Modelling and Control of a Spray Drying Processetd.dtu.dk/thesis/258819/sivarajingam.pdf ·...

Shayantharan Sivarajalingam

Modelling and Control of a Spray

Drying Process

Master’s Thesis, November 2009


Modelling and Control of a Spray

Drying Process

Master’s Thesis, November 2009

Modelling and Control of a Spray Drying Process,

This report was prepared by


Supervisors

Hans Henrik Niemann-Associate Professor, DTU Electrical EngineeringOle Ravn -Associate Professor, DTU Electrical EngineeringChrister Utzen- GEA Niro,GEA Process Engineering A/S,Process Control

Release date: 30 November 2009Category: 1 (public)

Edition: First

Comments: This report is part of the requirements to achieve the Master ofScience in Engineering (M.Sc.Eng.) at the Technical Universityof Denmark. This report represents 30 ECTS points.

Rights: c©Shayantharan, 2009

Department of Electrical EngineeringAutomation and ControlTechnical University of DenmarkElektrovej building 326DK-2800 Kgs. LyngbyDenmark

http://www.dtu.dk/centre/autTel: (+45) 45 25 35 50Fax: (+45) 45 88 12 95

Preface

This master’s thesis documents the process and results of the project Mod-elling and Control of a Spray Drying Process by Shayantharan Sivarajalingam.The project has been conducted at the Technical University of Denmark(DTU) at the Department of Electrical Engineering, Automation and Con-trol in the period from June till November 2009 and represents a workloadof 30 ECTS points.

I would like to express my sincere thanks and appreciation to my supervisorsAssociate Professor Hans Henrik Niemann and Associate Professor Ole Ravnfor their competent guidance and support throughout the development ofthe ideas in my thesis.

All at once I would like to say thanks to Christer Utzen, for his assistanceduring the thesis work and GEA Niro for giving me the opportunity to workon this real system, which has given me a lot of experience.

Last but not least, I will express my gratitude to my friends: Kristian, Lars,Soaban, Malcolm, Mickey, Varun and my Chellams for their patience andgreat support during the project.

Abstract

This Master thesis is about modelling of a spray drying process. In a spraydrying process a liquid feedstock is dried by spraying the feed into heatedair. This process is utilized in the dairy industry, where milk is dried intomilk powder. Moreover, this process is also applied in the chemical andmedical industries.

The quality of the final product can vary, depending on how the system iscontrolled. The purpose of modelling the spray dryer is to use the model fordevelopment and testing of control strategies to the dryer.

The point of reference is a steady state model, which has been developedto a dynamic model of a multi stage dryer with a mixed air flow. Themodel is based on mass and energy equations, as well as product dryingcharacteristics. The model describes the drying conditions in the dryingchamber with regards to temperature and humidity.

The developed model is verified with data from a genuine Multi stage dryerat GEA Niro’s test station. Furthermore, it has been demonstrated thatthe model can be applied in connection with a controller and thus examinevarious control systems.

Dansk Resume

Denne Master speciale omhandler modellering af et tørsprayingsanlæg. Iet tørspraying anlæg bliver et givent flydende stof tørret ved at sende detflydende stof gennem opvarmet luft. Det er anvendt i blandt andet mejeriindustrien, hvor blandt andet mælk tørres til mælkepulver. Dette er ligeledesanvendt i kemi og medicinal industrien.

Kvaliteten pa det færdigtørrede product kan variere alt efter hvordan an-lægget bliver styret. Malet med modelleringen af anlægget er at kunneanvende modellen til videre udvikling og test af reguleringssystemer til tør-spraying anlæg.

Med udgangspunkt i en steady state model, er der blevet en udviklet endynamisk model af en ”multi stage dryer med mixed air flow”. Denne erbaseret pa masse og energi balance ligninger og produkt tørrings karakter-stikker. Modellen beskriver tørringsforholdene i tørspraying kammeret medhensyn til temperatur og luftfugtighed.

Den udviklede model er blevet verificeret med data fra Multi stage dryeranlæg hos GEA Niro’s test station. Desuden er det blevet demonstreret atmodellen kan anvendes til at undersøge reguleringssystemer.

Contents

List of Figures xiii

List of Tables xviii

1 Introduction 3

1.1 Description of the Problem . . . . . . . . . . . . . . . . . . . 5

1.2 The objective of the project . . . . . . . . . . . . . . . . . . . 6

2 Introduction to the Spray Drying Process and Spray Dryers 9

3 Modeling 13

3.1 Black Box model . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 White Box model . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Grey Box model . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Modelling a Spray Dryer 17

4.1 Preparations and Assumptions for Modelling . . . . . . . . . 17

4.2 Steady State Mass and Energy Balances for Spray Dryers . . 20

4.2.1 Mass Balance . . . . . . . . . . . . . . . . . . . . . . . 24

4.2.2 Equilibrium Moisture Content . . . . . . . . . . . . . 25

4.2.3 Steady State Solution . . . . . . . . . . . . . . . . . . 29

4.3 Test on a Multi Stage Dryer- MSD20 . . . . . . . . . . . . . . 29

4.3.1 The Test on MSD-20 . . . . . . . . . . . . . . . . . . . 31

4.4 Steady State Calculations . . . . . . . . . . . . . . . . . . . . 33

4.4.1 Steady State Results . . . . . . . . . . . . . . . . . . . 35

4.4.2 Effect of varying Operation Variables . . . . . . . . . 37

5 Dynamic Modelling of a Mixed Flow Spray Dryer 43

5.1 Total mass of air in the Spray Dryer . . . . . . . . . . . . . . 44

5.2 Drying Kinetic Mechanism . . . . . . . . . . . . . . . . . . . . 47

5.2.1 Mass Transfer Rate . . . . . . . . . . . . . . . . . . . 49

5.2.2 Mass and Heat Transfer Coefficients . . . . . . . . . . 51

5.2.3 Droplet size . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3 Matlab Simulink Implementation . . . . . . . . . . . . . . . . 54

5.4 Test:Dynamic model . . . . . . . . . . . . . . . . . . . . . . . 54

5.4.1 Step: Temperature of main inlet air . . . . . . . . . . 57

5.4.2 Step: Feed Flow rate . . . . . . . . . . . . . . . . . . . 58

5.4.3 Step: Main inlet air flow rate . . . . . . . . . . . . . . 60

5.5 Test:Drying Time for particle . . . . . . . . . . . . . . . . . . 62

5.5.1 Test 1: particle sizes . . . . . . . . . . . . . . . . . . . 65

5.5.2 Test 2: Temperature . . . . . . . . . . . . . . . . . . . 66

5.5.3 Test 3: Effective Diffusivity . . . . . . . . . . . . . . . 67

5.5.4 Test 4: Critical Moisture Content . . . . . . . . . . . . 67

5.6 Summary: tests . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.7 Modifications in the Dynamic Model . . . . . . . . . . . . . . 69

5.7.1 Implementation of longer drying times and change inevaporation rate . . . . . . . . . . . . . . . . . . . . . 70

5.8 Summary: modifications . . . . . . . . . . . . . . . . . . . . . 73

6 Linearisation Analysis 75

6.1 Operating Point . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2 Linearised results . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4 Comparison of the linear model with the non-linear model . . 81

7 System Identification of Residual Moisture Content 85

7.1 Applied Identification Methods . . . . . . . . . . . . . . . . . 86

7.2 Estimation Data and Validation Data . . . . . . . . . . . . . 87

7.3 System identification Results . . . . . . . . . . . . . . . . . . 89

7.3.1 ARX model . . . . . . . . . . . . . . . . . . . . . . . . 90

7.3.2 ARMAX Model . . . . . . . . . . . . . . . . . . . . . . 91

7.3.3 State Space model . . . . . . . . . . . . . . . . . . . . 93

7.4 Summary: System identification . . . . . . . . . . . . . . . . 93

8 Control of spray dryers 95

8.1 Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 95

8.1.1 PI controller . . . . . . . . . . . . . . . . . . . . . . . 97

8.2 PI controller for disturbance rejection of solids content variation 98

8.2.1 PI controller design . . . . . . . . . . . . . . . . . . . 98

8.3 Results from PI controller implementation in dynamic model 101

8.3.1 Step on reference temperature . . . . . . . . . . . . . 101

8.3.2 Step on Solids content . . . . . . . . . . . . . . . . . . 101

8.4 Possible control strategies . . . . . . . . . . . . . . . . . . . . 102

9 Conclusion 105

Nomenclature 110

References 111

Appendix 114

A Appendix A 115

A.1 Desorption Isotherm at low and high humidity level . . . . . 116

A.2 General moisture Characteristic and food microbiology . . . . 117

B Appendix B 119

B.1 Modelling Variables . . . . . . . . . . . . . . . . . . . . . . . 120

B.2 Steady State Calculation . . . . . . . . . . . . . . . . . . . . . 121

B.3 Results from the Dynamic Model before modification . . . . . 123

B.3.1 Main inlet air temperature step up . . . . . . . . . . . 123

B.3.2 Feed Flow step down . . . . . . . . . . . . . . . . . . . 124

B.3.3 Temperature SFB step down . . . . . . . . . . . . . . 125

B.3.4 Temperature SFB step up . . . . . . . . . . . . . . . . 126

B.3.5 SFB air flow step down . . . . . . . . . . . . . . . . . 127

B.3.6 SFB air flow step up . . . . . . . . . . . . . . . . . . . 128

B.3.7 Main air flow step down . . . . . . . . . . . . . . . . . 129

B.4 Results from the Dynamic Model after modification . . . . . 130

B.4.1 Feed Flow step down with modefication . . . . . . . . 130

B.4.2 Temperature MAIN step down with modification . . . 130

B.4.3 Air flow MAIN step up with modification . . . . . . . 131

B.4.4 Absolute Humidity in Dryer For feed step up withmodification . . . . . . . . . . . . . . . . . . . . . . . . 132

B.4.5 Response for the system G(s)evap . . . . . . . . . . . . 132

B.4.6 Simulink model . . . . . . . . . . . . . . . . . . . . . . 133

C Appendix C 135

C.1 MSD-20 test 24-7-2009 . . . . . . . . . . . . . . . . . . . . . . 135

C.2 Test Step & Responses . . . . . . . . . . . . . . . . . . . . . . 136

C.2.1 Test Program MSD-20 week 30 2009 . . . . . . . . . . 136

C.2.2 Test Step & Results for the entire test on MSD-20 . . 138

C.2.3 Moisture content of the particle from the SFB dis-charge for the entire test on MSD-20 . . . . . . . . . . 139

C.2.4 Test Step & Results for change in feed rate on MSD-20 140

C.2.5 Feed flow rate and Nozzle pressure results from teston MSD-20 . . . . . . . . . . . . . . . . . . . . . . . . 141

C.2.6 Test Step & Results for change in Main inlet air tem-perature on MSD-20 . . . . . . . . . . . . . . . . . . . 142

C.2.7 Test Step & Results for change in Main inlet air flowon MSD-20 . . . . . . . . . . . . . . . . . . . . . . . . 143

C.2.8 Test Step & Results for change in SFB inlet air tem-perature on MSD-20 . . . . . . . . . . . . . . . . . . . 144

C.2.9 Test Step & Results for change in SFB inlet air flowon MSD-20 . . . . . . . . . . . . . . . . . . . . . . . . 145

C.2.10 Ambient Air Conditons At AIR intake (21/7-2009) . . 146

C.3 Logbook for MSD-20 test 24-7-2009 . . . . . . . . . . . . . . 147

D Appendix D 151

D.1 Humidity Calculation . . . . . . . . . . . . . . . . . . . . . . 151

D.2 Droplet calculations . . . . . . . . . . . . . . . . . . . . . . . 152

D.3 Thermal Conductivity Air . . . . . . . . . . . . . . . . . . . . 153

D.4 Thermal Diffusivity Air . . . . . . . . . . . . . . . . . . . . . 154

D.5 Kinematic Viscosity Air . . . . . . . . . . . . . . . . . . . . . 154

D.6 Mean Residense Time for the particle in the Spray dryer . . . 155

E Appendix E 159

E.1 Air and Particle Trajectory in Chamber . . . . . . . . . . . . 160

F Appendix F 161

F.1 Mass transfer and Drying time appendix . . . . . . . . . . . . 161

F.1.1 Default state operation condtion . . . . . . . . . . . . 161

F.1.2 TOut varied . . . . . . . . . . . . . . . . . . . . . . . . 161

G Appendix G 165

G.1 1st order system . . . . . . . . . . . . . . . . . . . . . . . . . 165

H Appendix H 167

xii

H.1 System Identification . . . . . . . . . . . . . . . . . . . . . . . 168

H.2 ARMAX models . . . . . . . . . . . . . . . . . . . . . . . . . 168

H.1.1 Model Misfit Vs Number parameters for ARX model . 169

H.1.2 Zero Pole plot for the ARX model . . . . . . . . . . . 170

H.2.1 ARMAX simulations . . . . . . . . . . . . . . . . . . . 171

H.2.2 ARMAX Zero-pole plot for 6th order model . . . . . 174

H.2.3 State Space- continous time zero-pole plot . . . . . . . 178

I Appendix I 179

I.1.1 Linearized model- State Space(Jacobians) . . . . . . . 179

I.1 Linearization of the dynamic Model - open loop . . . . . . . . 180

I.1.2 Frequency response - from inputs to output . . . . . . 181

I.1.3 Zero-Pole plot for the transfer functions - from eachinputs to output . . . . . . . . . . . . . . . . . . . . . 185

I.2 Comparison of linear and Non linear model . . . . . . . . . . 187

I.2.1 Feed flow . . . . . . . . . . . . . . . . . . . . . . . . . 188

I.2.2 Main inlet air flow . . . . . . . . . . . . . . . . . . . . 190

I.2.3 Main inlet air temperature . . . . . . . . . . . . . . . 193

I.2.4 Solids Content . . . . . . . . . . . . . . . . . . . . . . 196

I.2.5 Relative Humidity of Ambient air . . . . . . . . . . . . 197

List of Figures

1.1 Basic Spray drying process . . . . . . . . . . . . . . . . . . . 4

2.1 Spray drying process stages . . . . . . . . . . . . . . . . . . . 9

2.2 Multi Stage Dryer . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Agglomeration Process Schematic . . . . . . . . . . . . . . . . 11

4.1 Schematic of a CSTR and a plug flow reactor. . . . . . . . . . 18

4.2 Temperature profile for a mixed flow spray dryer . . . . . . . 20

4.3 Morphology of Particle with maltodextrin . . . . . . . . . . . 21

4.4 Basis Blockdiagram- variable description to the system . . . . 22

4.5 Desorption Isotherm Maltodextrin DE12 . . . . . . . . . . . . 27

4.6 MSD-20 Test Station Setup . . . . . . . . . . . . . . . . . . . 40

4.7 Test Centre at GEA Niro - Multi stage Dryer MSD-20 . . . . 41

5.1 Basic Dynamic Model . . . . . . . . . . . . . . . . . . . . . . 46

5.2 Particle Morphology . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Schematic of Drying mechanism . . . . . . . . . . . . . . . . . 48

5.4 Drying Proces of a Particle with a Shrinking Model . . . . . . 49

5.5 Dynamic model blockdiagram . . . . . . . . . . . . . . . . . . 55

5.6 Dynamic step response of the TOutAir for decrease in maininlet air temperature . . . . . . . . . . . . . . . . . . . . . . . 58

xiv LIST OF FIGURES

5.7 Dynamic step response of the TOutAir for a increase in feedflow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.8 Dynamic step response of the TOutAir for increase in Maininlet air flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.9 Mass tranfer rate and drying time test setup . . . . . . . . . 62

5.10 Drying time for a particle at default operation state . . . . . 64

5.11 Drying time for various particle sizes at default operation state 65

5.12 Drying time for various for a single particle for various effec-tive diffusivity coefficients . . . . . . . . . . . . . . . . . . . . 67

5.13 Drying time for various for a single particle for various criticalmoisture contents . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.14 Drying Time for single Particle of different sizes for Deff =8e− 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.15 Temperature response of the outlet air for the modified model(Feed step) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.1 Basic Dynamic Model . . . . . . . . . . . . . . . . . . . . . . 75

6.2 Bode plot- example: minimum phase & non minimum phase 79

6.3 Zero-Pole plot for the linearized model . . . . . . . . . . . . . 80

6.4 Comparison of linear and Non-linear model: Main inlet airtemperature. Step change= 10 from linearised input. Nochange difference is observed . . . . . . . . . . . . . . . . . . 82

6.5 Comparison of linear and Non-linear model: Feed step : 2& 10. For the small step no difference is observed. For thelarger step a small deviation is noted. . . . . . . . . . . . . . 82

6.6 Comparison of linear and Non linear model: Solids contentstep from 50 % to 80 % Such a large change is not possiblein reality. Small difference between the nonlinear and linearmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

7.1 Simulated ARX model output and measured output . . . . . 90

7.2 ARMAX model: 6th order & 10th order . . . . . . . . . . . . 91

7.3 State Space model : 4th order . . . . . . . . . . . . . . . . . . 93

8.1 Input and output variables for process control . . . . . . . . . 96

LIST OF FIGURES xv

8.2 Feed rate control . . . . . . . . . . . . . . . . . . . . . . . . . 97

8.3 The control system . . . . . . . . . . . . . . . . . . . . . . . . 99

8.4 Bode plot for the open loop transfer function . . . . . . . . . 100

8.5 PI controller:step on reference temperatur . . . . . . . . . . . 102

8.6 PI controller:step on solids content . . . . . . . . . . . . . . . 103

8.7 PI controller:Continuous Solids content Disturbance . . . . . 104

A.1 Desorption Isotherm Maltodextrin DE12 . . . . . . . . . . . . 116

A.2 General moisture Characteristic and Food microbiology . . . 117

B.1 Dynamic step response of the TOutAir for increase in maininlet air temperature . . . . . . . . . . . . . . . . . . . . . . . 123

B.2 Dynamic step response of the TOutAir for decrease in maininlet air temperature . . . . . . . . . . . . . . . . . . . . . . . 124

B.3 Dynamic step response of the TOutAir for decrease in SFBinlet air temperature . . . . . . . . . . . . . . . . . . . . . . . 125

B.4 Dynamic step response of the TOutAir for decrease in SFBinlet air temperature . . . . . . . . . . . . . . . . . . . . . . . 126

B.5 Dynamic step response of the TOutAir for increase in SFB inletair flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

B.6 Dynamic step response of the TOutAir for decrease in SFBinlet air flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

B.7 Dynamic step response of the TOutAir for decrease in Maininlet air flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

B.8 Dynamic step response of the TOutAir for decrease in maininlet air temperature . . . . . . . . . . . . . . . . . . . . . . . 130

B.9 Dynamic step response of the TOutAir for decrease in MAINinlet air temperature(modified) . . . . . . . . . . . . . . . . . 130

B.10 Dynamic step response of the TOutAir for decrease in MAINinlet air flow(modified) . . . . . . . . . . . . . . . . . . . . . . 131

B.11 Absolute Humidity in Dryer For feed step up with modification132

B.12 Response for the system G(s)evap . . . . . . . . . . . . . . . . 132

B.13 Simulink dynamic model . . . . . . . . . . . . . . . . . . . . . 133

xvi LIST OF FIGURES

C.1 Test Step & Results for the entire test on MSD-20 . . . . . . 138

C.2 Moisture content of the particle from the SFB discharge . . . 139

C.3 Test Step & Results for change in feed rate on MSD-20 . . . 140

C.4 Feed flow rate and Nozzle pressure results from test on MSD-20141

C.5 Test Step & Results for change in Main inlet air temperatureon MSD-20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

C.6 Test Step & Results for change in Main inlet air flow on MSD-20143

C.7 Test Step & Results for change in SFB inlet air temperatureon MSD-20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

C.8 Test Step & Results for change in SFB inlet air flow on MSD-20145

C.9 Ambient Air Condition at Intake . . . . . . . . . . . . . . . . 146

C.10 Logbook From Test on MSD-20 week 30 2009 . . . . . . . . . 147

C.11 Logbook From Test on MSD-20 week 30 2009 . . . . . . . . . 148

D.1 Thermal Conductivity of Air vs. Temperature . . . . . . . . . 154

D.2 Thermal Diffusivity of Air vs. Temperature . . . . . . . . . . 155

D.3 Kinematic Viscosity of Air vs. Temperature . . . . . . . . . . 156

E.1 Air Stream and particle trajectory in mixed flow chamber . . 160

F.1 Mass evaporated for various particles sizes . . . . . . . . . . . 161

F.2 Mass Transfer coefficient for various particles sizes . . . . . . 162

F.3 Crust resistance f for various particle sizes . . . . . . . . . . . 162

F.4 Drying time for particle -various feed flow . . . . . . . . . . . 163

F.5 Crust resistance f for various feed flow rates . . . . . . . . . . 163

F.6 Drying time for particle -various Main inlet air flow . . . . . 164

G.1 Control variable as a first order system . . . . . . . . . . . . . 165

H.1 Model Misfit Vs Number parameters for ARX model . . . . . 169

H.2 Zero-Pole plot for the 10th order ARX model . . . . . . . . . 170

H.3 ARMAX model 1 . . . . . . . . . . . . . . . . . . . . . . . . . 171

LIST OF FIGURES xvii

H.4 ARMAX model 1 . . . . . . . . . . . . . . . . . . . . . . . . . 172

H.5 ARMAX model 1 . . . . . . . . . . . . . . . . . . . . . . . . . 172

H.6 ARMAX model 1 . . . . . . . . . . . . . . . . . . . . . . . . . 173

H.7 ARMAX model 1 . . . . . . . . . . . . . . . . . . . . . . . . . 173

H.8 Zero-Pole plot for ARMAX 6th model . . . . . . . . . . . . . 174

H.9 Zero-Pole plot for ARMAX 6th model 1 . . . . . . . . . . . . 175

H.10 Zero-Pole plot for ARMAX 6th model 2 . . . . . . . . . . . . 176

H.11 Zero-Pole plot for State space model 4th order . . . . . . . . 177

H.12 Zero-Pole plot for State space model 4th order continuos time 178

I.1 Frequency response of the linearized model process input tooutput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

I.2 Frequency response of the linearized model- Feed flow inputto output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

I.3 Frequency response of the linearized model- disturbance input(Solids content) to output . . . . . . . . . . . . . . . . . . . . 183

I.4 Frequency response of the linearized model- disturbance input(Ambient Relative humidity) to output . . . . . . . . . . . . . 184

I.5 Zero-Pole plot for the transfer functions - from each processinput to output . . . . . . . . . . . . . . . . . . . . . . . . . . 185

I.6 Zero-Pole plot for the transfer functions - from disturbanceinputs to output . . . . . . . . . . . . . . . . . . . . . . . . . 186

I.7 Comparison of linear and Non linear model: feed flow . . . . 188

I.8 Comparison of linear and Non linear model: feed flow 1 . . . 189

I.9 Comparison of linear and Non linear model: feed flow 2 . . . 189

I.10 Comparison of linear and Non linear model: Main inlet air flow190

I.11 Comparison of linear and Non linear model:Main inlet air flow 1191

I.12 Comparison of linear and Non linear model: Main inlet airflow 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

I.13 Comparison of linear and Non linear model: Main inlet airtemperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193


xviii LIST OF FIGURES



I.17 Comparison of linear and Non linear model: Solids content . 196

I.18 Comparison of linear and Non linear model: Solids content . 196

I.19 Comparison of linear and Non linear model: Relative humid-ity of ambient air . . . . . . . . . . . . . . . . . . . . . . . . . 197

I.20 Comparison of linear and Non linear model: Relative humid-ity of ambient air . . . . . . . . . . . . . . . . . . . . . . . . . 197

List of Tables

3.1 Modelling Approach . . . . . . . . . . . . . . . . . . . . . . . 15

4.1 The manipulated variables in test of the dynamic process(MSD-20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 The manipulated range of the variables in test of the dynamicprocess(MSD-20) . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 Default Operation Variable Values for Testing . . . . . . . . . 34

4.4 Steady State Results for the drying air temperature TOutAir . 36

4.5 Steady State Results of absolute humidity and equlibriummoisture content . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.6 Energy Level of the components . . . . . . . . . . . . . . . . 38

5.1 Ranz-Marshall correlation Parameter Values . . . . . . . . . . 53

6.1 Operating Point for linearization: Stationary state . . . . . . 78

7.1 Sensor Description for Test system(MSD-20) . . . . . . . . . 88

B.1 Default Operation Variable Values for Testing APPENDIX . 120

B.2 Steady State Results for the drying air tempereture TOutAir

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

B.3 Steady State Results of absolute humidity and equlibriummoisture content . . . . . . . . . . . . . . . . . . . . . . . . . 122

xx LIST OF TABLES

C.1 Sensor Description for Test system(MSD-20) . . . . . . . . . 135

C.2 Test Program for Test On MSD-20 . . . . . . . . . . . . . . . 136

H.1 ARMAX models . . . . . . . . . . . . . . . . . . . . . . . . . 168

I.1 Operating Point for linearization: Stationary state . . . . . . 180

LIST OF TABLES 1

0

2 LIST OF TABLES

Chapter 1

Introduction

Baby food, milk powder, coffee whitener, flavours, and various other prod-ucts are produced in a spray drying process.

