Table of Contents
Preface vii
1 Introduction 1
2 The Loop Reactor Circulation Pump Power 4
2.1 Circulating Pure Liquid 4
2.2 Circulating the Slurry 6
2.3 Upsets in Pump Power 9
2.3.1 Realistic Pump Power Curve 9
2.3.2 Reactor Fouling 10
2.3.3 Hot Spots 12
3 The Functioning of the Settling Legs 19
3.1 Functioning of the Settling Legs 20
3.1.1 Description and Definitions 20
3.1.2 The Overall Reactor Mass Balance 22
3.1.3 The Volumetric Output Equation 23
3.1.4 Solids Removal Rate Equation 24
3.2 Correlations for the Settling Velocity 25
3.2.1 General Correlation 25
3.2.2 Specific Correlations 27
3.2.3 Correlation with the Terminal Falling Velocity 28
3.3 Control of the Solids Concentration in the Loop Reactor 29
3.3.1 The Solids Concentration Control Equation 29
3.3.2 Control of the Solids Concentration 30
3.3.3 Stability of the Solids Concentration Control 32
4 The Settling of the Polymer in the Settling Legs 36
4.1 Description and Definitions 37
4.2 Kynch's Sedimentation Theory 38
4.3 Growth Rate of the Zone of Thickened Slurry 40
4.4 Settling Behaviour of the Polymer 41
4.5 Maximum Filled Fraction of the Settling Legs 45
4.6 Settling Legs with a Change in Diameter 46
5 Catalyst Activity and Productivity 51
5.1 The Polymerisation Reaction 51
5.2 Polymerisation Rate Equation 54
5.3 Catalyst Activity 56
5.4 Catalyst Reactor Productivity 57
5.5 Catalyst Reactor Productivity in a Batch Reactor 58
6 The 1/1 Hypothesis 62
6.1 Silica Gel Particles 62
6.2 Catalyst Particle Fragmentation 64
6.3 Particle Productivity 66
6.4 Balance for the Number of Particles 66
6.5 Verification of the 1/1 Hypothesis 68
7 Catalyst Residence Time Distribution 73
7.1 Definitions and Assumptions 73
7.2 Perfect Mixing of the Catalyst 75
7.3 Catalyst Activity 76
7.4 Catalyst Reactor Productivity 78
7.5 Mass of Polymer Present in the Reactor 79
7.6 Catalyst Residence Time Distribution 80
7.7 Mass Balance for the Polymer 82
7.8 Measurement of the Catalyst RTD in the Loop Reactor 83
7.8.1 Cumulative RTD and Response to a Step Signal 84
7.8.2 Experiment 84
8 Catalyst Activity Profiles 88
8.1 Catalyst Activity Profiles 88
8.2 Catalyst Productivity Curve and Activity Profile 89
8.3 Particle Productivity 91
8.4 Experimental Results for Activity Profiles 92
8.5 Induction Time 96
9 Conversions 98
9.1 Calculating Conversions from Full Scale Reactor Data 98
9.2 The Conversion of Ethylene 100
9.3 The Conversion of Hydrogen 103
9.3.1 Hydrogen to Ethylene Ratios 103
9.3.2 Calculating the Hydrogen Conversion 104
9.4 The Conversion of 1-Hexene 106
9.4.1 1-Hexene to Ethylene Ratios 106
9.4.2 Calculating the 1-Hexene Conversion 108
9.5 Conversions and Polymer Properties 110
9.5.1 Correlations for Melt Index 110
9.5.2 Incorporated 1-Hexene and Density 111
9.6 In-situ Generation of 1-Hexene 114
9.7 Optimisation of Reactor Conditions 116
10 Ethylene Concentration Profile in the Loop 120
10.1 Reactor Geometry 120
10.2 Slurry Flow in the Reactor 121
10.3 Catalyst Activity 122
10.4 Rate of Reaction along the Loop 124
10.5 Ethylene Concentration Profile 125
10.6 Increasing Production Rates 128
11 Simple Reactor Model 132
11.1 Elements to Build the Model with 133
11.1.1 Overview of the Variables 133
11.1.2 Independent Variables 134
11.1.3 Dependent Variables 136
11.1.4 The Use of Conversions 137
11.2 Simplifying Assumptions 137
11.3 Mathematical Relations 138
11.3.1 Polymer Properties 138
11.3.2 Conversions 139
11.3.3 Physical Properties 140
11.3.4 Catalyst Activity 141
11.3.5 Flash Gas Flows 141
11.3.6 Reactor Feeds 142
11.3.7 Constraints 142
11.4 A Corrective Offline Model 143
12 Correlations by Linear Regression 147
12.1 The Data Set 147
12.2 Building the Data Set 152
12.3 Establishing the Correlations 154
12.3.1 Inspection of the Data Set 154
12.3.2 Cluster Analysis 154
12.3.3 Pearson Correlation Coefficients 156
12.3.4 Establishing the Correlation by Linear Regression 157
13 Scaling-Up from Bench to Loop 161
13.1 Bench Reactor Polymerisation Tests 161
13.2 Variables in Bench Reactor Tests 162
13.3 Catalyst Activity 165
13.4 Data Set and Correlations 167
13.5 From Bench Scale Variables to Loop Conditions 168
13.5.1 Type and Composition of the Catalyst 168
13.5.2 Ethylene Concentration 168
13.5.3 Reactor Temperature 169
13.5.4 Catalyst Activation Temperature 169
13.5.5 Hydrogen Concentration 169
13.5.6 Comonomer Concentration 170
13.5.7 Dosage of the Cocatalyst 171
13.5.8 Comparing Bench Results to Full Scale Loop Data 172
13.6 Molecular Weight Distributions 172
14 Two Loop Reactors in Series 177
14.1 Mass of Polymer Present in the Second Reactor 177
14.2 Residence Time Distribution in the Second Loop 178
14.3 Total Residence Time in Two Loop Reactors 180
14.4 Catalyst Productivity in a Second Loop Reactor 181
14.5 Bimodality Distribution 183
14.5.1 Ideal Bimodality Distribution 184
14.5.2 Realistic Bimodality Distribution 186
Index 193
