LOW DENSITY POLYETHYLENE GRADE TRANSITION CONTROL USING NEURAL WIENER MODEL PREDICTIVE CONTROL WITH SOFT SENSOR

LOW DENSITY POLYETHYLENE GRADE
TRANSITION CONTROL USING NEURAL
WIENER MODEL PREDICTIVE CONTROL

WITH SOFT SENSOR

DINIE BIN MUHAMMAD

UNIVERSITI SAINS MALAYSIA
2021

LOW DENSITY POLYETHYLENE GRADE
TRANSITION CONTROL USING NEURAL
WIENER MODEL PREDICTIVE CONTROL

WITH SOFT SENSOR

by

DINIE BIN MUHAMMAD

Thesis submitted in fulfillment of the requirements
for the degree of

Doctor of Philosophy

AUGUST 2021

ACKNOWLEDGEMENT

In the name of Allah, the Most Beneficent and the Most Merciful.

All praises are due to Almighty Allah, The Cherisher, and The Sustainer of the world.
Blessings and greetings of peace upon the prophet Muhammad (peace be upon him), his
families, companions, and followers. Praise be to Allah, who has bestowed His blessings,
guidance, and strength for me to complete this thesis successfully.

This PhD journey has been a great life experience for me. There are certain times
that I began to question myself, why am I doing this, how am I going to do this, and can I
able to finish this? Alhamdulillah, I was surrounded by many good people that helped and
motivated me along the way. Thus, it is fair that I took this small opportunity to thank
them.

Foremost, sincere thanks to my supervisor, AP Dr Norashid bin Aziz and co-
supervisor, Prof Ir Dr Zainal bin Ahmad for their guidance and comments in completing
my study. Thank you to Dr Fakhrony and Dr Sudibyo for their meaningful feedback and
comments to improve my work. My humble gratitude to my fellow research mates, Ashraf,
Nazaruddin, and Rasheed for always there to discuss and help me whenever I needed.
Special thanks to PETRONAS Chemicals LDPE process team, Madam Nora, Mr Fadzil,
Ms. Norfadhillah and Mr Aleh for sharing their expertise and knowledge in terms of LDPE
production in Kerteh, Terengganu.

My deepest gratitude for my beloved parents, Muhammad bin Awang and Azni
binti Che Ngah, for their unconditional love for their eldest son. Thank you, my dearest
wife, Noor Izah binti Shoparwe for your love, care, and support during my hard time
completing my study. Thank you for understanding my situation and help me along the

ii

way. Thank you to my lovely kids, Alif and Aqil, who may still not old enough to
understand why their dad is always busy but still managed to bear with it.

To my cherished friends: Imam, Nizam, Kak Fazliani, Kak Syura, Junaidi,
Hazwani, Noraini, Fadzil, Norazwan, Muaz, Tariq, Ihsan, Afiq, Izzudin, Muhammad,
Mahmood, Chamanti, Jackson, and anyone that has assisted and supported me for the past
years, thank you very much for your help. Without you, I would not have been here today.

Special acknowledgment to the Ministry of Higher Education (MOHE) and
Universiti Teknologi Mara (UiTM) under Tenaga Pengajar Muda (TPM) program for
sponsoring my study in USM. Thank you all. May Allah bless us all and grant us success
in this life and hereafter.

Dinie Muhammad
25th Zulhijjah 1442H / 4th August 2021

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENT......................................................................................... ii
TABLE OF CONTENTS.......................................................................................... iv
LIST OF TABLES .................................................................................................... ix
LIST OF FIGURES ................................................................................................... x
LIST OF SYMBOLS .............................................................................................. xvi
LIST OF ABBREVIATIONS .............................................................................. xviii
LIST OF APPENDICES ......................................................................................... xx
ABSTRAK ............................................................................................................... xxi
ABSTRACT ........................................................................................................... xxiii
CHAPTER 1 INTRODUCTION.......................................................................... 1
1.1 Research Background....................................................................................... 1
1.2 Problem Statement ........................................................................................... 2
1.3 Research Objectives ......................................................................................... 5
1.4 Scope of study .................................................................................................. 6
1.5 Thesis Outline .................................................................................................. 7
CHAPTER 2 LITERATURE REVIEW.............................................................. 9
2.1 LDPE production.............................................................................................. 9
2.2 LDPE polymerization..................................................................................... 14

2.2.1 Initiation ........................................................................................ 14
2.2.2 Propagation.................................................................................... 15
2.2.3 Termination ................................................................................... 15
2.2.4 Chain transfer ................................................................................ 16
2.3 LDPE process simulation ............................................................................... 19
2.4 LDPE tubular reactor control ......................................................................... 22
2.4.1 LDPE Control Scheme .................................................................. 23

iv

2.4.2 Process model................................................................................ 32
2.4.3 Soft sensor ..................................................................................... 35
2.5 Summary of review ........................................................................................ 39
CHAPTER 3 METHODOLOGY....................................................................... 41
3.1 Research Outline ............................................................................................ 41
3.2 Development of steady state model using Aspen Plus................................... 42
3.2.1 Tubular reactor model ................................................................... 43
3.2.2 Equation of State (EOS)................................................................ 45
3.2.3 Heat of Polymerization.................................................................. 47
3.2.4 Process flowsheet .......................................................................... 48
3.2.5 Heat Transfer Coefficient (HTC) .................................................. 49
3.2.6 Polymerization Mechanisms ......................................................... 49
3.2.7 Kinetic Parameters ........................................................................ 50
3.3 Dynamic model .............................................................................................. 52
3.4 MFI model...................................................................................................... 53
3.5 Model Analysis .............................................................................................. 54
3.5.1 Parametric Analysis....................................................................... 54
3.5.2 Degree of nonlinearity................................................................... 55

3.5.2(a) Asymmetric response.................................................... 56
3.5.2(b) Harmonic response ....................................................... 56
3.5.2(c) Input and Output multiplicity ....................................... 56
3.5.3 Nonlinearity Index (NLI) .............................................................. 57
3.6 Development of Neural Wiener MPC ............................................................ 58
3.6.1 Control structure............................................................................ 61
3.6.2 Neural Wiener Model.................................................................... 61
3.6.2(a) Model I/O selection ...................................................... 62
3.6.2(b) Data generation ............................................................. 62

v

3.6.2(c) Model structure............................................................. 63
3.6.2(d) Model identification...................................................... 64
3.6.3 Optimizer....................................................................................... 67
3.6.4 MPC Tuning.................................................................................. 68
3.6.5 Integrate with Aspen Dynamic...................................................... 70
3.7 Development of soft sensor............................................................................ 71
3.7.1 Soft sensor modeling..................................................................... 71
3.7.1(a) Input Selection .............................................................. 72
3.7.1(b) Training method............................................................ 74
3.7.2 Soft sensor scheme ........................................................................ 75
3.8 Controller performance test............................................................................ 77
3.8.1 Grade transition ............................................................................. 77
3.8.2 Conversion change ........................................................................ 79
3.8.3 Disturbance Rejection ................................................................... 80
3.8.3(a) Feed stream pressure loss ............................................. 81
3.8.3(b) Reduced feed stream flow rate ..................................... 81
3.8.3(c) Reduced ethylene gas feed purity ................................. 81
3.8.4 Robustness Test............................................................................. 82
3.8.4(a) Fouling.......................................................................... 82
3.8.4(b) Heat of polymerization ................................................. 83
3.8.4(c) Initiator efficiency ........................................................ 83
3.9 Performance criteria ....................................................................................... 83
CHAPTER 4 RESULTS AND DISCUSSION................................................... 85
4.1 Aspen Plus simulation results and validation................................................. 85
4.1.1 LDPE MFI grades ......................................................................... 88
4.2 Model analysis results .................................................................................... 89
4.2.1 Parametric study results ................................................................ 89

