery Optimisation
There are generally two types of mathematical formulations in refinery
optimisation: linear programming (LP) or mixed integer linear programming
(MILP), and nonlinear programming (NLP). LP formulation is that all the
197
objective and constraints are in linear form, while NLP formulation is that any of
the objective and constraints is nonlinear.
The state-of-the-art of LP/MILP is widely used in the overall refinery optimisation
for planning purpose. The advantages of LP/MILP are its robustness, speed and the
ease with which important solutions such as the complete value structure in terms
of marginal prices can be obtained. However, problems can be formulated as
LP/MILP only if the algebraic relationships between variables are linear or can be
closely approximated by linear equations. It is normally not the case for process
operations with highly nonlinear kinetics, thermodynamics, and hydromechanics,
etc. As a result, this kind of models cannot describe the nonlinear aspects
accurately. To mimic nonlinear behaviour while maintaining linear formulation,
recursion techniques in LP are commonly used, which requires sequential
execution of a number of LPs. 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 the confidence
(Hartmann, 1998). These in turn are restricted to long-term planning for plant-wide
optimisation, and not suitable for day to day operations. These LP based models
are well implemented in some commercial software packages, like RPMS
(Honeywell Hi-Spec Solutions), PIMS (Aspen Technology).
In principle, NLP models for the overall refinery optimisation can be formulated
by lumping all the rigorous process models. However, there is no established
commercial NLP software existing due to the great difficulties involved in
mathematics and computation to handle such complexities in the overall plant
modelling (Grossmann, 1995). In practice, normally NLP models are applied in the
process optimisation for the optimal operating conditions, which has a result close
to the reality. However, the process optimisation is with a stand-alone mode,
without the guidance from the overall refinery LP optimisation. Consequently, the
synergy between plant-wide aspects and process operations cannot be exploited
properly, which greatly limits the economic contribution of process optimisation.
198
6.1.2 Decomposition Strategy for Refinery Optimisation (Zhang, 2000)
In an effort to improve the accuracy and ability to tackle the nonlinear aspects
while maintaining the robustness and the speed in overall refinery optimisation, a
decomposition approach for overall refinery optimisation has been developed
(Zhang, 2000). The approach consists of two-level optimisation, namely the site-
level and process level, and more importantly, a strategy to coordinate two levels.
In this decomposition approach, all non-linear and discrete aspects are allowed to
be tackled in different levels with precise details and solvable mathematics.
In the site level, with given process performances, alternatively speaking, with
fixed operating conditions, the objective is to maximise the overall profit by taking
into account major aspects associated with plant-wide operations, which are
basically about how to manage resource distributions among processes. These
aspects have major impacts on overall economic performance, which include
selection of feeds and products, distribution of intermediate products, connections
between different processes and allocations of utilities. These aspects feature
nonlinear and/or discrete nature. In this level, processes are modelled with linear
yield correlations without the information of detailed process operating conditions.
In the process level optimisation, with given resource distribution, the objective is
to maximise process profit by optimising operating conditions. In this level, non-
linear and discrete aspects related to individual processes are fully addressed. The
main feature of this level optimisation is that feed conditions are fixed the same as
those determined from the current run of the site level optimisation.
The state-of-the-art of the approach is to coordinate two level models. To match
the real performance of refining processes, an iterative procedure is applied to
update the simplified linear yield correlations by the rigorous process simulation.
To guide the process optimisation, the marginal value of the intermediate product
is calculated to be used as the economic insight from the site level.
With this decomposition and coordination scheme, the problem of overall plant
optimisation can be modelled efficiently without the need of building an overall
plant model, and be solved efficiently without losing accuracy and interaction
199
between different systems. Furthermore, the rigorous process models can be
effectively integrated in the framework without the need of making simplifications.
6.2 Incorporating Molecular Management into Refinery
Optimisation
Based on the two-level decomposition approach (Zhang, 2000), molecular
modeling of refining streams and processes will be incorporated into the refinery
optimisation to investigate the benefits of the molecular techniques. The integrated
framework will be applied in two applications. The first is to explore the
integration of site and process level optimisation mainly focusing on material
processing system. In this application, molecular modelling technique are applied
in both site and process level models to monitor and control the molecular
specification of products properly, and simultaneously achieve the maximal
economic performance. The second application is to develop a method on how to
manage hydrogen utility more efficiently to improve economic performance rather
than saving hydrogen. Both applications include the basic idea of the two-level
decomposition approach: site level modelling, site level optimisation with
simulation/optimisation, and integration of site and process optimisation. The
developed methodologies are finally well illustrated in case studies.
6.3 Application I: Exploitation of Interaction between Refinery
Material Processing Network and Processes
6.3.1 Introduction
Obviously, material processing network has a strong interaction with each process.
The network will allocate materials to processes, while the process operating
conditions will determine the product quantity and quality fed back into the
network. By adopting the decomposition framework, the strong connection
between the network and processes can be fully exploited. To enhance the
accuracy of process models, simultaneously monitor and control molecules,
molecular modelling will be incorporated in both site and process levels.
200
6.3.2 Site Level Model
In the site level, the important aspects include the selection of crude oil (C), and
the allocation of intermediate refining streams (S) to refining units (U), as well as
refining products (P), together with the composition (K) represented by MTHS
matrix and properties (PP) of refining streams.
To differentiate the contribution from different crude oils, each flow is
decomposed into several flows based on their origins from the crude oils. For
instance, if a refinery has two crudes to choose from, VGO from AVU is
decomposed into two streams: VGO from Crude 1 and VGO from Crude 2
respectively. In this way, each crude is traced to its final products, and the
economical contribution of different crudes can be evaluated precisely.

Figure 6.1 A general connection
Figure 6.1 shows a general connection in a refinery. Streams (SS1, SS2… SSn)
from different processes (UU1, UU2… UUn) are fed into process U to produce
different products (S1… Sn), and then products such as S1 will be fed to different
processes (UUU1, UUU2… UUU3). The mass balance of these connections is:
( )
∑ ∑∑
= ×
uuu
uuu s u c
uu ss
s u ss c u ss uu c
F R F
, , , , , , , , ,
S s U u C c ∈ ∀ ∈ ∀ ∈ ∀ , ,
(6.1)
As mentioned, a process is modeled as simplified yield linear correlations.
s u ss c
R
, , ,

is the yield coefficients representing that one unit of feed ss will produce R of
UU
UU
UU
…
.
U
UUU
UUU
…
.
SS1
SS2
SSn
S1
UUU
UUU
….
Sn
201
product s through process u from crude oil c. This general connection includes
splitters. Decomposition of all process flows is based according to their crude oil
origin. The composition of the stream into a splitter has to be the same as that of
the streams leaving the splitter in all splitter operation, which is indicated as:
∑ ∑
=
uuu
uuu s u cc
uuu s u cc
uuu
uuu s u c
uuu s u c
F
F
F
F
, , ,
, , ,
, , ,
, , ,
S s U u C cc C c ∈ ∀ ∈ ∀ ∈ ∀ ∈ ∀ , , ,
(6.2)
The mass balance on each molecular composition of streams represented by MTHS
matrix can be written as:
( )
∑
∑∑
× ×
=
uu
uu , s , u , c
uu ss
k , s , u , ss , c s , u , ss , c u , ss , uu , c
k , s , u , c
F
y R F
y
K k S s U u C c ∈ ∀ ∈ ∀ ∈ ∀ ∈ ∀ , , , (6.3)
The composition in a blending process is as:
( )
∑∑
∑∑∑
× ×
=
c uu
uu s u c
c uu ss
k s u ss c s u ss c u ss uu c
k s
F
y R F
y
, , ,
, , , , , , , , , ,
,
K k P s C c ∈ ∀ ∈ ∀ ∈ ∀ , , (6.4)
Properties blending nonlinearly:
( )
k s p s
y f Pt
, ,
= NP p P s ∈ ∈ ∀ , (6.5)
Properties blending linearly:
∑
=
k
p k k s p s
Pt y Pt
, , ,
LP p P s ∈ ∈ ∀ , (6.6)
Utility consumption:
∑∑∑∑
× =
c uu s u
ut u s uu c u s uu c ut
F Q
, , , , , , ,
α UT ut ∈ ∀ (6.7)
Crude oil usage:
∑∑
=
s u
u s uu c c
F F
, , ,
CS uu C c ∈ ∀ ∈ ∀ , (6.8)
202
Crude oil is assumed to be loaded from a storage tank (CS).
Product quantity:
∑∑∑
=
c uu s
u s uu c p
F F
, , ,
PS u ∈ ∀ (6.9)
Products are assumed to be fed to products tank (PS).
Inequalities associated with limits on throughputs, product specifications, market
demands, etc. give the constraints associated with refinery operation.
Unit capacity:
U
u
c uu s
u s uu c
L
u
F F F ≤ ≤
∑∑∑ , , ,
U u ∈ ∀ (6.10)
Product specification:
p s p s
L
p s
Pt Pt Pt
, , ,
≤ ≤ PP p P s ∈ ∈ ∀ , (6.11)
Market constraints:
U
c c
L
c
F F F ≤ ≤ C c ∈ ∀ (6.12)
U
s p
L
s
F F F ≤ ≤ P p ∈ ∀ (6.13)
The objective of the site-level optimisation is to maximise the net profit that arises
from the sale of products and utilities minus the cost of purchasing raw materials
and utilities e.g. fuel, power, etc. This objective is a linear function of material and
utility requirements for given product prices and raw material and utility costs.
( )
∑∑∑∑ ∑ ∑ ∑
× − × − × − × =
u c uu ss
u u s uu c
ut
ut ut c
p c
c p p
C F C Q C F C F profit
, , ,
(6.14)
6.3.3 Site Optimisation with Process Simulation
To improve the feasibility of the overall solution, simulation is introduced in the
site level to form an iterative procedure to correct the error caused by the
simplified linear yield correlations. Based on the current operating scenario, the
first step is to carry out process simulation. Streams represented by MTHS matrix
203
in the site level will be transformed into molecular information according to the
bulk properties from the simulation. The developed methodology in Chapter 2 will
be applied. Besides that, the simulation also provides the initial linear correlations,
which are used in the site-level optimisation to determine the optimal material
allocation for processes. The new and improved operation may deviate from the
previous operating scenario on which the linear correlations are updated. This
indicates that although the overall profit may have risen, the point has deviated
from the actual operation. In other words, the correlations do not correspond with
current site-level results. In order to return to a feasible point, process simulation is
again carried out, in which the linear correlations are updated for the subsequent
site level optimisation. This iteration, between the site-level optimisation and the
process simulation is repeated until the differences between consecutive yields are
within the set tolerance. The whole iteration procedure is illustrated in Figure 6.2.