Spray drying is a process that transforms a given feedstock from a fluid stateinto a dried particulate form by spraying the feed into a gaseous hot dryingmedium. The feedstock can be a solution, emulsion or fluid paste, though itis required that the feed is pumpable so it can be atomised into droplets. Theextensive contact between the droplets and the drying medium is the mainprinciple of the spray drying process, where the drying medium provides theenergy for the evaporation of the solvent in the feed. The resulting driedproduct is conformed to a powder of either single particles, agglomerates,granules, or pellets. The shape and structure of the particles depends onthe physical and chemical properties of the feed, spray dryer design, and theoperation conditions used.

The spray drying process, compared to other drying processes, is unique inits ability to dry liquid feedstock to powder with specific physical properties,particle morphology, and moisture content. The broad range of spray dryerdesigns available fulfils the specifications stipulated by various industriesboth in terms of product properties and production capacity. The spraydried product reduces transportation cost, as there is less liquid to transport,but also simplifies storage and handling.

Furthermore the spray dryer has the great advantage due to the ability todry both non-heat sensitive and heat sensitive materials. Thus the productcan be dried without any loss or changes in the volatile compounds of theproduct. These compounds can be the aromatic characteristics of the prod-

4 Introduction

Drying

chamber

Sta�c

fluid bed

Par�culates

separa�on /

collec�on

Feed

Air Air

Total dried product disharge

Figure 1.1: Spray drying process is characterised by a liquid feedstock that issprayed into a chamber in which contact with the heated dryingmedium(air) results in evaporation of moisture from the droplets.Drying takes place as the droplet moves through the drying cham-ber. If the particle reaches the bottom of the chamber and the dryingis complete the product is discharged. Some feedstock requires posttreatment of the particles to reach a specific powder characteristic. Toreduce the amount of particles in the exhaust air, a particle collectoris used to ’clean’ the air before leaving the drying system.

uct or some proteins in the product, which is especially important in thefood and dairy industries. Here spray drying helps with preservation of theproduct which gives product stability and extended shelf life by reducingthe moisture content to levels where microbiological growth is not possible.

In addition to this the spray dryer can handle materials under aseptic andhygienic drying condition which makes it applicable in the pharmaceuticalindustry. It has also proved its worth in the protection of the environment asit is capable of evaporating organic solvents which are potentially explosiveor have toxic risks. Thus spray dryers have a variety of industrial andcommercial uses and just a few examples were named here.

1.1 Description of the Problem 5

1.1 Description of the Problem

The objective of the spray drying process is to produce a product of a desiredquality at minimum cost, with maximum throughput and sustain the desireddried product quality regardless of the disturbances in the drying operationand variations in feed supply. Appliance of automatic control systems offersan opportunity to improve the dryer operation and its efficiency. However,the product quality, which is the parameter that is wished to be controlled,consists of sub parameters such as moisture content, thermal degradation,aroma retention, and structure and size of the particles. These parametersare difficult to predict, but also to measure online in the system, with theaim to be used as a control variable in the controller.

By experience it is identified that the most effective parameter to controlquality is the moisture content in the product. This can be measured witha suitable moisture sensor, but these are not used for controller purposes inspray dryers yet as these are expensive and have a low reliability at presenttime. It is recognised that the quality of the final product is the outcomeof the drying conditions in the chamber, with respect to temperature andhumidity. Therefore the spray dryer uses the outlet drying air leaving thechamber to describe the drying condition and uses it as a control variablein a feedback control. So the moisture content is controlled indirectly bymaintaining a specific outlet drying air temperature by varying either thefeed flow into the dryer or the inlet drying air temperature.

So far the main spray drying operation controller is based on a single controlvariable and a single manipulated variable, a SISO control system, for whicha PI controller is utilised. The proportional gain and integral time constantsare selected from the experience of setting up previous spray dryers. Thisis often considered to be sufficient when the product moisture content canbe kept within a narrow limit. In case large variations or fluctuations areobserved these parameters are adjusted, which is an accepted and easy pro-cedure.

However, there is obviously potential in optimising the existing controlsystem or developing a more advanced control system by using analyticalmethods(MIMO- or Model Predictive Control System). This could minimisethe variations in moisture contents and improve the product quality. At thesame time this can lead to a more cost-effective drying, either by increasingthe throughput or reducing the energy consumption in the dryer, since spraydryers are known to have a relatively poor thermal efficiency compared toother drying processes.

With the purpose of being able to develop and analyse a control system, amodel of the spray drying system is required. There are two types of models:

6 Introduction

• An equipment model, which combines the factors that affects the spraydrying process and describes the environment the particles are expe-riencing as drying takes place.

• A particle model, which describes how the particles respond to thedrying environment.

There are several papers 1 on the study of how a single particle of a specificproduct reacts in certain conditions. There are also very detailed ’Compu-tational Fluid Dynamic’ (CFD) models that are able to illustrate the flowsof the particles and the air in the spray dryer very precisely. Common forboth cases are that the models have not been studied in a view to be usedin the development of the control systems in the spray dryer. But are moreused to examine the product for chemical purposes or in the developmentof the spray drying design. For the CFD models the calculation times arevery long, which is not acceptable.

1.2 The objective of the project

The object of this project is to construct a general dynamic equipment modelthat is fundamental and is able to predict and estimate the drying conditionsin the spray drying chamber as this is the factor that affects the quality ofthe powder. The model is developed in preparation to be further used inthe development of control systems for the spray dryer. However, the mainfocus in this project is the modelling and development process.

• The spray dryer that is modelled is of the type: multi stage dryer witha mixed air flow

– The focus is on the spray drying chamber and the condition in-side this for a running process. The start-up of the process isneglected.

– Modelling the temperature of the drying air is the main target.Subsequently the humidity level inside the chamber is of interest.These parameters have a significant influence on the drying of theproduct.

• The aim is to model the temperature and humidity levels in the cham-ber by using first principle methods.

1(Langrish and Kockel (2001)),( Shabde (2006)),( Ireneusz Zbicinski and Delag (2002)),(Ruud E.M. Verdurmen and JONG (2002)),( Lixin Huang and Mujumdar (2005)), (Kieviet(1997))

1.2 The objective of the project 7

– Mass and Energy balance equations are applied.

– Initially a steady state model of the spray dryer is examined.

– With the steady state model as the underlying basis a dynamicmodel is developed .

• The drying characteristics of the feed is examined.

– The equilibrium moisture content and the drying kinetics is stud-ied for maltodextrin which has been used as an example duringthe modelling.

– The particle behaviour, such as the agglomeration process andfines are neglected.

• For test and verification of the model, experiments on a multi stagespray dryer (MSD-20) at GEA Niro’s test station is conducted.

– step responses for this system was examined and data recorded.

– Data is used to compare steady state model results and the thedynamic response times for the dynamic model.

– The default operating settings for this dryer has been applied inthe models

• The dynamic model is linearised in order to analyse the system.

• System identification principles has been tried on the data collectedfrom the experiment on the MSD-20.

– A simple linear model of the moisture content in the particles asa function of the main process variables is tried to be estimated.

• In the last part of the project, the developed model is used to demon-strate that the model can be used for development and test of con-troller.

– A PI controller is applied to control the outlet temperature of thespray drying model.

8 Introduction

Chapter 2

Introduction to the Spray

Drying Process and Spray

Dryers

The spray drying process can be described by four stages: Atomization,spray and air contact, evaporation of the moisture from the droplets andproduct discharge.

ATOMIZATION SPRAY�AIR CONTACT DRYING OF SPRAY PRODUCT DISCHARGE

Liquid feed into

a spray of drop-

lets

Mixing and flow

pa"ern

Moisture

evapora#on

Separa#on of

dried product

from the air

STAGE 1 STAGE 2 STAGE 3 STAGE 4

Figure 2.1: Spray drying consists of four process stages. This involves sprayingof liquid, contact and mixing with drying air, droplet drying parti-cle formation and at last powder collection. These four stages areillustrated in figure 2.2

The plant in which the spray drying process takes place is a spray dryer.Spray dryers exists in various designs with regards to size, type(conventional,compact, tall-form, multistage etc), air flow characteristics (Co-current,counter, and mixed air flow) and mobility. The spray drying design andmode of operation, together with the physical and chemical properties of

10 Introduction to the Spray Drying Process and Spray Dryers

the feed determines the final characteristics of the dried product (particlesize and structure). The spray dryer used in this project is a Multi StageDryer (MSD) as illustrated in figure 2.2. The multi stage refers to the factthat post-treatment equipment for the powder is a part of the spray dryingsystem, which will be elaborated below.

Fan Heater

FeedExhaust air

Fines

Air outDrying air - Main

Drying air - SFB

Powder out

Cyclone /

Bag filter

Vibro Fluidizer

SFB

MULTI STAGE DRYER

STAGE 1

STAGE 2

STAGE 3

STAGE 4

Figure 2.2: Multistagedryer with mixed air flow. Feed enters the spray dryingchamber from the top. Air is drawn from atmosphere by a fan andheated with a heater. The heated air is mixed with the feed, whichfalls down while it dries. The base of the chamber is the static fluidbed(SFB) and is used for agglomeration and to finalize the drying of thepowder. Air outlet is at the top of the chamber. A cyclone and bagfilter is to filter the exhaust air for fine particles. The vibro fluidizeris for post treatment of powder [GEA Niro].

At the first stage the feed is pumped from the feed tank to the atomizer1.

1In some cases the feed is send through a preheater/evaporator with the intention of

11

The atomizer is either a rotary atomizer (rotating disc) or a nozzle whichmakes a spray of droplet. The nozzle atomizer which is operated in thesystem that is examined in this project utilizes pressure to create dropletsthrough an orifice. The atomizer is located at the ceiling of the chamber.The formed droplets are mixed with the drying air and evaporation com-mences.

The air is drawn from the atmosphere by a fan and passed through a heater.In this spray dryer setup the air flow is mixed, which means the drying airenters the dryer both from the top of the chamber and from the bottom.The drying air entering from the ceiling of the chamber is denoted as theMain inlet air. The air from the base of the chamber is the Static Fluid Bed(SFB) inlet air. The air leaves the chamber from the top of the chamber aswell, which is mentioned as the outlet air.

Following the evaporation of moisture from the droplets the majority of thedried particles fall down to the base of the drying chamber. A Multi stagedryer has a Static Fluid Bed at this place which serves to finalize the dryingof the product and for agglomeration. Agglomeration is the process wherewet or partially dried droplets get in contact with dry particles and formslarger particles. This is illustrated in figure 2.3. The air leaves the chamberfrom the top of the chamber as well, which is mentioned as the outlet air. Acyclone and/or a bag filter are used to filter out particles from the exhaustair. The filtered particles are referred to as fines and these are led back intothe chamber to increase the agglomeration process.

Figure 2.3: Agglomeration Process Schematic. Dry particles(fines)collision withwet particles, and thus gets into a structure or increase its size bygetting more layers[GEA Niro].

increasing the viscosity of the feed or increasing the solids content in the feed.

12 Introduction to the Spray Drying Process and Spray Dryers

The choice of spray drying setup, which includes drying chamber design,atomizer, air inlet and disperser has an influence on the resulting powdersize and how the product reacts to the temperature and humidity profilesexisting in the dryer due to the selected operation conditions. Besides thedesign of the spray dryer and its equipment, the chemical composition ofthe solids, affects the particle shape and formation during the drying.

Particles are continuously discharged from the SFB. These are led to a vi-brating fluid bed, which is equipment for post treatment of the powder.However, the focus in this project has only been on the spray drying cham-ber.A more detailed description of the spray dryer design and its equipmentis found in (Masters (2002)).

The terms droplet and particle has been alternately used throughout thereport to describe the element which is dried. To elaborate this: an elementwhich enters the drying chamber is at the outset a droplet and turns into aparticle as it solidifies.

Chapter 3

Modelling

With the intention to be able to evaluate more advanced or novel controlstrategies, an understanding of the static and dynamic properties of thespray drying process is needed. This can be obtained with an estimatedmathematical model of the plant. Describing and developing a completelyaccurate mathematical model of a spray drying process is a complicatedassignment due to high complexity of the physical, chemical, and mechanicalproperties in such a system. This embraces for instance the heat and masstransfer both within the particle at the boundary between the solid phaseand liquid phase, but also the particle and surroundings. Another aspectof this multifaceted process is the accounting for the various entrances ofthe drying medium into the spray dryer and the resulting flow patterns forthe gas and the particles. However, in all models some uncertainty in theprocess behaviour will arise due to unmeasured disturbances, unmodelleddynamics and nonlinearities. Although the mathematical model only willbe an approximation of the real process, it will be acceptable if it is capableof giving a practically realistic representation of the process and thus satisfythe previously defined objective.

The use of steady state models are well established in chemical engineeringfor plant analysis that can be used to calculate the necessary process condi-tions for an optimal exploitation of the system concerning powder propertiesand energy consumption. However, a dynamic model is an important partof operability study, both in assessing the consequences of plant malfunctionand in the mitigation of possible effects. Moreover it gives a better under-standing of process performance and is therefore a significant instrument forprocess optimisation.

14 Modeling

To decide which approach to use for a modelling task the required level offlexibility, time frame or validity goal, available resources , and the numberof approximations that is acceptable, has to be considered. In the forthcom-ing section different methods to develop or estimate a dynamic model areexplained (Labspace (2009)),(O’Callagan and Cunningham (2005)).

3.1 Black Box model

The black box modelling strategy is used for investigating a complex systemwith no or minimal knowledge and assumptions about the process and theinternal structure. Such a model is represented by an empirical descriptionor a set of transfer parameters that relate the output of the model to a setof inputs. With the sufficient data available, containing the significant dy-namics of the system, an estimate of a model is achievable and is known assystem identification. Thus the need of experimental data for this methodinvolves data collection, determination of model structure, parameter esti-mation, and model validation. However correct the dynamics are revealed inthe model, the physical details of the process are excluded. The determinedmodel is specific to the system, operating region, and the product whichdata is extracted from.

This lack of flexibility is the main disadvantage of black box modelling, sincethe effect of changes in any of the process conditions outside of those metduring the structuring of the model cannot be concluded. Another constrainton this type of model, is the lack of any form of physical meaning, whichmakes it difficult to relate it to the real object being modelled. Nonethelessit has proven its effectiveness in situations where important parameters arecomplicated to identify and measure online, such as the residual moisturecontent in the final powder. This subject will be elaborated in section 7.

3.2 White Box model

A white box model is the most detailed and comprehensive category withinmodelling. It is based on a first principle approach, which describes thephysical processes at the lowest level. The result will be a true nonlineardynamic model and as close as possible to the true description of the plant.In contrast to the black box model, this type of model will be fully predictive,even in the situation when changes in process conditions are outside thenormal operating conditions. In spite of the fact that the model is flexibleand realistic, the outcome could be a model of great complexity. The morecomplex a model is, the more difficult it will be to identify the increased

3.3 Grey Box model 15

number of parameter values. A pure white box model cannot exist as it isessentially a copy of the reality. So what is needed, is a model with a simpleapproach but which demonstrates realistic process phenomena. Thus themajority of simulation models are grey box models.

3.3 Grey Box model

A grey box model provides a physical representation of the system, thoughsome of the physical parameters are simplified or approximated by an em-pirical model. This hybrid model structure is the result of the combinationof the best properties from the white and black box model, and the methodthat is used in this project: the flexibility enables one to model the plantdesign and determine the effect of variations in chamber size or changes inmaterial parameters. In addition to this it is physically close to the real pro-cess, however, a convection heat transfer coefficient is utilized to describe theheat changes around a particle instead of a model of the actual laminar flowthat requires an airflow model. An empirical model is chosen for determi-nation residual powder moisture content. The reasonable trade-off betweencomplexity and performance is suitable from a control point of view.

3.4 Chapter Summary

Modelling ApproachType Advantage Disadvantage Time Frame

White box Extremely flexible High Complexity LongRealistic Large computer power

slowBlack box Parameter identification Low flexibility Short

Minimal computer power Non physicalFast

Grey Flexibility Error checking mediumphysicality

Table 3.1: Summing up the pros, cons and the time frame for the three modelingapproaches. The time frame is connected to flexibilty requirement.

16 Modeling

Chapter 4

Modelling a Spray Dryer

In this chapter the white box modelling method described in chapeter 3 isapplied to model the spray drying process. Explaining the reality completelyby physical equations is difficult. For that reason some simplification aremade which is elaborated in the follwing section.

4.1 Preparations and Assumptions for Modelling

Modelling the spray dryer can be done at various levels and degrees of details,from describing the flow, reaction rate and the effect on circumstances ofdroplet of a liquid to the overall energy flow and mass flow for the totalspray dryer. The purpose with modelling the spray dryer in this project isto be capable of estimating and predicting the temperature of the drying airin the spray drying chamber, which is to be used further in the control ofthe moisture content of the final product. There are four main phenomenain a spray drying operation:

1. Atomisation of the liquid feed

2. Drying of the droplets once they are formed

3. Motion of the droplet in the spray drying unit

4. Product discharge

The region of interest is the spray drying chamber and on the drying ofthe droplets once they are formed. Modelling the motion of the droplet is

18 Modelling a Spray Dryer

recognised as being dependent on the geometry of the chamber and the me-chanical setup of the system. Thus it is more of a mechanical problem, sincethe motion of the particles cannot be directly controlled with the flow andtemperature parameters we have at hand. To describe this class of prob-lems, ”‘rate based models”’, which are dynamic models that describe the rateat which the solvent removed from the droplets as they travel through thespray drying chamber can be used(Gauvin and Katta (1976)). Otherwise the”‘particle-source-in-cell”’ models, that assumes the droplets to be a sourceof mass, energy and momentum in a grid of the drying gas can also be usedPapadakis (1988). Due to the complexity of calculating the heated dryinggas flow and particle motion, it usually requires ”‘Computational Fluid Dy-namic”’ (CFD) techniques, which are tools that use numerical methods andalgorithms, to solve these models. The disadvantages using this approachare the long calculation times and model parameter values that may haveno physical meaning.

Therefore a simpler mass and energy balance model, incorporating equi-librium relationships on the amount of moisture in the particle is utilized.Chemical reaction engineering techniques have been considered and used tomodel the spray dryer, in view of the fact that the drying process can beviewed as a reaction (mixing) between gas and liquid/solids (vapour). Thereaction process can be represented either as in a ”‘Continuously StirredTank Reactor”’ (CSTR), a plug flow reactor or a sequence of these.(4.1)

Figure 4.1: Schematic of a CSTR and a plug flow reactor. The effluent com-position of the CSTR is identical to the conditions that exist in thereactor. For the plug flow reactor the outlet condition varies alongthe length of the tube.

In the CSTR the contents of the reactor are assumed to be ideally well mixedand the reactants and products flow into and out of the reactor continuously.This means that the temperature, pressure and concentration levels are in-

4.1 Preparations and Assumptions for Modelling 19

dependent of spatial position within the reactor. Accordingly it also impliesthat the composition and the temperature of the effluent flow are identicalto the gas in the chamber.

The plug flow reactor is an ideal flow assumption in a tube in which the fluidis well mixed in the radial and angular directions. The velocity, compositionand temperature of the fluid are functions of the axial position (along thelength of the tube) only. The plug flow can also be described as an infinitenumber of CSTR’s in a cascade connection. To model a co-current spraydryer (Air inlet from top and outlet air in the bottom), it is anticipated thatthis reactor type will give the best representation. But due to the fact that amodel of a mixed flow spray dryer is wanted, which has an inlet air flow fromthe top and the bottom of the chamber, it is expected that the well mixedCSTR reactor model is most suitable and will illustrate the inlet air mixingbest. Moreover the air leaving the dryer is from the top of the chamber andthus using a CSTR model, this temperature will not dependent on the travellength of the air flow.

Additionally, when looking at the temperature profile for a mixed flow spraydrying chamber (figure 4.2), it is observed that the chamber temperature toa great extent is the same and well mixed, except at the air inlet entranceswhere the temperature is higher due to the heated air. Therefore it is as-sumed that the spray dryer can be modelled as a CSTR process.

The model prepared is based on the following assumptions and simplifica-tions:

1. The Spray drying process is modelled as Continuously Stirred TankReactor (CSTR). In this the drying gas and the feed are continuouslyinjected into the chamber at uniform flow rates. The state of the gasin the chamber is identical to the state of the gas leaving the chamber.

2. The model will be based on mass and energy balance with equilibriumrelationship incorporated.

3. The gas is assumed to be a composition of dry air and vapour, whichbehaves as an ideal gas and flows as a perfect mixture. This has aninfluence on the calculations of the gas density and as well on therelation between absolute humidity and the partial vapour pressure.

4. The liquid feed is assumed to be completely atomised, that is all thedroplets are of uniform size and homogeneous. In figure 4.3 particleswith various amount of maltodextrin are depicted and as expectedthe particles are not perfectly spherical. However for simplicity theparticles are modelled as having a spherical shape. They are all wellmixed in the chamber and do not interact with one another. Because of


Figure 4.2: Temperature profile for a mixed flow spray dryer. The figure to theleft is the temperature profile given by Masters (2002). The arrowsindicate air flow. The dotted arrows point towards product flow di-rection. The figure to the right is a temperature profile with relativetemperatures(GEA Niro). Red is hot. Blue is less warm. It is seenon the figures that a great part of the chamber, except from the airinlet entrances, has the same temperature. Due to this information itis assumed that the spray dryer can be modelled as a CSTR process.

this simplification, the agglomeration process is disregarded, as therewill be no small particles (fines) nor will there be created any, due tono collisions of particles.

4.2 Steady State Mass and Energy Balances for

Spray Dryers

The spray dryer operating requirements are found by solving mass and heatbalance calculations in steady state which is very common in chemical en-gineering. With the production rate requests, feedstock, dried product, andambient air properties at hand, the air flow rate requirements can be es-timated. Correspondingly the moisture content of the final product, for apresented drying air flow, can be calculated at certain conditions. For thisto succeed it is presumed that the dryer is well mixed and hence the gascondition is uniform inside the drying chamber. It is expected that the out-let gas and outlet particles are in equilibrium, such that the temperaturesof these elements are equal. Accordingly the solids moisture content of theoutlet product is in equilibrium with the gas temperature and humidity. The

4.2 Steady State Mass and Energy Balances for Spray Dryers 21

Figure 4.3: Morphology of rice starch with little maltodextrin in particle on theleft picture and increased amount of maltodextrin on the right picture.Though the particles are not completely spherical, this is assumed inthe modelling. The density of the structure is also dependent on thedrying temperature.[GEA Niro]

equilibrium moisture content is the moisture content at which the product isneither gaining nor losing moisture; this however, is a dynamic equilibriumand changes with relative humidity and temperature.