vi

4.2.1(a) Effect of Initiator 1 (TBPPI)......................................... 89
4.2.1(b) Effect of Initiator 2 (TBPIN) ........................................ 94
4.2.1(c) Effect of Chain Transfer Agent (CTA)......................... 96
4.2.1(d) Effect of feed temperature ............................................ 97
4.2.1(e) Effect of feed pressure loss........................................... 98
4.2.1(f) Effect of feed flow rate ............................................... 100
4.2.1(g) Effect of impurity in feed composition....................... 101
4.2.1(h) Parametric study summary ......................................... 102
4.2.2 Degree of nonlinearity................................................................. 104
4.2.2(a) Asymmetric response.................................................. 104
4.2.2(b) Harmonic response ..................................................... 106
4.2.2(c) Multiplicity ................................................................. 108
4.2.3 Nonlinearity Index (NLI) ............................................................ 111
4.2.4 Summary for sensitivity analysis ................................................ 111
4.3 Neural Wiener modeling results................................................................... 111
4.3.1 Input-Output selection................................................................. 111
4.3.2 Data Generation results ............................................................... 113
4.3.3 Model Identification results ........................................................ 116
4.4 Soft sensor modeling results ........................................................................ 122
4.4.1 Input selection results.................................................................. 122
4.4.2 Model identification results......................................................... 125
4.5 NWMPC control results ............................................................................... 127
4.5.1 Control Schemes ......................................................................... 128
4.5.2 Tuning results.............................................................................. 130
4.5.3 Linear controller performance results ......................................... 131
4.5.4 Nonlinear controller performance results.................................... 134
4.5.4(a) Grade transition .......................................................... 134

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4.5.4(b) High Grade transition ................................................. 136
4.5.4(c) Conversion change...................................................... 138
4.5.4(d) Disturbance rejection 1: Feed stream pressure loss .... 140
4.5.4(e) Disturbance rejection 2: Reduced feed stream flow

rate .............................................................................. 142
4.5.4(f) Disturbance rejection 3: Reduced ethylene gas feed

purity........................................................................... 144
4.5.4(g) Robustness Test 1: Fouling......................................... 146
4.5.4(h) Robustness Test 2: Heat of polymerization ................ 149
4.5.4(i) Robustness Test 3: Initiator efficiency ....................... 151
4.5.4(j) Performance remarks .................................................. 153
4.5.5 Controller performances with delay............................................ 155
4.5.5(a) Bias update.................................................................. 155
4.5.5(b) Control performance evaluation ................................. 157
4.5.5(c) Performance with delay remarks ................................ 161
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS ................... 162
5.1 Conclusions .................................................................................................. 162
5.2 Recommendations for future research.......................................................... 164
REFERENCES....................................................................................................... 166
APPENDICES
LIST OF PUBLICATIONS

viii

LIST OF TABLES

Table 2.1 Page
Table 3.1 Review of LDPE high-pressure polymerization control scheme.......28
LDPE tubular reactor operating and feed conditions (Asteasuain et
Table 3.2 al., 2001) ............................................................................................46
List of kinetic parameters used in this study (Agrawal et al., 2006)
Table 3.3 ............................................................................................................52
Table 3.4 Process input-output...........................................................................55
Table 3.5 Maximum and minimum values for MV ...........................................63
Table 4.1 Parameters for soft sensor model input-output selection ...................74
Table 4.2 LDPE conversion and properties validation ......................................88
Table 4.3 Generated LDPE MFI grades.............................................................89
Table 4.4 Overview of the input effects towards reactor outputs ....................103
Table 4.5 Summary of nonlinearity test results................................................112
Table 4.6 Selected input and output variables for Neural Wiener model ........113
Table 4.7 Summary of model identification results for SS and NW model ....122
Table 4.8 PCC results for parameter outputs ...................................................124
Table 4.9 Finalized soft sensor input parameters.............................................126
Table 4.10 MPC and PID tuning parameters .....................................................131
Heat transfer coefficient (HTC) for clean and fouled tubular
Table 4.11 reactor based on zones (in BTU unit) ..............................................147
Performance test results using NWMPC and SSMPC based on ISE
..........................................................................................................153

ix

LIST OF FIGURES

Page

Figure 2.1 Ethylene undergo polymerization process to produce polyethylene
.............................................................................................................. 9

Figure 2.2 Overview of Polyethylene processing technology.............................10

Figure 2.3 PE polymer structure: LDPE, LLDPE and HDPE (Kupolati et al.,
2017) ..................................................................................................11

Figure 2.4 Schematic diagram of LDPE tubular reactor production
(Kiparissides et al., 2010) ..................................................................12

Figure 2.5 LDPE molecular structure with long-chain branching (LCB) and
short-chain branching (SCB) (Boopathy, 2006) ................................17

Figure 2.6 Simulation model development phase (Krallis et al., 2010)..............20

Figure 2.7 Elements needed for polymerization model (Pladis et al., 2015) ......20

Figure 3.1 Research methodology flow chart......................................................41

Figure 3.2 Steps for developing steady state model using Aspen Plus ...............42

Figure 3.3 A schematic diagram of the tubular reactor (Agrawal et al., 2006)...43

Figure 3.4 Branching index for LDPE molecular weight (Dietrich et al., 2019)
............................................................................................................53

Figure 3.5 Block diagram of MPC workflow (Khaled and Pattel, 2018)............60

Figure 3.6 Neural Wiener model in MPC control scheme ..................................61

Figure 3.7 Wiener model (L-N) structure............................................................63

Figure 3.8 Flow chart for Wiener model identification using L-N approach......64

Figure 3.9 The structure of the neural network model used as the nonlinear
part of the Wiener model (Lawryńczuk, 2013)..................................66

Figure 3.10 Flow chart for MPC tuning procedure ...............................................69

Figure 3.11 NWMPC control scheme with Aspen Dynamic ................................71

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Figure 3.12 Feedforward NN model with input delays .........................................72

Figure 3.13 Dual MISO model scheme for soft sensor model ..............................73

Figure 3.14 Flowchart for input parameter selections for soft sensor
development .......................................................................................73

Figure 3.15 Soft sensor model scheme..................................................................76

Figure 3.16 Comparison of two different routes of grade transition effect
towards molecular weight distribution (Ohshima and Tanigaki,
2000) ..................................................................................................78

Figure 4.1 LDPE tubular reactor model in Aspen Plus .......................................86

Figure 4.2 LDPE reactor temperature validation profile.....................................87

Figure 4.3 Effect of Initiator 1 flow rate deviations ............................................90

Figure 4.4 Polymer conversion profile based on different initiator 1 flow rate ..91

Figure 4.5 Reactor temperature profile based on different initiator 1 flow rate
............................................................................................................92

Figure 4.6 (a) Initiator 1 (TBPPI) and Oxygen composition inside Zone 3; (b)
Zone 4 using initiator 1 flow rate at 2.6 kg/h. ....................................93

Figure 4.7 Effect of Initiator 2 flow rate deviations ............................................95

Figure 4.8 Effect of CTA flow rate deviations....................................................96

Figure 4.9 Effect of feed temperature changes towards selected rector outputs
............................................................................................................98

Figure 4.10 Effect of feed pressure loss variations towards selected rector
outputs ................................................................................................99

Figure 4.11 Effect of Feed flow rate deviations towards selected rector outputs
..........................................................................................................100

Figure 4.12 Effect of impurity in ethylene feed composition towards selected
rector outputs....................................................................................102

Figure 4.13 Asymmetric response for peak temperature in Zone 3 (in
deviation)..........................................................................................105

xi

Figure 4.14 Asymmetric response for LDPE mass fraction in product stream
(in deviation) ....................................................................................105