Site-level optimisation
|Yiel d
k +1
- Yiel d
k
| < ε
Feasible and optimal solution
Updated correlations
at k=k+1
No
Yes
Process simulation
Process arrangement
Yieldk +1
Process superstructure
Use linear yield correlations
Transformation of bulk property
into mole cular information

Figure 6.2 Site level optimisation with process simulation
It is important to note that at this stage, simulation is carried out under fixed
process operating conditions. The only change is in the distribution of feeds and
intermediate products determined via the site-level optimisation.
204
6.3.4 Integrated Site and Process Optimisation

Process Level Optimisation
Creating Objectives for Process
Optimis ation (mar ginal value calculation)
Curre nt Proces s Operations
k , n
P
X , n=0,
Site Level Optimis ation/Simulation
Site Level Optimis ation/Simulation
Under fixed res ource alloc ations
ε ≤ −
+ k , n 1 k , n
Obj Obj
k , n
r
X ,
k , n
Ob j , n=0, k=0
1 k , n
Ob j
+

ε ≤ −
+ 0 , 1 , n k n
Obj Obj
k=k+1
0 , n
r
0 , n
r
0 , 1 n
r
d X X λ + =
+

n=n+1
Yes
No
No
Yes
Stop
Tr ansformation of bulk properties into
molecular compos ition
Transformation of bulk pr oper ties into
molecular composition

Figure 6.3 Integration of site level optimisation and process optimisation
Site level optimisation determines the optimal allocation of materials and utilities
based on the fixed operating conditions of processes, which means it does not
consider the interaction between site level issues and individual processes, and thus
lose some opportunities to further improve the overall economic performance. The
developed approach (Zhang, 2000) integrated process optimisation with site level
optimisation. Marginal values of intermediate products obtained from site level
optimisation are used in process optimisation to maximise the process profit. The
changes of operating conditions from process optimisation are updated through the
simplified linear correlations, which are used in site optimisation. In this way, a
205
loop is created effectively to incorporate site and process optimisation together.
Figure 6.3 shows the diagram of integration of site and process optimisation.
6.3.5 Case Study
6.3.5.1 Problem Definition

Figure 6.4 Flowsheet of a refinery
Table 6.1 Unit capacity
Process Capacity, bpd
Low Limit High Limit
AVU 120,000 200,000
CCRU 8,000 24,000
RFCCU 50,000 80,000
DCU 50,000 80,000
CNHTU 6,000 20,000
DHTU 12,000 140,000
206
To investigate the benefit of integrating process optimisation with site optimisation
and molecular modelling techniques, a case is studied. Figure 6.4 shows the
flowsheet of a refinery, consisting of an Atmosphere/Vacuum Distillation Unit
(AVU), a Catalytic Reforming Unit (CRU), a Residue Fluid Catalytic Cracking
Unit (RFCCU), a Delayed Coker Unit (DCU), several hydrotreating units and
product blending units. The capacity of each unit is listed in Table 6.1.
Table 6.2 Properties of two crudes
Crude 1 Crude 2
API 33.1 24.9
Viscosity @50 C, mm2/s 20.19 83.36
Freeze Point, C 30 28
Wax, wt% 26.2 14.6
Gum, wt% 8.9 19
Conradson Carbon Residue, wt% 2.9 6.4
Element Analysis, wt%
Carbon 85.87 86.26
Hydrogen 13.73 12.2
Surphur 0.1 0.8
Nitrogen 0.16 0.41
Ni, ppm 3.1 26
Table 6.3 Availability of crudes
Crude Selection, bpd
Low Limit High Limit
Crude 1 0 120,000
Crude 2 0 120,000
There are two crudes for the refinery to select from. Both of the crudes are heavy
sweet with crude 2 being slightly heavier and sourer than the crude 1. The
properties of these two crudes are listed in Table 6.2, as well as the availability of
these two crudes in Table 6.3. The major products of the refinery are four grades of
gasolines (including gasoline90, gasoline93, gasoline 95 and gasoline 97), diesel,
207
liquefied petroleum gas (LPG), jet fuel, fuel oil and coke. Table 6.4 shows the
market conditions of gasoline and diesel products.
Table 6.4 Major market conditions of refining products
Major Market Conditions, bpd
Low Limit High Limit
Gasoline 90# 20,000 30,000
Gasoline 93# 4,000 10,000
Gasoline 95# 4,000 10,000
Gasoline 97# 2,000 10,000
Diesel 40,000 62,000
6.3.5.2 Modelling of Refining Streams and Processes
The developed molecular models of gasoline blending and CRU in Chapter 3 and
Chapter 4 will be applied in the case study. For the rest units, the non-linear
models are based on the correlations published by HPI Consultants, Inc. (1999) in
Appendix F. As for the streams, they are lumped in terms of the products generated
and feedstock depending on processes. For instance, the distillation products will
be lumped into the main fractions e.g. gas, light and heavy naphtha, jet fuel, diesel,
vacuum gas oil and vacuum residue, and for fluid catalytic unit, these include dry
gas, gasoline, liquefied petroleum gas (LPG), light cycle oil, coke and slurry, etc.
In the stage of process optimisation, the corresponding developed molecular
optimisation models are applied.
Since both the traditional lumped models and molecular models are preset, the
streams connecting these two kinds of units should have a proper interface to
incorporate both. MTHS matrix representation will be applied as the developed
molecular process models are also based on MTHS matrix, and they are easily
transformed to bulk properties, which the conventional model needs. Therefore,
streams flowing from units with conventional models to units with molecular
modelling are needed to transform into molecular composition by the developed
approach in Chapter 2, and vice visa. For instance, naphtha from DHT will be
transformed into molecular information before fed into CRU, and gasoline from
CRU in the form of MTHS matrix is directly used in gasoline blending units.
208
6.3.5.3 Strategy of Case Study
Table 6.5 Investigation modes of case study
Case 1 Case 2 Case 3 Case 4
Simulation Yes Yes Yes Yes
Site level optimisation Yes Yes Yes
Specification Yes Yes Yes
Raw material allocation Yes Yes
Process level optimisation Yes
Not only will the benefits from the integration of site and process optimisation be
illustrated, but also the benefits of incorporating molecular management. The case
study is investigated in four scenarios as Table 6.5.
Case 1, also base case, is applying rigorous molecular models to simulate current
operation. With only considering octane specification for gasolines and cetane
number for diesels, the products may violate the specifications on the molecular
information such as olefin, aromatic and benzene contents. In this step, RFCCU is
operated in the maximal gasoline mode with 70% of the conversion level.
Table 6.6 Gasoline specification
Gasoline Type G90 G93 G95 G97
RON (min) 90 93 95 97
RVP(psi) (max) 7.8 7.8 7.8 7.8
Sulphur(wt ppm) (min) 100 100 100 100
Aromatics (vol%) (max) 55 55 55 55
Olefins (vol%) (max) 25 25 25 25
Benzene (vol%) (max) 5.5 5.5 5.5 5.5
Table 6.7 Diesel specification
CN (min) 50
Sulphur(wt ppm) (max) 300
209
In case 2, given the same crude oil selections as case 1, the product specifications
(given as Table 6.6 and Table 6.7) are considered, which will reallocate the
intermediate products between processes to maximise the profit with the product
specifications. In this step, molecular modelling techniques show its advantages to
monitor and control the molecular contents in the products.
Based on case 2, the degree of freedom of site level optimisation is increased by
allowing the changes of crude oil selection to demonstrate it is crucial to the
overall economic performance. Finally, process optimisation is integrated based on
case 3 to form case 4, to fully investigate the maximal profit.
In this refinery, the RFCC unit is the key process for the plant economics, since it
can convert low-value VGO and part of VR to high-value gasoline and diesel. It is
necessary to optimise RFCC operation in the overall refinery. The optimised
variable of RFCCU is the conversion level for HPI correlations. On the other hand,
the gasoline from CRU has desired high octane number, but also with the high
restricted aromatic and benzene contents. Therefore, the proper control of
operating conditions of CRU is crucial to gasoline blending, and should be
considered in process optimisation. The operating temperature and pressure of
CRU will be optimised in the process level.
6.3.5.4 Optimisation Results
Table 6.8 Total profit of the refinery in the different modes
Total profit of the refinery, MM$/yr Improvement (%)
Case 1 152.19 0.00
Case 2 114.37 -24.85
Case 3 126.63 -16.79
Case 4 156.36 2.74
Table 6.8 compares the total profit of the refinery of these four cases. Compared
with base case, the profit is reduced dramatically by 24.85% from 152.19 MM$ to
114.37 MM$ after imposing environmental constraints on product quality, if with
the fixed operating conditions and crude selection. The total profit then is increased
210
to 126.63 MM$ after allowing crude selection, further to 156.36 MM$ with a great
improvement by integrating process optimisation.
Because of low sulphur, crude 1 is favored with the configuration of the refinery as
Table 6.9 shows the crude selections. Crude 1 favoring is also well illustrated as
the throughput of DHT reaches the maximal capacity showed in Table 6.10. Due to
the high aromatic/benzene content of product from CRU and aromatic/benzene
specification of gasoline, the throughput of CRU is reduced.
Table 6.9 Crude oil selection in the different modes
Crude oil selection, bpd Crude 1 Crude 2
Case1 54000 120000
Case2 54000 120000
Case3 120000 54095
Case4 120000 55922
Table 6.10 Process utilisation in the different modes
Process Utilisation, bpd
Case1 Case2 Case3 Case 4
AVU 174000.00 174000.00 174095.05 175922.82
CCR 18172.85 13748.63 14166.05 16215.89
RFCC 60247.33 52488.49 54811.65 75527.54
DCU 50000.00 50000.00 50000.00 50000.00
DHT 124968.00 140000.00 140000.00 140000.00
CNHT 20000.00 17096.89 17501.49 19857.89
Table 6.11 gives the main product distribution in different cases. Table 6.12 and

Table 6.13 selectively present the properties of gasoline90 and gasoline97
respectively. Without the restriction of environmental specification, gasoline90
product in base case has 34.53% of the olefin content, and gasoline97 has 57.76%
of aromatic content, higher than the maximal specified contents. Table 6.14 shows
that sulphur content of diesel product of base case also violates the specification.
Therefore, 152.19 MM$/yr of the overall profit for base case is unrealistic,
211
producing high profitable product gasoline97 as much as maximal market demand,
but with violated quality. Table 6.11 also exhibits that the production of diesel
reaches the maximal market demand since low sulphur crude oil is available.
Table 6.11 Main product distribution in different modes
Main product, bpd Case 1 Case 2 Case 3 Case 4
Light Naphtha 787.87 0.00 0.00 0.00
Jet Fuel 6870.00 10560.98 11391.95 9239.40
Fuel Oil 0.00 6531.85 0.00 0.00
LPG 11099.78 9711.60 10199.12 11862.94
Coke 3359.43 2926.40 2904.39 4363.74
G90 27620.03 30000.00 30000.00 29407.57
G93 4000.00 4137.94 5637.93 10000.00
G95 4402.55 4000.00 4000.00 8731.65
G97 10000.00 2000.00 2000.00 2000.00
Diesel 55343.85 53492.73 53954.76 62000.00
Gas 8091.06 7756.97 5869.25 6288.91
Table 6.12 Gasoline90 product properties in different modes
G90 Product property
Case 1 Case 2 case 3 case 4
RON 90.00 90.00 90.00 90.00
MON 77.33 77.77 77.82 77.74
RVP 3.99 4.73 4.96 4.82
Sulphur(wt ppm) 81.13 59.64 68.27 82.91
Nitrogen(wt ppm) 179.31 129.44 197.98 209.53
Aromatics(vol%) 32.72 34.60 34.14 34.83
Olefin(vol%) 34.53 25.00 25.00 25.00
Benzene(vol%) 0.62 1.59 1.55 1.43


212
Table 6.13 Gasoline97 product properties in different modes
G97 Product property
Case 1 Case 2 case 3 case 4
RON 97.00 97.00 97.00 97.00
MON 86.80 87.08 87.05 87.14
RVP 5.23 5.53 5.50 5.76
Sulphur(wt ppm) 0.27 0.30 0.30 0.36
Nitrogen(wt ppm) 0.14 0.18 0.12 0.09
Aromatics(vol%) 57.76 55.00 55.00 55.00
Olefin(vol%) 0.00 0.00 0.00 0.00
Benzene(vol%) 4.35 5.05 4.85 4.49
Table 6.14 Diesel product properties in different modes
Diesel property
Diesel Case 1 Case 2 Case 3 Case 4
CN 54.45 54.81 55.16 53.72
Sulphur(wt ppm) 1150.64 300.00 300.00 300.00
G90 composition
0%
20%
40%
60%
80%
100%
Case 1 Case 2 Case 3 Case 4
NHTNAP
DHTNAP
F_PET
CR_PET