In the following the equations of the mass and energy balances, for an opencycle mixed flow spray dryer with an aqueous feedstock, are illustrated. Theconservation of mass and energy in a steady state flow process is expressedas: the rate of mass/energy flow into the system is equal to the rate ofmass/energy flow out of the system. First the energy balance is consideredin (4.1). In figure 4.4 a diagram illustrating input and output to the systemand a variable description for the following equations.

FMaindryHairIn + FSFBdryHairIn + FfeedHfeedIn

= FOutdryHairOut + FpowderHpowderOut (4.1)

Where FMaindry is the Main inlet air flow, FSFBdry is the inlet air flow from

the SFB while FOut is the outlet air flow, all of them in dry form(Kgs ).

The dry components are easier to handle in the equations and later in thischapter it is shown, how these are determined from the true humid air flow.The humid air is a mixture of mv mass of water vapour and mass mdryAir

of dry air. FFeed is the flow rate of the feed in (Ls ) and Fpowder is the flow

of powder out of the system(Kgs ). The enthalpy H is a composite energy of

the internal energy of the constituent atoms and the flow work associatedwith forcing streams in and out of a system against a pressure. It has theunit energy per unit mass( J

Kg ). The enthalpy of mixtures such as the humiddrying medium, the feedstock etc. is the sum of the partial enthalpies ofthe components and a residual enthalpy term which for example takes intoaccount the heat of mixing. However, in this report the influence of the

22

ModellingaSprayDryer

SPRAY

DRYER

WEEL MIXED

MAIN INLET DRYING AIR

Flow

Absolute humidity

Enthalpy

Temperature

Specific heat capacity dry air

SFB INLET DRYING AIR

OUT LET AIR

FEED IN

Moisture content

Feed (liquid)

AMBIENT AIR

Rela!v humidity

Temperature

OUT LET PRODUCT

Specific heat capacity vapour

Flow

Absolute humidity

Enthalpy

Temperature



Flow

Enthalpy

Temperature

Specific heat capacity solid

Specific heat capacity water

Flow

Absolute humidity

Enthalpy

Temperature



Moisture content

Flow

Enthalpy

Temperature

Specific heat capacity solids

Specific heat capacity water

Kg/s

Kgmoist

/Kg dry air

KJ/Kg

°C

J/Kg"K

J/Kg"K

Kg/s

Kgmoist

/Kg dry air

KJ/Kg

°C

J/Kg"K

J/Kg"K

Kg/s

Kgmoist

/Kg solids

KJ/Kg

°C

J/Kg"K

J/Kg"K

Kg/s

Kgmoist

/Kg dry air

KJ/Kg

°C

J/Kg"K

J/Kg"K

Kg/s

Kgmoist

/Kgsolids

KJ/Kg

°C

J/Kg"K

J/Kg"K

Fmain

Yin

Hmain

Tmain

Cdry air

Cvapour

FSFB

Yin

HSFB

TSFB

Cdry air

Cvapour

Ffeed

Xin

Hfeed

Tfeed

Csolid

Cwater

Fout

Yout

Hout

Tout

Cdry air

Cvapour

Fout

Xout

Hout

Tout

Csolid

Cwater

Powder out

Figure 4.4: Basis Blockdiagram- variable description for the system used in energy and mass balance equation. The block describes theinput and output for air and product. The block shows the true flows of the air flow and feed flow. In the calculations theseare modified into dry flows for easier use.


residual enthalpy is neglected as this value often is very small comparedto the enthalpy of the main components (≈ 1%). With this definition thehumid air enthalpy for both inlet and outlet airflow is defined in 4.2:

HhumAir = HdryAir + Y Hvapor (4.2)

Y is the absolute humidity or moisture content in the air expressed by the

relation between mass of vapour and dry air mv

mdryAir,(

KgvapourKgdryAir

)

. From being

YIn at the inlet it increases during the spray drying operation to Yout. Interms of specific heat the enthalpy is given by:

HhumAir = CdryAir(Tair − Tref ) + Y (λ+ Cvapor(Tair − Tref )) (4.3)

where CdryAir is the specific heat capacity of dry air ( KjKg·K ), Cvapor is the

specific heat capacity for water vapor KjKg·K . The heat capacity is defined

as the energy required to raise the temperature a unit mass of a substanceby a unit temperatur. The specific heat capacity is temperature dependent,however, it is convenient to use mean values for this parameter, which isthe heat capacity evaluated at the arithmetic mean temperature for a giventemperature range. This has been used through the entire project. Tair isthe air temperature(oC), Tref is the reference temperature. (0oC), is usedas the reference temperature at which there is zero enthalpy. λ is the latentheat of vaporization, which is the heat required for water to change fromliquid- to gas phase (vaporize).

(4.3) is a simplification since it is assumed that the final enthalpy is inde-pendent of the vaporisation path, accordingly the vaporisation is assumedto take place at (0oC) at which the enthalpy is chosen to be zero and thensuperheated to the air temperature Tair. Originally to reach vapour state,the vaporisation occurs at the dew point temperature, which is the temper-ature at which the air become saturated and then heated up to the final airtemperature. This becomes of practical importance for the calculations ifthe absolute humidity is above 0.05 Kgwater

kgdry(Mujumdar (2007)). The en-

thalpy of the feed entering the dryer is the sum of the enthalpy of the drysolid and the moisture liquid in the product

Hfeed = Csolid(Tfeed − Tref ) +XInCwater(Tfeed − Tref ) (4.4)

Hpowder = Csolid(Tpowder − Tref ) +XoutCwater(Tpowder − Tref ) (4.5)

where Csolid and Cwater are the specific heat capacity of dry solid and water.XIn/out is the solids moisture content and is based on a unit weight of dry


product (Kgwater

Kgsolids) . The reason for using a dry basis in the equations above

for the air and powder moisture content is that the flow rates of the dryair and the dry solids is the same at both the inlet and outlet, which makesthe calculations more straightforward as the moisture now is directly relatedto the dry substance. (4.5) for the enthalpy of powder leaving the dryer issimilar to the enthalpy of feed (4.4). It is assumed that all the moistureevaporated from the feed is absorbed by the outlet air and taken out of thedryer. Hence the moisture content in the final powder can be related to theoutlet humidity of the dryer by a mass balance.

4.2.1 Mass Balance

The mass balance over the spray dryer relates the moisture entering thedryer with the outgoing moisture and gives (4.6). Due to the assumption ofa well mixed dryer and equilibrium state between outlet air and solids, theoutlet moisture content of the powder X0 is expected to be the equilibriummoisture content of the solid in the respective air conditions. The outletabsolute humidity Yout is then isolated.

FMainDryYIn + FSFBDryYIn +MsInXIn = FOutDryYOut +MsOutXOut

(4.6)

FMainDry + FSFBDry = FOutDry

MsIn =MsOut

Ms(XIn −Xout) = FOutdry(YOut − YIn)

YOut = YIn +Ms

FOutdry(XIn −Xout) (4.7)

(4.7) is inserted into the previously stated energy balance equation, whichresults in (4.8). Hereafter the unknown and unspecified parameters are:Primary and secondary inlet airflows, FMain and FSFB respectively and thebelonging air temperatures, TMain and TSFB, the moisture content of theair going into the system YIn, the moisture contents of the feed XIn and thefinal product XOut, and the in- and outlet solids rate MsIn and MsOut.

FMainDry(CdryAirTMain + YIn(λ+ CvaporTMain))

+ FSFBDry(CdryAirTSFB + YIn(λ+ CvaporTSFB))

+Ms(CsolidTfeed +XInCwaterTfeed)

= FOutDry(YIn +Ms

FOutDry(XIn −Xout))(λ+ CvaporTOutair)

+ CdryAirTOutair) +Ms(CsolidTpowder +XoutCwaterTpowder) (4.8)


TOutair = Tpowder (4.9)

In our present situation, the temperature of the outlet drying air and theresulting moisture content of the final product are the variables that arerequired to be estimated. As it can be seen from the two equations abovethese variables are influenced by the input operational variables and materialparameters outlined in the block diagram in figure 4.4. In the calculationprocess the input operational variables to the plant are assumed to be knownand predetermined. Thus by first determining the outlet powder moisturecontent, (4.7) can be solved for the outlet drying air humidity. Taking theassumption into account that the temperature of the gas and the product issimilar, this temperature can be computed from (4.8).

4.2.2 Equilibrium Moisture Content

The moisture content of the outlet powder is approximated to be the equi-librium moisture content. The equilibrium moisture content is the result-ing state of an interaction between the environment and the substance, towhich the moisture content of the substance converges to either by moistureuptake(adsorption) or by drying(desorption). It is noted that equilibriummoisture content may vary depending on whether the substance is exposed toadsorption or desorption. So changes in the moisture content of a substanceare dependent on the surrounding partial vapour pressure and temperaturecondition, but also on the nature of the solids. After an adequate amount oftime has passed with steady state condition an internal moisture diffusionbalance takes place until the equilibrium moisture content is attained. Thusfor the vapour pressure at a given temperature the substance will have astate where it will neither gain nor lose any moisture.

This relationship between the equilibrium vapour pressure and the moisturecontent in the substance can be presented by a moisture sorption isothermfunction. This sorption isotherm designates the equilibrium moisture con-tent for a certain humidity value, at a constant temperature and herebygives a description of a products ability to bind water. Due to the complex-ity of the sorption process, the isotherm cannot be determined analytically,but instead measured experimentally. Different products and materials havedifferent hygroscopic properties, which is affected by their molecular struc-ture and their solubility. There are various empirical relations describingthe sorption characteristics for food ingredients using different models inliterature.

The desorption isotherm for maltodextrin, which is the test material that hasbeen used in this project, is determined in (Jesus M. Frıas and Schittkowski


(2001)). Maltodextrin is a polysaccharide and consist of dextrose(glucose)molecules connected in a chain of variable length. The length of the moleculechain is described by a DE(Dextrose equivalent) number and explains itsproperties(flavour). The sorption isotherm found in (Jesus M. Frıas andSchittkowski (2001)) is for maltodextrin DE 12 and the maltodextrin usedin our test setup is of type DE 10. The difference was discussed with achemist from GEA NIRO and it was found acceptable to use the sorptionisotherm for maltodextrin DE 12.

As explained there will be a slight dissimilarity in moisture binding proper-ties though it is insignificant and can be neglected. The equilibrium mois-ture content model is based on Guggenheim-Anderson-de Boer (GAB) modelequation, as recommended by the ”‘European Project Group COST 90 onthe Physical Properties of Foods”’ 1 for the characterisation of water sorptionin food materials.

Xeq(T, aw) =CeqKeqWeqaw

(1−Keqaw)(1 −Keqaw + CeqKeqaw)(4.10)

Where the model parameters Wm, Ceq and Keq are determined by (JesusM. Frıas and Schittkowski (2001)). All the parameters are dependent on thetemperature of the solid in celsius.

Ceq = 0.04exp(1257.14

Tsolid + 273) (4.11)

Keq = 0.65exp(144.57

Tsolid + 273) (4.12)

Weq = 0.05exp(−99.27

Tsolid + 273) (4.13)

To characterise equilibrium vapour pressure in the sorption isotherm therelative humidity content of the drying air is applied, as the vapour pressurein the solid is equal to the partial vapour pressure in the drying air whenno more moisture can be lost to the surroundings and thus be equilibrium.This is also known as the water activity of the product aw. The equilibriummoisture content model is derived from desorption isotherm measurementsperformed at four different temperatures (4oC, 25oC, 37oC, 50oC). Sinceit is expected that the spray dryer will work at higher temperature rates,the behaviour of the model is tested at higher temperatures. In figure (4.5)a graph is produced in which the equilibrium moisture content is plotted

1http://www.esf.org/ (2/10-09)


against the relative humidity for various temperatures. If the relative hu-midity of the surrounding air is close to zero, then the equilibrium moistureinside the dry product also is nearly zero independent of the temperature.At higher temperatures a larger variation in equilibrium moisture contentis noted. The model is unrealiable for water activities above 0.9. For largevalues of water activities values (4.10) gets negative.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Water activity aw

Equ

ilibr

ium

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Desorption Isotherm for Maltodextrin DE12 at various Temperatures

4oC

25oC

37oC

50oC

65oC

85oC

100oC

115oC

increasing T

Figure 4.5: Desorption Isotherm Maltodextrin DE12: Equilibrium moisture con-tent as function of water activity for temperatures between 40C and1150C. If the relative humidity of the surrounding air is close tozero, then the equilibrium moisture inside the dry product also isnearly zero independent of the temperature. At higher temperaturesa larger variation in equilibrium moisture content is noted. The modelis unrealiable for water activities above 0.9

The relative humidity ψ of the vapour gas mixture is measured as the frac-tional saturation with moisture and is defined as the ratio of the partialvapour pressure Pv to the saturated pressure Psat at the same temperature:

ψ =Pv

Psat(4.14)

For drying to take place the relative humidity of the surrounding drying airmust be lower than the water activity of the product. The partial vapour


pressure is related to the absolute humidity of the surrounding air and isrecalled to be the ratio of vapour mass mv to mass of dry air mdryAIR. Usingthe gas law for the two fractions at constant temperature T and total volumeV results in (4.15). R is the universal gasconstant (8.314 J

(mol·K)

mv =PvV

RTMw

mdryAir =PdryAirV

RTMdryAir

Y =Pv

PdryAir

Mw

MdryAir(4.15)

Dalton’s law (4.16) states that the total pressure exerted by mixture of gasis equal to the sum of the partial pressures of each fraction in the mixtureand knowing the molar mass of water is Mw = 18.01 g

mol and and dry airMdryAir = 28.96 g

mol (4.15) becomes:

Ptotal = Pv + PdryAir (4.16)

Y = 0.622Pv

Ptotal − Pv(4.17)

The outcome of rearranging the above written equation is the partial vapourpressure as function of absolute humidity Y, since Ptotal is assumed to beequal to the standard atmospheric pressure : 101325 Pa(Langrish (2008)).

Pv =( Y0.622 )Patm

1 + ( Y0.622 )

(4.18)

At 100 % relative humidity, the partial vapour pressure equals the vapourpressure of liquid and the drying air or the surface of the substance is saidto be saturated with vapour. There are many formulations to calculate thesaturation vapour pressure.(4.19) (Richard Shelquist (2009)) used here issimple with only 3 parameters and still offers good results when comparedto the Smithsonian reference table for vapour pressure found in (Wiederholt(1997)). A deviation of 1 percent at high temperatures (above 100oC) andmuch less for lower temperatures from reference value is acceptable, as thiswill only have a very small effect on the relative humidity calculation andequilibrium moisture content (see appendix A).

4.3 Test on a Multi Stage Dryer- MSD20 29

Psat = 100 · C0 · 10C1T

C2+T (4.19)

C0 = 6.1078

C1 = 7.5

C2 = 237.3

With the system of equations put forward in this section, the temperatureand moisture content of the outlet air, Tout and Yout respectively can bedetermined. To that, the moisture content of the final product is estimated.The procedure is written in a Matlab script and solved with Matlab.

4.2.3 Steady State Solution

There are six unknown variables (Xout, Yout, ψ, Pv , Psat, and Toutair) and sixcorresponding equations ((4.19), (4.18), (4.14), (4.10), (4.8) , and (4.7))which means the system has a unique solution that is found by the followingiterative process.

1. X0 is initialised to have the same value as XIn, moisture in the feed

2. Yout is calculated using equation (4.7)

3. ToutAir is solved for equation (4.8), where Tpowder is set to be equal toToutAir.

4. Pv is calculated using equation (4.18)

5. Psat is calculated using equation (4.19)

6. ψ is calculated using equation (4.14)

7. Xout is calculated using equation (4.10). Hereafter the process is re-turned to the second step and a new outlet moisture value Yout iscalculated. This is reiterated until the process converges to the finalvalues. In the Matlab script the process stops when the differencebetween the previous determined temperature and the presently cal-culated temperature is less than (1/1000).

4.3 Test on a Multi Stage Dryer- MSD20

With the purpose of being able to validate the correctness of the dynamicsand the steady state values of the created model, a test has been prepared


and completed on a real spray dryer system. The tests was basically aboutputting in step changes at the most important input operation variables andexamine the resulting step responses for some significant output variables.Such a test on an actual system would depict the known but also the hiddendynamics of the system and thus explain its behaviour for certain changesin the system.

The test was completed on a Multi Stage Dryer(MSD)-20 open cycle2 systemat GEA NIRO’s test station in Soeborg, Denmark. Maltodextrin DE 10 wasused as the material to be spray dried. As drying gas atmospheric air wasapplied with the use of an electric heater. The system setup was as shownin figure 4.6.

The drying chamber has a diameter of 2 m and a height of 2.30 m, witha total volume of approximately 10.3 m3. Compared to the largest spraydryers used in the dairy industry which can be up to 16 m in diameter witha total volume of 1920 m3, this is a small one. This spray dryer can produceapproximately 70 kg

hour of powder.

The input variables which are chosen to be manipulated are the most signif-icant ones and have the greatest effect on the spray drying process. That isthe feed flow rate, given by sensor 1626, the Main inlet airflow and temper-ature, (sensor 1701) and 1702 respectively. Similarly the SFB inlet airflow(1703) and temperature (1704) are controlled. In the end the airflow intothe Vibrofluidizer is operated, but this is only commented superficially giventhat the focus in this project has been on the drying chamber and the processin it. The central output variables are the outlet air temperature (1709),outlet powder particle size and residual moisture content. (see table in app.C.1 and figure 4.6)

Furthermore in the figure the variables are marked as either manually (M) orautomatically (A) controlled. Automatical control indicates that a variableis controlled by a PI regulator when the specific variable value is set. Forthe manually controlled variable an operator sets the controller output value.As described previously, under normal circumstances the moisture contentof the powder leaving the dryer, is controlled indirectly by maintaining aconstant outlet drying air temperature through the regulation of the speedon the feed rate pump.

Throughout the test this feedback loop was disconnected, so the main sys-tem functioned as an open loop and the feed rate was controlled manuallywith pumps 1639 and 1606. The inlet air flows and temperatures were au-tomatically controlled, likewise the pressure inside the chamber. This isto prevent the chamber from crumpling up due to the air flows. The PI

2In a open cycle spray dryer the drying medium is not reused. Air enters one placeand exits at another place

4.3 Test on a Multi Stage Dryer- MSD20 31

parameters are shown in the logbook from the test in appendix C.3. The

Manipulated variablesSensor Name Description Control Unit

MAINKGH Main air flow into chamber Auto Kg/hT1702 Temperature of MAINKGH Auto oC

SFBKGH SFB air flow into chamber Auto Kg/hT1704 Temperature of SFBKGH Auto oCF1626 Feed flow into chamber Manual L/h

Table 4.1: The manipulated variables in test of the dynamic process(MSD-20).Auto= automatic control (PI), manual: Manual control

blue lines in figure 4.6 depict air flows, while the yellow lines show productflow. A cyclone was used to filter out the fines from the outlet air. Thesewere returned at the top of the chamber to be applied in the agglomerationprocess. The bag filter shown was disengaged.

Each variable is controlled in a number of steps within a maximum andminimum range(step up and step down) which is predetermined by the Testengineers at ’GEA Niro’, so the system stays in stable and workable pro-cess states. The standard values indicate the value the variables are keptat in normal operation. The variables are changed one at a time, while allthe others are kept constant and the entire dynamic process is recorded.It is essential that nothing else is modified throughout the test, thus onlythe response due to the specific step change is observed. However, distur-bances both measurable and immeasurable are still present which can affectthe responses. As disturbances the relative humidity of the ambient air(measured by sensor 1618), fluctuations in feed concentration and height ofpowder layer in SFB can be mentioned (1706).

The feed that was used in the test was a mixture of 50% solids and 50%water with variations within the measurement uncertainty (2%). Five tanksof mixture were used during the entire test and with no stirring of the feed,which contributes as a small disturbance. In an industrial dryer there isoften a preheater/evaporator on the feed input, which is advantageous notonly from a bacteriological point of view, but it also decreases the viscosityto improve atomizer performance. Moreover, increasing the solids concen-tration in the feed is a more energy effective, since less moisture has to beevaporated in the spray dryer.

4.3.1 The Test on MSD-20

The total number of test steps are 22 included those for the VFB. Fromrehearsal tests (24/6-2009) the settling time for the responses of the output


Manipulated variables Step rangeSensor Name Min Default Max

MAINKGH 1600 1800 2000T1702 150 160 170

SFBKGH 350 500 600T1704 80 90 100F1626 - 65 75

Table 4.2: The manipulated range of the variables in test of the dynamicprocess(MSD-20). The standard values indicate the value the vari-ables are kept at in normal operation. Min and Max values are thestep values used for test. In total there was 22 test steps includedthose for the VFB

variables for step changes was experienced. From this the test period for astep change in Feed rate and Main inlet air was estimated to have a lengthof 1 hour and 30 minutes as it was expected that the responses would havereached their final states. For SFB and VFB the length of the test periodwas 1 hour, since their influence on the final output values are small andless time is required for the response to settle.

The experiment was carried out in a continuous process (≈ 30 hours) inorder to avoid spending unnecessary amount of time on both system start-upand terminating the process. All the variables are sampled and logged everysecond and every tenth second. The moisture content and particle size ofthe outlet powder though is measured off-line, for this reason a sample of thepowder from the SFB outlet and the VFB outlet is taken every fifth minuteand send to the laboratory. The result from the laboratory is an averageparticle size and moisture content. Triple tests in the laboratory of samplesverified, that the results from the used method for determining the moisturecontent has a measurement uncertainty of 1 percent when tests are repeated.For the particle size determination the uncertainty is 2 percent. The powderdata is linearly interpolated in the intervals between two samples, in thisway the data can be applied with the one or ten second measurements ofthe system.

The tests were completed successfully, despite small adjustments on an os-cillating controller and on the height of the powder layer in the SFB whichis an indirect description of the powder residence time in the SFB. This iscontrolled by setting the time on how often powder is sent out from the SFBthrough a lock.

The results are used in the further study of the spray dryer and for modelverification in the steady state and dynamic modelling (see section 4.2 and5.4), where the results are examined and discussed. Furthermore they are

4.4 Steady State Calculations 33

used for estimating a model for the prediction of the powder moisture contentby system identification (see section 7). Since some of the steps have beenrepeated, some part of the tests could be applied as estimation data and therest of the test data is used as validation data for the identified model. Theentire test program and graphical plots of the time responses are found inappendix C

4.4 Steady State Calculations

It is desired to compare the results derived from the model with the resultsfrom the experiment on the real system MSD-20(see section (4.3) for testdescription). Hence the same operation conditions, as were used on thereal plant, were applied to the steady state model to create similar processconditions. The operation parameters and the specific values for the plant towork at a default normal state are explained in table 4.3. It should be notedthat the flow rates are given in mass per hour. These have to be divided by3600 sec to get the flow rate in seconds. As drying gas atmospheric air isapplied and the solvent in the feed is water.

As stated previously the air and feed flow rates in the mass and energyequations are based on dry gas and dry solids flow, which are calculatedfrom the initial moisture content in air YIn and feed XIn. The dry air flowrate is decided by determining the ratio of mass of dry air to the mass oftotal air as displayed in (4.20).