Figure 4.15 Asymmetric response for LDPE polymer MFI (in deviation) .........106

Figure 4.16 Harmonic response of Initiator 1 flow rate towards Peak
temperature in Zone 3 ......................................................................107

Figure 4.17 Harmonic response of Initiator 2 flow rate towards LDPE
conversion ........................................................................................107

Figure 4.18 Harmonic response of CTA flow rate towards polymer MFI ..........107

Figure 4.19 Distinct temperature profiles in Zone 3 by increasing initiator 1
flow rate ...........................................................................................108

Figure 4.20 Distinct temperature profiles in Zone 5 by increasing initiator 2
flow rate ...........................................................................................109

Figure 4.21 Steady state operation points by changing the initiator 1 flow rate
in ascending and descending routine................................................110

Figure 4.22 Steady state operation points by changing the initiator 2 flow rate
in ascending and descending routine................................................110

Figure 4.23 Steady state operation points by changing the CTA flow rate in
ascending and descending routine....................................................110

Figure 4.24 Process input excitation data; (a) Initiator 1 flow rate (b) Initiator
2 flow rate (c) CTA flow rate...........................................................114

Figure 4.25 Process output variable results: (a) reactor peak temperature in
Zone 3 (b) reactor peak temperature in Zone 5 (c) LDPE
conversion ........................................................................................115

Figure 4.26 Process output variable results (a) polymer molecular weight (b)
MFI...................................................................................................116

Figure 4.27 Linear model order selection based on Hankel Singular Values .....117

Figure 4.28 Number of hidden neurons selection for NW static nonlinear block
for (a) LDPE conversion (b) MFI ....................................................117

xii

Figure 4.29 Regression plot for LDPE conversion (Y1) for (a) Neural Wiener
model (b) State space model ............................................................119

Figure 4.30 Regression plot for MFI (Y2) for (a) Neural Wiener model (b)
State space model.............................................................................120

Figure 4.31 Model validation results from 1900 to 2000 minutes: (a) LDPE
conversion (b) MFI ..........................................................................121

Figure 4.32 The input and output data plotted using Box plot; (a) feed
temperature (b) peak temperature zone 1 (c) peak temperature zone
2 (d) peak temperature zone 3 (e) peak temperature zone 4 peak (f)
temperature zone 5 (g) temperature valley (h) temperature exit
temperature (i) initiator 1 flow rate (j) initiator 2 flow rate (k) CTA
flow rate (l) polymer exit density (m) LDPE conversion (n) MFI...123

Figure 4.33 Number of hidden neurons selection for (a) TDNN conversion
model and (b) TDNN MFI model ....................................................127

Figure 4.34 Regression plot for (a) TDNN model conversion and (b) TDNN
model MFI........................................................................................127

Figure 4.35 PID control scheme inside Matlab Simulink ...................................128

Figure 4.36 NWMPC control scheme inside Matlab Simulink...........................129

Figure 4.37 NWMPC control scheme with a soft sensor inside Matlab
Simulink ...........................................................................................130

Figure 4.38 Grade transition profile for PID and SSMPC (a) CV profile (b) MV
profile ...............................................................................................132

Figure 4.39 LDPE conversion profile for PID and SSMPC (a) CV profile (b)
MV profile........................................................................................133

Figure 4.40 Comparison of grade transition control using NWMPC and
SSMPC: (a) MFI profile (b) CTA flow rate profile.........................135

Figure 4.41 Comparison of grade transition control using NWMPC and
SSMPC: (a) Conversion profile (b) Initiator 2 flow rate profile (c)
Initiator 1 flow rate profile...............................................................135

xiii

Figure 4.42 Comparison of high-grade transition control using NWMPC and
SSMPC: (a) MFI profile (b) CTA flow rate profile.........................137

Figure 4.43 Comparison of high-grade transition control using NWMPC and
SSMPC: (a) Conversion profile (b) initiator 2 profile (c) initiator 1
profile ...............................................................................................137

Figure 4.44 Comparison of conversion change control using NWMPC and
SSMPC: (a) MFI profile (b) CTA flow rate profile.........................139

Figure 4.45 Comparison of conversion change control using NWMPC and
SSMPC: (a) Conversion profile (b) initiator 2 profile (c) initiator 1
profile ...............................................................................................140

Figure 4.46 Comparison of disturbance rejection results for pressure loss in the
feed stream using NWMPC and SSMPC (a) MFI profile (b) CTA
profile ...............................................................................................141

Figure 4.47 Comparison of disturbance rejection results for pressure loss in the
feed stream using NWMPC and SSMPC (a) LDPE conversion (b)
initiator 2 flow rate (c) initiator 1 flow rate .....................................141

Figure 4.48 Comparison of disturbance rejection results for reduced flow rate
in the feed stream using NWMPC and SSMPC (a) MFI (b) CTA
flow rate ...........................................................................................143

Figure 4.49 Comparison of disturbance rejection results for reduced flow rate
in the feed stream using NWMPC and SSMPC (b) initiator 2 flow
rate (c) initiator 1 flow rate ..............................................................143

Figure 4.50 Comparison of disturbance rejection results for reduced ethylene
impurity in the feed stream using NWMPC and SSMPC (a) MFI
(b) CTA flow rate.............................................................................145

Figure 4.51 Comparison of disturbance rejection results for reduced ethylene
impurity in the feed stream using NWMPC and SSMPC: (a) LDPE
conversion (b) initiator 2 flow rate (c) initiator 1 flow rate .............145

Figure 4.52 Performance comparison of fouling effect in LDPE tubular reactor
using NWMPC and SSMPC (a) MFI (b) CTA flow rate.................148

xiv

Figure 4.53 Performance comparison of fouling effect in LDPE tubular reactor
using NWMPC and SSMPC (a) LDPE conversion (b) initiator 2
flow rate (c) initiator 1 flow rate ......................................................148

Figure 4.54 Performance comparison of the heat of polymerization effect in
LDPE tubular reactor using NWMPC and SSMPC (a) MFI (b)
CTA flow rate ..................................................................................150

Figure 4.55 Performance comparison of heat of polymerization effect in LDPE
tubular reactor using NWMPC and SSMPC (a) LDPE conversion
(b) initiator 2 flow rate (c) initiator 1 flow rate................................150

Figure 4.56 Performance comparison of initiator efficiency effect in LDPE
tubular reactor using NWMPC and SSMPC (a) MFI (b) CTA flow
rate....................................................................................................152

Figure 4.57 Performance comparison of initiator efficiency effect in LDPE
tubular reactor using NWMPC and SSMPC (a) LDPE conversion
(b) initiator 2 flow rate (c) initiator 1 flow rate................................152

Figure 4.58 Close-loop grade transition test using delay measurement ..............155

Figure 4.59 Comparison of the different correction factor for close-loop grade
transition test ....................................................................................156

Figure 4.60 The NWMPC and NWMPC-SS comparison in controlling grade
transitions with delayed information: (a) MFI profile (b) CTA
profile ...............................................................................................158

Figure 4.61 The NWMPC and NWMPC-SS comparison in controlling grade
transitions with delayed information: (a) LDPE Conversion (b)
initiator 2 flow rate (c) initiator 1 flow rate .....................................158

Figure 4.62 The NWMPC and NWMPC-SS comparison in controlling
conversion changes with delayed information: (a) LDPE
Conversion (b) initiator 2 flow rate (c) initiator 1 flow rate ............160