Figure 6.5 Composition of gasoline90 in different modes
Figure 6.5 - Figure 6.8 give the components of gasoline products. In the refinery,
gasoline from RFCCU and RCU comprises the major contribution of gasoline
products. For example, in base case, around 97% of gasoline90 is from RFCC,
which also explains the violated high olefin content. Along with the increase of
octane specification, the percentage of gasoline from CRU is increased as well.
213
G93 composition
0%
20%
40%
60%
80%
100%
Case 1 Case 2 Case 3 Case 4
NHTNAP
DHTNAP
F_PET
CR_PET

Figure 6.6 Composition of gasoline93 in different modes
G95 Composition
0%
20%
40%
60%
80%
100%
Case 1 Case 2 Case 3 Case 4
NHTNAP
DHTNAP
F_PET
CR_PET

Figure 6.7 Composition of gasoline95 in different modes
G97 Composition
0%
20%
40%
60%
80%
100%
Case 1 Case 2 Case 3 Case 4
NHTNAP
DHTNAP
F_PET
CR_PET

Figure 6.8 Composition of gasoline97 in different modes
Figure 6.9 shows the components of diesel products. Straight run diesel, which has
2900 wt ppm sulphur content, is the main contribution to diesel product with 1150
wt ppm in base case.
214
Diesel Composition
0%
20%
40%
60%
80%
100%
Case 1 Case 2 Case 3 Case 4
HD
LGO
LCO
AV_DIE
J_DIE

Figure 6.9 Composition of diesel in different modes
The large increase in profit is achieved by exploiting the synergies between the site
level aspects and process operating details. In this case, RFCC operation is no
longer fixed at the maximum gasoline mode. Instead, the best compromise between
different operation modes is exploited with the integrated optimisation. As a result,
the RFCC conversion level is changed from 70 LV% to 64.71 LV%. As for CRU,
the operating temperature is decreased to lower aromatic contents in products.
Table 6.15 shows the optimal operating conditions of RFCCU and RCU
respectively.
Table 6.15 Operating conditions of processes in different modes
Case 1 Case 2 Case 3 Case 4
Temperature -Reactor1(K) 783.50 783.50 783.50 763.15
Temperature -Reactor2(K) 793.50 793.50 793.50 763.15
Temperature -Reactor3(K) 793.50 793.50 793.50 763.15
Pressure(psi) 120.00 120.00 120.00 80.00
FCC Conversion Level 70.00 70.00 70.00 64.71


215
6.4 Application II: Exploitation of Interactions between
Hydrogen Network and Hydroprocesses
6.4.1 Introduction
A hydrogen network may be described as a system of these refinery processes
interacting with each other through a hydrogen distribution system. The refinery
processes operating with hydrogen as a shared commodity constitute the
components of a hydrogen network.
The existing tools and methods for design of refinery hydrogen networks target
minimising the hydrogen utility of a given hydrogen network by assuming constant
operating conditions of refinery processes. The operating conditions of refinery
processes are changing from time to time depending on the feedstock and market
demands. Therefore, the hydrogen balance of a given hydrogen network may also
vary resulting in changing performance of refinery processes. A window of
opportunity that requires further research is the improvement of performance of
hydrogen consuming processes by utilising the hydrogen freed-up using hydrogen
management techniques. The hydrogen consumption of refinery processes is bound
to keep increasing in this era of cleaner transportation fuels, and consequently
design approaches are needed that can provide not only flexible hydrogen
distribution systems but also optimal utilisation of hydrogen for increasing the
overall profit margins of refineries.
6.4.1.1 Hydrogen Network in Refinery
Hydrogen network in refinery usually involves hydrogen producers that supply
hydrogen such as hydrogen plant and catalytic reforming process, hydrogen
consumers that consume hydrogen such as diesel hydrotreater and hydrocracker,
compressors that assure the pressure of hydrogen sink is met, and purifiers that
purify the hydrogen streams, as well as pipelines that transport hydrogen between
units. Figure 6.10 shows a typical hydrogen network (Singh, 2004) without the
consideration of pressure difference between processes.
216
HCU DHT KHT
CNHT NHT
HDA
H
2
Plant
CRU
Fuel
CRU Catalytic Reformer Unit
HCU Hydrocracker Unit
DHT Diesel Hydrotreater
KHT Kerosene Hydrotreater
CNHTCracked Naphtha
Hydrotreater
NHT Naphtha Hydrotreater
HDA Hydrodealkylation
Fuel Fuel Gas System

Figure 6.10 A typical hydrogen network
Hydrogen is supplied as a product of stream reformers (H
2
plant in Figure 6.10),
and a by-product of catalytic reformers (CRU), and a number of offgas or purge
streams in a refinery that contain hydrogen. There are various hydrogen consumers
in a refinery, which possibly include hydrocracking (HCU), diesel hydrotreater
(DHT), kerosene hydrotreater (KHT), cracked naphtha hydrotreater (CNHT),
naphtha hydrotreater (NHT) and hydrodealkylation (HDA) as Figure 6.10 shows.
Normally, the purities and pressures of these hydrogen consumers are different
because of the process characteristics, and the hydrogen source streams coming out
of the different units also have different pressures and purities. The difference in
operating pressure and hydrogen purity in the various hydroprocessing units can be
arranged in a downward sequence as Figure 6.10.
6.4.1.2 Hydrogen Network Management
Refinery hydrogen network management refers to the optimal allocation of
hydrogen distribution network. The methodology for hydrogen network
management has been developed intensively in this decade due to the stricter
environmental regulations on the transportation fuels. A brief review of these
methodologies would be present, together with some concepts used in this work.
Alves (1999) developed a framework of sinks and sources for classification of
components of a hydrogen distribution system. A sink is a stream that consumes
217
hydrogen from the hydrogen distribution system while a source is defined as a
stream supplying hydrogen to the system. The hydrogen producing processes form
the sources of a hydrogen distribution system with given purities and pressure
levels. The hydrogen consuming processes are represented in the framework of
sinks and sources as shown in Figure 6.11.
Purge (F
P
,y
P
)
Liquid
feed
Liquid
product
Make-up (F
M
,y
M
)
Recycle (F
R
,y
R
)
Reactor
Separator
Sink
Source

Figure 6.11 Simplified diagram of a hydrogen consumer (Alves, 1999)
Hydrogen pinch approach (Alves, 1999) to target the minimal hydrogen utility is
based upon the pinch technology and takes advantage of an analogy with heat
exchanger network synthesis (Linnhoff, 1993). In this method, sources and sinks of
hydrogen are similar to hot and cold streams in heat exchanger networks.
Sources and sinks of a hydrogen network can be plotted in a two-dimensional
graph by the flowrate and the purity as composite curves. Figure 6.12 displays a
hydrogen demand profile and a supply profile plotted in the order of decreasing
purity. There are regions where the source profile lies above the sink profile
indicating an excess of hydrogen available in that particular range of purity
(marked as +). On the other hand if the source profile is beneath the sink profile
then we have a deficit of available hydrogen in that purity range (marked as -). The
availability of hydrogen at different purity levels is represented as the hydrogen
surplus which is defined as the net cumulative excess of hydrogen in the purity
profile at a given flow rate (Alves et al., 2002). A hydrogen surplus diagram is a
plot of the hydrogen surplus against different purity levels of a hydrogen network.
Figure 6.13 shows a hydrogen surplus diagram generated by plotting the hydrogen
surplus or deficit, from purity profiles, at different purity levels.
218

Figure 6.12 Composite curves (Liu, 2002)

Figure 6.13 A hydrogen surplus diagram (Liu, 2002)

Figure 6.14 Balanced hydrogen surplus cascade diagram (Liu, 2002)

219
The hydrogen pinch is determined by moving this surplus curve towards the
vertical axis that is minimising the surplus amount of hydrogen available in the
hydrogen network. The sink in the segment touching the vertical axis is defined as
the hydrogen pinch. In this way, the minimum demand of hydrogen is determined.
If the hydrogen surplus curve passes the purity axis, the supply of hydrogen
sources can not satisfy the demand of hydrogen sinks.
The hydrogen network approaches discussed do not provide a framework for
optimal utilisation of hydrogen to improve the economic performance of refinery
processes (Hallale et al., 2002). The change of operating conditions plays an
important role in product quality as well as hydrogen consumption. For example,
increasing hydrogen partial pressure may enhance the reactor conversion,
throughput, product yields and catalyst life of hydrogen consuming processes. The
interaction between a hydrogen network and hydroprocessing processes could be
described as:
• Hydrogen sources affect hydrogen consumers by providing hydrogen at
different flowrates and purities;
• Changes of sources result in different process performance;
• Hydrogen consumers affect hydrogen sources by requiring certain amounts
of hydrogen at certain purities;
• Changes of operating conditions result in different hydrogen consumption;
Sun (2004) developed a series of procedures to investigate the interaction between
hydrogen network and diesel hydroteater. The approach (Sun, 2004) is far from
systematic. First of all, the effect of purity of hydrogen source was not
investigated, which has a significant impact on both a hydrogen network and diesel
hydrotreaters. Secondly, the effect of the change of operating conditions of diesel
hydrotreater on the economic performance is a complex problem, and not easily
identified by analysing the results from the different combinations of operating
conditions of a diesel hydrotreater. Last, a multi-period hydrogen network due to
catalyst deactivation was not considered yet.
220
6.4.2 Integrating Hydrogen Network and Hydroprocesses
The reason that the approach (Sun, 2004) to investigate the interaction between
hydrogen network and diesel hydrotreater is based on the analysis of the results
from the different combinations of operating conditions, is that the model relating
to process operations of a diesel hydrotreater are highly non-linear. This then led to
the great difficulty to handle the non-linearities related to the kinetics,
thermodynamics, etc. The challenge of this work then was to develop a model that
can account for both highly non-linear process models (containing detailed
descriptions of operating conditions) and at the same time optimise the overall
performance of a multi-period model of a hydrogen network.
The framework developed by Zhang (2000) forms the basic idea of the proposed
approach for the investigation of the interaction. The site-level optimisation is the
management of a multi-period hydrogen network, which is built to find the optimal
operations in each period: the changes of feeds fed to the processes, the hydrogen
purities and amounts, and the allocation of hydrogen between hydrogen sources
and sinks. In this level of optimisation, processes are modelled with linear
correlations and the information of detailed operating conditions is not needed. The
detailed procedure about these correlations building is explained in the late section.
The process-level optimisation tries to improve process performances based on the
allocated resources. Take diesel hydrotreater as an example, the process-level
optimisation would target on maximising the process profit based on the allocated
feed flowrate and hydrogen purity by changing the operating temperature and
hydrogen flowrate satisfying the product specifications. In this level of
optimisation, non-linear and discrete aspects related to individual processes are
fully addressed, and the rigorous process model can be employed. The main
feature of this level optimisation is that feed conditions and the hydrogen purity
determined on the site level are fixed.
6.4.3 Site Level Model
The target of this work is to switch the objective from saving hydrogen to
improving the economic performance by utilising hydrogen more efficiently. There
221
are several potential ways to increase the economic performance: feeding cheaper
feedstocks, increasing throughput, and reducing hydrogen and catalyst cost. To
include these potential ways, the representation of a hydrogen consuming process
is changed as illustrated in Figure 6.15, which allows the consideration of changing
feedstock composition and flowrate, as well as the hydrogen flowrate and purity.