Fdry =1

YIn + 1Fflow (4.20)

Ms = FFeed · ρfeedSconc (4.21)

Likewise the dry solids flow is estimated from the amount of solid, Sconc,in the feed (4.21). The feed flow process value is given in L

s on the real

plant and therefore also used in the model. This is converted into kgs by

multiplying the feed flow with the density of the feed, ρfeed. Since it has notbeen possible to find any functions describing the density of the maltodextrinthat was used in the experiment, the density function is approximated, afterconsultancy with Chemists from GEA NIRO, to be the same as for milkconcentrate without any fat and is given in (4.22). The total feed densityis a combination of solids amount in percentage of total feed S, the densityof lactose (Carbonhydrate)D1 , and density of water D2, which are both


Default Operation ValuesVariable Name Description Value Unit

FMAIN Main air flow IN 1800 Kg/hTmain Temperature of MAIN 160 oCFSFB SFB air flow IN 500 Kg/hTSFB Temperature of SFB 90 oCFfeed Feed flow IN 65 L/hρfeed Density of feed 1.208 Kg/LSconc Solid concentration 0.5 Kg/KgfeedTfeed Temperature of feed 50 oCTamb Temperature of ambient air 30 oCψamb Rel. humidity ambient air 28 %Solid solids of total feed 50 %XIn Initial Moisture Content 1 Kg/KgsolidPatm Standard Atmospheric pressure 101325 PaYIn Absolute Humidity air IN 0.0079 Kg/Kgdryair

Specific Heat Capacity

Cdryair Dry air 1 KJ/(Kg ·K)Cvapour vapour 1.8 KJ/(Kg ·K)Cdryair Maltodextrin 1.5 KJ/(Kg ·K)Cwater water 4.2 KJ/(Kg ·K)λ latent heat of vaporisation 2500 KJ/(Kg)

Qloss

UChamber heat transfer coefficient (chamber) 16.75 KJ/m2/hAChamber Surface area(chamber) 26.2 m2

Table 4.3: The manipulated variables’ default operation values for test of themodels. These are equal to the operation values used at the test ofMSD-20.Note that the flow rate are not on dry basis, but the totalamount(sum of Moist and either dry air or dry solids.)

functions of the feed temperature Tfeed (Refstrup).

ρfeed =100

S( 1D1 − 1

D2) +100D2

(4.22)

D1 = 1.635 − 0.0026 · Tfeed + 2 · 10−5Tfeed2 (4.23)

D2 = 1.0020825 − 1.14 · 10−4Tfeed − 3.325 · 10−6Tfeed2 (4.24)

S = Solids in % (4.25)

The initial moisture contents XIn is known as the ratio of water to solids inthe feed.

XIn =0.5kg water

kg feed

0.5kg solidkg feed

(4.26)


Moreover the table shows the ambient air humidity and temperature condi-tion that are used in the model calculation. Obviously these circumstanceschanged during the 11

2 day experiment as it can be seen on the plot of thetemperature and humidity in appendix C.2.10. Therefore an approximatedaverage value for ambient temperature and relative humidity are chosen forthe calculations of the absolute humidity in the air going into the chamber,YIn((eq. 4.14), (4.19),and (4.7)).

4.4.1 Steady State Results

The model has been exposed for the same tests and changes on the processvariables as for the experiment on the real spray dryer and followed the sametest procedure. At the outset the model is at the default state given by theparameters in table 4.3. For each test a process variable was changed, whileall the other variables were kept at default state. The resulting estimate ofthe outlet air temperature compared to the results from the tests on MSD-20 is shown in table 4.4. To this point the heat losses from the spray dryerhave been neglected in the energy balance equation. Nonetheless, as it isobserved from the results, the temperature calculated without any heat lossis significantly higher than the temperatures measured on MSD-20.

In view of the fact that the model is ideal and the drying is complete (allpossible moisture is evaporated), the drying course is not the possible reasonfor the higher temperature at the outlet, as more energy cannot be used onevaporation and thus decreasing the temperature. It is expected that thelower temperatures from the experiment to some extent can be attributedto the heat losses through the spray dryer outer cladding and structuralsupports. Another possible reason for the lower temperatures in the realexperiment is due to the cooling air for the air disperser at the top of thechamber which has been omitted in the model. Moreover the system ismodeled as a CSTR, in which the temperature is well mixed through theentire chamber. However, on the real system the outlet temperature ismeasured at the exit of the chamber, while at the inlet air entrances, thetemperature is a little higher. Thus there are some small regions in thechamber that will have a higher temperature than the rest of the chamber,which the model does not take into account.

The heat loss is expressed by the standard heat transfer equation in (4.27)and added to the right hand side in the energy balance equation (4.8).

Qloss = UchamberAchamber∆T (4.27)

∆T = TOutAir − Tamb (4.28)

The heat transfer coefficient Uchamber for properly insulated drying chambers


Steady State ResultsNo Loss Loss Included TEST

Test TOutAir TOutAir TOutAir

Description Temperature Temperature Temperature

Default System 101.5 oC 86.1oC ≈ 86oCFfeed = 75 L/h 95.3 oC 80.6oC ≈ 81oCTmain = 150 oC 94.2 oC 79.9oC ≈ 79oCTmain = 170 oC 108.9 oC 92.4oC ≈ 90oC

FMAIN = 2000 kg/h 106 oC 90.9oC ≈ 89oCFMAIN = 1600 kg/h 96.3 oC 80.6oCFSFB = 600 kg/h 101.1 oC 86.2oC ≈ 84oCFSFB = 350 kg/h 102.3 oC 85.9oC ≈ 83oCTSFB = 80 oC 99.5 oC 84.4oC ≈ 82.5oCTSFB = 100 oC 103.6 oC 87.9oC ≈ 85.6oCTamb = 50 oC 102.1 oC 86.7oCTamb = 10 oC 101.3 oC 85.9oCRHamb = 75 % 102 oC 86.7oCRHamb = 10 % 101.4 oC 85.9oC

Sconc = 0.8 Kg/Kg 124.7 oC 105.7oCSconc = 0.2 Kg/Kg 78.6 oC 66.7oC

Table 4.4: Steady State Results for the drying air temperature TOutAir calculatedwith the operation variables values as used in the real test on MSD-20, with an energy loss function included and without a loss function.These are compared with the results from the Test on MSD-20

with mineral wool or similar materials is in the order of 1-2 Kcalm2h

(1 Kcal(m2h)

=

4.187 KJ). For non isolated drying chambers the heat transfer coefficient isaround 5-7 Kcal

m2h. The heat transfer coefficient is in the model chosen to be

equal to 4 Kcalm2h

, although the MSD-20 spray dryer is non-isolated and pre-sumably have a higher heat transfer coefficient than the chosen value. Butto compensate for the complete drying of the powder, which gives the lowestpossible drying air temperature due to more energy being used for evapora-tion, the lower value is selected. Including this into the calculations of theiterative process with a loss equal to the initial temperature of the chamber,reveals the modelled outlet temperature to be much closer to reality.

The reason for the grand effect of including heat loss is explained by theenergy levels of the various components. The energy level lost throughthe chamber wall is high compared to energy from the incoming feed andthe outlet powder, which is the reason for its great effect on the the airtemperature in the chamber ToutAir (see tabel 4.6).

In table 4.5 the resulting humidity and moisture contents are listed.


Steady State Results for humidityLoss Included Loss Included TEST

Test Eq Moist. YOut Abs. HumDescription Content Abs. Hum Outlet Air

Default System 0.0033 0.0251 ≈ 0.010Ffeed = 75 L/h 0.0047 0.0277 ≈ 0.012Tmain = 150 oC 0.0045 0.0251 ≈ 0.011Tmain = 170 oC 0.0024 0.0251 ≈ 0.010

FMAIN = 2000 kg/h 0.0025 0.0237 ≈ 0.010FMAIN = 1600 kg/h 0.0047 0.0267FSFB = 600 kg/h 0.0032 0.0244 ≈ 0.0115FSFB = 350 kg/h 0.0035 0.0263 ≈ 0.012TSFB = 80 oC 0.0036 0.0251TSFB = 100 oC 0.0030 0.0251Tamb = 50 oC 0.0051 0.0397Tamb = 10 oC 0.0026 0.0198RHamb = 75 % 0.0050 0.0386RHamb = 10 % 0.0026 0.0199

Sconc = 0.8 Kg/Kg 7.75e-4 0.0148Sconc = 0.2 Kg/Kg 0.0135 0.0354

Table 4.5: Steady State Results of absolute humidity and equlibrium moisturecontent calculated with the variables and values as used in the realtest on MSD-20. Calculated with a energi loss funtion included. Theseare compared with the results from the Test on MSD-20. The absolutehumidity is calculated from sensor 1616 and 1614.

4.4.2 Effect of varying Operation Variables

Feed Flow

It is observed that the outlet air temperature is inversely proportional to thefeed flow rate. An increase in the feed flow decreases the temperature andvice versa. This is explained by the fact that an increase in feed flow resultsin more water to be evaporated which requires a lot of energy. This resultsin an increased absolute humidity value in (4.7) and the relative humidityincreases, which causes the moisture content in the final powder to increase.(See table 4.5)

Feed solids content

The change in feed solids content resulted in a change in outlet temperaturedue to the same reason as for the feed flow rate. Decreasing the solids contentin the feed obviously gives rise to an increased amount of solvent (water)per unit weight of feed that requires more energy to evaporate. From the


Energy level of the components (Default)Energy

Test KJ/s=KW

FMAIN Inlet 90.33Ffeed Inlet 3.10

Fpowder Outlet 1.4Fout outlet 96.8Qloss 10.5

Table 4.6: Energy Level of the components at default state. Energy in the air isvery high compared to the other parts. However it is noted that theenergy lost in the chamber compared to the energy in the feed andpowder is high as well, and therefore has an important effect on thetemperature in the chamber ToutAir. The energy is shown in KJ

s.

large changes in temperature it is noted that evaporation of water is energyexpensive. Therefore from an energy perspective it is wished that the feedhas maximum solids content when it is fed to the spray dryer, but still is ableof being completely atomised. However sometimes it is necessary to run thespray dryer with a low solids content in the feed and low outlet temperaturein order to avoid any degradation in powder quality or to meet a specificproduct specification .

Concerning the feed temperature, and increase in the feed temperature re-duces the heat required to dry the product, which means the temperaturein the chamber is higher than at default state. Moreover an increased feedtemperature reduces viscosity which makes the feed easier to atomize.

Inlet Air Flow and Temperature

It is from the results table noted that the changes in outlet air temperatureis proportional to the changes in the operation condition for the inlet air.But the Main inlet air has more effect on the system than the SFB, dueto the higher flow rate and temperature. Increase in any one of the inletair flow rates or temperatures signifies an increase in the amount of energyavailable for evaporation, and since there is no change in the amount of waterto be evaporated the energy used for the evaporation will be the same. Asa result there is energy in excess which is seen as a rise in the outlet airtemperature. Likewise the temperature falls in the chamber when one ofthe operation condition values is reduced. As stated before the absolutehumidity depends on the flow rates ,(4.7) , consequently a fall in the flowrate causes the absolute humidity to increase.

Generally it can be stated that the lower the outlet air temperature is,the more effective utilisation of the heat, however the lower temperatureincreases the moisture content in the outlet powder. The explanation for


this is that the differences in the outlet air temperature affect the saturationvapour pressure (4.19), which descends with a falling temperature. So airwith a lower temperature can contain less water. For a constant absolutehumidity, that is the vapour pressure is constant, it means an increase inrelative humidity. The moisture content in the final product will also increaseas seen in the equilibrium moisture contents in table 4.5.

Ambient Humidity

The ambient humidity is viewed to have a minor impact on the temperatureof the air in the chamber. Nevertheless it affects the spray dryer’s ability todry a product. As a consequence of the increased humidity level in the ambi-ent air, the resulting moisture content in the outlet product is increased. Itdoes not seem to be a problem in this case, but for other products, which aremore hygroscopic, it can be difficult to reach the wanted moisture contentin the powder, if the ambient humidity is too high. In such case, dehumidi-fication of the inlet air is necessary prior to use or the plant capacity can bereduced.

Ambient temperature

The ambient temperature affects the moisture content of the inlet air. Atconstant relative humidity, as in the test, a higher ambient temperatureresults in an increase of moisture content of the drying air. Simultaneouslythe higher ambient temperature has a positive effect on the heat loss giventhat heat transfer through the chamber wall will be less significant when thetemperature difference between wall and ambient temperature is small.

The results of the steady state model have revealed that it is possible toestimate the outlet air temperature using mass and energy balance equa-tions. However, the model is ideal and describes a complete drying of theproduct, such that gas and particles reach an equilibrium state. This is alsonoted when the moisture content of the air from the real test is comparedto moisture content from the model. The humidity level in the model issomewhat higher, due to the complete drying which means more vapour isreleased into the drying air.

From having evaluated the steady state results a dynamic model of the spraydryer is described in the subsequent chapter.


Figure 4.6: MSD-20 Test Station Setup for test of the dynamic process on mal-todextrin (21/7-2009). The red boxed marks the manipulated vari-ables. The green boxes are disturbances. The arrows show the direc-tion of flow. Blue line is the air flow. Yellow Lines are feed / productflow. A cyclone filters the outlet air for fines and returns these intothe chamber


Figure 4.7: Test Centre at GEA Niro - Multi stage Dryer MSD-20


Chapter 5

Dynamic Modelling of a Mixed

Flow Spray Dryer

In the previous section a steady state model of the spray drying system wasdeduced. It is able to estimate the final drying conditions for certain stepchanges of the system and its drying environment. However, in an actualsystem the drying environment and conditions vary with respect to time.Under these circumstances a steady state model is insufficient. A dynamicmodel, which describes the responses of the system over time for certainchanges in the settings is necessary. This also essential with regards to theselection and simulation of control systems for the spray dryer.

The main setup of the drying chamber model is similar to the one madeuse of in the previous section as seen in figure 4.4. But in the dynamicmodel the difference between the input and out flow expresses the rate ofaccumulation of a component in the system; this could be mass or energy.The accumulation rate represents the rate of change in the total mass orenergy of the system with respect to time. At steady state there is no rateof change and this term (time derivative) will be equal to zero: flow rate inis equal to flow rate out.

A dynamic model of the temperature changes over time in the spray dryingchamber is derived from the unsteady state energy balance model given forCSTR process. It is still assumed that the internal energy is the dominantcontribution to the total energy. However it is more convenient to work withenthalpy to describe energy. Hence the chamber is of constant volume andthe drying air is analysed as an ideal gas, the energy balance equation is

44 Dynamic Modelling of a Mixed Flow Spray Dryer

given in (5.1).

mCdT

dt=

∑

FjInHjIn −∑

FjOutHjOut + Q+ W (5.1)

The enthalpy equations for the air (Main and SFB) (4.3), feed (4.4), andfinal product flow (4.5) known from the steady state model are still validand are used in the above written equation. Q denotes the rate of heatadded to the system and W is the rate of work done on system. Yet theinfluence of the variables on the system are ignored given that the chamberis not externally heated and the pressure is kept constants in the chamber.Thus there is no additional work done on the chamber. Isolating the timederivative of the temperature, results in a model specifying the temperaturedevelopment over time in the chamber (5.2).

dTOutAir

dt=

1

mtotalAirC(FMain(CdryAirTMain + YIn(λ+ CvaporTMain))

+ FSFB(CdryAirTSFB + YIn(λ+ CvaporTSFB))

+Ms(CsolidTfeed +XInCwaterTfeed)

− FOutDry(YOut(λ+ CvaporTOutair) + CdryAirTOutair)

−Ms(CsolidTpowder +XoutCwaterTpowder)) (5.2)

Where mtotalAir is the total mass of air in the chamber as a mixture of dryair and vapour. At the initial state, without any flow entering or leaving thedryer, this value is calculated from the density of the ambient air pressureand the volume of the chamber. C is the specific heat capacity of the moistand dry air in the chamber.

5.1 Total mass of air in the Spray Dryer

The total air density is simplified to be the sum of dry and moist air densi-ties, neglecting the errors due to non-ideal compressibility of gas and usingthe ideal gas law ((5.4))(Node (2009)). The density equation is derived inappendix D. Thus the density is a function of the total pressure P, vapourpressure Pvapour of the air and temperature T in Kelvin (5.4). From theequation it is noted that an increase in vapour pressure at constant temper-ature causes the air density to decrease. This is due the fact that the molarmass of water is smaller than for dry air.

ρtotalair = ρdry + ρvapour (5.3)

=MdryAirP − Pv

RT+Mw

Pv

RT(5.4)

5.1 Total mass of air in the Spray Dryer 45

The volume of the spray drying chamber is determined by using (5.5) (Ref-strup and NIRO),where Dchamber symbolises the diameter of the chamber;Hchamber, the height of the chamber; ACeiling angle of the chamber ceiling,and ACone is the angle of cone on chamber.

V =π

4Dchamber

2Hchamber (5.5)

+ πDchamber

3

24(

1

tan( π180

ACone

2 )+

1

tan( π180 (90−ACeiling))

)

With the density and the volume of the chamber at hand the mass of airat the beginning of the process is computed. The mass is separated intothe mass of dry air and mass of moisture in the air, which is determined byusing the same approach as in section 4.2.3 for calculating the inlet dry- andvapour air flow.

mChamberAirStart = ρtotalairVchamber

mChamberAirStart = mdryAir Start +mvapour Start

mdryAir Start = mChamberAirStart1

YIn + 1

mvapour Start = mChamberAirStart −mdryAir Start

When the process has begun, the total mass of drying gas in the chamberis equal to the accumulated change of air mass added to the air mass at theprocess start, as in (5.6). The flow rates are, as in the steady state model,calculated on the dry air basis and assumed to be identical at the inlet andoutlet which means the mass of dry is constant. This implies that a changein mass of air is due to the increase or decrease of vapour in the air only.The rate of the change in vapour mass is expressed by vapour entering andleaving the chamber with the airflows and the air vaporised from the feed(5.7). All flow rates and the vaporisation rate are described by kg/seconds.

mtotalAir = mChamberAirStart + ˙mvapour (5.6)

d ˙mvapour

dt= FMainDryYIn + FSFBDryYIn +Ms(XIn −XOut)− FOutYOut

(5.7)

YOut =mvapour Start + ˙mvapour

mdryAir Start(5.8)

By dividing the total amount of vapour mass with the unchanged amountof dry air the absolute humidity in the chamber is estimated, which is theabsolute humidity of the outlet air YOut as well due to our assumption of thechamber being well mixed. The effect of this is that the total outlet air flowrate varies according to the amount of vapour, and thus the vapour pressure,


which causes a change in chamber air temperature. An increase in outletair flow results in less energy accumulated in the chamber and therefore thetemperature in the chamber will decrease. On the contrary there will be anincrease in temperature with a decrease in outlet flow.

With a description of the change of total mass of air in the chamber,(5.2),can be solved to estimate the temperature development over time. But firstthe outlet moisture content XOut has to be determined from the equilibriummoisture content from (4.10), which is dependent on the relative humidityof the chamber, which can be found from (4.14). This equation is a functionof the temperature of the chamber and the absolute humidity. This is solvedby an iterative procedure, setting the initial state of the temperature. Onthe block diagram in figure 5.1 this basic dynamic model is illustrated.

Figure 5.1: Basic Dynamic Model: The model of the chamber is connected to therelative humidity equation and the equilibrium moisture content. Thefigure shows the main operational variables processed in the spray dry-ing chamber and the output variables that are inputs to the relativehumidity equation and moisture content blocks.

As stated above the flow rates and vaporisation rates in the model are de-scribed by kg

seconds . In the model it is therefore assumed the feed particles areheated and dried such that vaporisation process is completed within a sec-ond from the time the feed enters the dryer (vapour changeMs(XIn−XOut)(5.7)). To validate this hypothesis and estimate the general drying timesand the heat and mass transfer equations between single feed particles anddrying gas are examined.

5.2 Drying Kinetic Mechanism 47

5.2 Drying Kinetic Mechanism

TheMSD dryer is the preferred dryer for creating agglomerated powder. Butdue to lack of information regarding the statistical properties for agglomera-tion, like the collision frequency of particles in the spray dryer and how oftenthese are combined into larger particles or destroyed into smaller pieces, onlythe evaporation process of the single droplets entering the chamber beforethey get agglomerated are examined. This follows our earlier assumptionsthat all droplets are of equal size, homogenous and spherical.

Figure 5.2: Particle Morphology: When a particle is dried it can end up havingdifferent surface forms, which is dependent on the spray dryer de-sign, its setup and the operation conditions.Depending on the spraydryer the particles can be combined into various structures: singleparticles,agglomerates, granules, or Pellets(layered structure)

Solid particles can have different sort of behaviour when reacting with gas.Some have an unchanged size and some shrinks over time in various ways.For the drying process for a single particle a shrinking core model is used,as it is accepted as being the best simple model that describes the reactionbetween gas and solids, even though it does not precisely represents themechanisms of gas-solid reactions (Levenspiel (1999)) and (Shunji Hommaand Matsumoto). Here it is visualised that the reaction first occurs at thesurface of the particle and then the reaction moves into the particle leavingbehind dried inert solid. Thus the unreacted moist core shrinks while theshell thickness increases.

The evaporation of the water from the atomized droplets to form dry par-ticles involves simultaneous heat and mass transfer ( (figure 5.3). The heat


Figure 5.3: Schematic of Drying mechanism

and mass transfer is a function of temperature, humidity, diffusion proper-ties of the surrounding air, relative velocity between droplet and air, anddroplet diameter. The process is described by two drying periods. In thefirst period of drying the moisture content in the particles is assumed to beevenly distributed and the moisture is removed at constant rate. Heat istransferred by convection from the air to the droplets and converted intolatent heat during moisture evaporation. This heat transfer rate is given bya heat transfer coefficient hheat and driving force calculated as the differencebetween the drying air temperature and the particle temperature , (5.9).

˙Qheat = hheat(TOutair − Tfeed) (5.9)

m = Kmass(Psurface − Pv) (5.10)

The vaporised moisture is transferred into the air by convection through theboundary layer that surrounds each droplet. This vapour flux in this periodis expressed by an external mass transfer coefficient Kmass and a vapourpressure driving force (vapour pressure difference between the drying airPv and pressure at droplet surface Psurface, which is saturated). Due tocapillary and diffusion mechanisms moisture migrates to the surface fromthe interior of the droplet at a rate sufficient to maintain saturation on thesurface. The shrinkage model is ideal and it is therefore assumed that thedroplets remain perfectly spherical and the droplet solution is homogenousin this period. The change in particle volume corresponds to the amount ofwater evaporated.


Figure 5.4: Drying Proces of a Particle with a Shrinking Model.First period theparticle shrinks. Second period the core shrinks and no change inparticle volume.

When the critical moisture contentXC is reached within the droplet, the sur-face wetness cannot be maintained which results in a porous crust formation.This acts as some resistance to water vapour diffusion and consequently thedrying rate will fall. The drying rate is estimated as vapour diffusion froma moist core through a dry shell. In this second drying period the particlecan change its formation to any type shown on figure 5.2. However here thespherical form is kept and when the specified surface condition is reached,the volume of the particle does not change, but the crust thickness increasesas moisture content decreases. Because the vapour pressure at the surfacedescends to the vapour of the surrounding air the moisture content in thecrust is the equilibrium moisture content with the surrounding drying airhumidity.

5.2.1 Mass Transfer Rate

For a spherical particle the mass transfer equation given in (5.11) is devel-oped by (K.H. Clement and Thomsen (1991)). It is a combination of the


vapour transfer from the moist core to the particle surface and the externalvapour transfer at the surface and describes the mass transfer rate per unitof the particle surface area (Kg/(s ·m2)).

˙mtransfer =PMw

RToutAir+Tfeed

2

2Deff

ddrop(f +2Deff

kmassddrop)ln(

P − Pv

P − Psat(Tfeed)) (5.11)

f = 0 ; for Xparticle > Xcr 1st drying period

f =

(

Xparticle −Xeq

Xcr −Xeq

)

−1/3

− 1 for Xparticle ≤ Xcr2nd drying period

(5.12)

• Ddrop is the diameter of a single droplet.

• P is the pressure in the chamber(standard air pressure).