Figure 4.63 The NWMPC and NWMPC-SS comparison in controlling
conversion change with delayed information: (a) MFI profile (b)
CTA profile ......................................................................................160

xv

LIST OF SYMBOLS

Specific heat of mixture J/kg.K
̂ Predicted error J/kmol
Activation energy J/kmol
Polymer molar enthalpy
Objective function BTU
Control horizon K
Prediction error Watt/m2.K
2 Coefficient of determination
Fouling resistance 1/sec
Process stream temperature kg/min
Heat transfer coefficient J/s
Tuning weight for controller output rate K
Tuning weight for setpoint tracking
Model mismatch
̃ Branching index
Pre-exponential factors
̇ Mass flow rate
Heat transfer rate
Coolant stream temperature
Input signal
Intermediate signal
Neural network weight

xvi

Output signal

̃ Corrected prediction

̂ Uncorrected prediction

Process model output
Process output

Greek symbols

∆ Heat of polymerization J/kmol
m3/kmol
∆ Logarithmic mean temperature difference
∆ Activation volume

Δ Controller output change

Correction factor

Process delay or lag

Nonlinear transfer function (neural network
model)

Correlation function or model

xvii

LIST OF ABBREVIATIONS

APC Advanced process control
CH2 Ethylene
CTA Chain transfer agent
CV Control variable
DCS Distributed control system
EOS Equation of state
FFNN Feedforward Neural Network
FPM First principle model
HDPE High density polyethylene
HOP Heat of polymerization
I/O Input-Output
INIT Initiator
ISE Integral squared error
LCB Long-Chain Branching
LDPE Low density polyethylene
LLDPE Linear low-density polyethylene
MFI Melt flow index
MPC Model predictive control
MV Manipulated variable
MWN Number Average molecular weight
MWW Weight Average molecular weight
NLI Nonlinearity Index

xviii

NMPC Nonlinear model predictive control
NN Neural network
NRMSE Normalized root mean square error
NW Neural wiener
NWMPC Neural Wiener model predictive control
NWMPC-SS Neural Wiener model predictive control with soft sensor
PCA Principle Component Analysis
PCC Pearson correlation coefficient
PC-SAFT Perturbed-chain statistical fluid theory
PEM Prediction error estimate
PID Proportional integral derivative
PLS Partial least square
QDMC Quadratic Dynamic Matrix Control
SCB Short-Chain Branching
SP Set point
SQP Sequential quadratic programming
SS State space
SSMPC State space model predictive control
TBPIN tert-butyl 3,5,5 trimethyl-peroxyhexaonate
TBPPI tert-butyl peroxypivalate
TDNN Time delayed neural network
Z Zone

xix

LIST OF APPENDICES

Appendix A Modifying Heat of Formation in Aspen Plus
Appendix B NWMPC S-function script
Appendix C Properties regression using PC-SAFT EOS
Appendix D NWMPC process model results
Appendix E PID Tuning using Matlab PID Autotuning

xx

KAWALAN TRANSISI GRED POLIETILENA BERKETUMPATAN
RENDAH MENGGUNAKAN KAWALAN MODEL RAMALAN NEURAL

WIENER DENGAN PENDERIA LEMBUT

ABSTRAK

Polietilena berketumpatan rendah (LDPE) adalah polimer komoditi yang
bernilai dengan permintaan tinggi kerana aplikasinya yang pelbagai. Disebabkan oleh
pasaran LDPE yang kompetitif, pengeluar perlu meningkatkan pengeluaran mereka
dengan menerapkan skema kawalan proses lanjutan (APC) seperti kawalan model
ramalan tak linear (NMPC), untuk mengawal transisi gred dan meningkatkan
penukaran polimer. Baru-baru ini, NMPC berdasarkan model prinsip pertama (FPM)
telah diaplikasikan untuk mengawal proses reaktor tubular LDPE. Walau
bagaimanapun, model tersebut memerlukan usaha yang signifikan untuk dibangunkan
dan kurang sesuai bagi pelaksanaan dalam industri. Selain itu, terdapat masalah
kelewatan masa dengan pengukuran kualiti LDPE secara praktikal, iaitu, indeks
pengaliran leleh (MFI) dan penukaran polimer, yang dapat mempengaruhi prestasi
kawalan NMPC.

Oleh itu, kajian ini bertujuan untuk membangunkan dan menilai prestasi
kawalan model ramalan Neural Wiener (NWMPC) dalam mengawal transisi gred dan
penukaran LDPE. Tambahan pula, model penderia lembut (soft sensor) dengan skema
bias yang dikemaskini telah dibangunkan untuk mengagak ukuran kelewatan dan
sekaligus dapat mengemaskini isyarat model keluaran dengan ukuran semasa. Untuk
mendapatkan data input-output untuk membina model NW, model simulasi dinamik
reaktor tubular LDPE telah dibangunkan dengan menggunakan perisian Aspen Plus
dan Aspen Dynamic. Model NW telah menghasilkan korelasi penentuan (R2)

xxi

bersamaan 0.989 untuk penukaran LDPE dan R2 0.986 untuk profil MFI hasil daripada
pengesahan model. Semasa pembinaan model penderia lembut, pemilihan input telah
dilakukan berdasarkan pekali korelasi Pearson (PCC) dan pengetahuan pakar. Hasil
pengesahan model penderia lembut menunjukkan R2 bersamaan 0.999 dan 0.998 untuk
penukaran polimer dan MFI, masing-masing.

Dalam kajian ini, skim kawalan NWMPC telah dibangunkan dalam Matlab
Simulink dan bersepadu dengan Aspen Dynamic untuk kawalan reaktor tubular LDPE
atas talian. Untuk menilai prestasi NWMPC, pengawal telah dinilai dalam ujian
transisi gred, transisi penukaran, penolakan gangguan, dan keteguhan dengan
menggunakan State space MPC (SSMPC) sebagai perbandingan. Daripada analisis
profil proses dan kamiran ralat kuasa dua (ISE), NWMPC telah berjaya untuk
mengatasi SSMPC. Kombinasi NWMPC dengan penderia lembut (NWMPC-SS) telah
menunjukkan prestasi yang sangat baik dalam menangani transisi gred dan perubahan
penukaran LDPE meskipun terdapat kelewatan masa dalam gelung kawalan.
Berdasarkan prestasi ini, kemampuan NWMPC-SS untuk mengawal reaktor tubular
LDPE telah dibuktikan, yang menyerlahkan potensinya setanding dengan NMPC
berdasarkan FPM.

xxii

LOW DENSITY POLYETHYLENE GRADE TRANSITION CONTROL
USING NEURAL WIENER MODEL PREDICTIVE CONTROL WITH SOFT

SENSOR

ABSTRACT

Low density polyethylene (LDPE) is a valuable commodity polymer with high
demands because of its versatile applications. Due to the competitive LDPE market,
manufacturers need to improve their production by implementing advanced process
control (APC) schemes such as nonlinear model predictive control (NMPC) to control
grade transition and increase polymer conversion. Recently, NMPC based on first
principle model (FPM) has been implemented to control the LDPE tubular reactor
process. However, such a model requires significant effort to be developed and is less
feasible for industrial implementation. Moreover, there are time delay issues with the
practical LDPE quality measurement, i.e., melt flow index (MFI) and polymer
conversion, that affect the NMPC control performance.

Thus, this study aims to develop and evaluate the performance of the Neural
Wiener MPC (NWMPC) in controlling LDPE grade transition and conversion. In
addition, a soft sensor model with a bias updated scheme was developed to estimate
the delay measurements and simultaneously update the model output signal with the
current measurements. In order to obtain the input-output data to develop the NW
model, a dynamic simulation model of the LDPE tubular reactor was developed using
Aspen Plus and Aspen Dynamic software. The NW model produced a correlation of
determination (R2) of 0.989 for the LDPE conversion and R2 of 0.986 for the MFI
profile from the model validation results. During the development of the soft sensor
model, the input selection was conducted based on the Pearson correlation coefficient

xxiii

(PCC) and expert knowledge. The validation results of the soft sensor model showed
R2 of 0.999 and R2 of 0.998 for polymer conversion and MFI, respectively.