Figure 6.15 Representation change of a process for new method

Figure 6.16 Modified diagram of a hydrogen consuming process
For a process, the operating condition such as temperature and pressure is
changeable to satisfy the product specifications as Figure 6.16 shows.
In this research, to simplify the problem, the practical constraints are not
considered such as pressure differences between hydrogen sources and sinks, and
compressors, purifiers are not included. The constraints on hydrogen network are
the overall mass balance and hydrogen mass balance. The proposed model can be
easily integrated with the consideration of practical constraints.
A nonlinear programming model is formulated to account for the mass balance of a
hydrogen distribution network. The important aspects related to the multi-period
hydrogen network include processes to be optimised (CPO), hydrogen sinks (SK)
and hydrogen source (SR), different types of (FD), multi-stage because of catalyst
deactivation (ST), hydrogen utility (HU). In the following mathematical model, the
Sink
(F
Sk
, y
Sk
)
Liquid feed
(F, y
i
)
Hydroprocesses
(T, P, Catalyst)
Source
(F
sr
, y
sr
)
Liquid Product
Separator
Recycle
(F
R
, y
R
)
Purge
(F
P
, y
P
)
Make-up
(FM, yM)
F
in
, y
H2,in
F
out
, y
H2,out
F
in
, y
H2,in
F
out
, y
H2,out
F
in
, y
i,in
F
out
, y
i,out
222
symbol with an over-bar represents a parameter, which value is fixed in the current
site-level optimisation, and may be different in different iterations, and a symbol
without an over-bar is a variable.
The objective function of site-level optimisation is the annualised overall profit.
( )
cat H t feed income
Ns
s
shutdown s
C C C C
L L
profit − − −
+
=
∑
=
2 cos
1
365
(6.15)
where L
s
is the run length of period s,
shutdown
L represents the duration for replacing
catalyst, Ns is the period number in one run. C
income
is the income of selling
products, C
feedcost
stands for the cost of the consumed feedstock, C
H2
is the
operating cost of hydrogen utility, and
cat
C is the catalyst cost for one run.
∑
∈
∆ + =
FD f
f s
L
f s s s
F L L
, , , 0
α
ST s ∈ ∀
(6.16)
∑
∈
=
ST s
s
P
s
P
income
L F c C (6.17)
∑ ∑
∈ ∈
=
ST s FD f
s
F
f s
F
f t feed
L F c C
, cos
(6.18)
∑
∈
=
ST s
s
H
s
H
H
L F c C
2 2
2
(6.19)
where
2
, ,
H F
f
P
c c c are the prices of product, feedstock f of CPO, and hydrogen
utility respectively.
F
f , s
P
s
F , F are the flowrates of product and feedstock f of CPO
respectively, given as:
∑
∈
∆ + =
FD f
f s
P
f s
P
s
P
s
F F F
, , , 0
α ST s ∈ ∀ (6.20)
f s
F
f s
F
f s
F F F
, , , 0 ,
∆ + = , ST s ∈ ∀ FD f ∈ ∀ (6.21)
∑
∈
=
SK j
s j u
H
s
F F
, ,
2
, ST s ∈ ∀ HU u ∈ ∀ (6.22)
223
where
P
s , 0
F is the product flowrate of CPO at stage s from the previous iteration.
P
f , s
α is the coefficient updated from the process optimisation.
f , s
F ∆ stands for the
change of feed f at stage s.
s , j , u
F is the hydrogen flowrate fed to hydrogen sink j
from hydrogen utility u at stage s.
As mentioned previously, the process models on the site level are simplified linear
correlations, which are derived from the process optimisation (explained later)
based on the rigorous models by using finite difference approximation. These
aspects include the period length, product yields, flowrate and hydrogen purity of
offgas, as well as the demand hydrogen flowrate.
Hydrogen distribution is constrained by overall hydrogen stream mass balance and
hydrogen mass balance. The overall mass balance on a hydrogen sink is as:
∑ ∑
∈ ∈
= +
SR i CPO ii
sink
j s j ii s j i
F F F
, , , ,
, ST s ∈ ∀ SK j ∈ ∀ (6.23)
∑ ∑
∈ ∈
= +
SR i CPO ii
sink
s jj s jj ii s jj i
F F F
, , , , ,
, ST s ∈ ∀ CPO jj ∈ ∀ (6.24)
where
s , jj , ii s , jj , i s , j , ii s , j , i
F , F , F , F all stand for the flowrates of hydrogen from the
sources i or ii to the sinks j or jj.
sink
j
F is the demand flowrate of hydrogen for sink
j which is fixed in all periods, and
sink
s , jj
F stands for the demand flowrate of
hydrogen of CPO in period s, which would be changed depending on the selected
feedstock and hydrogen purity.
By assuming the demand hydrogen quantity remains same for different hydrogen
purity, the flowrate of hydrogen stream is calculated as:
sink
s jj
sink
s jj
sink
s jj
sink
s jj
y
y F
F
,
, , 0 , , 0
,
= , ST s ∈ ∀ CPO jj ∈ ∀ (6.25)
where
sink
s , jj , 0
y is the hydrogen purity from the previous iteration, and
sink
s , jj
y is the
hydrogen purity (to be optimised) of CPO at stage s.
sink
s , jj , 0
F is the flowrate of
hydrogen if with
sink
s , jj , 0
y of the hydrogen purity for the change of feed as:
224
∑
∈
∆ + =
FD f
f s
H
f s
sink
s jj
sink
s jj
F F F
,
2
, , , 0 , , 0
α , ST s ∈ ∀ CPO jj ∈ ∀ (6.26)
where
sink
s , jj , 0
F is the result of flowrate of hydrogen stream from previous iteration,
and
2 H
f , s
α is the coefficient standing for the flowrate change of hydrogen stream
with feed f change at stage s of CPO.
Consequently, the purity of hydrogen sink is allowed to be changed leading to
another degree of freedom. The change of sink hydrogen purity will impact the
hydrogen purity of the offgas, which is also affected by changing feed.
∑
∈
∆ + ∆ + =
FD f
sink
s jj
Sr
s jj
Sk
s jj f s
y
f s
Sr
s jj
Sr
s jj
y
y
y F y y
, , 0
, , 0
, , , , , 0 ,
α , ST s ∈ ∀ CPO jj ∈ ∀
(6.27)
where
Sr
s , jj , 0
y is the hydrogen purity of offgas from the previous iteration,
y
f , s
α is
the coefficient that represents the impact of feed f change on the hydrogen purity of
offgas at stage s of CPO.
sink
s , jj , 0
sink
s , jj
Sk
s , jj
y y y − = ∆ , ST s ∈ ∀ CPO jj ∈ ∀ (6.28)
The hydrogen mass balance on sinks is described as:
∑ ∑
∈ ∈
= +
SR i
sink
j
sink
j
CPO ii
Sr
s ii s j ii
Sr
i s j i
y F y F y F
, , , , ,
, ST s ∈ ∀ SK j ∈ ∀
(6.29)
sink
s jj
sink
s jj
SR i
sink
s jj
sink
s jj
CPO ii
Sr
s ii s jj ii
Sr
i s jj i
y F y F y F y F
, , 0 , , 0 , , , , , , ,
= = +
∑ ∑
∈ ∈
, ST s ∈ ∀
CPO jj ∈ ∀ (6.30)
where
Sr
i
y is the hydrogen purity of the source i, which is fixed.
The overall mass balance on hydrogen sources is given as:
∑ ∑
∈ ∈
= + +
SK j CPO jj
Sr
i
Fuel
s i s jj i s j i
F F F F
, , , , ,
, ST s ∈ ∀ SR j ∈ ∀ (6.31)
225
∑ ∑
∈ ∈
= + +
SK j CPO jj
Sr
s , ii
Fuel
s , ii s , jj , ii s , j , ii
F F F F , ST s ∈ ∀ CPO ii ∈ ∀ (6.32)
where
Sr
i
F is the flowrate of hydrogen source i, which is fixed.
Fuel
s , i
F is the
flowrate from source i to fuel at stage s.
∑
∈
∆ + =
FD f
f s
Sr
f s
Sr
s ii
Sr
s ii
F F F
, , , , 0 ,
α , ST s ∈ ∀ CPO ii ∈ ∀ (6.33)
where
Sr
s , ii , 0
F is the offgas flowrate of CPO at stage s from the previous iteration,
Sr
f , s
α is the coefficient representing the effect of feed f change on the offgas flowrate
of CPO at the stage s.
Some practical constraints can be considered such as the capacity of processes, the
run length of process etc.
∑
∈
≤ ≤
FD f
Feed Feed
f , s
Feed
U F L ST s ∈ ∀ (6.34)
∑
∈
≤ ≤
ST s
run
s
run
U L L (6.35)
As discussed previously, the process model on the site-level optimisation is a
simplified linear model. These correlations could only be applied for a small
change of variables. Otherwise it could lead to big deviations from the reality.
Therefore, all independent variables are allowed to be changed in a certain range.
∑ ∑
∈ ∈
≤ ≤
fD f
Feed
f , s
U
f , s f , s
FD f
Feed
f , s
L
f , s
F F F β ∆ β ST s ∈ ∀ (6.36)
sink
s , ii
U
s
sink
s , ii
sink
s
L
s
y y y β ∆ β ≤ ≤ , ST s ∈ ∀ CPO ii ∈ ∀ (6.37)
The coefficient β is controlled depending on the previous iterations with a
maximum and minimal value. The way to update the bounds of variation follows:
• If
sink
s , ii f , s
y , F ∆ ∆ has changed sign from the last site-level optimisation and
the latest one is positive,
2 /
L
i
L
1 i
β β ←
+

226
• If
sink
s , ii f , s
y , F ∆ ∆ has changed sign from the last site-level optimisation and
the latest one is negative,
2 /
U
i
U
1 i
β β ←
+

• If
sink
s , ii f , s
y , F ∆ ∆ has touched the upper bound for the three consecutive
iterations,
U
i
U
1 i
2β β ←
+

• If
sink
s , ii f , s
y , F ∆ ∆ has touched the lower bound for the three consecutive
iterations,
L
i
L
1 i
2β β ←
+

6.4.4 Site Optimisation with Process Simulation
Since the site level uses the simplified correlations to model process operation, it is
expected to cause obvious errors to realistic results. Therefore, it is necessary to
combine a rigorous process simulation/optimisation with the site level
optimisation, which can correct these errors. The stage is named as stablisation. To
satisfy product specifications on process level, the process optimisation based on a
rigorous process model is needed. Then, hydrogen flowrate and reactor
temperature will be optimised to achieve the product specification. The main
feature in this stage is that the process optimisation is performed with the fixed
feed selection, and the site-level optimisation is with the fixed hydrogen purity.
What the site-level optimisation gets from the process-level optimisation is the
update of the simplified correlations. To simplify, the site-level optimisation in the
stabilisation is just a traditional hydrogen network distribution optimisation with
the fixed hydrogen source and purity, hydrogen sink and purity.
227

Figure 6.17 Site optimisation with process simulation/optimisation
The stabilisation is performed in an iterative procedure as Figure 6.17. To differ
the optimisation in different stages, site-level optimisation I represents site-level
optimisation with the allowable change on feed selection and hydrogen purity, and
site-level optimisation II stands for the traditional hydrogen network optimisation.
6.4.5 Integrated Site and Process Optimisation
The procedure of integrating site-level and process-level optimisation starts with a
base case, which is the current operation. Based on current feed selection, a small
deviation on different types of feed is performed. Then, a process optimisation is
performed to update the linear correlations for process model. Thereafter, the site-
level optimisation I is applied to optimise the hydrogen distribution network, and
simultaneously the feed selection and hydrogen purity of sinks, followed by
stabilisation step to correct the unrealistic errors. The new value of objective
function, as well as the feed selection and hydrogen purity is compared with the
Site-level
optimisation I
Process-level
optimisation
Update
P
s , ii , 0 s , 0
Sr
s , jj , 0
Sr
s , jj , 0
sink
s , jj , 0
F , L , F , y , F

Site-level optimisation II
ε ≤ dif
Stop
Yes
No
Stabilisation
228
previous one. If the difference between these two results is within the specified
tolerance, the procedure would terminate, otherwise, a new iteration will start.