• The f factor characterizes the resistance to vapour diffusion throughthe crust, which only has an influence in the second drying periodwhere the average moisture content of the particle Xparticle < Xcr

Until the critical moisture (Xcr) content is reached, (5.11) is a descriptionof the external mass transfer resistance only. The fraction in the f factoris an explanation of the ratio of the core volume to the particle volume byvolumetric averaging of the moisture content (relation between the moisturecontent left (Xparticle −Xeq) since crust formation began (Xcr −Xeq)). Sothe inverse of this illustrates crust thickness. This simplification is possibledue to the assumption of a spherical particle and shrinking core model:

Vsphere =4

3· π ·

d

2

3

Xparticle −Xeq

Xcr −Xeq=

(

dcoreddrop

)3

(5.13)

At the commencement of drying the droplet has a diameter of DdropInit.During the first drying period the diameter of the droplet decreases, equalto the amount of water evaporated, due to the assumption of ideal shrinking(5.14)(see appendix D.12). In the second drying period the diameter of thedroplet is constant as given in (5.15).

Ddrop =

(

DdropInit3 −

6Ms(XIn −Xparticle)

πρwater

)1/3

(5.14)

Ddrop =

(

DdropInit3 −

6Ms(XIn −Xcr)

πρwater

)1/3

(5.15)


It is noted that the mass transfer model also presents an adjustable param-eter, coefficient of effective vapour diffusion through the particle crust Deff ,which is dependent on the solid material and describes how well moisture isdiffused through this.

The average mositure content of the particle Xparticle is determined by set-ting up a water balance model as in eq.eq:waterbalance, which describes the

rate of change in moisture content calculated on dry basis(

kgmoist

kgdrySolid

)

.

MsdXparticle

dt= −πDdrop

2 ˙mtransfer (5.16)

5.2.2 Mass and Heat Transfer Coefficients

The mass transfer coefficient Kmass and heat transfer coefficient hheat areestimated from the Nusselt number, Nu and the Sherwood number Sh (di-mensionless). The Nusselt number, Nu, is a measure of the heat transferoccurring at the droplet surface and is the ratio of convective to conductiveheat transfer defined in (refeq:nusselt). Kair in this equation defines thethermal conductivity of air (W/(m ·K)) and by regression analysis of datagiven from (Box (2009)) the thermal conductivity as function the tempera-ture is estimated (See appendix D.3).

The Sherwood number is the mass transfer equivalent to the Nusselt numberand characterises the ratio of convective mass transport to diffusive masstransport and expressed in (5.18). Dair is the diffusion coefficient of watervapour in air and is obtained by regression curve fit to data from Bolz andTuve (Nellis and Klein (2009)). It is a function of the air temperature inKelvin and is given in (5.19).

Nu =hheatDdrop

kair(5.17)

Sh =kmassDdrop

Dair(5.18)

Dair = −2.775 · 10−6 + 4.479 · 10−8(Tair + 273) + 1.656 · 10−10 · (Tair + 273)2

(5.19)

The external transfer coefficients are isolated in the equations above (5.20)and the Nusselt and the Sherwood number are obtained from the Ranz-Marshall correlation (5.22), in which they are determined from the Reynolds


number, Re, Prandtl number, Pr, and the Schmidt number ,Sc.

hheat = NukairDdrop

(5.20)

kmass = ShDair

Ddrop(5.21)

Nu = 2 + 0.60Re1/2Pr1/3 (5.22)

Sh = 2 + 0.60Re1/2Sc1/3 (5.23)

The Reynolds number provides a measure of the ratio of inertial forces (re-sistant to change or motion) to viscous forces, which for the air and dropletgives equation (5.24) (Benson (2009)). V is the relative velocity betweenthe air and particle and µair is the absolute viscosity of the air. µair

ρair, which

is known as the kinematic viscosity ν is determined in appendix D.5. Dueto lack of information about the relative velocities between air and particle,it is assumed due to the small size of particles that the relative velocity isalmost zero ( 0.01m/s) (particles follows the air see appendix E) (Shabde(2006)).

The Schmidt number is a dimensionless number known as is the propor-tion between the kinematic viscosity and the mass diffusivity (5.25). ThePrandtl number is analogous to the Schmidt number and represents the ratioof kinematic viscosity to thermal diffusivity αair. In table 5.1 the parame-ters are estimated within the temperature range 300C − 1200C and with aconstant droplet size Ddrop = 76µm. It is noted that the values are small,which means that their contribution to the Nusselt and Sherwood numberin (5.22) is small. This demonstrates that the viscous forces do not havea big influence and the main mechanism in the heat and mass transport isconduction and diffusion.

Re =ρairV Ddrop

µair(5.24)

Sc =µair

ρairDair(5.25)

Pr =nuairαair

(5.26)


Ranz-Marshall correlation Parameter valuesParameter Value

Re 5.2−2 − 3.4−2

Sc 61.8−2 − 62.4−2

Pr 71.2−2 − 69.9−2

Table 5.1: Ranz-Marshall correlation Parameter Values. For droplet Ddrop =76µm and in the temperature range 300C − 1200C. Relative Veloc-ity between particle and air is estimated to 0.01m/s.

It is observed from the equations in (5.20), that the transfer coefficients varywith the size of the droplet. A decrease in droplet size implies an increase inthe transfer coefficients. This indicates faster heat and mass transfer, whichin the end gives quicker drying times

5.2.3 Droplet size

Droplet and dried particles are by no means of equal size as assumed inthe calculations with a constant droplet diameter, but have a range of sizescharacterized by their size distribution. To portray the size distribution in aspray dryer, various mathematical functions have been suggested. Howeverthe complex nature of feed atomisation and the subsequent drying makes itdifficult to fit the size distribution to a mathematical function. The mostcommon distributions are:

• Normal distribution (Both rotary and nozzle atomisers)

• Log-Normal distribution (rotary atomisers)

• Square Root Normal distribution (Nozzle atomiser)

• Empirical distribution function

– Nukiyama-Tanasawa distribution (Nozzle atomiser)

– Rosin Rammler distribution (Nozzle atomiser)

Some distributions give a better fit for nozzle atomisers while others arebetter for describing rotary atomisers (Masters (2002)). The MSD-20 op-erates with a pressure nozzle, but there is no information available aboutits particle size distribution. This would have made it possible to identifythe particle sizes that should be used in the examination of the feed dryingtime.

Instead the mean particle size is estimated from a function which is basedon the nozzle dimension(Orifice diameter), atomizing pressure, spray angle,


nozzle capacity, and feed characteristics(viscosity and density), given byGEA NIRO (OLK and NIRO). The nozzle which is used in the calculationis of the type : 4931 cof which has an orifice diameter of 2.2mm and thespray angle is chosen to be the standard 65 degrees. The viscosity is decidedto be 20 centipoise(cp)1, which is approximately the viscosity of milk. Anincrease in viscosity increases the droplet size.

The atomising pressure is determined from the pressure that was used throughthe test on MSD-20(sensor 1616. see appendix C.2.5). The feed rate is con-trolled by setting this pressure. As seen in the plot in appendix the feedrate increases when the pressure is increased and decreases correspondinglywhen pressure is decreased. The droplet size is inversely proportional tothe pressure but at the same time the increase in feed rate has the oppositeeffect on the size. The pressure is chosen to 240 bar.

This results in a mean droplet size equal to 76µm, which is within theexpected range given that pressure nozzle is known to be able to producedroplet in the range 10− 300µm. Moreover the program estimated that 98percent of the created particles have a particle size less than 298µm(3·Ddrop).The mean droplet size found here is chosen to de be the default particle sizein the following tests of the drying time.

5.3 Matlab Simulink Implementation

The dynamic model has been in implemented in Simulink/Matlab. Twoseparate models have been implemented: the model of the spray dryer anda model of the drying kinetics for a single particle. These two models areat present time not combined, thus the drying times for a particle and theevaporation rate is not directly used in the model of the spray drying cham-ber. Nonetheless the temperature and humidity results from the spray dryermodel are used to estimate the drying time for a single particle. For the spraydryer model process variables, feed characteristics, ambient air characteris-tic, spray dryer chamber sizes can be varied. A block diagram illustratingthe model construction in Simulink. The blocks show what they use as inputand give as output.5.5

5.4 Test:Dynamic model

In this section the dynamic model of the spray drying chamber describingthe outlet air temperature ToutAir given in (5.2) is tested and compared with

1visocosity is dependent on temperature. Viscosity of water at 200C = 1 cp and oliveoil = 84 cp (Chieh (2009))

5.4

Test:D

ynamic

model

55

FEED SUBSYSTEM

INPUT

Feed Kg/h

Diameter droplet

OUTPUT

Feed flow l/s

Ndrop

Surface area (droplet)

Mass solid

INPUT

Ddroplet

Tout air

Rela!ve humidity

Equilibrium moisture content

Tfeed

OUTPUT

Mass evaporated

Moisture content Xpar!cle

INPUT

Ddroplet

Tout air

Rela!ve humidity chamber

OUTPUT

Kmass

MASS

TRANSFER PARAMETERS

INPUT

Chamber air (ini!al)

Feed rate

Feed temperature

Main flow

Main temperature

SFB flow

SFB temperature

DRYING

CHAMBER

RELATIVE

HUMIDITY

EQUILIBRIUM

MOISTURE

CONTENT

OUTPUT

Abs. humidity

Tout air

INPUT

Abs. humidity

Tout air

INPUT

Water ac!vity

Tout air

MASS TRANSFER RATE

SINGLE PARTICLE

More precise model

(not included in this project)

Figure 5.5: Block Diagram of the dynamic model.The 3 block to the left describes the particle drying model. The three blocks on theright hand side describe the spray dryer model. They are at present time implemented separately in matlab. Combiningthe two models will give a more precise white box model of the system.The physical description will be exact. But verydifficult the drying of each particle precisely.


the results from the experiment on the MSD-20 spray dryer. The model isexposed to the same changes in the operation variables as for the experimenton the real system, for which the test program can be found in appendix C.Only one operation variable is manipulated at a time while all the othersare kept constant at default state(B.1). Thus the dynamic response of thetemperature development in the chamber is examined for step changes forthe following operation variables:

1. FMAIN Main inlet air flow rate

2. TMAIN Temperature of main inlet air flow

3. Ffeed Feed flow rate

4. FSFB SFB inlet air flow rate

5. TSFB Temperature of SFB inlet air flow

Generally it is not possible to manipulate the operation variables directly,but through another device such as a heater or a fan for the air inlets and apump for the feeding system. Each one of the elements is normally controlledby a PI controller. When the set point is exposed to a step change, it takessome time for the operation variable to settle at the correct value. For thatreason the changes in the operation variables are simplified and modelled asbeing a first order system with a time constant τ .

This value is approximately determined as being the time constant for theprocess value in the experiment(see fig G.1 in appendix). The static gain,which is the relation between the stationary value of the output and theinput is 1 for the systems controlling the operation variables. Both theoriginal step change and the first order step change have been modelled toexamine the effect, the delay has on the model and its response.

1st order system

1

τs+ 1(5.27)

Start-up of a spray drying process and to get the process in a stable statetakes time and requires experienced technicians. However this is kept ata basic level in the model since the main focus has been on modelling thespray dryer in a running state and to estimate the effect when it is exposedto changes. Therefore as an initial condition the moisture content of the airin the chamber Yout, is set to be equal to the moisture content at steadystate, for the default operation conditions. The steady state value is alsoapplied as the initial temperature of the outlet air TOutAir.

5.4 Test:Dynamic model 57

In addition to the included heat loss through the chamber cooling air isincluded in the model which is used for the air disperser. This supplementaryair is an additional energy term (4.3) in the dynamic model (5.2). Moreoverit contributes to the total amount of vapour in the chamber, exactly like theother inlet air (5.6) and the total amount of dry air leaving the chamber.

The step change is applied to the system after 1000 seconds, while the de-velopment of TOutAir, Relative humidity in the chamber, and equilibriummoisture content Xeq data is recorded for the analysis. In all tests the stepchange has been applied directly on the manipulated variable. The resultsare compared and validated against the test results from the MSD-20.

5.4.1 Step: Temperature of main inlet air

The inlet air temperature is at default operation state 1600C. First a stepchange down to TMain = 1500C is accomplished, where after a simulationwith a step change up to TMain = 1700C is performed. The step change andthe resulting response of the temperature TOutAir for a decrease in main inletair temperature is plotted in figure 5.6, top and bottom plot respectively. Forcomparison the result from the similar experiment on the MSD-20 is shownin the same figure (red). It is seems that correlation between the main inletair temperature and outlet air temperature is high, since the temperatureresponse of the outlet follows the changes in the operation variable veryprecisely (oscillation). The outlet air temperature is directly proportionalto the inlet air temperature.

For a direct step change in the main inlet temperature (blue) it is observedthat the model responses too fast compared to the results from the truespray dryer. However, when the manipulated variable is modelled as beingthe step response of a first order system with a time constant τ (green) theoutcome appears to be more realistic. The time constant is here chosento be 180 sec, which is approximated by examining the rise time for thevariable in the spray dryer(time it takes the electric heater to increase the airtemperature). Thus after 180 seconds the heater would have reached 63.2%of its final value. The model reaches the new steady state after 1000 sec. Dueto the oscillations in the real dryer the settle time is longer. The oscillationsis due to an incorrectly tuned PI controller to the heater. Probably theproportional gain was set too large, which results in the overshoot.

Besides the imperfections in the settling time, which may be solved by acorrection of the time constant in the first order system describing the heater,it can be concluded that the model gives a good estimate of the outlet airtemperature for a change in the main inlet air temperature. Modelling theheater as a first order system seems sufficient. The figure shows that control


signal has a fall before it starts to rise. This is because of a small mistakeby the technician when changing the value of the feed pump. Furthermoreit is observed that the inclusion of the cooling air has reduced the outlet airsteady state temperatures with approximate 0.50C.

A similar behaviour of the response is observed when the main inlet airtemperature is stepped up from 1500C to 1700C The response for a step upin temperature is found in appendix 5.6.

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000140

145

150

155

160

165

Main Air Temperature step Tmain

=160−>150 oC

Time [sec]

Tem

pera

ture

[oC

]

Model: No delayModel: with delay τ=180TEST 6 MSD−20

1000 1500 2000 2500 3000 3500 4000 4500 5000

78

80

82

84

86

Temperature TOut Air

for Main Inlet air Temperature change

Time [sec]

Tem

pera

ture

[oC

]


Figure 5.6: Dynamic step response of the TOutAir for decrease in main inlet airtemperature from 1600C to 1500C. The top figure shows the appliedstep change. Heater is a first order system τ = 180. The bottomfigure is step response. Model results are compared with data fromMSD-20

5.4.2 Step: Feed Flow rate

The effect of changing the feed flow rate is tested in two cases: increase infeed flow rate from 65L

h to 75Lh and for a decrease in feed flow rate from

75Lh to 65L

h . The results from the steady state model proved that the outlettemperature is inversely proportional to the feed flow rate. The dynamicresponse of the outlet air temperature for the step change increasing feed flowis illustrated in figure 5.7. The feed pump is modelled as a first order system


with a time constant τ = 5, which react much faster to changes comparedto the heater. It is seen that the responding feed flow rate builds up in thesame way as in the real system. Correspondingly the model estimates thetemperature response of the outlet air to be fast (150 sec. to reach steadystate). On the contrary, the result from the MSD-20 demonstrates that whenthe increased amount of feed enters the dryer the outlet air temperature firstreacts as expect and falls some degrees with the expected rate. But hereafterthe temperature response decreases in speed, thus it takes more than 3000seconds to reach steady state.

900 950 1000 1050 1100 1150 1200 1250 130060

65

70

75

80

Feed flowrate step Ffeed

=65−>75 L/h

Time [sec]

Fee

d F

low

[L/h

our]

Model: with delay τ=5TEST 2 MSD−20

1000 1500 2000 2500 3000 3500 4000 4500 500080

81

82

83

84

85

86

87Temperature in Spray Dryer Chamber Spray Dryer for a Feed Step Change

Time [sec]

Tem

pera

ture

[oC

]


Figure 5.7: Dynamic step response of the TOutAir for a increase in feed flow ratefrom 65L

hto 75L

h. The top figure shows the applied step change.

Pump is a first order system τ = 5. The bottom figure is the stepresponse. Model results are compared with data from MSD-20(red)

The much faster response from the dynamic model can be explained by thefact that it is assumed the spray dryer behaves completely as a CSTR, whichmeans the feed particles are evenly distributed in the chamber immediatelyafter the entry into the dryer. However, in a spray dryer the trajectoriesof the particles are much more complex as seen in figure E.1 in appendix.It is seen the main part of the feed falls straight down in the chamber andstays down in the SFB for agglomeration. Thus the effect of the increasedamount of particles in the lower part of the chamber might be a reason forthe slower response time.

The increase in feed results in an increase of the moisture content in theair inside the chamber. This affects the agglomeration rate, which createslarger particles. A large particle means longer drying times, which implies


less water is evaporated and less energy is used within a specific time interval.The slower the evaporation process takes place the longer will it take to reachsteady state, which is what is observed in the MSD-20. Thus the assumptionof drying times of a second and the lack of the dynamics describing the longerdrying times and the change in the amount of particles to be dried are themain reasons for the deviation between the model and the real spray dryer.

A step change down in feed flow rate shows a similar behaviour with a longsettle time in appendix B.2.

Generally it can be concluded that changes in feed flow rate can be madevery quickly due to the fast response of the feed pump (5 sec) and a changein temperature will be observed after less than 100 sec. However the timeto reach a stable steady state is longer, compared to a change in main inletair temperature for which the heaters response time is 180 sec but the settletime is only 1000 sec. This has to be considered when the control system isdeveloped.

5.4.3 Step: Main inlet air flow rate

The main inlet air flow rate is increased to 2000 Kgh for which the response

of Tout is shown in figure 5.8 and stepped down again back to 1800 Kgh (result

is found in appendix B.3.1). The fan is modelled as first order system withthe time constant τ = 40. Hereby the change in flow rate appears to followthe true change in flow rate.

Nonetheless the dynamics of the recorded responses for the true spray dryerseems to behave somewhat different than expected by the model. First ofall the explanation for this deviation may be found in the flow pattern ofthe air. The model assumes the dryer to be well mixed which is not truein reality. However the most important factor may be the change in dryingcondition and drying time of the particle as for change in feed rate. A changein air flow inversely affects the moisture content of the air inside chamber,but the rate of change in humidity condition is too fast compared to thereality.

The results of the variations in the SFB variables are given in appendixB.3.1.The responses are the same as for the main inlet air, although their effect onthe total system is much less due to the small amount of energy that entersthe system this way. This is expected since the main purpose of the SFB isto control the agglomeration process and final product in the fluid bed.


900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20001750

1800

1850

1900

1950

2000

2050

Main Air inlet flow step Fmain

=1800−>2000 kg/h

Time [sec]

Air

Flo

w [K

g/h]


800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

84

86

88

90

92Temperature in Spray Dryer Chamber Spray Dryer for Main Inlet air Temperature change

Time [sec]

Tem

pera

ture

[oC

]


Figure 5.8: Dynamic step response of the TOutAir for increase in Main inlet airflow from 1800Kg

hto 2000Kg

h. The top figure shows the applied step

change. Fan is a first order system τ = 40. The bottom figure is stepresponse. Model results are compared with data from MSD-20


5.5 Test:Drying Time for particle

Figure 5.9: Mass tranfer rate and drying time test setup. The red block is theMass tranfer rate system. Orange blocks are mass transfer rate coef-ficients and droplet characteristic. Blue box’ are process variables asstep functions.

5.5 Test:Drying Time for particle 63

The drying time is evaluated as being the time from evaporation beginsand until it ends when the droplet reaches equilibrium moisture content.The examination is accomplished by implementing the mass transfer equa-tion (5.11), with a changing diameter function during evaporation(red) intoSimulink as in figure 5.9. The operation conditions (blue), TOutair, RHchamber,and Xeq are the steady state values calculated in the previous chapter forcertain process inputs. These are also applied to calculate the transfer coef-ficients and the belonging parameters (orange). The simulink models of thesubsystems and function are illustrated in appendix F

The initial droplet size is by default determined to be 76µm from the cal-culation in the previous section. This is, together with the feed flow rate,used to calculate the mass of solid in a single droplet. The feed flow and thedroplet size is not linked, which means that changes in the feed flow doesnot have an effect on the droplet size in the drying tests. The reason for thisis, that the main purpose with this test is to examine how certain processconditions affect the drying time of a single particle and estimate the limitsfor the dynamic drying chamber model.

Four different test cases have been completed. In each test one of the fol-lowing parameters were varied in order to estimate the drying time for aparticle:

• Droplet

• Temperature

– Feed

– Main inlet air

• Effective diffusivity Deff

• critical moisture content XC

By varying these parameters information about the effect of changing processconditions and the importance of the product characteristics is obtained.The process condition for the experiments is the default state condition,which was also used for the tests at steady state (app.B.1). At default statethe temperature Toutair = 86.10C, RH = 6%, and the equilibrium moisturecontent Xeq = 0.0033kg

kg .

The effective diffusivity constantDeff is as a standard selected to be 5e−9 m2

s ,which is an approximate value for the effective diffusivity for milk(empiricallydetermined in (V. S. Birchal a and Passos (2008))). The critical moisturecontent for maltodextrin is in (I. Zbiciski and Prajs (2005)) estimated to be


0.54kgkg . These two parameters characterise the product that is dried and

therefore it seemed essential to examine the importance of the parameters.

With these parameter values used in the calculations, the drying processfor single particle in the default process condition is graphically plotted infigure 5.10.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.2

0.4

0.6

0.8

1Drying Time for Particle at Default steady state Operation

Time [sec]

Mo

iostu

re C

on

ten

t (K

gH

2O

/Kg

so

lid

)

Particle Ddrop

= 76 µ m

2 4 6 8 10 12 14 16 18

x 10−5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Drying Time for Particle at Default steady state Operation(Zoom)

Time [sec]

Mo

iostu

re C

on

ten

t (K

gH

2O

/Kg

so

lid

)

Particle Ddrop

= 76 µ m

1st drying period

Constant Drying Rate

2nd Drying period− falling dryingrate

Xcr

critical moisture content

1st drying period

Xcr

critical moisture content

Figure 5.10: Drying time for a particle with a Ddrop = 76µm at default operationstate(steady state). Moisture Content vs. time in seconds. Thefigure is similar to the top, but zoomed in to show the change indrying period. The 2 drying periods are illustrated. The first dryingperiod is at constant drying, almost. The second drying period startsat Xcr which for maltodextrin is 0.54 kg/kg and has a falling dryingrate. It shows that the crust formation takes place almost instantly.Drying ends when particle reaches the equilibrium moisture content.

The figure illustrates the moisture content, Xparticle,in a particle as a func-tion of time. As described the drying process has two periods. The firstperiod takes place until the particle reaches its critical moisture content andcrust is formed. This happens almost instantly, since there is no ”resistance”for the moisture transfer and the mass transfer coefficient value is relativelyhigh (see app F). In the lower figure, which is a zoomed version of the topfigure, the constant drying rate is noted. When moisture content reaches


0.54 kg/kg the second period begins and drying rate falls significantly. Ittakes about 0.3 sec for a particle of this size to reach equilibrium moisturecontent.(see modification in sec 5.7)

5.5.1 Test 1: particle sizes

The effect of the particle size on the drying time is examined in this section.This is done by computing the moisture content development over time forparticles of different sizes. The process conditions were kept at default state.The outcome of the calculation is seen in figure 5.11.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Drying Time for Particles at Default steady state Operation

Time [sec]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Particle Ddrop

= 57 µ m

Particle Ddrop

= 76 µ m

Particle Ddrop

= 114 µ m

Particle Ddrop

= 152 µ m

Particle Ddrop

= 228 µ m

Particle Ddrop

= 304 µ m

IncreasingParticlesize

Limit

Figure 5.11: Drying time for various particle sizes at default operationstate(steady state). Moisture Content vs. time in seconds. Dry-ing times are increased for increasing particles size. Particles largerthan 150 µm takes more than one second to dry. This means largeparticle will not have completed the drying within 1 second as thedynamic model takes for granted. This means less vapour in cham-ber and results in a higher TOutair temperature. It is recalled thatthe dynamic model is ideal.