In this work, the NWMPC control scheme was developed inside Matlab
Simulink and integrated with Aspen Dynamic for online LDPE tubular reactor control.
In order to evaluate the NWMPC performance, the controller was tested in grade
transition, conversion change, disturbance rejection, and robustness tests using State
space MPC (SSMPC) as a comparison. The tests’ process profiling and integral
squared error (ISE) analysis showed that the NWMPC successfully outperformed the
SSMPC. Furthermore, the combination of the NWMPC with soft sensor (NWMPC-
SS) demonstrated excellent performance in handling LDPE grade transitions and
conversion changes despite a time delay in the control loop. Based on these
performances, the ability of the NWMPC-SS to control the LDPE tubular reactor is
established, which highlights its potential comparable with FPM based NMPC.

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CHAPTER 1
INTRODUCTION

1.1 Research Background
Low Density Polyethylene (LDPE) is one of the world’s largest produced

polymers in terms of volume (Patel, 2017). It is a flexible material with high ductility
and low tensile strength and is primarily applied in packaging, films, adhesives, and
coatings. LDPE is usually categorized by its density or melt flow index (MFI). MFI is
the measure for the polymer flow characteristic under conditions related to its
processing. LDPE has a density ranging from 0.91 to 0.93 kg/m3. It is reported that the
global demand for LDPE is at 50.4 million tons with an annual growth of 3.7%
(Bühler-Vidal, 2017). In Malaysia, LDPE is also a significant petrochemical industry,
contributing to the national gross revenues in the domestic and export market
(Malaysian Petrochemicals Association, 2018). LDPE and its copolymers have been
commercially produced in high-pressure tubular and autoclave reactors for more than
50 years (Taheri et al., 2020).

LDPE is produced from ethylene gas polymerization at a high pressure and
temperature environment using free radicals from organic initiators. The LDPE
produced from the high-pressure free radical polymerization process has a distinct
rheological and physical property due to its complex polymer branching structure. This
complex branching characteristic distinguishes this polymer with a similar LDPE
production using low-pressure transition metal-catalyzed polymerization (Saldívar-
Guerra et al., 2016). There are specific differences in the polymer’s branching
distributions for the autoclave and tubular reactor process. The autoclave process
typically would produce a branching distribution that is more root-like while the
tubular process produces a distribution that is more comb-like. The production of

1

LDPE using a tubular reactor is preferred due to its higher conversion process per pass
compared to the autoclave reactor (Patel, 2017). Moreover, in terms of the economic
perspective, the initial capital investment and operational cost for the autoclave reactor
is much higher than the tubular reactor (Burdett and Eisinger, 2017b).

Despite its economic significance and widespread usage, the LDPE high-
pressure tubular reactor still presents several operational challenges to plant engineers.
This is primarily due to the complex physico-chemical phenomena in the reactor, its
relationship to polymer quality, and its dependency on process conditions (Boopathy,
2006). As a result, researchers from both the industrial and academic fields have
carried out research and development in LDPE tubular reactors over the years (Azmi
and Aziz, 2016). Since controlling polymer quality can be considered a critical task in
the plant, the LDPE research themes mainly cover the development of a
comprehensive polymerization model to predict polymer quality (Kiparissides et al.,
2010), reactor control (Skålén et al., 2016), and quality monitoring (Sharmin et al.,
2006).

1.2 Problem Statement
The polymer industry’s current trends and competition have forced the

polymer plants to adopt an efficient production strategy (Fraunhofer-Gesellschaft,
2019). For the LDPE manufacturers, this translates into the continuous production of
different polymer grades using the same production line to save capital and production
costs. This requires a seamless transition operation between the polymer grades to
avoid costly production start-ups and shutdowns (Mahadevan et al., 2002). Since each
polymer grade has different end-use properties, frequent shifting between them can

2

cause excursions outside the desired product range, resulting in an off-specification
(off-spec) product (Dünnebier et al., 2005).

Another aspect that can improve the LDPE plant economically is by increasing
its polymer conversion (or production rate). Polymer conversion refers to the ratio of
the amount of the polymer produced compared to the supplied monomer. Typically,
LDPE polymer conversion using a tubular reactor is about 10% to 30%, as reported in
the literature (Yao et al., 2004). In practice, LDPE polymer conversion can be
controlled by regulating specific reactor parameters such as initiator flowrate (Ham
and Rhee, 1996). Thus, by properly controlling the parameters of the reactor, product
variability and transition time can be minimized while production capacity can be
maximized (Naidoo et al., 2007).

However, controlling the LDPE polymerization process is not a trivial task as
it is known to show complex nonlinear dynamic behaviors (Disli and Kienle, 2012;
Häfele et al., 2005). Moreover, the availability of multiple reactor parameters to be
controlled and monitored has made the LDPE tubular reactor production a
multivariable system. The need to produce multiple polymer grades requires the plant
controller to control a broad operating region (BenAmor et al., 2004). Thus, the
application of advanced controllers such as nonlinear model predictive control
(NMPC) is more suitable in the polymer plants such as LDPE (Qin and Badgwell,
2003). One of the main features associated with the NMPC is its process model. The
process model acts as the actual process to provide the controller with unbiased
estimations of the current process. Thus, the performance of the NMPC controller
depends on the accuracy of the developed process model.

3

In order to produce an accurate process model, the option of the first principle
model (FPM) is often selected (Skålén et al., 2016). The FPM is developed based on
mathematical mass, energy, and momentum equations of the process. However, its
development consumes a great deal of time, effort, and resources (Zhao et al., 2006).
Moreover, such a model is hard to accept by the average industrial practitioner due to
its mathematical complexity (Forbes et al., 2015). In this matter, nonlinear system
identification serves as a comparable alternative for developing process models
(Schoukens and Ljung, 2019). In nonlinear system identification, the process model is
developed by obtaining the empirical relationship of input and output data using a
nonlinear optimization technique. One of the well-known nonlinear model
identification techniques is block-oriented models (Schoukens and Tiels, 2017).

Unlike black-box modeling, the block-oriented modeling approach is more
transparent due to its straightforward physical interpretation based on its combined
block gains (Lawryńczuk, 2019). In addition to that, the identification method for
block-oriented models is more straightforward, requires a low computational effort,
and easy to incorporate a priori process knowledge (Lawryńczuk and Tatjewski, 2020).
The block-oriented model class comprises a wide range of model configurations,
which involves a linear dynamic and nonlinear static element. The most widely
implemented block-oriented model is the Wiener model, which has been applied in
many modeling case studies and displayed the capability to describe a broad class of
nonlinear systems (Bai and Giri, 2010; Janczak, 2005). To date, the application of the
empirical models in NMPC, such as Wiener model, is still new for the LDPE
polymerization reactor control.

4

Another issue in polymer manufacturing is the online monitoring of the
polymer quality end-use properties such as melt flow index (MFI) (Ohshima and
Tanigaki, 2000). Although the online analyzer is set up in the plant, the measurement
and physical delay in the LDPE production line have hindered the results from being
available at each sampling time (Rallo et al., 2002; Sharmin et al., 2006). A similar
situation has also occurred with the LDPE polymer conversion measurement. A delay
in the control loop can affect the controller performance in handling grade transition
operations and rejecting process disturbances properly. Therefore, the application of
quality and polymer conversion monitoring using a soft sensor is a viable method to
solve this issue (Nogueira et al., 2017).

1.3 Research Objectives
This research aims to develop and evaluate the Neural Wiener MPC (NWMPC)

performance in controlling the industrial LDPE tubular reactor during grade transitions
and conversion changes. A soft sensor model is combined with the NWMPC to handle
the delayed quality and conversion measurement signal. In order to achieve the
proposed goal, several research objectives are constructed:

1. To develop a dynamic LDPE tubular reactor simulation model that is
embedded with Melt Flow Index (MFI).

2. To develop a nonlinear process model for the NWMPC using Neural
Wiener model identification technique.

3. To develop a soft sensor with bias update for the LDPE quality and polymer
conversion monitoring using neural network model.