Figure 6.18 Integration of hydrogen network and hydroprocesses
It is worthy to note about the feasibility of site-level optimisation. The optimal
hydrogen sinks (optimised from process-level optimisation) and the hydrogen
purity of sinks (from the previous site-level optimisation) possibly cannot be
satisfied by the available hydrogen sources. Therefore, to avoid the infeasibility of
hydrogen distribution network, one pure hydrogen source if without any hydrogen
utility in system and one zero hydrogen source (the hydrogen purity is zero) are
introduced. The penalty strategy is applied to make the site-level optimisation use
these two introduced hydrogen sources as little as possible.
6.4.6 Case Study
The case employed by Sun (2004) would be used to demonstrate the performance
of the proposed framework. The developed process level optimisation model of
diesel hydrotreater in Chapter 5 would be applied.
Base case
Coefficients update
Site-level optimisation
Stabilisation
ε ∆ ≤ obj

Stop
Yes
No
229
NHT HC
HDT
RHT
IS4
CCR
Fuel
CCR: Catalytic Cracking
Reformer
NHT: Naphtha Hydrotreater
RHT: Residue Hydrotreater
HC: Hydrocracker
HDT: Di esel hydrotreater
IS4 : Isomerisation process

Figure 6.19 The hydrogen network of the case (Sun, 2004)
Table 6.16 Calibrated data of hydrogen sinks (Sun, 2004)
Unit Flowrate (t/day) Purity (mass fraction)
NHT 3.108 0.2620
RHT 5.081 0.2624
HC 3.251 0.2624
ISOM 5.913 0.2596
CCR fuel 0.446 0.2624
Figure 6.19 shows the hydrogen network. There is only one hydrogen producer –
CCR, and five hydrogen consumers: NHT, RHT, HC, HDT, and IS4. The
calibrated data about hydrogen network is listed as Table 6.16 and Table 6.17,
which give the information about hydrogen sources and sinks respectively.
Table 6.17 Calibrated data of hydrogen sources (Sun, 2004)
Unit Flowrate (t/day) Purity (mass fraction)
CCR 13.73 0.2624
NHT 2.24 0.2857
RHT 4.95 0.2436
HC 3.16 0.2436
ISOM 4.58 0.2588
230
Due to the catalyst deactivation, the run cycle of DHT is divided into three stages,
and only temperature is increased to compensate the loss of activity of catalyst.
The throughput remains same along stages. Table 6.18 shows the related operating
conditions of DHT. Hydrogen surplus diagram of base case, which is current
operation, and balanced hydrogen surplus given as Figure 6.20 based on pinch
analysis, shows a positive surplus. The balanced hydrogen cascade diagram shows
that the pinch concentration is 0.2015, which corresponds to the DHT sink
concentration shown in Table 6.18. That means DHT is most likely to become the
bottleneck within the system. The overall profit of base case is 13.03 M$/yr.
Table 6.18 Operating conditions of DHT for base case
Stage Purity (wt) Sink flowrate(t/d) SRGO(t/d) Temperature(K)
S 0.2015 28.58 350 677.1
M 0.2015 28.58 350 687.5
E 0.2015 28.58 350 700.0
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Surplus
P
u
r
i
t
y

-

w
t

f
r
a
c
t
i
o
n
BASE CASE
BALANCED HYDROGEN SULPLUS

Figure 6.20 Hydrogen surplus diagram
To utilise hydrogen in system more efficiently, light cycle oil (LCO), cheaper than
SRGO, is allowed to be used as another feedstock of DHT but remaining the same
throughput. The hydrogen purity and flowrate fed to DHT, as well as operating
temperature can be changed to satisfy the product specification of the maximum
50wt ppm sulphur content. The proposed integration methodology is applied to
exploit the maximum profit, together with the developed rigorous model of DHT
on molecular level. Some practical constraints are given in Table 6.19.
231
Table 6.19 Constraints of operating conditions for DHT
Constraint Bound
Maximum reactor Temperature (K) 700
Minimum catalyst life(days) 300
Maximum product sulphur content (wtppm) 50
Table 6.20 Optimal operating conditions of diesel hydrotreater in each period
Stage Purity Flowrate SRGO LCO Temperature
S 0.155 94.062 90.4 259.6 700
M 0.192 101.267 133.4 216.6 700
E 0.236 78.785 215.1 134.9 700
The achieved overall profit is increased to 17.60 M$/yr, by 35.1% compared with
the profit of base case. The big increase in profit indicates that if the degrees of
freedom in the process level are exploited together with the degrees of freedom in
the site level, it provides significant synergy for economic improvement. The
optimal operating conditions for DHT are given in Table 6.20, which are quite
different from those of base case. The hydrogen purity is increased to compensate
the activity loss, and the operating temperatures reach the upper bound, which may
be because of the higher hydrogen consumption of aromatic hydrogenation
reactions and hydrodesulphurisation favoured by higher temperature.
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1 1.2
Surplus
p
u
r
i
t
y

-

w
t

f
r
a
c
t
i
o
n
Hydrogen surplus (S)
Hydrogen surplus (M)
Hydrogen surplus (E)

Figure 6.21 Hydrogen surplus diagrams of periods

232
The run cycle length of DHT is decreased dramatically from 707 to 339 days due
to higher operating temperature and higher aromatic contents of LCO. Cheaper
feedstock of LCO is blend as feedstock of DHT, which enhances the economic
performance. LCO blend ratio decreases along with the loss of catalyst activity
from 259 to 134 t/day. The hydrogen surplus diagrams of the optimal result in
three periods (Figure 6.21) all show that the hydrogen purity of DHT sink is the
pinch point, which means that hydrogen is utilised efficiently in each period.
6.5 Summary
Molecular modelling is firstly integrated into the two-level decomposition
optimisation approach (Zhang, 2000), and then the incorporated framework is
successfully applied in two exploitations, the interaction between material
processing network and refining processes, and the interaction between hydrogen
network and hydrogen consuming processes. With the integration of the process
and the site-level models, a better perspective is obtained with regard to material
processing system. By applying molecular modelling of the refining streams and
processes, the integrated approach not only controls the molecules in products
properly, but also increases the overall refinery performance.
In the second application, a novel framework for the integration of hydrogen
network with hydroprocesses is developed to target the maximum profit. It
allocates hydrogen on the hydrogen network level and utilise hydrogen efficiently
on the process level. The proposed methodology switches the objective from
saving hydrogen to improving the economic performance. Throughput could be
increased to make full use of hydrogen surplus, and cheaper feedstock could be
blended into feedstock of hydroprocesses to reduce the cost. The hydrogen purity
fed to hydroprocesses, which significantly impacts sulphur/nitrogen conversion,
throughput, and catalyst life, is optimised as well. The case study demonstrates that
the proposed methodology is capable of not only handling the complexity of non-
linearity of rigorous process models, but also improving the economic performance
greatly. Consequently, the extent of achieving the maximum profit could be fully
exploited with optimal hydrogen utilisation.
233
6.6 Nomenclature
6.6.1 Application I
List of sets
C crude oil
U, UU, UUU refining unit
S, SS refining stream
P refining products
K component represented by MTHS matrix
PP property of refining streams
UT utility
List of symbols
s , u , ss , c R yield coefficients representing that one unit of feed ss will produce
R amount of product s through process u from crude oil c
u , ss , uu , c
F mass flow from unit uu to unit u through stream ss from crude oil c
k , s , u , c
y composition of component k in the stream s produced by unit u
from crude oil c
k , s , u , ss , c
y composition of component k in the stream s produced by unit u
from the feedstock ss coming from crude oil c
c p
F , F flow rate of product p and crude oil c
p , s
Pt blending property p of stream s
k , s
y composition of component k in blending component s
u ut c p
C , C , C , C prices of product p, crude oil c, utility ut, and the operating cost of
unit u
6.6.2 Application II
List of sets
S stage of multi-period
CPO hydrogen consuming process to be optimised
P product
234
F feedstock
i hydrogen source
j hydrogen sink
u hydrogen utility
List of symbols
Ls run length of period s
shutdown
L
duration for replacing catalyst
Ns period number in one run
Cincome income of selling products
Cfeedcost cost of the consumed feedstock
CH2 operating cost of hydrogen utility
cat
C
catalyst cost for one run
2
, ,
H F
f
P
c c c
prices of product, feedstock f of CPO, and hydrogen utility
respectively.
F
f , s
P
s
F , F
flowrates of product and feedstock f of CPO respectively
P
s , 0
F product flowrate of CPO at stage s from the previous iteration
P
f , s
α coefficient updated from the process simulation/optimisation
f , s
F ∆ change of feed f at stage s
s , j , u
F hydrogen flowrate fed to hydrogen sink j from hydrogen utility u at
stage s
s , jj , ii s , jj , i s , j , ii s , j , i
F , F , F , F flowrates of hydrogen from the sources i or ii to the sinks j
or jj
sink
j
F demand flowrate of hydrogen for sink j which is fixed in all periods
sink
s , jj
F demand flowrate of hydrogen of CPO in period s
sink
s , jj , 0
y hydrogen purity from the previous iteration
sink
s , jj
y hydrogen purity to be optimised, of CPO at stage s
sink
s , jj , 0
F flowrate of hydrogen if with
sink
s , jj , 0
y of the hydrogen purity for the
change of feed
235
sink
s , jj , 0
F result of flowrate of hydrogen stream from previous iteration
2 H
f , s
α coefficient standing for the flowrate change of hydrogen stream
with feed f change at stage s of CPO
Sr
s , jj , 0
y hydrogen purity of offgas from the previous iteration
y
f , s
α coefficient that represents the impact of feed f change on the
hydrogen purity of offgas at stage s of CPO
Sr
i
y hydrogen purity of the source i, which is fixed
Sr
i
F flowrate of hydrogen source i, which is fixed
Fuel
s , i
F flowrate from source i to fuel at stage s
Sr
s , ii , 0
F offgas flowrate of CPO at stage s from the previous iteration
Sr
f , s
α coefficient representing the effect of feed f change on the offgas
flowrate of CPO at the stage s

236
Chapter 7 Conclusions and Future Work
7.1 Conclusions...........................................................................................237
7.2 Future Work ..........................................................................................239