As anticipated the larger the particles are the longer does it take to completethe drying. The dynamic model of the chamber condition expects the dryingto be completed within one second, in order to be exact. The consequence of


this is that the dynamic model is only correct for particle sizes below 150 µm.For larger particles for which the drying is incomplete after 1 second in thechamber, this means less moist is evaporated to the chamber from them thanthe model expected. They will naturally continue the drying in the chamber,which theoretically should end up in the same amount moist evaporated tothe chamber at steady state. However, there is a possibility that someparticles leave the chamber before drying is complete, which means lessvapour in the chamber. Less vapour in the chamber is equal to the fact thatless moisture is evaporated and the consequence is a higher temperature inthe chamber due to less energy has been used on evaporation. In this casethe dynamic model is imperfect, since it models an ideal drying process.

5.5.2 Test 2: Temperature

Two methods has been employed for examination of the drying time forvarying temperature of ToutAir :

• Changing the feed flow rate

• Changing the Main inlet air flow rate

The feed flow rate has been changed to the standard test values(65 − 75Lh )

but also to more extreme values to see the effect on drying times (35−105Lh ).

The results are plotted in a graph and shown in app. F.1.2.

It is known that an increase in feed rate causes the air temperature todecrease and vice versa. As expected the drying time increases for lowerdrying temperatures. For a feed rate of (105L

h ⇒ ToutAir = 660C) thedrying time is now 0.35 second compared to 0.3 sec at default state for themean particle size, and seems not to be a problem. Moreover it is noted thatthe increase in feed amount increases the equilibrium moisture content.

However the drying model is not fully describing reality since only the dryingof a single particle is examined. The higher feed flow rate will increase thenumber of particles and as a consequence the possibility of collision betweenthe particles increases. This will for the most part give larger particlesand thus larger drying times. Larger drying times could be a problem insome cases due to the stickiness of the product that could lead to walldeposits and trouble at powder discharge. This topic has been neglected inthis project but more information into this found in (Masters (2002)) and(Pilairuk Boonyai and Howes (2004)).

Similar behaviour of the drying times was observed when the drying tem-perature is changed by varying the main inlet air flow with a constant tem-perature. The result is shown in app. F.1.2.


5.5.3 Test 3: Effective Diffusivity

The significance of the effective diffusivity for the drying process is examined,as this variable represents the type of product that is dried. The variable hasbeen varied by a factor of 10 both up and down. The operation conditionswere kept at default. The results of the simulations is presented in figure5.12 which shown the moisture content in a particle over time.

0.5 1 1.5 2 2.5 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Drying Time for Particle by varying the effective diffusivity Deff

Time [sec]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Deff

= 5.9e−9 m2/s

Deff

= 5.9e−10 m2/s

Deff

= 5e−8 m2/s

Deff

= 1e−9 m2/s

Deff

= 3e−9 m2/s

Deff

= 2e−9 m2/s

DecreasingD

eff

Figure 5.12: Drying time for various for a single particle for various effective dif-fusivity coefficients. Moisture Content vs. time in seconds. Dryingtimes are increased for decreasing Deff .

It is observed that the effective diffusivity has a great effect on the dryingprocess, which is expected as this describes the speed the liquid mass canbe transported in the specific product. This means that for a lower value ofDeff gives a longer drying time since it will take more time for the waterto diffuse through the particle, which is also seen in the results. Thus forproducts with a low effective diffusivity, for which the particle will take moretime to dry than one second the dynamic model is not completely accuratefor the same reason as explained earlier.

5.5.4 Test 4: Critical Moisture Content

The critical moisture content is the point at which crust formation begins totakes place. In this test the point of critical moisture content is controlledfor the dried product, thus to examine what effect the point at which the


critical moisture occurs has on the drying time. For maltodextrin this valueis Xcr = 0.54, this value is both decreased and increased in the test. Theoperation conditions are kept at default state. The particle size is the meansize determined earlier 76µm. The result of the simulations is shown infigure 5.13.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Drying Time for Particle by varying the critical mositure content Xcr

Time [sec]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

xcr

=0.54

xcr

=1.00

xcr

=0.75

xcr

=0.25

xcr

=0.10

Increasing X

cr

Figure 5.13: Drying time for various for a single particle for various critical mois-ture contents. Figure shows Moisture Content vs. time in seconds.Drying times are increased for products with a higher critical mois-ture content value.

5.6 Summary: tests

It can be concluded from the results, the before the particle reaches criticalmoisture content the longer will it take to complete the drying of the particle.Apparently the reason for this is the increase in resistance which beginsmuch earlier for higher critical moisture contents due to crust formation. Inappendix F.5 the development of the resistance during the drying process isshown. When the critical moisture content is reached the resistance f startsto increase and converges to a final value when the moisture content goes toequilibrium.

Modelling the particle as being perfectly spherical is a way of keeping themodel simple as the vapour diffusivity through the crust will be the samefrom the boundary of the moist core to the surface in the entire particle andthus the resistance of the crust in all directions is simplified. In the article(Stephen R.L. Werner and Paterson), it has been tried to model the drying

5.7 Modifications in the Dynamic Model 69

of a collapsed(shrivelled) particle. An effective diffusivity coefficient and anappertaining constrictivity factor, which accounts for the structural influenceon the pore system is estimated from experimental data. Compared to theideal shrinkage model the model of a shrivelled particle model is slightlymore realistic as expected, but also more complicated because it is difficultto measure and predict the surface stress on particles and requires moreresearch in this field.

5.7 Modifications in the Dynamic Model

In the previous sections the equipment model, describing the dynamic changesin the spray dryer, and a single particle drying model has been evaluatedand compared to data from a real spray dryer. The particle model demon-strated that the drying time of a single particle is dependent on the size ofthe particle, but also on it chemicals and physical properties, especially theeffective diffusivity.

The test of the dynamic model of the spray drying chamber illustrated thatchanges in drying condition affects the evaporation rate and that it had animmense effect on the outlet air temperature response. Thus the assumption,that all the moist is transferred to the surrounding drying air in a second,does not completely describe the true process. Therefore few modificationsare made to the dynamic model of the temperature condition in chamber,which will be described in this section.

From the test of the drying times for single particles it was found out that adecrease in the effective diffusivity increases the drying time of a single par-ticle. It has come to knowledge that the effective diffusivity for maltodextrinof the type DE 10 is in the range 8 · 10−11 m

s at 80 0C, and even less forsmaller temperatures (J.G. Baez-Gonzalez and Vizcarra-Mendoza (2004)).This is nearly 100 times less than first estimated. The drying time for par-ticles with the new effective diffusivity constant is estimated and illustratedin figure 5.14.

It is immediately noticed that the total drying time for the particle hasincreased, in view of the fact that transportation of liquid through the crustnow is slower. For the default droplet size Ddrop = 76µ the drying time isnow 20 seconds compared to a drying time of less than one second before.Due to agglomeration of the particles the possibility of larger particles ispresent. Thus for droplets with a size of 300 µ the drying size is about300 seconds. However collision of particles, both dry and wet, can vary thedrying time and the dynamics of the drying process.


50 100 150 200 250 300 350 400 4500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Drying Time for single Particle of different sizes for Deff

=8e−11

Time [sec]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Particle Ddrop

= 76 µ m

Particle Ddrop

= 150 µ m

Particle Ddrop

= 300 µ m

Particle Ddrop

= 400 µ m

Figure 5.14: Drying Time for single Particle of different sizes for Deff = 8e −11 at default operation condition. The lower effective diffusivity isfor maltodextrin gives longer drying times. For a particle with adiameter of Ddrop = 76µ is 20 sec. For a particle with a diameter ofDdrop = 76µ is 20 sec.

5.7.1 Implementation of longer drying times and change inevaporation rate

So far in the spray dryer model the evaporation of water is expressed tohappen in one second, Ms(XIn −XOut)(difference between the moisture infeed in and product out) in (5.7) which describes the addition of vapour fromthe feed to the chamber per second. This is correct in steady state and whenthe drying time is less than one second, however, variations in the dryingtimes also changes the time for the evaporation rate to reach steady state.It is observed from the results (figure 5.7 & C.2.4) for the true spray dryerthat the temperature response for a variation in the feed rate appears to bea composite of both a slow and fast dynamic. The fast dynamic comes fromthe rapid change in the amount of feed entering the chamber, compared tothe slower dynamics that is a consequence of the slow evaporation as seenfor the drying time for a particle in figure 5.14.

A possible way to achieve this is to keep track of the number of particlesthat enters the chamber and estimate how much each particle evaporatesper second until a steady state is reached, although it is very complicated.

5.7 Modifications in the Dynamic Model 71

To maintain the simplicity of the model, the amount of moisture evaporated(Ms(XIn−XOut)) is send through a first order dynamic system with a timeconstant τevap that describes the slow dynamic from the evaporation. Thusthis time constant τevap is a function of the drying time of the particle,agglomeration rate and residence time of particles in the chamber.

The fast dynamic is included by inserting a zero in the transfer functionwhile keeping the static gain to 1. Thus the transfer function G(s)evap canbe written as:

G(s)evap =τfasts+ 1

τevaps+ 1

G(s)evap =τfasts

τevaps+ 1+

1

τevaps+ 1(5.28)

Now the system is given as the sum of two first order systems. Assess-ing the rewritten transfer function the effect of the included zero is easilyunderstood, when the initial and final value theorem is applied. These the-orems can be used to estimate the initial and final value of a function in thetime domain by examining its Laplace transform, in the frequency domain.Though this requires the poles of a transfer function are in the left half planeso the system is stable. For this to be fulfilled τevap has to be positive.

Thus the transfer function G(s)evap is evaluated by applying the theoremson the step response Y (s) for this system. h0 is the value of the step.

Y (s) = G(s)h0s

(5.29)

Initial value theorem:

limt→0+

y(t) = lims→∞

sY (s) =τfastτevap

h0 (5.30)

final value theorem:

limt→∞

y(t) = lims→0

sY (s) = 1 · h0 (5.31)

It is noticed that in the beginning of the response, for s → ∞, the value ofthe second fraction in (5.28) will go to 0, so only the first part of the systemhas an influence on it, due to the zero in the nominator. Thus the zero hasan effect on the gain of the system and consequently how fast it reacts in themoments just after the step has occurred τfast/τevap. The larger the zero isthe larger the gain will be which means a faster response. However whenthe time t → ∞ the first fraction in (5.28) will go to 0 and the influenceof the second fraction increases. At steady state the gain in the system isequal to 1(static gain) and the time to reach this only depends on τevap.

To demonstrate that this system is able to give an acceptable descriptionof the change in evaporation rate, this is implemented in the model and


simulations are to be compared to the real data. By inspection of the tem-perature response of the outlet air temperature for MSD-20 when feed isvaried the time constant τevap is estimated to be around 1000 sec (see fig.5.7 & appendix C.2.4). τfast is guessed to be approximately half of the valueof τevap. If the value is decreased the system will be slower and vice versa.But a value larger than τevap will result in an overshoot, since the gain willbe larger than one in (5.30). The simulation of the outlet temperature fora step in feed rate from 65L

h → 75Lh for the modified model and the similar

true data from MSD-20 is shown in figure 5.15.

7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 8000

65

70

75

80

Feed flowrate Ffeed

step 65−>75 L/h

Time [sec]

Fee

d F

low

[L/h

our]


7000 7500 8000 8500 9000 9500 10000 10500 11000

78

80

82

84

86

Temperature in Spray Dryer Chamber Spray Dryer for a Feed Step Change(Modified model)

Time [sec]

Tem

pera

ture

[oC

]

τ

evap=1000 & τ

fast=500

τevap

=1300 & τfast

=600

τevap

=1000 & τfast

=100

τevap

=1000 & τfast

=1500

TEST 2 MSD−20

Figure 5.15: Temperature response of the outlet air for the modified model whena feed step from 65 L

hto 75 L

his applied. The top figure shows the

manipulated variable in the model (1st order) and the true dryer.Thefigure below is the response for different pole and zero in G(s)evap.It shows the effect of a zero too high or too low and the resultingchange in the dynamic. Best fit in this case compared to the truedata (purple) is for τevap = 1300 and τfast = 600(light green)

The figure shows that the response from the model is reasonably in agree-ment with the true system for the correct values of the zero and the pole.For this system the best fit is reached for τevap = 1300 and τfast = 600.The figure also shows how the value of the zero affects the dynamics of thesystem. Figure B.12 in the appendix B.4 illustrates the output of the sys-tem G(s)evap, which is the evaporation rate per sec and the effect of variouszero- pole combination is seen. The change in the evaporation rate affectsthe absolute humidity of the air in the spray dryer. This is also shown inthe appendix (B.11).

Moreover the effect of this modification on the other operation variables has

5.8 Summary: modifications 73

been studied and the result is seen in B.4.2. A change in the main inlet airtemperature is still well estimated. However changes in the air flow rate areyet less precisely estimated. The dynamics of the air flow is complex andneeds further study to be modelled by a simple approach.

5.8 Summary: modifications

The change in evaporation rate is modelled by applying a first order systemwith a zero and a pole. The modification that has been implemented inthe model results in a more exact estimate of the behaviour for a change infeed rate. However, this part of the model is determined empirically and byexperience like a black box model in chapter 3. The consequence of this isthat the model is only correct for the specific spray dryer(MSD-20) and thespecific product. Thus an alteration of the spray dryer that is wished to bemodelled requires new experiments. In the long term time scale applying theevaporation times of the particles and evaluate the agglomeration processwill make the model sustainable.


Chapter 6

Linearisation Analysis

For most control design and model analysis applications a linear time in-variant model is needed. In this chapter the dynamic spray dryer modelof environment inside the dryer, described in chapter 5 is linearised andanalysed in order to prepare the model for control design.

Feed rate

Feed temperature

Main flow

Main temperature

SFB flow

SFB temperature

Drying

chamber

Tout air

Rela!ve

humidity

Equilibrium

moisture

content Abs. humidity X

out Water ac!vity

Solidcontent

Tfeed

Tamb

RHamb

Figure 6.1: Dynamic Model of the spray drying chamber, illustrating the ma-nipulated process variable inputs: Feed rate, inlet air flow, inlet airtemperature. Disturbance inputs: Solids contents in feed, ambient airtemperature, relative humidity of ambient air. Output : Toutair

76 Linearisation Analysis

A linearised model is a linear approximation of a nonlinear system. Thisapproximation is only valid within a specific region around a chosen oper-ating point of the system. The operating point is a set of inputs u, outputsy, states x, and disturbances v that describe the operating condition of thesystem. Thus when the state values and inputs of the linearised system areclose to the operating point, the system will behave approximately linearly.

The system is linearised numerically by applying the linmod function inMatlab on the Simulink model for a certain operating point. This functioncomputes the linearised state space model, which is given in (6.1) in termsof δx(t), δu(t), δv(t), and δy(t). The δ-variables denotes the deviations fromthe selected operating point. The matrices A, B, Bv

1, C, and D are definedas the Jacobians of the system evaluated at the operating point (6.2).

δx·(t) = Aδx(t) +Bδu(t) +Bvδv(t) (6.1)

δy(t) = Cδx(t) +Dδu(t)

A =∂f

∂x|x0,u0,v0

, B =∂f

∂u|x0,u0,v0

, Bv =∂f

∂v|x0,u0,v0

(6.2)

C =∂g

∂x|x0,u0,v0

,D =∂g

∂u|x0,u0,v0

6.1 Operating Point

The operating point is a set of inputs u, outputs y, states x, and distur-bances v. The model has 5 inputs to the system, which are used to controlthe drying process: Main inlet air, SFB inlet air, their respective temper-atures and feed flow. The temperature of the outlet air is the output ofthe model. Additionally 2 disturbance inputs are chosen for the model,which are estimated to have the largest impact on the drying process andthe outputs: The relative humidity of the ambient air and Solids content infeed. These parameters vary independent of the spray drying operation andtherefore seen as disturbances. The model has in total 8 states: 5 of thestates describe the process operating variable, which are modelled as firstorder systems. 2 states describe the evaporation rate of the feed and thetotal amount vapour in the chamber, respectively. The last state expressesthe outlet air temperature.

The operating point is selected to be a stationary state for the system, forwhich the time derivative of the states are equal to zero. In this state thesystem is stable and the Jacobians are constant matrices, hence the modelis time invariant. For various input and mean disturbance values stationary

1Simulink regards disturbance v as in input to the system.Bv is therefore a part of the

determined matrix B. 6.1 is then B

[

δu(t)δv(t)

]

6.2 Linearised results 77

states can be determined by following the iterative process given in section4.2.3. The mass and energy balances do not have any constraints for possiblestationary states during the calculations of these, however there are physicalconstraints which have to be considered:

• Spray Dryer System: The performance limitations on the componentssuch as heater, fan, and pump. Also the ratio of amount of feed to airflow and the ratio of Main air flow to SFB air flow is essential for thedrying process and for the system to work properly. Nonetheless theratio of air temperature to air flow rate is in particular of interest forthe drying process, since the amount of energy entering the system fora certain air flow rate and temperature can be obtained, by decreasingthe flow rate and increase the temperature or vice versa. This willchange the properties of the drying air and the drying process.

• Air properties: The humidity level of the drying air is vital for thedrying process. The amount of vapour that can be absorbed by thedrying air is limited by the saturation vapour pressure. Hence therelative humidity cannot be larger than one in reality.

• Feed properties: E.g. the amount of solids decides whether the feed iscapable of being atomised, which the model does not consider.

The operating point for the linearization is chosen to be the stationary statefor the default operation condition used for the experiment (B.1). Theperformance of the dryer in this operating point is known to be stable and itis observed that the spray dryer is capable of step up and step down aroundthis state with regards to air flow, feed flow and temperature, without anydegradation in its performance and stability useful. This state is thereforeestimated to be applicable as the operating point for the linearization. Theoperating point for linearization is listed in table 6.1.

The stationary states and outputs are determined by running a simulationwith the chosen process condition. The disturbances input are the meanvalues experienced for the process.

6.2 Linearised results

The state space matrices for the linearised model, for the operating pointspecified above, is given in app. I. Also the transfer functions from eachinput to the output are determined, for which the zero and poles are shownand their respective frequency responses are illustrated in bode plots(app.I).


Operating Point for LinearizationVariable Name Description Value Unit

Input u0u01 Main air flow IN 1800 Kg/hu02 SFB air flow IN 500 Kg/hu03 Temperature of MAIN 160 oCu04 Temperature of SFB 90 oCu05 Feed flow IN 65 L/h

Disturbance input v0 (mean)

v01 solids of total feed 50 %v02 Rel. humidity ambient air 28 %

State x0x01 Tout 85.44 oCx02 Main air flow IN 1800 Kg/hx03 SFB air flow IN 500 Kg/hx04 Temperature of MAIN 160 oCx05 Temperature of SFB 90 oCx06 Feed flow IN 65 L/hx07 evaporation rate 0.0108 Kg/sx08 Vapour in chamber 0.1933 Kg

output y0y01 Tout 85.44 oC

Table 6.1: Operating Point for linearization: Stationary state

It is observed that the transfer function for the inlet air flow and temperatureprocess inputs (u01−u04) and relative humidity disturbance input (v02) areminimum phase systems2, since all the poles and zeros are in the left halfplane (LHP) (app I.1.3). This means that there is a unique relation betweenthe gain and the phase for the frequency responses. As none of the transferfunctions have pure integrators the slope of the gain at low frequencies is 0.

The slope of the high frequency gain asymptote depends on the differencein the number of zeros and poles. A zero adds 20 dB

dec and a pole -20 dBdec .

to the slope. The transfer function for the process inputs (u01 − u04 −inlet air characteristics) has 2 poles and 0 zeros which results in a highfrequency gain slope of -40 dB

dec . The transfer function for the feed flow inputu05 to output is a 4 order, 4 poles and 2 zeros, with one in RHP. The highfrequency gain slope is -40 dB

dec . The disturbance input v1(solids) have 3

poles and 2 zeros and therefore causes a gain slope of -20 dBdec . The relative

humidity of the ambient air is a first order system which also descends with-20 dB

dec . (The bode plots are found in app. I.1.2).

2minimum phase lag for the given magnitude respose

6.2 Linearised results 79

A LHP pole and a RHP zero adds a −90o phase shift to the high frequencyphase asymptote and a LHP zero and RHP pole adds −90o phase shift. Asseen in the appendix this results in a larger phase shift for the non minimumphase transfer functions. The non minimum phase for feed flow and solids isa result of how the model is build. A change in either the feed rate and solidscontent(both non minimum phase) changes the amount of energy(liquid orvapour conditions) entering system faster than the amount of energy leavingthe system. The amount of energy leaving the system is based on the totalamount of vapour in the system (5.7).

10−4

10−2

100

−180

−135

−90

−45

0

45

90

135

180

To:

Out

(1)

From: In(5)

10−4

10−2

100

Bode Diagram− minimum phase (u1) vs. non minimum phase (u5)

Frequency (Hz)

Mag

nitu

de (

dB)

; Pha

se (

deg)

−150

−100

−50

0From: In(1)

To:

Out

(1)

Figure 6.2: Bode plot- example for a minimum phase transfer function(processinput main inlet air flow u01) (left)and non minimum phase transfer(process input feed flow u05)(right). Both transfer function have 4poles and 2 zeros. For the minimum phase transfer function the phaseshift= −90o · (4 − 2) = -1800. For the non minimum phase transferfunction the total phase shift = −90o · (4) + 90o = −360o

Thus as an example when the feed flow rate increases the amount of energyentering the system increases, which theoretically means the temperaturerises until the vapour level in the chamber has increased and more energy isleaving the chamber, which gives the fall in temperature.

To get a more accurate model only the energy of the evaporated amount ofvapour should be added to the system instead of the difference in input feedand output powder. This is an extension to the modifications made on themodel in section 5.7, which has not been implemented yet.


The poles and zeros for the transfer function for the different input has beenexamined. In the next it is examined how these look for the entire system.

6.3 Stability

A linear dynamic system is stable only if all its poles are in the LHP (Skoges-tad and Postlethwaite (2005)). The poles are determined by calculating theeigenvalues for the system matrix A and inserted in figure 6.3(app. I.1.1).The system can be concluded to be stable since all the poles are in the LHP.The pole in -0.2 denotes the fastest dynamic in the system, which is for thefeed flow. The slowest dynamics in the system is the evaporation, which hasa pole in -0.0008 .

It is denoted that the system does not have any multivariable zeros.

Poles[

-0.0676 -0.0008 0-0.0563 -0.0250 -0.0063 -0.0056 -0.0020 -0.2000]

Pole−Zero Map− for the Multivariable system :7 inputs 1 output

Real Axis

Imag

inar

y A

xis

−0.2 −0.18 −0.16 −0.14 −0.12 −0.1 −0.08 −0.06 −0.04 −0.02 0−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Figure 6.3: Zero-Pole plot for the linearized model. The linearized system con-tains only poles. There are 8 poles and describes the dynamics at eachstate.There are no multivariable zeros, which mean there is no com-mon zero for all the transfer functions. The columns in the transferfunction are not linearly dependent

6.4 Comparison of the linear model with the non-linear model 81

6.4 Comparison of the linear model with the non-linear model

In this section the linear model is compared to the non linear model by ap-plying various steps on the process - and disturbance inputs. The linearisedmodel describes how far the result is from the linearised operating point fora certain change. The step change applied is also given as the deviation fromthe inputs used for linearization. Thus at the operating point the outputis equal to zero and to compare it with the non-linear model the stationaryoutput value is added to the output.

The results of the comparison of the models for the various steps on bothprocess and disturbance inputs are given in app. I.2. Generally it is observedthat the linear model is a reasonably good estimate of the non-linear modelfor the same step changes on the process inputs as used in the previous testsof the non-linear model (table C.2).

The largest discrepancies between the linear and non linear model are ob-served when the step values are great compared to the stationary inputs.As seen in figure 6.4 the step change of 10oC in the temperature of the inletair, for which the stationary value is 160 oC, gives a close estimate. Whilea step change of 10 L

h for the feed flow results in a dissimilarity (figure 6.5).Also changes in the disturbance input have resulted in good estimates. Theresult of a step change in the solids content is seen in figure 6.6. However,this is only a theoretical test as a change in solids content from 50% to 80% percent is very unlikely in reality.