5

4. To develop and evaluate the performance of the NWMPC in handling
control scenarios in the LDPE tubular reactor process.

1.4 Scope of study
The scope of this study is to investigate the performance of the NMPC using

an empirical process model, namely the Neural Wiener model, in controlling the LDPE
tubular reactor process based on selected control scenarios. Thus, this investigation
focuses on the NMPC nonlinear process model performance compared with the MPC
with a linear process model. For the initial model development stage, it is common to
compare the nonlinear model performance with a linear model as described by Nelles
(2001) and Shariff et al. (2014). Thus, a similar concept can be applied in the controller
development as well.

This study is limited to LDPE production using a high-pressure free radical
polymerization process. The LDPE can also be produced using the transition metal
catalyst polymerization in solution, slurry, or gas phase. However, the LDPE polymer
using such a process has a lower number of branches, which makes it structurally
different from the conventional LDPE. Hence, this catalyst-based LDPE polymer is
commonly known as Linear LDPE (LLDPE). Moreover, there is no recycle stream is
considered in the tubular reactor process. This is because no data is available in the
case study literature to perform process validation for such operations.

One of the industrial end-use properties for LDPE is the Melt Flow Index
(MFI). MFI is a complex property and is influenced by many parameters, such as
reactor pressure, reactor temperature, monomer concentration, and CTA feed (Skålén
et al., 2016). Typically, the MFI measurement is obtained from an online rheometer or
laboratory test. However, due to unavailable MFI data from the chosen case study in

6

the literature, this value is estimated using a correlation equation based on the LDPE
weight average molecular weight (MWW) (Rokudai and Okada, 1980) and branching
index (Dietrich et al., 2019).

1.5 Thesis Outline
This thesis is divided into five chapters. Chapter 1 serves as a general

introduction to LDPE polymerization control and the current issues associated with it.
A problem statement that discusses this matter more in-depth is then presented. Next,
several research objectives are constructed to solve the problem systematically. The
scope and limitations of this current study are explained at the end of the chapter.

Chapter 2 presents a general review related to the LDPE literature. It covers
LDPE production, polymerization mechanisms, and reactor control development.
Under the reactor control development, the review emphasizes further details in the
LDPE process simulation, modeling, and soft sensor development. A list of
implemented LDPE control schemes in both the tubular and autoclave reactors is
presented to provide an overview of the control development progress in the area.
Insights from the literature review would establish the foundation for the proposed
problem.

Chapter 3 focuses on the research methodology adopted to achieve the research
objectives. The research methodology can be divided into data generation, model
development, and controller development. In the data generation part, the development
of the LDPE process model, model analysis, and data excitation method is presented.
Model development covers the procedure for the Neural Wiener and soft sensor model
development. Lastly, the controller part describes the development of the NWMPC

7

controller, control scheme, and tuning method. A set of control scenarios is created to
evaluate the final controller performance.

Chapter 4 presents the results obtained from this study. The modeling results
include the LDPE tubular reactor simulation, Neural Wiener, and soft sensor model
validation. In addition, the control results consist of the PID and State Space MPC
(SSMPC) control comparison, SSMPC and NWMPC control comparison, and
NWMPC performance during delayed measurement. The SSMPC and NWMPC
controller performances are evaluated in handling LDPE grade transition, conversion
changes, process disturbance, and uncertainty. The control performance results are
discussed and analyzed based on the controller profiles and the calculated integral
square error (ISE) values.

The final chapter, i.e., Chapter 5, summarizes the entire research development
and findings. Several recommendations are also proposed to further improve the
current study.

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CHAPTER 2
LITERATURE REVIEW
2.1 LDPE production
Low Density Polyethylene (LDPE) is a well-known thermoplastic from the
polyethylene (PE) family with diverse final applications due to its branching properties.
In order to produce LDPE, ethylene is required as the raw material. Ethylene is a
colorless gas with a slightly sweet smell obtained by cracking ethane or naphtha at high
temperatures in a steam cracker. Figure 2.1 shows the ethylene molecule structure
(C2H4), a stable molecule with two carbon atoms connected by a double bond. LDPE is
produced based on the polymerization of ethylene molecule in the presence of free
radicals, which breaks the double bond and connects the carbon atoms into a chain. The
letter n in the figure represents the number of ethylene repeat segments in the polymer
chain. The longer the chain, the higher the molecular weight. LDPE polymerization
releases a significant amount of heat due to the breaking of ethylene’s double bond
connection.

Figure 2.1 Ethylene undergo polymerization process to produce polyethylene
An overview of the PE processing technology is presented in Figure 2.2. From

the figure, PE can be produced from two different process routes, which are low-
pressure conditions using catalysts and high-pressure conditions using free radicals. The
low-pressure process is used to produce linear LDPE (LLDPE) and high-density PE

9

(HDPE), while LDPE is produced from a high-pressure process. The low-pressure PE
process can be conducted from three reaction conditions: slurry, solution, and gas phase.
For the LDPE production, the bulk (or mass) polymerization process is used, which
involves combining the monomer and initiator into the main mixture without any
solvent. In the industry, an autoclave or tubular reactor can be used to produce LDPE.
However, the application of tubular reactor has certain benefits in terms of design
simplicity, good heat transfer capability, and narrow molecular weight distribution
(MWD) due to minimal back mixing compared to the autoclave reactor (Pladis and
Kiparissides, 2014). Moreover, the application of tubular reactor is preferred over the
autoclave reactor due to its lower capital and operation cost, yet has higher production
capacity (Dobbin, 2017).

Polyethylene process

Low pressure High pressure

LLDPE & HDPE LDPE

Solution Slurry Gas Bulk

Tubular reactor Autoclave reactor

Figure 2.2 Overview of Polyethylene processing technology
The polymer structure of LDPE, LLDPE, and HDPE is illustrated in Figure 2.3.
From the figure, LDPE has the highest number of chain branches (long and short),
followed by LLDPE and HDPE. By convention, short-chain branching (SCB) implies
branches of six or fewer carbon atoms, while long-chain branching (LCB) can contain

10

hundreds of carbon atoms (Malpass, 2010). Such a condition means LDPE has the
lowest density property compared to LLDPE and HDPE. Thus, the number and
distribution of the polymer branches can affect the end-use properties such as density,
crystallinity, melting temperature, yield strength, and melt flow index (MFI).

Figure 2.3 PE polymer structure: LDPE, LLDPE and HDPE (Kupolati et al.,
2017)

An example of an industrial LDPE production plant using a tubular reactor is
presented in Figure 2.4. The tubular reactor consists of a spiral-wrapped metallic pipe
with a large length-to-diameter ratio. Its typical length ranges from 0.5 to 1.5 km long
with 2.5 to 7.6 cm (1 to 3 inches) of the inside diameter (Burdett and Eisinger, 2017a).
In Figure 2.4, the ethylene gas feed stream and recycle streams are introduced into the
hyper-compressor unit. The mixture is compressed in two stages (primary and
secondary), increasing the pressure from 0 to 275 bar and then from 275 to 2900 bar
(Butler, 2010). Next, a chain transfer agent (CTA) is injected into the mixture to regulate
the LDPE molecular weight by prohibiting long-chain polymer formation during the
polymerization process. Thus, the CTA amount can be used to control specific LDPE
end-use properties such as melt flow index (MFI).