237
7.1 Conclusions
In this work, four aspects of molecular management in oil refineries are
investigated respectively.
First of all, a novel methodology to characterise light and middle distillates into the
molecular level is developed on the basis of MTHS matrix framework. The method
comprises of the enhancements of both representation matrix construction and
transformation methodology of bulk properties into molecular composition. To
improve the accuracy and adequacy of the representation model, different
strategies are set up separately for light and middle distillates for the consideration
of isomers. By introducing statistical distribution and applying extensive bulk
properties, the transformation approach is revolutionised to increase the usability,
and tackle the challenge of possibly achieving significantly different molecular
compositions from the same bulk properties of refining streams by the existing
transformation approach.
Regarding molecular modelling of refining processes, gasoline blending, catalytic
reforming, and diesel hydrotreating are investigated in the representative of MTHS
matrix for feedstocks and products, together with the consideration of critical
issues related to each process. Based on the developed molecular models, process
level optimisation is also presented, which is integrated into overall refinery
optimisation.
On the modelling of gasoline blending processes, firstly a new methodology is
proposed to predict ON/RVP properties of blending components based on easily
obtainable properties. To tightly control the property giveaways in gasoline
blending, a molecular model of gasoline blending on PIONA lumps is developed
based on a detailed composition-based octane model, and then integrated into the
recipe optimisation. A case study demonstrates the economic improvement from
the tighter control on property giveaways compared with the conventional
approaches. The significance of this work is that the detailed property
consideration during optimisation helps to find better solutions and meet with the
238
product specifications more closely, and the proposed methodology can be
integrated into the overall site-level optimisation.
As for the molecular modelling of catalytic reforming, a rigorous molecular model
of a semiregenerative catalytic reforming process has been developed. Pressure
drop is taken into account due to the non-negligible cost for the power
consumption of compressing the recycle hydrogen gas. Composition, temperature
and pressure have been obtained to provide information about the extent of
conversion in the reactors. A case study demonstrates that the developed model is
capable of simulating the reactions in a catalytic reformer accurately. Furthermore,
sensitivity analysis of operating conditions exhibits different characteristics on the
process performances. Thereafter, a multi-period process level optimisation model
has been formulated with the consideration of catalyst deactivation, by correlating
coke yield with reaction rate. The optimisation model targeting different objectives
by varying the operating temperatures of the reactors in the periods is successfully
implemented by assuming the temperature profile follows a smooth function with
respect to time.
Regarding a diesel hydrotreater, firstly a molecular model of hydrotreating
reactions with a three-phase trickle-bed reactor has been developed. Structural
contribution approach is used to obtain kinetics and adsorption parameters. The
concept of reaction family is applied. A case study shows that the developed model
is capable of simulating the reactions in a diesel hydrotreater accurately.
Furthermore, a process level optimisation model is developed with the
consideration of catalyst deactivation in stages independent from each other. The
optimisation model targeting the minimum operating cost with production
specifications is successfully implemented. The developed model enhances the
possibility to explore the interactions between hydrotreaters and a hydrogen
network by the integration of the site and the process level optimisation.
After the build-up of the molecular models of individual refining processes and
streams, the overall refinery optimisation can be taken into account. Molecular
modelling is integrated into the two-level decomposition optimisation approach
(Zhang, 2000), and then the incorporated framework is applied in two aspects.
Firstly, with the integration of the process and the site level models, a better overall
239
perspective is obtained with regard to material processing system. Together with
molecular modelling of the refining streams and processes, the integrated approach
not only provides better controls over molecular flows in products properly, but
also increases the overall refinery performance. In the second application, a novel
framework to integrate hydrogen network with hydroprocesses is developed, which
allocates hydrogen at the hydrogen network level, and utilise hydrogen efficiently
at the process level. The proposed methodology targets improving the economic
performance, rather than saving hydrogen. Case studies illustrate that the
incorporated framework can help improve the overall refinery performance
significantly.
In summary, systematic molecular management is successfully implemented step
by step, which hence efficiently tackles the stricter environmental regulations, and
more importantly, enhances the refining profitability and competitiveness through
managing molecules effectively.
7.2 Future Work
The present work mainly focuses on molecular management of streams and
refining processes related to gasoline and diesel. There is still a massive to enhance
and expand the work done in this thesis, as a few outlined as follows.
First of all, as the basis of molecular management, the proposed methodology of
molecular characterisation need to be properly extended to heavier fractions, and
integrated to characterise a refining stream covering a broader list of properties. As
expected, the number of molecular species as well as the possible structural
arrangements in molecules increases exponentially as boiling point increases.
Therefore, the MTHS representative matrix could be modified based on boiling
point rather than carbon number for very heavy fractions due to the difficulties of
dealing with high carbon numbers for process modelling.
Secondly, in this work, although process modelling is constrained to the processes
handling gasoline and diesel streams, the methodology can be extended to other
refining processes. With the proper modelling of refining processes, they can be
applied in the overall refinery modelling at a molecular level to track the path of
240
each individual molecule as it is processed, which provides a better understanding
of a refinery configuration, and therefore the possibility to get the most value out
of any molecular species through proper process design and operation.
Last but not least, refinery optimisation can be done in many aspects. As a
molecule can be tracked as it is processes, the target of molecular management,
allocating the right molecule to be at the right place at the right time and at the
right price could be explored potentially. On the other hand, the integration of
utility systems into plant-wide operation can be investigated. In this work,
hydrogen management are incorporated with hydroprocessing processes to find
more opportunities of enhancing the economic performance. More opportunities
can be found with the consideration of energy system.
241
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258
Appendix A Joback Group Contribution
Table A.1 Joback group contribution for boiling point and Gibbs energy
Property tbk Gfk
Units K cal/mol
Group k
CH3(1) 23.58 -43.96
CH2(2) 22.88 8.42
CH(3) 21.74 58.36
C(4) 18.25 116.02
=CH2(1) 18.18 3.77
=CH(2) 24.96 48.53
=C(3) 24.14 92.36
=C=(2) 26.15 136.7
≡CH(1) 9.2 77.71
≡C(2) 27.38 109.82
CH2(ss)(2) 27.15 -3.68
CH(ss)(3) 21.78 40.99
C(ss)(4) 21.32 87.88
=CH(ds)(2) 26.73 11.3
=C(ds)(3) 31.01 54.05
NH2(1) 73.23 14.07
NH(2) 50.17 89.39
NH(ss)(2) 52.82 75.61
N(3) 11.74 163.16
=N-(2) 74.6 X
=N-(ds)(2) 57.55 79.93
=NH(1) X 119.66
SH(1) 63.56 -22.99
S(2) 68.78 33.12
S(ss)(2) 52.1 27.76
259
Appendix B Parameters of Kinetic Model of
Catalytic Reformer
Table B.1 Factors for pressure effect (Ancheyta, 1994)
Reaction k αk
isomerisation 0.370
dehydrocyclization -0.700
hydrocracking 0.433
hydrodealquilation 0.500
Table B.2 Activation energies for each reforming reaction (Henningsen, 1970)
Reaction j EAj(kcal/mol)
paraffins
Pn → Nn 45
Pn → Pn-I + Pi 55
naphthenes
Nn → An 30
Nn → Nn-I + Pi 55
Nn → Pn 45
aromatics
An → An-i + Pi 40
An → Pn 45
An → Nn 30




260
Table B.3 Kinetic constants of the model (Ancheyta, 2000)
Reaction step k reaction step k reaction step k
P11->N11 0.0356 P8->P4 0.007 N8->N7 + P1 0.0007
P10->N10 0.0243 P7->P6 + P1 0.0027 N11->A11 0.6738
P9->N9 0.05 P7->P5 + P2 0.0018 N10->A10 0.3198
P8->N8 0.0266 P7->P4 + P3 0.0043 N9->A9 0.2205
P7->N7 0.0076 P6->P5 + P1 0.0018 N8->A8 0.215
P6->N6 0 P6->P4 + P2 0.0016 N7->A7 0.0788
P6->MCP 0.0042 P6->2P3 0.0025 N6->A6 0.1368
P11->P10+P1 0.0075 P5->P4 + P1 0.0018 A11->P11 0.0016
P11->P9 + P2 0.01 P5->P3 + P2 0.0022 A10->P10 0.0016
P11->P8 + P3 0.0135 N11->P11 0.005 A9->P9 0.0016
P11->P7 + P4 0.0135 N10->P10 0.0054 A8->P8 0.0011
P11->P6 + P5 0.0191 N9->P9 0.0054 A7->P7 0.0016
P10->P9 + P1 0.0015 N8->P8 0.0025 A11->A10 +P1 0.0006
P10->P8 + P2 0.0054 N7->P7 0.0019 A11->A9 + P2 0.0006
P10->P7 + P3 0.016 N6->P6 0.0204 A10->A9 + P1 0.0006
P10->P6 + P4 0.0095 MCP->P6 0.0008 A1->A8 + P2 0.0006
P10->2P5 0.0095 N11->N10+P1 0.0134 A10->A7 + P3 0
P9->P8 + P1 0.003 N11->N9 + P2 0.0134 A9->A8 + P1 0.0005
P9->P7 + P2 0.0039 N11->N8 + P3 0.008 A9->A7 + P2 0.0005
P9->P6 + P3 0.0068 N10->N9 + P1 0.0134 A8->A7 + P1 0.0001
P9->P5 + P4 0.0058 N10->N8 + P2 0.0134 A6->N6 0.0015
P8->P7 + P1 0.0019 N10->N7 + P3 0.008 MCP->N6 0.0238
P8->P6 + P2 0.0056 N9->N8 + P1 0.0127 N6->MCP 0.004
P8->P5 + P3 0.0034 N9->N7 + P2 0.0127




261
Appendix C Parameters of Group
Contribution Approach
Table C.1 Numerical values for the structural contributions for (s)DBT at 573K
(Froment, 2004)
Hydrogenolysis Hydrogenation
310 . 0 ) 0 ; 0 ; 4 ( K
, ST
=
σ
04 . 1 ) 0 ; 0 ; (
,
=
+
m K
ST EL τ

238 . 0 ) 0 ; 6 ; 4 ( K
, ST
=
σ
11 . 1 ) 0 ; ; (
,
=
+
n m K
ST EL τ

588 . 0 ) 0 ; 0 ; 4 (
,
=
σ ST
k 05 . 6 ) 0 ; 0 ; (
,
=
+
m k
ST EL τ

050 . 0 ) 0 ; 6 ; 4 (
,
=
σ ST
k 07 . 6 ) 0 ; ; (
,
=
+
n m k
ST EL τ

000 . 1 ) ; ; (
,
= p n m k
EL σ

000 . 1 ) ; ; (
,
= p n m K
EL σ

The structural contributions approach also could be applied for benzothiophene. A
methyl substituent in position 2 and/or 7 decreases the hydrogenolysis rate with
respect to that of benzothiophene. This is due to the steric hindrance of the methyl
groups on the vertical adsorption through the sulphur atom and the surface reaction
between the adsorbed species on the σ-sites. A methyl group in position 2 is closer to
the sulphur atom than a methyl group in position 7; therefore its effect on the
hydrogenolysis rate is more pronounced than that of a methyl group in position 7.
Methyl substituents in positions 3, 4, 5, and/or 6 have almost no influence on the
hydrogenolysis rate compared to that of benzothiophene. The substituted
benzothiophenes the presence of methyl groups leads to a higher adsorption
equilibrium constant on the τ istes, regardless of their position. Furthermore, in
benzothiophenes with a methyl group in position 2, the C2-C3 bond, which is
hydrogenated before hydrogenolysis occurs, has a lower bond order than that in
benzothiophene.

262
Table C.2 Rate and adsorption parameters related to HDS of DBT (Froment, 2008)
Parameter Units
(
(
¸
(


¸

× −
× =
T R
k
gas
DBT
3
10
,
10 770 . 122
exp 10 44336 . 2
σ

kmol/kg
cat
h
(
(
¸
(


¸

×
× =
−
T R
K
gas
H
3
11
,
10 232 . 113
exp 10 36312 . 3
σ

m
3
/kmol
1
,
10 56868 . 7 × =
σ DBT
K
m
3
/kmol
(
(
¸
(


¸

× −
× =
T R
k
gas
DBT
3
16
,
10 190 . 186
exp 10 86757 . 2
τ

kmol/kg
cat
h
(
(
¸
(


¸

×
× =
−
T R
K
gas
H
3
15
,
10 693 . 142
exp 10 40255 . 1
τ

m
3
/kmol
(
(
¸
(


¸

×
× =
−
T R
K
gas
DBT
3
7
,
10 840 . 76
exp 10 50395 . 2
τ

m
3
/kmol
(
(
¸
(


¸

× =
−
T R
K
gas
S H
105670
exp 10 47118 . 1
8
, 2 σ

m
3
/kmol
This is also true for benzothiophenes with a methyl group in position 3. Methyl
groups in the positions 4, 5, 6 and/or 7 increase the hydrogenation rate compared to
that of benzothiophene. Based on these information, the structural constributions were
estimated as follows (Vanrysselberghe and Froment, 1998):
(
(
¸
(


¸

× = =
−
T R
K k m K m k f
gas
sBT
ST
sBT
ST
sBT
EL
sBT
EL
2745
exp 10 84047 . 3 ) 0 ; 0 ; 0 ; 2 ( ) 0 ; 0 ; 0 ; 2 ( ) 0 ; 0 ; 0 ; ( ) 0 ; 0 ; 0 ; (
2
, , , , , 2 σ σ σ σ σ
(
(
¸
(


¸

− × = = = = =
T R
m K m k f f f f
gas
sBT
EL
sBT
EL
17896
exp 10 81232 . 4 ) 0 ; 0 ; 0 ; ( ) 0 ; 0 ; 0 ; (
1
, , , 6 , 5 , 4 , 3 σ σ σ σ σ σ

