Dynamic Model and Microcalorimetric Soft Sensor Developments

................................................................................................3.2 3.1 DYNAMIC MODELLING........................................................................3.3 3.1.1 Radical Balances in the Aqueous Phase ...................................................... 3.5 3.1.2 Particle Population Balance ......................................................................... 3.7 3.1.3 Molecular Weight Distribution .................................................................... 3.8 3.1.4 Rates of Polymerisation Reactions .............................................................. 3.9 3.1.5 Reactor Material Balance........................................................................... 3.10 3.1.6 Physical Parameters ................................................................................... 3.10 3.1.6.1 Monomer Concentrations in Multiple Phases................................. 3.10 3.1.6.2 Volumes of Phases .......................................................................... 3.12 3.1.6.3 Swollen Radius of a Particle ........................................................... 3.13 3.1.6.4 Probability Functions ...................................................................... 3.14 3.1.6.5 Concentration of Micelles............................................................... 3.14 3.1.6.6 Critical Degrees of Polymerisation ................................................. 3.15 3.1.7 Rate Coefficients........................................................................................ 3.15 3.1.7.1 Rate Coefficient of Volume Growth............................................... 3.16 3.1.7.2 Entry and Exit Rate Coefficients .................................................... 3.16 3.1.7.3 Termination Rates ........................................................................... 3.18 3.1.7.4 Transfer Rate Coefficient................................................................ 3.19 3.1.7.5 Propagation Rate Coefficients ........................................................ 3.20 3.1.7.6 Efficiency of Initiator Dissociation Constant.................................. 3.22 3.1.8 Physical Parameters ................................................................................... 3.22 3.1.8.1 Average Density and Molar Fraction.............................................. 3.22 3.1.8.2 Terpolymer Composition ................................................................ 3.23 3.1.8.3 Conversion and Polymer Volume Fraction..................................... 3.23 3.1.8.4 Glass Transition Temperature......................................................... 3.24 Chapter 3 Dynamic Model and Microcalorimetric Soft Sensor Developments 3. 1 3.2 MODEL SOLUTION TECHNIQUES....................................................3.24 3.3 THE EFFECT OF MANIPULATED VARIABLES ................................3.26 3.4 MICROCALORIMETRIC SOFT SENSOR DEVELOPMENT...............3.27 3.5. CALORIMETRIC DYNAMIC MODELING ..........................................3.28 3.5.1 Reactor Species Balance ............................................................................ 3.28 3.5.2 Reactor Energy Balance............................................................................. 3.29 3.5.2.1 Heat Flow Due to Feed Input.......................................................... 3.30 3.5.2.2 Heat Flux across Reactor Wall........................................................ 3.30 3.5.2.3 Heat Loss to Surroundings.............................................................. 3.31 3.5.2.4 Heat Flow due to Stirrer.................................................................. 3.32 3.5.3 Monomer Conversion and Terpolymer Composition ................................ 3.33 3.6 CONCLUSION.....................................................................................3.35 BIBLIOGRAPHY .......................................................................................3.37 Chapter 3 Dynamic Model and Microcalorimetric Soft Sensor Developments 3. 2 Dynamic Model and Microcalorimetric Soft Sensor Developments