11

12

Figure 2.4 Schematic diagram of LDPE tubu

ular reactor production (Kiparissides et al., 2010)

In this process, the tubular reactor is divided into several reactor zones, namely
preheater, reaction, and cooling zones, which are arranged based on the initiator
injection location, heating, or cooling requirement. A typical commercial tubular
reactor can consist of two to six reaction zones and six to twelve cooling zones (Pladis
and Kiparissides, 2014). Initiators (such as peroxides or oxygen) are injected at multiple
locations along the reactor to initiate the polymerization reaction. The initiator feed
stream usually contains a mixture of two to four initiators with different activation
temperatures. This would further prolong the polymerization reaction since each
initiator would be decomposed at different temperatures inside the reactor (Dhib and
Al-Nidawy, 2002). Since ethylene polymerization is an exothermic reaction, a cooling
jacket is wrapped around the reactor to remove the excessive heat and maintain the
reactor temperatures.

Afterward, the polymer mixture in the exit stream is sent into the high pressure
and low-pressure separators to remove the unreacted monomer (ethylene). The
unreacted monomer is then recycled back into the reactor via the compressors to
improve the process conversion. Before entering the extruder, LDPE grade quality, i.e.,
MFI and conversion, is measured (Rallo et al., 2002). In addition, additives are injected
to improve the polymer in terms of thermal-oxidative stability, flow instabilities, film
blocking, film friction, crystallinity rate, flame retard, and color (Spalding and
Chatterjee, 2017). After the extrusion process, the LDPE pellets are dried, degassed,
and sent to the storage silos.

LDPE has been produced using high-pressure tubular reactor technology for
over 50 years (Malpass, 2010). Overall, LDPE production involves several stages, from
compressed ethylene gas to produce LDPE solid pallets. Nevertheless, the most critical
stage of LDPE production is the polymerization process inside the tubular reactor. The

13

LDPE end-use properties depend on ethylene polymerization and process conditions.
Therefore, the understanding of the LDPE polymerization is crucial in producing
polymer within the desired specification.

2.2 LDPE polymerization
LDPE is produced via free radical polymerization of ethylene gas under high

pressure and temperature conditions inside a tubular reactor. Free radical
polymerization is a type of chain-growth polymerization by which a polymer is formed
by the successive addition of monomers onto the active site of growing polymer chains.
LDPE free radical polymerization typically involves four fundamental reactions:
initiation, propagation, termination, and chain transfer. The explanation for these
reactions is presented in the following sections.

2.2.1 Initiation

The initiation reaction consists of two steps; the formation of initiator radicals
and addition to monomer molecule. The initiator radicals (or primary radicals) are
generated from the thermal decomposition of chemical initiators such as organic
peroxides or azo compounds.

→ ∗
initiator radical

Next, the reactive primary radicals ( ∗) react with ethylene to form chain radicals of

unit length (or live polymer chain):

∗ + 2 = 2 → − 2 − 2 ∗

radical ethylene chain radical

14

The chain radicals grow with the successive addition of ethylene molecules to form long
backbone chain polymers.

2.2.2 Propagation

The initial propagation step consists of the chain radical of unit length reacting
with another ethylene molecule to form a new polymer radical. The new polymer radical
then reacts with other ethylene molecules and this cycle continues. The propagation
reaction can be described as follows:

− 2 − 2 ∗ + 2 = 2 → − 2 − ( 2 − 2) − 2 ∗

chain radical ethylene polymer radical

2.2.3 Termination

The bimolecular termination of radicals may involve primary radicals and chain
radicals. However, the concentration of primary radicals is usually much lower than the
concentration of chain radicals. Hence, only bimolecular termination involving chain
radicals is considered. When the termination reaction leads to two terminated (dead)
chains, the mechanism is called disproportionation, while termination by combination
leads to a single dead chain.

Termination by combination
Two growing polymer molecules, both with a radical at the growing end, combine to
form one long chain. Consequently, the polymerization reaction of these two molecules
is stopped (terminated).

15

− ( 2) − 2 ∗ + − ( 2) − 2 ∗ → − 2 − ( 2) + − 2 ∗ − ′

polymer radical polymer radical polymer

Termination by disproportionation
One of two growing polymer molecules, both with a radical at the growing end, takes
the radical from the other molecule and forms an unsaturated polymer molecule. The
other growing polymer molecule loses its radical and forms a saturated polymer
molecule.

2 {~ 2 − 2 ∗} → ∼ = 2 + ∼ 2 − 3
polymer radical unsaturated polymer saturated polymer

2.2.4 Chain transfer

Chain transfer involves the transfer of reactivity from the growing chain to other
molecules, such as polymer, monomer (i.e., ethylene), solvent, or agent (e.g., propane
and propylene). The chain radical abstracts hydrogen from another molecule, leading to
the termination of the live chain. Simultaneously, a new primary radical is formed that
can start chain polymerization. As a result, chain transfer to monomer and chain transfer
to agent leads to lower (average) molecular weight. In contrast, chain transfer to
polymer and intramolecular chain transfer lead to more branching. In general, chain
transfer reaction results in broad molecular weight distribution of the produced
polymers. Two types of chain branching are distinguished; long-chain branching and
short-chain branching, as illustrated in Figure 2.5:

 Long-chain branching can be due to chain transfer to polymer or reactions
involving a live chain and a terminal double bond on another polymer chain.
Polymer chains with terminal double bonds are formed by chain transfer to

16

monomer or termination by disproportionation. A typical long chain branching
length is 100 to 2000 carbon atoms.
 Short-chain branching or backbiting is an intramolecular radical transfer
followed by the propagation of the backbone radical. A typical short chain
branching length is 1 to 10 carbon atoms.

Figure 2.5 LDPE molecular structure with long-chain branching (LCB) and short-
chain branching (SCB) (Boopathy, 2006)

The polyethylene produced under high pressure is highly branched, with both short-
chain branches and long-chain branching, with the first one being the most dominant.
The various types of chain transfer mechanisms are described in more detail below:
Chain transfer to monomer
In the case of chain transfer to monomer, a dead polymer with either a terminal double
bond or saturated polymer and a new chain radical of unit length are formed. This
reaction occurs through a hydrogen abstraction mechanism and leaves an unsaturated
end segment on the dead polymer chain.

~ 2 − 2 ∗ + 2 = 2 → ∼ = 2 + 3 − 2 ∗

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~ 2 − 2 ∗ + 2 = 2 → ∼ 2 − 3 + 2 = ∗
polymer radical ethylene
polymer radical

Chain transfer to agent
In the LDPE polymerization process, saturated modifiers such as propane or propylene
are used as the chain transfer agent (CTA). During this reaction, the active radical from
a live polymer is transferred to the CTA molecule, generating a dead polymer chain and
a new radical. Such reactions occur via the exact mechanism as chain transfer to
monomer

~ 2 − 2 ∗ + 3 − 2 − 3 → ∼ 2 − 3 + 3 − ∗ − 3

polymer radical propane polymer radical

Chain transfer to polymer
Chain transfer to polymer is the intermolecular chain transfer reaction between a
polymer radical and a dead polymer chain. The active radical from the polymer radical
is transferred to the dead polymer chain and is terminated. Consequently, the new
polymer radical can continue to propagate to develop a long chain branch.

~ 2 − 2 ∗ + ∼ 2~ → ∼ 2 − 3 + ~ ∗ ~
radical
polymer radical polymer polymer

Intramolecular radical transfer
Intramolecular radical transfer or backbiting is chain transfer within the same polymer
molecule, which generates short chain branching. The radical at the chain end is
transferred to a hydrogen atom attached to a chain carbon of five or six carbon atoms
from the chain end. As the active site propagates, a short-chain branch (i.e., butyl
branch) is formed on the backbone chain. A possible second intramolecular chain
transfer can also occur to produce another short chain branch in the exact location.