(
(
¸
(


¸

× = =
−
T R
K k m K m k f
gas
sBT
ST
sBT
ST
sBT
EL
sBT
EL
17073
exp 10 20070 . 3 ) 0 ; 0 ; 0 ; 7 ( ) 0 ; 0 ; 0 ; 7 ( ) 0 ; 0 ; 0 ; ( ) 0 ; 0 ; 0 ; (
3
, , , , , 7 σ σ σ σ σ
(
(
¸
(


¸

− × = =
T R
K k m K m k f
gas
sBT
ST
sBT
ST
sBT
EL
sBT
EL
26327
exp 10 37053 . 8 ) 0 ; 0 ; 0 ; 2 ( ) 0 ; 0 ; 0 ; 2 ( ) 0 ; 0 ; 0 ; ( ) 0 ; 0 ; 0 ; (
1
, , , , , 2 τ τ τ τ τ
263
(
(
¸
(


¸

− × = =
T R
K k m K m k f
gas
sBT
ST
sBT
ST
sBT
EL
sBT
EL
9932
exp 10 33432 . 2 ) 0 ; 0 ; 0 ; 3 ( ) 0 ; 0 ; 0 ; 3 ( ) 0 ; 0 ; 0 ; ( ) 0 ; 0 ; 0 ; (
0
, , , , , 3 τ τ τ τ τ
(
(
¸
(


¸

− × = = = = =
T R
m K m k f f f f
gas
sBT
EL
sBT
EL
9903
exp 10 24161 . 1 ) 0 ; 0 ; 0 ; ( ) 0 ; 0 ; 0 ; (
1
, , , 7 , 6 , 5 , 4 τ τ τ τ τ τ

As for the adsorption equilibrium constants for P, N, A, AA and AN are assumed as
zero, which is confirmed by Froment (Froment, 1998).
264
Appendix D Physical Properties Calculation
In terms of the calculation of heat capacity of pure real compounds, procedure 7D3.6
(1997) from American Petroleum Institute (API) technical data book is successfully
applied. The equation to be used is
(
(
¸
(


¸

|
|
¹
|


\
|
−
−
|
|
¹
|


\
|
−
+
|
|
¹
|


\
|
−
=
|
|
¹
|


\
|
−
) 0 (
0
) (
0
) (
) 0 (
0 0
~ ~ ~ ~ ~ ~ ~ ~
R
C C
R
C C
R
C C
R
C C
p p
h
p p
h
p p p p
ω
ω
(D.1)
where:
|
|
¹
|


\
|
−
R
C C
p p
~ ~
0
= the dimensionless effect of pressure on isobaric heat capacity;
) 0 (
0
~ ~
|
|
¹
|


\
|
−
R
C C
p p
= effect of pressure on the isobaric heat capacity for the simple fluid, to
be calculated from Equation D.2
) (
0
~ ~
h
p p
R
C C
|
|
¹
|


\
|
−
= effect of pressure on the isobaric heat capacity for the heavy reference
fluid, to be calculated from Equation D.2.
ω
= acentric factor of the compound for which the pressure effect on isobaric heat
capacity is sought
) (h
ω
= acentric factor of the heavy reference fluid = 0.3978
The dimensionless effect of pressure on the isobaric heat capacity of the simple and
heavy fluid is to be calculated from the following equations:
265
) (
2
) (
0 ~
1
~ ~ i
V
Tr
r
r
Vr
r
r
r
i
p p
R
C
V
p
T
p
T
R
C C
|
|
¹
|


\
|
∆
+
|
|
¹
|


\
|
∂
∂
|
|
¹
|


\
|
∂
∂
+ =
|
|
¹
|


\
|
−
(D.2)
Where
¦
)
¦
`
¹
¦
¹
¦
´
¦
(
(
¸
(


¸

|
|
¹
|


\
|
−
|
|
¹
|


\
|
+ − +
−
+
+ +
+ =
|
|
¹
|


\
|
∂
∂
2 2 2 3
4
5
1
2
3
3 1
3
4
2
3 1
exp
2 / 2 / 2 /
1
1
r r v r r r
r
r
r r
r
Vr
r
r
V V V T
c
V
d
V
T c c
V
T b T b b
V T
p γ γ
β
¦
)
¦
`
¹
¦
¹
¦
´
¦
|
|
¹
|


\
|
−
|
|
¹
|


\
|
¦
)
¦
`
¹
¦
¹
¦
´
¦
|
|
¹
|


\
|
+ − + + + + + − =
|
|
¹
|


\
|
∂
∂
2 2 2 2 3
4
5 2 2
exp 2 5 3
6 3 2
1
r r r r r r r r r
r
Tr
r
r
V V V V T
c
V
D
V
C
V
B
V
T
V
p γ γ γ
β β
) (
0
) (
~ ~ ~
i
V V
i
V
R
C C
R
C
|
|
¹
|


\
|
−
=
|
|
¹
|


\
|
∆
which can be calculated by the following equations.
(
(
¸
(


¸

|
|
¹
|


\
|
−
−
|
|
¹
|


\
|
−
+
|
|
¹
|


\
|
−
=
|
|
¹
|


\
|
−
) 0 (
0
) (
0
) (
) 0 (
0 0
~ ~ ~ ~ ~ ~ ~ ~
R
C C
R
C C
R
C C
R
C C
V V
h
V V
h
V V V V
ω
ω
(D.3)
The effect of pressure on the isochoric heat capacity for the simple and heavy fluid
can be calculated by Equation D.4.
( )
¦
)
¦
`
¹
¦
¹
¦
´
¦
|
|
¹
|


\
|
−
|
|
¹
|


\
|
+ + − + + +
+
− =
|
|
¹
|


\
|
−
2 2 3
4
2 3
3
2
4 3
) (
0
exp 1 1
2
6
3 / 3 2
~ ~
r r r r r r r
r
i
V V
V V T
c
V T
c
V T
T b b
R
C C γ γ
β β
γ
(D.4)
In those equations,
C r
T T T = is the reduced temperature,
c C r
RT V p V = is obtained
by solving Equation D.5.
|
|
¹
|


\
|
−
|
|
¹
|


\
|
+ + + + + =
2 2 2 3
4
5 2
exp 1
r r r r r r r r
r r
V V V T
c
V
D
V
C
V
B
T
V p γ γ
β (D.5)
Where
C r
p p p = = the reduced pressure,
3
4
2
3 2 1
/ / /
r r r
T b T b T b b B − − − = ,
3
3 2 1
/ /
r r
T c T c c C + − = ,
r
T d d D /
2 1
+ = .
266
Two sets of constants are given below, one for the simple fluid, and the other for
heavy reference fluid.
Table D.1 Constants for the simple and heavy reference fluid
Constant Simple fluid Heavy reference fluid
b
1
0.1181193 0.2026579
b
2
0.265728 0.331511
b
3
0.154790 0.027655
b
4
0.030323 0.203488
C
1
0.0236744 0.0313385
c
2
0.0186984 0.0503618
C
3
0.0 0.016901
C
4
0.042724 0.041577
4
1
10 × d
0.155488 0.48736
4
2
10 × d
0.623689 0.0740336
β 0.65392 1.266
γ
0.060167 0.03754
Equation D.5 is solved iteratively for Vr. The problem is that without a proper bound
and initial guess on Vr, the iterative procedure always fails to find the solution. In
order to get a proper bound, a Lee-kesler table (Lee and Kesler, 1975) is successfully
applied combining a bisection method to find the solution.
Chung (1988) developed an empirically correlated function of density and
temperature for viscosity of dense fluids as Equation D.6.
p
µ µ µ
κ
+ = (D.6)
Where
(
¸
(

¸

+ = Y A
G
6
2
0
1
µ µ
κ

( )
|
¹
|

\
|
+ +
(
(
¸
(


¸

× =
−
2 *
10
*
9
8 2
2
7
3 / 2
2 / 1
6
exp 10 344 . 36
T
A
T
A
A G Y A
V
MT
C
C
p
µ
267
( )
C
C
F
V
MT
* 3 / 2
2 / 1
5
0
10 0785 . 4
Ω
× =
−
µ
ω 2756 . 0 1− =
C
F
( )
( ) H ST GT
FT
E
DT
C
T
A
W B
B
− + + + = Ω
* *
* * *
*
sin
) exp( exp

4
10 435 . 6 , 43787 . 2 , 16178 . 2 , 77320 . 0 , 52487 . 0 , 14874 . 0 , 16145 . 1
−
× − = = = = = = = G F E D C B A
76830 . 0 , 0323 . 18 , 27371 . 7 − = = = W S H
C
T
T
T
2593 . 1
*
=
6
C
V
Y
ρ
=
( )
3
1
1
5 . 0 0 . 1
Y
Y
G
−
−
=
( ) [ ] ( ) { }
3 2 4 1
1 3 5 1 2 4 1
2
exp / exp 1
A A A A
G A Y A G A Y Y A A
G
+ +
+ + − −
=
ω ) ( ) (
1 0
i a i a A
i
+ =
Table D.2 Constants used for the generalised viscosity correlation
i
) (
0
i a ) (
1
i a
1 6.32402 50.41190
2
2
10 12102 . 0
−
×
-0.0011536
3 5.28346 254.20900
4 6.62263 38.09570
5 19.74540 7.63034
6 -1.89992 -12.53670
7 24.27450 3.44945
8 0.79716 1.11764
9 -0.23816 0.067695
10 0.068629 0.34793
The same approach was employed by Chung (1988) to develop the thermal
conductivities of pure fluids and mixtures. The equation is an empirically correlated
function as Equation D.7.
268
p
k k k + =
κ
(D.7)
Where
(
¸
(

¸

+ = Y B
H
k k
6
2
0
1
κ

Ψ =
M
k
0
0
452 . 7
µ

αβ β
β α
α
061 . 1 6366 . 0
26665 . 0 0161 . 1 28288 . 0 215 . 0
1
+ +
+ − +
+ = Ψ
Z
Z

2
3
0
− =
R
C
V
α
2
3168 . 1 7109 . 0 7862 . 0 ω ω β + − =
2
5 . 10 0 . 2
r
T Z + =
R C C
p V
− =
( )
2 / 1
2
2
7
3 / 2
2 / 1
4
10 039 . 3
r
C
p
T H Y B
V
M Tc
k
−
× =
( ) [ ]
3 2 4 1
1 3 5 1 2 4 1
2
) exp( exp 1
B B B B
G B Y B G B Y Y B B
H
+ +
+ + − −
=
ω ) ( ) (
1 0
i b i b B
i
+ =
b
0
, b
i
are given in Table D.3.
Table D.3 Constants used for the generalised correlation for thermal conductivity
i
) (
0
i b ) (
1
i b
1 2.41657 0.74824
2 -0.50924 -1.50936
3 6.61069 5.62073
4 14.54250 -8.91387
5 0.79274 0.82019
6 -5.86340 12.80050
7 81.17100 114.15800
269
It is necessary to know the molecular diffusivity
L
i
D in the liquid which would be
used to calculate the mass transfer coefficients. Assuming infinite dilution, the
diffusivity can be estimated by a Tyn-Calus correlation (Reid et al., 1987) as equation
D.8.
L i
L L
i
T
v
v
D
µ
433 . 0
267 . 0
8
10 93 . 8
−
× = (D.8)
Gas-liquid mass transfer coefficient is the function of the liquid superficial mass flow
velocity.
L
G . For its determination, the correlation developed by Goto and Smith
(1975) is used as Equation D.9.
2 / 1 4 . 0
7
|
|
¹
|


\
|
|
|
¹
|


\
|
=
L
i L
L
L
L
L
i
L L
D
G
D
a K
ρ
µ
µ
(D.9)
The liquid-solid mass transfer in the low interaction regime can be estimated by the
van Krevelen-Krekels equation (1948) as Equation D.10.
3 / 1 2 / 1
8 . 1
|
|
¹
|