The linearised system has made it possible to analyse the system. This isutilized in the design of a PI controller for the system in chapter 8.


0.95 1 1.05 1.1

x 104

79

80

81

82

83

84

85

86

Tout

outlet air temperature Linear model compared to Non linear model: main air temperature step Tmain

Time [sec]

Tem

pera

ture

[oC

]

Linear model: ∆ Tmain

=−10

Nonlinear model

Figure 6.4: Comparison of linear and Non-linear model: Main inlet air tempera-ture. Step change= 10 from linearised input. No change difference isobserved

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

80

81

82

83

84

85

86

Tout

outlet air temperature Linear model compared to Non linear Feed flowrate step Ffeed

Time [sec]

Tem

pera

ture

[oC

]

Linear model: ∆ F

feed =10

Nonlinear model

Linear model: ∆ Ffeed

=2

Nonlinear model

Figure 6.5: Comparison of linear and Non-linear model: Feed step : 2 & 10. Forthe small step no difference is observed. For the larger step a smalldeviation is noted.

6.4 Comparison of the linear model with the non-linear model 83

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

x 104

85

90

95

100

105

Tout

outlet air temperature Linear model compared to Non linear model: Solids content step Scont

Time [sec]

Tem

pera

ture

[oC

]

Linear model: ∆ Scont

=0.3

Nonlinear model

1.3 1.4 1.5 1.6 1.7 1.8 1.9

x 104

103.5

104

104.5

105

Zoomed in

Time [sec]

Tem

pera

ture

[oC

]


=0.3

Nonlinear model

Figure 6.6: Comparison of linear and Non linear model: Solids content step from50 % to 80 % Such a large change is not possible in reality. Smalldifference between the nonlinear and linear model.


Chapter 7

System Identification of

Residual Moisture Content

In the previous chapter a grey box model describing the temperature con-ditions of the drying air (environment) in the chamber using a combinationof first principle equations and observations, from the experiment on theMSD-20 spray dryer, has been developed. The purpose was to estimate thesurrounding conditions the particles are experiencing during the drying pro-cess as an indirect measure for the final product quality. A model that isable to estimate the operations condition in the dryer, and is able to estimatethe moisture content of the final product would have a distinct preferencewhen developing new control systems. However, as declared earlier due thecomplexity of the product behaviour and drying parameters it is difficulttoexpress the moisture content of the product leaving the dryer by a whitebox model.

In this chapter a black box model, as described in chapter 3, of the finalmoisture content in outlet powder is modelled by applying system identifi-cation principles. This is another way of getting a linear model of the systemas it was completed for temperature model of the spray dryer in chapter 6.The black box model makes it possible to create a mathematical model ofthe dynamic process based on the measured data from the experiment onthe MSD-20, and then be able to estimate the changes in the moisture con-tent when the process condition are changed. Nonetheless this subject isonly handled superficially in this project, to prove that black box modellingis a proficient tool to model parts of a system which are problematical tomodel, such as the moisture content of the product leaving the chamber.Thus only linear models are evaluated and only parametric and state space

86 System Identification of Residual Moisture Content

identification methods are used.

7.1 Applied Identification Methods

Parametric identification is a matter of estimating numerically the valuesof the parameters in a given model structure that gives the best agree-ment between the output of the model and the measured data. The systemidentification toolbox in Matlab is able handle a variety of diverse linearpolynomial model structures, which can be given in the general form as in(7.1).

The model structure shown is for discrete time, due to the fact that it isstraightforward to estimate the model in discrete time and then convert itto continuous time. A, B, C, D, and F are polynomials that contains thetime shift operator q(1 sample). The coefficients in each polynomial are theparameters that are to be found. ui is the ith input to the model and thetotal number of inputs is nu. nki is the input delay for the ith input whichcharacterise the number of samples it takes for the output to respond to theinput. y(t) is the output and e(t) is white noise. (Ljung (2001), Mathworks(2009))

A(q)y(t) =

nu∑

i=1

Bi(q)

Fi(q)ui(t− nki) +

C(q)

D(q)e(t) (7.1)

Thus the output at the time t depends on the input and output values atprevious time instants. The order of the model is determined by the num-ber of coefficients in the polynomials. Herafter when the model order ismentioned it is thought to be the number of coefficients in the A polyno-mial. The model structures vary by how many of the polynomials that areincluded in the structure or whether they are set to 1. Hereby they pro-vide some flexibility for modelling the dynamics and noise characteristics.In this project the main emphasis is on modelling the dynamic changes inthe moisture content when the operation conditions change.

Moreover due to the very few real samples (∆ 10 min) of the moisturecontent in the powder, compared to the number of samples in the processdata from the spray dryer (1-10 sec), which is used as input data, it isdifficult to evaluate the direct influence of the noise at the inputs. Thereforeit has been decided that a detailed model of the noise is not necessary andconsequently the F and D polynomials are not included in the models thatare estimated here.

The model structures that will be examined is an ARX 1 model, which is

1Auto Regressive with eXogenous input

7.2 Estimation Data and Validation Data 87

described by the A and B polynomial, and an ARMAX 2 model, whichprovides some flexibility for modelling the disturbance dynamic with theinclusion of the C polynomial. The parametric identification method min-imises a performance function which is based on the sum of squared errors.It can therefore experience many local minima in the performance functionand thus not converge to the global minima and problems with instabilitycan occur. For this reason state space identification method is examined,which gives a model that is well conditioned. The state space model (7.2)describes the same linear difference relationship between the input and out-put as the ARX model, but on the contrary only one delay is used. Insteadstate variables are introduced corresponding to the model order and a Knoise

matrix that determines the noise properties

x(t+ 1) = Ax(t) +Bu(t) +Knoisee(t) (7.2)

y(t) = Cx(t) +Du(t) + e(t)

The focus of the estimated models is on simulation purposes (dynamic prop-erties) rather than prediction purposes (stochastical properties).

7.2 Estimation Data and Validation Data

For estimation of a linear model, time domain data is used. The data iscollected from the experiment on the MSD-20 spray dryer (section 4.3). Asdescribed in the test description, most of the tests on an operation variablewere repeated. In this way the first part of a test can be used as estimationdata, which is the data set that is used to train the model to fit givendata. The repeated test data is appropriate to be used as validation data tovalidate the estimated model. Thus the model is simulated using the inputdata from this data set and the result is compared to the output data inthis data set.

The moisture content is the parameter that is wished to be modelled basedon essential inputs (single output multiple inputs system). The data set,for both estimation and validation data, contains data from 9 inputs and 1output and is listed in table 7.1. The variables that are chosen to be inputsare first of all the most significant parameters for the drying process. Thesecond criteria is that it should be able to model the input parameter values,thus the moisture content can be estimated without the need for real dataonce the model is up running. The input parameters used can therefore beobtained from the dynamic model of the chamber developed in this project.

2Auto Regressive Moving Average with eXternal input


Data SetSensor Name Description Value Unit

Input Data

MAINKGH Main air flow into chamber PV Kg/hSFBKGH SFB air flow into chamber PV Kg/hT1702 Temperature of MAINKGH PV oCT1704 Temperature of SFBKGH PV oCF1626 Feed flow into chamber PV L/hP1706 Pressure difference of powder layer in SFB PV mmH2OT1624 Temperature of ambient temperature PV oCP1618 Relative humidity of ambient air PV %T1709 Temperature of air flow out of chamber PV oCT1616 Temperature of air leaving system PV oCP1614 Relative humidity of air leaving system PV %

INHUMABS Absolute humidity air IN PV Kg/Kgbased on sensor values (T1624 & P1618)

OUTHUMABS Absolute humidity air OUT PV Kg/hbased on sensor values (T1616 & P1614)

Output Data

Moisture content of Powder (SFB outlet) %water/kg

Table 7.1: PV:process value, Out: Controller Output value

Accordingly five of the nine input parameter are the feed and inlet air pa-rameters that have been extensively used during this project. Moreover theoutlet temperature of the chamber and the absolute humidity of the ambientair at air intake are chosen, as these affects the evaporation. The absolutehumidity of the air leaving the chamber gives a description of the amountof water evaporated. The last parameter is the pressure difference aboveand below the powder in the SFB, which is an estimate of the height ofthe powder layer in the SFB. This parameter is indirectly a measure of theresidence time of the powder in the chamber and included in the data set,despite the fact that is not found in the model of the chamber. If the amountof powder discharged the varied according to feed flow rate this parametercan be modelled as a constant.

Two data sets are available. In the first one data is logged every secondand in the other one data is logged every tenth second. The noise in theone second data set is more apparent than for the 10 sec. data set, whichdue to the lower sampling frequency does not capture the high frequencyvariations. For that reason the 10 sec data set is used in the identificationprocess. The moisture content of the powder at the outlet of the SFB isonly sampled every fifth (feed flow tests) or tenth minute (the rest of tests)for offline measurement. These data are linearly interpolated to be able

7.3 System identification Results 89

estimate the moisture content with a 10 sec interval and combined with the10 sec data from the system.(see figure C.2.3 in appendix C)

The estimation data set is the combination of all data from the tests shownin the logbook in app. C.3. The validation data set is decided to be datafor the entire test, including the part which has been used to train themodel. This way the model is tested both with known and unknown data.Furthermore the point of reference for the step change will be similar to theone which has been used to train the model.This will make it easier for themodel to recognise the change and respond to it in a correct way.

7.3 System identification Results

The best model between the selected model structures according to the givendata is wished to be determined. However, the quality of the model can bedefined and measured by various parameters (Mathworks (2009)):

• Loss function - value of the identification criterion at the estimate,thus it indicates how well the model is fitted to the estimation data.

• Best fit - sum of the squared error between the validation data outputand the model output

• Final Prediction Error (FPE)- Akaike’s critierion is another way todescribe the difference between the model and validation data.

• Model Order

All the parameters are aimed to be as low as possible. But concerning theloss function, a value too low can also indicate over fitting of the model to theestimated data, which can have a negative effect when the model is used onnew data. Also an increased model order in normal cases gives a better fit,but this increases the possibility for zero pole cancellations and over fittingto the noise. Hence these parameters can be used as guiding indicator aboutthe quality of the estimated model, nonetheless it is essential that the modelhas captured the dynamic and therefore a graphical view of the simulatedoutput and measured out will be used as well. Since there is no previousknowledge about the dynamics of the final moisture content, the trial-and-error approach is used to determine the model order and delays necessaryto get the best model.


7.3.1 ARX model

The ARX model is the simplest polynomial model and fast to be calculated.A function in the System Identification Toolbox in Matlab allows one tomodel a range of orders and delays simultaneously and compare the resultingmodels. This was used to estimate model orders from 1 to 10 and likewise forthe delay. The result showed that a model of the order 10 with one coefficientfor each input (B polynomial coefficient) and a time delay of 8, gives thebest fit(FPE = 0.00105) (see appendix H.1.1). The model is simulated forthe validation data set and compared to measured output in figure 7.1. Forcomparison a similar ARX model of order 15 is simulated and included inthe same figure.

0 1 2 3 4 5 6 7 8 9 10

x 104

0.5

1

1.5

2

2.5

Time [sec]

Res

idua

l moi

stur

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nt [%

wat

er/k

gpo

wde

r]

Measured and simulated ARX model output of the moisture content

Model order 10 & 1 input coeffcients

Measured

Model order15 & 1 input coeffcients

Figure 7.1: Simulated ARX model output and measured output(moisture content(%water/kgpowder) for a 10th order model and a 15th order model.Both describe the input with one coefficient and time delays for theseare 8 sec.

It is noticed that the simulated model has captured some of the trends butthe result is far from acceptable. This is mainly due to the fact that thesystem dynamic and the stochastic dynamics are coupled by having the sameset of poles. Thus the model is deficient when it comes to distinguishing noisefrom the system dynamics. Increasing the model order could give a betterfit. The zero-pole plot for this model illustrates a zero-pole cancellation andincreasing the model order is not desired, which increases the possibility of

7.3 System identification Results 91

more zero-pole cancellations (app. H.1.1).

7.3.2 ARMAX Model

The ARX model has given a good starting point for estimating ARMAXmodels, which unlike the ARX model describes the stochastic dynamics withadditional polynomial C (7.1). Starting with a 10th order ARMAX model,the estimated model was successfully decreased to a 6th order ARMAXmodel. It has 7 input coefficients (nb) and 8 time delays (nk). At the sametime it gives a better fit according to quality parameters. The simulatedoutputs and the coefficients for both models is illustrated in figure 7.2. A

0 1 2 3 4 5 6 7 8 9 10

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−0.5

0

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Measured and simulated ARMAX model output

na=6 nb=7 nc=2 nk=8na=10 nb=5 nc=8 nk=8Measured data

MAINKGH1702SFBKGH &1704

END ofTEST

Feed Flow1626

Figure 7.2: ARMAX model of order 6 and 10 with the coefficients given in thena, nb, nc, nk). 6th order: FPE = 0.00017, Loss = 0.000169. 10thorder: FPE = 0.0010, Loss = 0.00109. The tests periods are shownas well. In the last part of the main inlet air flow test (MAINKGH)the PI controller on the air temperature was turned off.

few of the estimated ARMAX models and their quality parameter is listedin table H.1 the simulated outputs are given in app. H.1.1.

The first part of the tests is used for estimation of the model. As it isseen the models fits well to this part. The second part is the new data for


validation, which at first sight may not look excellent, but acceptable andthe deviations may be explained.

In the feed flow test it observed that the moisture contents decreases inspite of the fact that the same step changes are applied and the outlet airtemperature is almost constant (app. C.2.4). The explanation could not befound in any of parameters used for the identification of the system. Butthis may be due to the changes in the amount of fines collected and thechanges in the agglomeration process when the feed flow is changed. Theseare unmeasured parameters. it notes that the model has estimated the stepchange similar to the behaviour of the training data.

The deviation between the measured and simulated value in the temperaturetest (sensor 1702. see app. C) for main air inlet is due to the fact thatdifferent steps are applied in the estimation data set and the validation dataset. In the estimation data the steps applied are from 1600C → 1500Cand 1500C → 1700C. In the validation data set the step used is from1700C → 1600C. (C.3). This illustrates the fact that a black box model isonly useful in the operating region which data is extracted from and used inthe identification process (see modelling section 3).

The effect of changing the main inlet air on the final moisture content is notdistinct. Moreover the validation data set for this test cannot be used toevaluate the model, because in this part the controller to 1702 was turnedoff. This means the effect from the electric heater is constant. Consequentlyan increase in air flow decreases the inlet temperature. The model thereforemisinterprets the situation and estimates the fall in temperature to be equalto a rise in the moisture content. The outcome of changing the SFB inlet airflow is indistinguishable as for the Main inlet air. So the model estimatesnoise more than the actual dynamic. But the temperature of the SFB isobserved to have a great impact on the moisture content and model estimatesit well.

It is observed that the 6th and the 10th order model behave identically.The main difference is how the noise is described. The 10th order modelincludes more noise, while for the 6th order model only 2 coefficients areused to describe the noise. This seems satisfactory in a situation where thesystem dynamics is of main interest. The zero-pole plot of the 6th ordermodel is illustrated in figure H.8 in appendix. The model is stable since thepoles of the system lies within the unit circle and no zero-pole cancellationis observed. In the same appendix results from other ARMAX models areshown and what effect the number of polynomial coefficients has on theestimated model.

7.4 Summary: System identification 93

7.3.3 State Space model

For the state space model structure the best model is estimated to be of 4thorder. The results from simulating this model is shown in figure 7.3. Forcomparison the ARMAX model is also given in the figure. It is observedthat the state space model experience the same problem as the ARMAXmodel. Both models are able to capture the most dominant dynamics.

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Measured and simulated model output

ARMAX model 6th orderState Space model 4th ordermeasured data

Figure 7.3: State space model of 4th is identified as being the best for this modelstructureFPE = 0.00030, Loss = 0.0003.. Here the model is com-pared to the ARMAX model of 6th order and the measured data.

7.4 Summary: System identification

ARX, ARMAX, and state space model structures has been examined. TheARMAX model and state space model gave the best simulation results, butsince the estimation data and validation data are not based on the same stepchanges for all tests, it is difficult to estimate the quality of the estimatedmodel. Nonetheless this confirmed that a black box model only is acceptablewithin the operation region that has been used to train the model.

Another problem appears to be, that the test periods are too short with onlya few measurements. Longer test periods would give time for the moisturecontent to settle around a point, which might help the model to distinguish


between a noise and the system dynamics. For a short test period with onlya few measurements the observed changes may be assumed as being a partof the noise dynamics than a part of the system dynamics.

In the models investigated in this section the number of coefficients (nb)for the input has been chosen to be the same for all of them. This is notnecessarily the best, since each input can go through different orders ofdynamic in reality. Further studies of the inputs are necessary to optimisethe model. This same applies for the time delay of the input coefficient.The system identification is only superficially handled in this project. Thisalso means that the model order has been reduced by the trial-and -errormethod. Model reduction can also be done analytically for example by usingthe Hankel norm approximation.

A black box model is a fast and straightforward way to model a system.It needs a great number of data for different operation regions both forestimation and validation. Otherwise the developed model will be too simpleand ineffective for modelling. The disadvantage of this type model is thelack of flexibility as it cannot be used for other systems. The conclusionis that a complete black box model is also difficult to estimate without theappropriate data. However, it might be possible to estimate some simplerparameters, that can be combined with the white box model. For examplethe time it takes for the system to settle after a step change, which gavedifficulties for the white box model in chapter 5.4.

Chapter 8

Control of spray dryers

In this chapter it is demonstrated that the developed model of the spraydryer is relevant for examining control strategies. This is realised by imple-menting the main feed rate control strategy with a PI controller which isused on most of the spray dryers at present time. The input, output, anddisturbance variables associated with the spray dryer for process control isshown in figure 8.1. Though, only control on a single operation variable isdescribed in this section.

8.1 Control Strategy

As described in the introduction in chapter 1, the control system of a spraydryer has many objectives:

• Maintenance of a desired dried product quality, irrespective of thedisturbances in the drying operation.

• Stable drying process

• Optimisation of the performance of the drying process- maximisationof throughput at optimal energy efficiency and at minimum cost

• safety system- in case of system failure.

The target of the inspected controller in this project is only to keep theprocess stable and disturbance rejection. Thus the dried product quality,

96 Control of spray dryers

Feed rate

Main flow

Main temperature

SFB flow

SFB temperature

Drying

chamber

Tout air

Solidcontent

Tfeed

Tamb

RHamb

Figure 8.1: Illustration of the process input and outputs to the spray drying sys-tem and disturbances which can be used in the controller design pro-cess

measured as the moisture content in the final powder, is maintained anduniform. Since the moisture content is not directly measurable, it is indi-rectly controlled by maintaining the outlet air temperature at a set value byvarying either the feed rate to the dryer or the main inlet air drying tem-perature (feedback control strategy). Maintaining a constant outlet dryingair temperature through feed rate control is mostly used, in which the feedpump/nozzle pressure is varied to counteract any temperature deviations.The time constant for a change in the manipulated variables is smallestfor the feed rate, as observed from the test results from the MSD-20(app.C.2.4), which is the reason to use this as the main control loop. While themain control loop is used to control the drying process the other input vari-ables are kept constant by the relation between air flow and the heated air.However for some systems it is required to keep a constant nozzle pressure,due to the product characteristics of the feed. In such cases the outlet airtemperature is controlled by the inlet air temperature.

8.1 Control Strategy 97

HEATERDRYING

CHAMBER

PUMP

Variable

speed drive

Feedstock

Drying air

Powder

Tout air

PI

PI

Tin air

Disturbance:

Solides content

Tamb

RHamb

Figure 8.2: Illustration of feed rate control by using a PI controller. Inlet airtemperature is kept constant by a PI controller, which measures thetemperature of the inlet air and controls the heater.

8.1.1 PI controller

The control strategy used in the spray dryer is feedback control with a PIcontroller, in which an error signal e(t) is used to generate the proportionaland integral actions. The resulting signals are weighted and summed toshape the control signal u(t) to the plant model. The algorithm for the PIcontrol is given in (8.1). Kp is the proportional gain and τi is the integral/re-set time which weights the influence of the integral term. When the feedrate is controlled the error signal is defined as e(t) = rtemp − Toutair. Thelaplace transformed transfer function of the PI controller is given in (8.2).

u(t) = Kp

[

e(t) +1

τi

∫ t

0e(τ)dτ

]

(8.1)

Gc(s) =U(s)

E(s)= Kp

(

τis+ 1

τis

)

(8.2)

The controller has a pole in origo and a zero in s = − 1τi, which results in

the controller to have its cutoff frequency at ωb =1τi.


8.2 PI controller for disturbance rejection of solidscontent variation

A PI controller for feed rate control is determined, for which the objectivesare given as:

• Reference tracking: The controller should be able to hold the outlet airtemperature value at a set point. For a certain change in the referencethe controller should manipulate the feed rate to obtain the desiredeffect.

• Disturbance rejection: The disturbances shown in figure 8.1 should berejected. The disturbance from the ambient air characteristics have aslow dynamics, as it takes time for the temperature and humidity levelto change. However the disturbances from the feed is somewhat faster,as this depends on the preheater/evaporator. The solids content hasa major impact on the drying process and the final moisture content,which is the reason for examining this disturbance.

The general requirements for the control system:

• Stability and Accuracy: In order to obtain powder with a constantlevel of moisture content, no oscillation in the system is desired, asthis result in fluctuations in the output moisture content. A constantoutlet air temperature is wanted.

• Response speed: The response speed is of less importance, since thespray dryer in general is a slow system, due to the long evaporationtime of the feed and the time for the evaporation rate to settle asnoticed in chapter 5.7. Hence it is not necessary for the controller tobe as fast for some servo system.

8.2.1 PI controller design

The temperature control system by feed rate variation is shown in figure8.3. The transfer function Gfeed(s) from the feed input to the outlet airtemperature output was found in chapter 6 and given in (8.3). The transferfunction from disturbance input to the output, Gsolid(s), is given in (8.4).

Gfeed(s) =0.00042s2 − 0.0002213s − 3.736 · 10−7

s4 + 0.3247s3 + 0.02885s2 + 0.0007841s + 6.095 · 10−7(8.3)

Gsolid(s) =−0.4735s2 + 0.09684s + 0.0001852

s3 + 0.1247s2 + 0.003905s + 3.047 · 10−6(8.4)

8.2 PI controller for disturbance rejection of solids content variation 99

CONTROLLER

Gc(s)G

feed�s

Gsolid

�s

d

r+

-

e + +T

out airu

Figure 8.3: The temperature control system by feed rate variation. Gfeed(s) is thetransfer from feed input to output. Gc - controller transfer function.Gsolid(s) is the transfer function of the disturbance.

It is noticed that the static gain for the disturbance is Gsolid(0) ≈ 60, whichmeans that the response to a unit disturbance will be 60 times larger thanacceptable. The Bode plot of this transfer function shows that this decreasesfor larger frequencies, but the gain remains larger than 1 up to ωd = 0.5 rad

secat which frequency Gsolid(jωd) = 1 (see app. I.3).

In order to be able to reject the disturbances the cross over frequency, ωc, forthe controller is chosen to be equal to ωd. It is known that the PI controllerincludes a phase shift of −900 at low frequencies and 00 at higher frequencies.To reduce the impact of the introduced negative phase shift on the closedloop systems phase margin, the cutoff frequency ωb of the controller is chosento be four times lower than the determined cross over frequency ωc (8.5).Hence the phase shift of the controller will be close to zero at this frequency(Jannerup and Sørensen (2004)).