18

~ 2 − 2 − 2 − 2 − 2 ∗ → ~ ∗ − 2 − 2 − 2 − 3

polymer radical polymer radical

2.3 LDPE process simulation
Polymer simulation has become an essential aspect of LDPE polymerization

research since the beginning (Pladis et al., 2015). Due to extreme conditions of high
pressures and temperatures for the LDPE polymerization process, performing an
experimental analysis regarding the polymer’s process-properties relationship is time
and cost-intensive (Peikert et al., 2019). Moreover, conducting the open-loop
experiment on the manufacturing plant has the consequences of disturbing the polymer
production operation, safety issues, and economic considerations (Meintanis et al.,
2017). Thus, the application of the mathematical model to simulate the LDPE
polymerization process is well justified.

A process simulation study begins with the definition of the goals. It is
sequentially conducted in several phases, as shown in Figure 2.6. From the figure, the
simulation model development needs to undergo three phases, which are the conceptual
phase, the development phase, and the post-development phase. The conceptual phase
involves defining the problem, collecting or generating data, and describing the
conceptual model. The middle phase, i.e., the development phase, serves as the stage
for the model to be developed, simulated, and validated. A typical simulation of an
industrial-scale LDPE tubular reactor requires integrating various mathematical
models, describing the complex physical and chemical phenomena occurring at
different lengths and time scales. In order to develop a proper polymerization model,
the following elements are required; (1) comprehensive kinetic mechanism (2) mass,
energy, and momentum balances (3) thermodynamic properties calculation and (4)

19

transport properties calculation, as illustrated in Figure 2.7. Finally, the post-
development phase is where the developed model is implemented. The model can be
used in the optimization study, model-based process control, and safety analysis. The
presence of such a model can be a good substitute for the actual process to be used in
an integrated simulation environment.

Figure 2.6 Simulation model development phase (Krallis et al., 2010)

Comprehensive
kinetic mechanism

Transport Mass,
properties energy, and
calculation momentum

balances

Thermodynamic
properties calculation

Figure 2.7 Elements needed for polymerization model (Pladis et al., 2015)
20

Many of the LDPE models available in the present literature are based on the
mechanistic or first principle model (FPM) (Azmi, 2019). These models are developed
based on mathematical equations of mass, energy, and momentum balance. However,
the development of such a model requires a considerable investment in time, effort, and
cost to develop it from the beginning (Bezzo et al., 2004). Thus, the application of a
process simulator to develop the polymer model is a convenient approach to overcome
this challenging task (Chen, 2002; Krallis et al., 2010). With a process simulator, a
polymer model can be developed with minimal effort and time since many of the FPM
properties are already available in the software. Several applications of polymer process
simulators for the LDPE tubular reactor have been reported in the literature. Among the
recognized ones are Aspen Plus (Bokis et al., 2002), gPROMS (Asteasuain and
Brandolin, 2008), and Predici (Fries et al., 2016; Neuhaus et al., 2014; Peikert et al.,
2019).

The Aspen Plus software provides a user-friendly interface, a wide range of
components database, and an object-oriented programming environment, which allows
the users to simulate any polymer process efficiently and comprehensively (Al-Malah,
2017). Nevertheless, most of the developed models, as mentioned earlier, are based on
steady state conditions. Compared to a steady state model, a dynamic model can track
process variables’ changes as a function of time. Such a model is essential in a process
control study to determine the best control action route to achieve or/and maintain the
desired process targets, especially in grade transitions. One of the limitations of the
current Aspen Plus software is in terms of estimating the polymer MFI. To estimate
MFI in Aspen Plus, the user needs to develop and compile the equations using the user
FORTRAN subroutine. Alternatively, one can develop the equation in Matlab Simulink
and connect the software with Aspen Dynamic for online MFI estimation. This method

21

is better since the FORTRAN subroutine can only be used in Aspen Plus, which is in
steady state form.

2.4 LDPE tubular reactor control
The polymerization reactor (i.e., tubular reactor) is the core of the LDPE

manufacturing plants, which significantly influences downstream processing and
polymer end-use properties. The amount or type of initiators, CTA amount, reactor
configurations, and process conditions can directly influence the produced LDPE
polymer’s quality. Richards and Congalidis (2006) have reported several factors that
contribute to the significance of polymer reactor control:

i. The need to improve plant productivity by optimizing reactor yield and
uptime.

ii. The trend towards shorter and frequent multiple grade transitions from the
same reactor.

iii. Global competition, which requires the production of uniform polymer
grades and shorter commercialization time for new polymers.

iv. Abiding by safety considerations and environmental regulations from
operating a potentially thermal unstable process.

However, the inherent characteristics of the LDPE polymerization process, such
as nonlinear behavior (Kiparissides and Mavridis, 1986; Kiparissides et al., 1993b),
oscillation (Ray and Villa, 2000) and multiplicity (Häfele, 2006), have become a
challenge to the polymer manufacturers. Additionally, the real-time measurement of
these characteristics is not feasible due to time delay, high analyzer installation cost,
and maintenance routine (Cheng and Liu, 2015). Hence, to operate the LDPE tubular
reactor economically, process automation or control must be employed to enable

22

stringent compliance with the required polymer specification and fast response to
market demands at minimal costs.

One of the strategies to improve LDPE production productivity is to control
operation conditions during grade transition and polymer conversion (Na and Lee,
2006). This can be achieved by minimizing the resources (such as initiators and CTA)
and reducing polymer grade variability, which can save a considerable amount of plant
expenses (Naidoo et al., 2007). Moreover, the improvement in polymer quality can
reduce the need for downstream polymer blending or other post-processing operations
to treat the off-spec product during grade transition (Valappil and Georgakis, 2002).
One of the approaches in controlling the LDPE tubular reactor is using advanced
process control (APC), particularly model predictive control (MPC).

Based on a survey by Qin and Badgwell (2003) on industrial MPC applications,
most of the polymer plants implement nonlinear MPC (NMPC) compared to linear
MPC (LMPC). This finding also concurs with the latest review by Nogueira et al.
(2020) on polymerization process control. From their review, NMPC is the most used
controller for polymer control in the last two decades. Due to the complexity of the
polymerization process, coupled with the need to produce multiple polymer grades with
board operating conditions, the NMPC is a better option than LMPC (Bindlish, 2020).

2.4.1 LDPE Control Scheme

In the past, several researchers have conducted the LDPE high-pressure
polymerization control study, whether in tubular or autoclave reactors. Thus, a brief
explanation of their work is presented here. Singstad et al. (1992) proposed a two-level
control strategy, which comprised quality optimization and basic level controllers, for

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an industrial multi-zone LDPE autoclave reactor. However, only the development of a
basic level controller was discussed in their paper. The basic controller was a
multivariable controller developed based on an internal nonlinear decoupling method.
The controller was used to control the reactor temperature by regulating the monomer
feed streams. Based on the disturbance rejection tests, the controller had performed
better by presenting a faster and smaller damping of the disturbance than a multi-loop
PID controller. The controller was also implemented in the plant, which led to a
significant overall reduction in the off-spec products.

Ham and Rhee (1996) applied pole placement or full state feedback (FSF)
control on an adiabatic slim type autoclave reactor for the LDPE polymerization
process. In their study, the bifurcation diagram was used to show the existence of
multiple steady state conditions. The FSF controller was implemented to control the
reactor exit temperature by regulating the initiator flow rates and it was updated using
the recursive least square method. Compared to a conventional PID controller, the FSF
controller displayed a better performance without overshoot and used a lesser amount
of initiator.

Berber and Coşkun (1996) investigated the performance of Quadratic Dynamic
Matrix Control (QDMC) controller for an industrial LDPE autoclave reactor model.
The QDMC is an improved version of DMC controller with constraints and utilizing
quadratic programming (QP) to solve the controller’s objective function. A step
response model was utilized as the process model in the QDMC control scheme. Based
on the performance tests, the QDMC outperformed the conventional PI controller in
controlling the reactor temperatures, especially during setpoint tracking. In the tests, the

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