\
|
|
|
¹
|


\
|
=
L
i L
L
L s
L
s
L
i
S
D a
G
a D
k
ρ
µ
µ
(D.10)
Where
s
a is the specific surface area of the packing.
) 1 (
6
ε − =
p
s
d
a (D.11)
where
p
d is the equivalent particle diameter, and ε is the void fraction of the catalyst
bed.
By postulating that “the ratio of the momentum lost by skin friction between two
sections a differential distance apart to the total momentum of the fluid will be the
same as the ratio of the heat actually supplied by the surface to that which would have
been supplied if the whole of the fluid had been carried up to the surface”, Chilton
and Colburn (1934) developed an equation to correlate the mass and heat transfer
coefficients as Equation D.12.
270
|
|
¹
|


\
|
= =
|
|
¹
|


\
|
=
k
C
u C
h
J
D u
K
J
p
p
L
H
e
L
D
µ
ρ ρ
µ
3 / 2
(D.12)


271
Appendix E Boundary Value Problem
As for boundary value problem, an approximate method – orthogonal collocation
method is applied to solve the ordinary differential equations. Orthogonal collocation
method is one of methods of weighted residuals (Rice, 1995). The method of
weighted residuals has been used in solving a variety of boundary value problems,
ranging from fluid flow to heat and mass transfer problems. It is popular because of
the interactive nature of the first step, that is, the user provides a first guess at the
solution and this is then forced to satisfy the governing equations along with the
conditions imposed at the boundaries. The left-over terms, called residuals, arise
because the chosen form of solution does not exactly satisfy either the equation or the
boundary conditions. How these residual terms are minimized provides the basis for
parameter or function selection. Of course, the optimum solution depends on the
intelligent selection of a proposed solution.
∫
V
k
dx x w x R Min ) ( ) ( (E.1)
The residual R is in general nonzero over the whole domain of interest, so that it will
be dependent on x, in the usual case. V is the domain of interest, and w
k
is some
selected set of independent functions, which are called the test functions. Various
methods of weighted residuals differ selecting the test functions. The collocation
method use the Dirac delta function (Equation E.2) at N interior points (called
collocation points) within the domain of interest.
) (
k k
x x w − = δ (E.2)
where δ is the trial function,
k
x is the kth collocation point.
The full potential of the collocation method can only be realised by judicious
selection of the collocation points. Moreover, the choice of functions is critical.
272
orthogonal functions, such as Jacobi polynomials, are particularly attractive, since
they are compact and contain only a few terms. If these N interior collocation points
are chosen as roots of an orthogonal Jacobi polynomial of Nth degree, the method is
called the orthogonal collocation method.
The Jacobi polynomial of degree N has the power series representation
∑
=
−
− =
N
i
i
i N
i N
N
x x J
0
,
) , (
) 1 ( ) ( γ
β α
(E.3)
Here,
i N,
γ are constant coefficients, and α and β are parameters characterising the
polynomials.
) , ( β α
N
J is the polynomial orthogonal with respect to the weighting
function
α β
) 1 ( x x − .
The explicit solution for γ is as follows:
( ) ) 1 ( ) 1 (
) 1 ( ) 1 (
! !
!
,
+ + Γ + + + Γ
+ Γ + + + + Γ
−
=
β β α
β β α
γ
i N
i N
i N i
N
i N
(E.4)
To obtain the roots of Jacobi polynomial, which are collocation points, Newton-
Raphson method is applied to solve the equations iteratively.
After obtaining the collocation points, an interpolation polynomial as Equation E.5 is
used to calculate the corresponding y value at x point by assuming an unknown data
set.
∑
+
=
=
1
1
) ( ) (
N
i
i i N
x l y x y (E.5)
Where
N
y is the N degree polynomial,
i
y is the value at point
i
x , and ) (x l
i
is called
the Largrange interpolation polynomial as Equation E.6.
∏
+
≠
=
−
−
=
1
1
) (
N
i j
j j i
j
i
x x
x x
x l (E.6)
Then the first and second derivates of the interpolation polynomial at the interpolation
points are as Equations E.7 and E.8.
273
∑
+
=
=
1
1
) (
) (
N
j
i
i j
i N
y
dx
x dl
dx
x dy
(E.7)
∑
+
=
=
1
1
2
2
2
2
) (
) (
N
j
i j
i N
dx
x l d
dx
x y d
(E.8)
The function vector is defined as values of y at N + 1 collocation points as
T
N N
y y y y y y ] , ,..., , , [
1 3 2 1 +
= (E.9)
The first and second derivate vectors can be written in terms of the function vector y
using matrix notation
y A y ⋅ =
'
(E.10)
y B y ⋅ =
"
(E.11)
where
)
`
¹
¹
´
¦
+ = = = 1 , ,... 2 , 1 , ;
) (
N N j i
dx
x dl
a A
i j
ij
(E.12)
¦
)
¦
`
¹
¦
¹
¦
´
¦
+ = = = 1 , ,..., 2 , 1 , ;
) (
2
2
N N j i
dx
x l d
b B
i j
ij
(E.13)
By applying the orthogonal collocation method, Equation 5.31 is converted into a set
of equations in terms of collocation points as Equation E.14.
0 ) ( 6 4 ) (
2
1
1 ,
1
1 ,
= −
(
¸
(

¸

+ +
(
¸
(

¸

+ =
∑ ∑
=
+
=
+ i
N
j
N i j ij
N
j
N i j ij i i
y G a y a b y b u y F φ (E.14)
where:
2
|
¹
|

\
|
=
R
x
u
i
i

S
i
i
C
x C
y
) (
=
274
[ ]
∑
=
=
Nr
k
S k
S e
s
C r m k S
C D
R
1
2
2
) ( ,
ρ
φ
The Newton-Raphson method is applied to solve these equations iteratively to obtain
the concentration profile in a catalyst particle.
Quadrature defines the process of expressing the continuous integral as an
approximate sum of terms as Equation E.15.
∫
∑
=
≈
N
k
k k
x f w dx x f x W
1
) ( ) ( ) ( (E.15)
Effectiveness factor defined as Equation 5.34 is calculated by the Guass-Jacobi
quadrature technique (1995) as Equation E.16.
∫
∑
+
=
= =
1
0
1
1
0 0
) (
) ( 2
3
) (
) ( 2
3
N
k
k k i
C r w
C r
du u C r
C r
η (E.16)
where:
∫
− =
1
0
0 2 / 1
) ( ) 1 ( du u l u u w
k k

∑
=
=
N
k
k k
u l C r C r
1
) ( ) ( ) (
k
w can be obtained using the properties of the Lagrangian interpolation polynomials.

275
Appendix F RFCC Model
This RFCC model is developed based on the FCC model published by HPI
Consultants, Inc. The RFCC model takes into account the influence of an additional
feed property – Conradson Carbon Residue, apart from the other properties that have
already been considered in HPI correlations. The new model is then regressed using
unpublished industrial data.

Data requirement
Conversion level, LV% C
Feed specific gravity, 60°F/60°F SG
f

Feed API gravity API
f

Feed volumetric average boiling point, °F VABP
f

Feed aniline point, °F AP
f

Feed sulphur content, wt% S
f

Feed characterisation factor K
f

Feed Conradson carbon residue content, wt% CCR
f


RFCC model
Feed quality parameter
f f f f f f
CCR SG AP AP S VABP FQP 15 . 0 / 26 . 0 6 . 0 9 . 0 065 . 0 70 − − + − − =
276
Yield of C3 to 400°F product, LV%
) ) 100 / ( 762 . 0 100 / 82 . 1 0667 . 0 )( 0076 . 0 88 . 1 6 . 25 ( 400 _ 3
2 2
FQP FQP C C C − + − + − =
Ratio of C5/400°F to C3/400°F
f
2
CCR 015 . 0 ) 100 / FQP ( 738 . 0 100 / FQP 628 . 0 713 . 0 RGASO − − + =
Gasoline yield, LV%
400 _ 3 C * RGASO GASOV =
LPG yield, LV%
GASOV 400 _ 3 C LPG − =
Ratio of C4 LPG to C3 LPG
2
) 100 / FQP ( 611 . 0 100 / FQP 272 . 0 879 . 1 3 C _ 4 RC − + =
C3 LPG yield, LV%
) 1 3 C _ 4 RC ( LPG 3 C + =
C4 LPG yield, LV%
3 C LPG 4 C − =
Ratio of propylene to total C3 LPG
5864 . 0 FQP 001425 . 0 3 C _ RC
3
+ =
=

Propylene yield, LV%
3 * 3 _
3 3
C C RC C
= =
=
Propane yield, LV%
=
− =
3
3 3 C C nC
Ratio of butylenes in C4
3573 0 FQP 001775 0 4 C RC
4
. . _ + =
=

277
Butylene yield, LV%
4 C RC 4 C C
4 4
_ *
= =
=
Normal butane yield, LV%
4 C 125 0 4 nC * . =
Isobutane yield, LV%
4 4 4
4
nC C C iC − − =
=

Coke and fuel gas yield, wt%
2158 0 FQP C 462 2 FG Coke . / * . ) _ ln( − =
Ratio of coke yield to the yield of coke plus fuel gas
2
100 FQP 556 0 100 FQP 441 0 766 0 C 000978 0 RCoke ) / ( . / . . * . − + + − =
Coke yield, wt%
RCoke FG Coke Coke * _ =
Fuel gas yield, wt%
Coke FG Coke FG − = _
Ratio of H2S yield to feed sulphur
76 0 FQP 005075 0 S RH
2
. . + − =
H2S yield, wt%
f 2 2
S S RH S H * =
API gravity of gasoline
2 2
g
100 FQP 6 35 100 FQP 2 31 100 C 33 9 100 C 5 15 84 66 API ) / ( . ) / ( . ) / ( . / * . . + − + − =
Specific gravity of gasoline
) . /( .
g g
API 5 131 5 141 SG + =
278
Gasoline yield, wt%
f g
SG GASOV SG GASOW / * =
Total cycle oil yield, LV%
C 100 TCOV − =
Ratio of heavy cycle oil to total cycle oil
f
2
f f
S 10 K 003 0 K 053 0 931 0 RHCO ) ( . . . − + − =
Heavy cycle oil yield, LV%
RHCO TCOV HCOV * =
Light cycle oil yield, LV%
HCOV TCOV LCOV − =
Weight factor for total cycle oil
) ) 100 / ( 22 . 2 100 / * 66 . 1 804 . 0 )( ) 100 / ( 25 . 3 100 / * 5 . 6 4 . 1 (
2 2
FQP FQP C C WF − + − + − =

Weight yield of total cycle oil
WF TCOV TCOW + =
Gravity factor for light cycle oil
FQP 111 0 C 1185 0 6919 10 FQP C 000965 0 LCOGF . * . . * * . ) ln( + + − − =
Light cycle oil API gravity
LCOGF API API
f lco
− =
Light cycle oil specific gravity
) . /( .
lco lco
API 5 131 5 141 SG + =
Light cycle oil yield, wt%
f lco
SG LCOV SG LCOW / * =
279
Heavy cycle oil yield, wt%
LCOW TCOW HCOW − =
Heavy cycle oil specific gravity
HCOV HCOW SG SG
f hco
/ * =
Sulphur in gasoline, wt%
GASOW S 5 5 S
f g
/ . =
Sulphur in light cycle oil, wt%
LCOW S 21 S
f lco
/ =
Sulphur in heavy cycle oil, wt%
HCOW S 21 S
f hco
/ =
Sulphur in coke, wt%
Coke HCOW S LCOW S GASOW S S H 12 94 S 100 S
hco lco g 2 f coke
/ ) * * * . ( − − − − =
Research octane number of gasoline
3 101 FQP 187 0 C 0384 0 FQP C 00139 0 RON . . . * . + − − =
Motor octane number of gasoline
5 9 RON 778 0 MON . . + =
Reid vapour pressure of gasoline, psia
f f
S 3 0 K 5 2 8 23 RVP . . . + + − =
Aniline point of light cycle oil, °F
lco lco
API 34 4 AP . =
Aniline point of heavy cycle oil, °F
86 API 65 4 AP
hco hco
+ = .