ωk =1

τi=

1

ωc(8.5)

τi =1

0.25 · 0.5 radsec

= 8 sec (8.6)

Inserting the integral time in (8.2) and the open loop transfer function can


be written as:

Gopen(s) = Gc(s)Gfeed(s)

Gopen(s) == Kp

(

8s+ 1

8s

)

0.00042s2 − 0.0002213s − 3.736 · 10−7

s4 + 0.3247s3 + 0.02885s2 + 0.0007841s + 6.095 · 10−7(8.7)

The bodeplot for the open loop system Gopen for proportional gains Kp =1−10 is given in figure 8.4. The phase margin, which is a description of howmuch phase lag can be added to the system before the phase at the gaincrossover frequency becomes −1800, is for Kp = 1 is ≈ 1400. Phase marginfor Kp = 10 is ≈ 700. Normally a phase margin larger than 300 is required,which is seen to be satisfied for the examined proportional gains.

Furthermore the system fulfils Bode’s stability condition for closed loop sys-tem, since |Gopen(jω180)| < 1. (Skogestad and Postlethwaite (2005))

Bode Diagram− Open loop transfer function with PI control, (Kp =1−10)

Frequency (rad/sec)

−150

−100

−50

0

50

100

150

System: G_openFrequency (rad/sec): 0.0238Magnitude (dB): 0.745

Mag

nitu

de (

dB)

System: G_openFrequency (rad/sec): 0.103Magnitude (dB): −0.203

10−5

10−4

10−3

10−2

10−1

100

101

102

−180

−135

−90

−45

0

45

90

System: G_openFrequency (rad/sec): 0.0238Phase (deg): 49.6

Pha

se (

deg)

System: G_openFrequency (rad/sec): 0.103Phase (deg): −20.8

Kp = 1

Kp =10

ωc for K

p =10

ωc for K

p = 1

Figure 8.4: Bode plot for the open loop transfer function for various proportionalgains Kp. It seen the frequency response is close to each other for thedifferent gains. Phase margin for Kp = 1 is ≈ 1400. Phase margin forKp = 10 is ≈ 700.

8.3 Results from PI controller implementation in dynamic model 101

8.3 Results from PI controller implementation indynamic model

In this section a PI controller with the previous determined integral timehas been implemented in the dynamic model. Step tests on the referencetemperature and in solids contents has been conducted for the lowest andthe highest proportional gain (Kp = 1 and Kp = 10) has been conducted.

8.3.1 Step on reference temperature

In this test the reference temperature is stepped up from steady state tem-perature 84.440C → 870C. The resulting control signal u, which is theoutput of the PI controller, and the response of the outlet air temperatureis shown in figure 8.5.

It is seen that the rise time is shorter for Kp = 10 is approximately 50 sec,while it takes 100 sec for Kp = 1. It is noticed that the overshoot of theoutlet air temperature is lower than for the smaller gain, nonetheless moreoscillations are observed and it requires more of the feed pump due to thelarge variations in the control signal. This is not desired, since changes infeed rate also affects the structure of the particle and the agglomerationprocess, which can result in a non uniform product. The settle time isequal for both gains. The outlet air temperature is within 0.10C of the finaltemperature after 200 sec. Temperature is completely settled after 1500 sec.This is due to the change in evaporation rate, with a very slow pole (seesection 5.7). It has to be emphasized that an increase in the control signalis a decrease in feed rate, since Ffeed − u is the input to the system.

8.3.2 Step on Solids content

The solids content can vary ± 2% from the mean solids content in the feed.(Westegaard (2004)). In this project, the mean solids content has beencalculated to 50%. At first a step change is applied on the solids contentvalue. This is only of theoretical interest as this does not occur in reality.The step applied is from the mean value of 50% to 52% solids in feed. Thetarget is to keep the default outlet air temperature at 85.440C. The resultof the temperature control and the disturbance rejection is shown in figure8.6.

Again it is observed that the controller with the larger proportional gainhas the fastest response. Due to the slower response from the controllerwith Kp = 1 the outlet air temperature increases more than for the othercontroller. This controller is also noted to have larger oscillations, but the


7 7.05 7.1 7.15 7.2 7.25

x 104

0

5

10

15

Step on reference temperature r= 85.44 −>87 0C

Time [sec]co

ntro

l sig

nal u

PI Control signal Kp =1

PI Control signal Kp =10

7 7.02 7.04 7.06 7.08 7.1 7.12 7.14 7.16 7.18 7.2

x 104

85

85.5

86

86.5

87

87.5

Temperature Tout air

Time [sec]

Tem

pera

ture

[oC

]

Tout air

Kp =1

Tout air

Kp =10

Figure 8.5: PI controller: reference temperature is stepped up from steady statetemperature 84.440C → 870C. Controller is examined for Kp = 1and Kp = 10. Top figure shows the control signal. The figure belowillustrates the outlet air temperature response. The settle time isequal for both gains. The rise time is shorter for Kp = 10 is ca. 50sec, while it takes 100 sec for Kp = 1. Outlet air temperature iswithin 0.10C of the final temperature after 200 sec.

settle time is similar for both controllers: 400 sec.

Continuous Disturbance in solids content The effect of the controlleris examined by simulating a continuous disturbance in solids content. Thisis completed by using a uniform random block in Simulink, which gener-ates uniformly distributed random numbers over a specifiable interval. Theinterval in this test is specified to be from 48% to 52%. In figure 8.7 the tem-perature response of a process with a continuous disturbance in which thePI controller is turned off and then switched on is illustrated. For the pro-cess running without the PI controller the temperature variation is ∓0.70C.When the PI controller is turned on the temperature variation decreases toless than ∓0.30C.

8.4 Possible control strategies

In this chapter a PI controller has been designed, implemented in the dy-namic model of the spray dryer and tested for reference tracking and distur-bance rejection to demonstrate that the model can be used to evaluate theperformance of a controller for a spray drying process.

8.4 Possible control strategies 103

7 7.005 7.01 7.015 7.02 7.025 7.03 7.035 7.04 7.045 7.05

x 104

−3

−2.5

−2

−1.5

−1

−0.5

0

Step on solids content Sconc

= 50% −>52%

Time [sec]

cont

rol s

igna

l u

control signal u− Kp =1

control signal u Kp =10

7 7.005 7.01 7.015 7.02 7.025 7.03 7.035 7.04 7.045 7.05

x 104

85.2

85.3

85.4

85.5

85.6

85.7

85.8

85.9

86


Time [sec]

Tem

pera

ture

[oC

]

Tout air

Kp =1

Tout air

Kp =10

Figure 8.6: PI controller:step on solids content is stepped up from the mean valueof 50% to 52% solids in feed . Top figure shows the control signal. Thefigure below illustrates the outlet air temperature response. Kp = 1gives a slower response and therefore larger temperature oscillations.settle time is similar for both controllers: 400 sec

The PI controller is a good basic controller with no steady state error, butto optimise the performance of the spray drying process it is expected morevariables has to be controlled. During the development of the dynamicmodel, it was experienced that the humidity level in the dryer is an essentialparameter for the drying process and the final moisture content in the prod-uct. Applying the air humidity as a control variable in the control systemgives some possibilities.

At present time single input single output control is used. But multivariablecontrol is estimated to have a great potential for spray drying systems. Ithas been observed that the air inlet temperatures has relatively fast responsetime and has a great effect on the moisture content. Moreover it is knownthat the relative humidity is dependent on the temperature and the differ-ence in vapour pressure between the feed and air determines the drying rate.Manipulating the inlet air temperature will therefore give a better controlof the drying condition in the chamber.

Especially the SFB inlet air temperature was observed, during the systemidentification process, to have a great effect on the moisture content. In amultistage dryer the SFB part gives, during the fluidisation, the powder itsspecific characteristics. Using temperature from this part of the spray dryer


1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 2.06 2.08 2.1

x 104

0.47

0.48

0.49

0.5

0.51

0.52

0.53

Continuous Disturbance in solids content Sconc

= 48% −52%

Time [sec]S

olid

s co

nten

t [kg

solid

s/k

gfe

ed]

Solids content

1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3

x 104

85.35

85.4

85.45

85.5

85.55


Time [sec]

Tem

pera

ture

[oC

]

Tout air

Kp =10PI controller OFF PI controller ON

Figure 8.7: PI controller:Continuous Solids content Disturbance. The figureabove is the simulated variation solids content. The figure belowshows the temperature response. Before the time reaches 20000 sec.the PI controller is turned off and the outlet air temperature varies∓0.70C. After 20000 sec PI controller is turned on. The temperaturevariation decreases to less than ∓0.30C.

to control the SFB air temperature is assumed to result in a more uniformpowder quality.

The linearised model provides the possibility for LQG control and the Kalmanfilter. Otherwise more advanced H2 optimal control can be used, in whichthe output error of the system is minimized. Another possibility is toshape the sensitivity function, as this is a good indicator for closed loopperformance(H∞ control). Further description of multivariable control canbe found in (Skogestad and Postlethwaite (2005))

Chapter 9

Conclusion

The objective of the spray drying process is to produce dried product of adesired quality regardless of the disturbances in the drying operation andvariations in feed supply. In order to improve the dryer operation and its effi-ciency, alternative control strategies than the classical PI control are wishedto be examined. However, the design of a controller has not been the focusof the project. The aim of this project was to construct a dynamic model ofthe drying process in a multistage spray dryer with a mixed air flow, thatcan be utilised in the future study of new control strategies for the spraydryer.

In this project a dynamic model describing the drying environment, withregards to the air temperature and humidity, inside the chamber has beendeveloped based on white box modelling methods. The underlying basis forthis dynamic model is mass and energy balance equations. It is assumedthat the air and particles in the drying chamber are well mixed, due to themixed air flow, and the spray dryer is therefore modelled as a continuouslystirred reactor tank. The outlet air temperature is for that reason equalto temperature in the chamber. The calculated steady state temperatures,when heat loss through the chamber is included, is very close to the temper-atures measured from the experiment on the Multi Stage Dryer-20 at GEANiro’s test station(deviation ≈ 1− 2oC).

The absolute humidity of the air in the chamber is determined from theamount of vapour evaporated from the feed. In the model it is assumedthat the final product leaving the spray dryer has reached its equilibriummoisture content. This is a simplification, since some of the powder leaves

106 Conclusion

the dryer before this state is reached in reality, which gives a lower humiditylevel than the model estimate.

The dynamic model has been implemented in MATLAB/Simulink, in whichthe input process variables, size of the spray drying chamber, disturbanceand product characteristics can be varied and the process simulated. Thedynamic model has been validated by comparing the simulation results withthe experimental results from MSD-20.

The temperature response for step changes in the input process variablesdryer has been examined. For a step change in main inlet air temperaturethe model behaved similar to what was observed for the real spray dryer.The time for the outlet air temperature to settle for a step in main inlet tem-perature is 1500 sec. Modelling the temperature response for a step changein air flow appears to be more complicated due to the complex behaviourof the air flow around the inside of the chamber. The model presents aresponse which is twice as fast the MSD-20 test results. For a change infeed flow rate into the chamber, the temperature response is sensitive tothe changes in evaporation rates. In this project the change in evaporationrate is modelled as a first order system by inspecting the drying times fora single particle and the experimental results. The outcome of using thismethod has shown good results for the temperature response when the feedrate changes. The time for the temperature to settle for step in feed rate isapproximately 2500 sec.

The model has been linearised in order to analyse the model. It is seenthat the behaviour of the linear model is close to the non-linear model forsmall steps. Moreover the frequency response was examined and used in thedesign of a simple PI controller.

An estimate of a black box model, which is another way of examining a lin-ear model, of the moisture content as a function of input process variables,ambient air disturbances and outlet air temperature, has been attemptedby using the system identification toolbox in Matlab. However lack of esti-mation and validation data for moisture content assessment resulted in lessoptimal models. However it is expected that these methods can be used todetermine some parameters for the white box mode, which will result in agray box model.

In the end it was demonstrated that the model can be used with a PI con-troller. The PI controller used here was for reference tracking of the outletair temperature and rejection of disturbances from the variation in solidscontent, which it accomplished successfully.

Nomenclature

˙mtransfer mass transfer rate, page 50 (Kg/(s ·m2))

λ latent heat of vaporization, page 25 Kj/Kg

µair absolute viscosity, page 52 -

ν kinematic viscosity, page 52 -

ωb break frequency, page 99 -

ωc Cross over frequency, page 99 -

ωd Cross over frequency for disturbance-for rejection, page 99 -

ψ relative humidty of vapour gas mixture, page 27 %

τi integral time for PI control, page 97 -

τevap time constant for the slow dynamics in evaporation rate, page 71

τfast time constant fast response in evaporation , page 71 -

ACeiling angle of the chamber ceiling, page 45 -

AChamber surface area, page 34 m2

ACone angle of cone on chamber, page 45 -

CdryAir heat capacity of dry air, page 23 Kj/Kg ·K

CdryAir specific heat capacity of dryAir, page 25 Kj/(Kg ·K)

Ceq parameter for Xeq calculations, page 26 -

Csolid specific heat capacity of dry solid, page 23 Kj/(Kg ·K)

108 Conclusion

Cvapour heat capacity for water vapour, page 23 Kj/Kg ·K

Cwater specific heat capacity of water, page 23 Kj/(Kg ·K)

CSTR Continuously Stirred Reactor Tank, page 20 -

Dair diffusion coefficient of water vapour in air, page 51 -

Dchamber diameter of the chamber, page 45 m

ddrop diameter of a single droplet, page 50 m

Deff effective diffusivity, page 50 m2/s

e(t) error signal to controller, page 97 -

F1626 Sensor:Feed flow into chamber, page 94 L/h

FFeed feed flow rate, page 21 L/s

FMaindry Main dry air flow into chamber, page 21 Kg/s

FOutdry outlet dry air flow , page 21 Kg/s

Fpowder powder flow out of system, page 21 Kg/s

FSFBdry SFB dry air flow into chamber, page 21 Kg/s

Gc Controller transfer function, page 100 -

Gfeed Transfer function- feed input to outlet temperature, page 99 -

Gsolid Transfer function- solid input to outlet temperature, page 99 -

Hair enthalpy of air, page 21 J/Kg

Hchamber height of the chamber, page 45 m

HdryAir enthalpy of dry air, page 23 J/Kg

Hfeed enthalpy of feed, page 21 J/Kg

hheat heat transfer coefficient, page 48 W/(m2 ·K)

HhumAir enthalpy of humid air, page 23 J/Kg

Hpowder enthalpy of powder, page 21 J/Kg

Kp proportional gain, page 97 -

Keq parameter for Xeq calculations, page 26 -

Kmass mass transfer coefficient, page 48 m/s

109

mv mass of vapour, page 28 Kg

Mw molar mass of water, page 28 g/mol

mw mass of water, page 28 Pa

MdryAir molar mass of dry air, page 28 g/mol

mdryAir mass of dry air, page 28 Kg

Ms dry solid flow, page 24 Kg/s

MAINKGH Main air flow into chamber, page 94 Kg/h

Nu Nusselt number, page 51 -

P1614 Sensor:Relative humidity of air leaving system, page 94 %

P1618 Sensor:Relative humidity of ambient air, page 94 %

P1706 Sensor:Pressure difference of powder layer in SFB, page 94 mmH2O

Pv partial vapour pressure, page 27 Pa

Patm standard atmospheric pressure, page 28 Pa

PdryAir partiel pressure of dry air, page 28 Pa

Psat Saturated vapour pressure, page 27 Pa

Psurface pressure at surface, page 48 Pa

Ptotal Total Pressure, page 28 Pa

Pr Prandtl number, page 52 -

Qheat heat transfer rate, page 48 J/(s ·m2)

Qloss heat loss through chamber, page 35 KW

R Universal gas constant, page 28 8.314J/(mol ·K)

Re Reynolds number, page 52 -

rhodry density for dry air, page 44 Kg/m3

rhofeed density of feed, page 33 Kg/m3

rhototalair density for air, page 44 Kg/m3

rhovapour density for vapour, page 44 Kg/m3

S Solids in, page 33 %

110 Conclusion

Sconc amount of solid in feed, page 33 Kgsolids/Kgfeed

Sc Schmidt number, page 52 -

SFBKGH SFB air flow into chamber, page 94 Kg/h

Sh Sherwood number, page 51 -

T Temperature, page 28 oC

T1616 Sensor:Temperature of air leaving system, page 94 oC

T1624 Sensor:Temperature of ambient temperature, page 94 oC

T1702 Sensor:Temperature of MAINKGH, page 94 oC

T1704 Sensor:Temperature of SFBKGH, page 94 oC

T1709 Sensor:Temperature of air flow out of chamber, page 94 oC

Tair air temperature, page 23 oC

TMain temperature of Main air flow, page 24 oC

TOutair temperature of outlet air, page 25 oC

Tpowder temperature of powder, page 25 oC

Tref reference temperature, page 23 oC

TSFB temperature of SFB air flow, page 24 oC

UChamber heat transfer coefficient, page 34 KJ/m2/h

V volumen, page 28 m3

Weq parameter for Xeq calculations, page 26 -

X0 initial moisture content, page 24 Kgwater/Kgsolids

Xeq equilibrium moisture content, page 26 Kgwater/Kgsolid

XIn/out moisture content of particle, page 23 Kgwater/Kgsolids

XIn moisture contents of feed, page 24 Kgwater/Kgsolids

Xout final product, page 24 Kgwater/Kgsolids

Xparticle average mositure content of the particle, page 51(

kgmoist

kgdrySolid

)

YIn absolute humidty inlet air, page 24 Kgwater/KgdryAir

Yout absolute humidity outlet air, page 24 Kgwater/KgdryAir

Y Hvapour moisture content in air, page 23 Kgvapour/KgdryAir

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Kurichi Kumar Lixin Huang and Arun.S. Mujumdar. Computationalfluiddynamic simulation og droplet drying in a spray dryer. Drying 2004 Pro-

ceedings of the 14th International Drying Symposium IDS 2004, A:326–332, 2005.

Lennart Ljung. System identification Toolbox users guide. The Mathworks,5th edition, 2001.

Keith Masters. Spray drying in Practice. SprayDryConsult, 2002.

Mathworks. System identification toolbox, 11 2009. URL http://

www.mathworks.com/access/helpdesk/help/toolbox/ident/ident_

product_page.html.

Arun S. Mujumdar. Handbook of Industrial Drying. CRC Press, third edi-tion, 2007.

Gregory Nellis and Sanford Klein. chapter EXAMPLE 9.2-1. CambridgeUniversity Press, 2009. URL http://cambridge.org/us/engineering/

author/nellisandklein/downloads/examples/EXAMPLE_9.2-1.pdf.Diffusion Coefficient for Air-Water Vapor Mixtures.

PDS: The Planetary Atmospheres Data Node. Humidity, 9 2009. URLhttp://atmos.nmsu.edu/education_and_outreach/encyclopedia/

humidity.htm.

Donal O’Callagan and Peter Cunningham. Modern process control tech-niques in the production of dried milk products a review. EDP Sciences,2005.

OLK and GEA NIRO. Nozzle program.

http://labspace.open.ac.uk/mod/resource/view.php?id=361363&direct=1

http://labspace.open.ac.uk/mod/resource/view.php?id=361363&direct=1

http://www.mathworks.com/access/helpdesk/help/toolbox/ident/ident_product_page.html



http://cambridge.org/us/engineering/author/nellisandklein/downloads/examples/EXAMPLE_9.2-1.pdf

http://cambridge.org/us/engineering/author/nellisandklein/downloads/examples/EXAMPLE_9.2-1.pdf

http://atmos.nmsu.edu/education_and_outreach/encyclopedia/humidity.htm

http://atmos.nmsu.edu/education_and_outreach/encyclopedia/humidity.htm

BIBLIOGRAPHY 113

Spyridon E. Papadakis. Air temperature and humidity profiles in spraydrying. 1. features predicted by the particle source in cell model. IndustrialEngineering Chemistry Research, 27,11:2111–2116, 1988.

Bhesh Bhandari Pilairuk Boonyai and Tony Howes. Stickiness measurementtechniques for food powders: a review. Powder Technology, 145:34–46,2004.

Ejnar Refstrup. Density of milk concentrate.

Ejnar Refstrup and GEA NIRO. Gea niro data.

Shelquist Engineering Richard Shelquist. Air density and density alti-tude calculations, 9 2009. URL http://wahiduddin.net/calc/density_

altitude.htm.

Maykel VERSCHUEREN Jan J. VAN HAREN Erik SMIT Gerrald BARGE-MAN Ruud E.M. Verdurmen, Han STRAATSMA and Peter DE JONG.Modelling spray drying processes for dairy products. EDP Sciences, 82:453–463, 2002.

Vikram Shabde. Optimal design and control of a spray drying process that

manufactures hollow micro particles. Ph.d, Texas Tech University, Chem-ical Engineering, December 2006.

Jiro Koga Shunji Homma, Shinji Ogata and Shiro Matsumoto. Gas solidreaction model for a shrinking spherical particle with unreacted shrinkingcore.

Sigurd Skogestad and Ian Postlethwaite. Multivariable Feedback Control-

Analysis and Design. Wiley, 2nd edition, 2005.

Jim R. Jones . John E. Bronlund Stephen R.L. Werner, Richard L. Edmondsand Anthony H.J. Paterson. Single droplet drying: Transition from theeffective diffusion model to a modified receding interface model.

A. S. Mujumdar b V. S. Birchal a, L. Huang bc and M. L. Passos. Spraydryers: Modeling and simulation. Drying Technology, 24,3:359–371, 2008.

Vagn Westegaard. Milk powder technology- Evaporation and Sparay drying.Niro A/s, 5th edition, 2004.

Pieter R. Wiederholt. Water Vapor Measurement: Methods and Instrumen-

tation. Marcel Dekker INC, 1997.

http://wahiduddin.net/calc/density_altitude.htm

http://wahiduddin.net/calc/density_altitude.htm

114 BIBLIOGRAPHY

Appendix A

Appendix A

116 Appendix A

A.1 Desorption Isotherm at low and high humid-ity level

0.79 0.8 0.81 0.82 0.83 0.84

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

X: 0.83Y: 0.2023

Water activity aw

Eq

uilib

riu

m M

oio

stu

re C

on

ten

t (K

gH

2O

/Kg

so

lid


X: 0.82Y: 0.1893

4oC

25oC

37oC

50oC

65oC

85oC

100oC

115oC

0.02 0.022 0.024 0.026 0.028 0.03 0.032

0.5

1

1.5

2

2.5

3

x 10−3

X: 0.03Y: 0.001541

Water activity aw

Eq

uilib

riu

m M

oio

stu

re C

on

ten

t (K

gH

2O

/Kg

so

lid

)


X: 0.02Y: 0.0008069

4oC

25oC

37oC

50oC

65oC

85oC

100oC

115oC

Increasing Temperature

Increasing Temperature

Figure A.1: Desorption Isotherm Maltodextrin DE12: Equilibrium moisture con-tent as function of water activity for temperatures between 40C and1150C. First figure at low water activity level and the second figureis for high water activity level

117

A.2 General moisture Characteristic and food mi-

crobiology

Figure A.2: General moisture Characteristic and Food microbiology. Mositurecontent vs. Water activity is the product characteristic. Chemicalreaction are slow for water activities below 0.5. Micro biologicalgrowth does not take place for water activity levels below 0.75.

118 Appendix A

Appendix B

Appendix B

120 Appendix B

B.1 Modelling Variables

Default Operation ValuesVariable Name Description Value Unit

FMAIN Main air flow IN 1800 Kg/hTmain Temperature of MAIN 160 oCFSFB SFB air flow IN 500 Kg/hTSFB Temperature of SFB 90 oCFcool Cooling air flow IN 80 Kg/hTcool Temperature of cooling air 60 oCFfeed Feed flow IN 65 L/hρfeed Density of feed 1.208 Kg/LTfeed Temperature of feed 50 oCTamb Temperature of ambient air 30 oCRHamb Rel. humidity ambient air 28 %Solid solids of total feed 50 %XIn Initial Moisture Content 1 Kg/KgsolidPatm Standard Atmospheric pressure 101325 PaYIn Absolute Humidity air IN 0.0079 Kg/Kgdryair

Specific Heat CapacityCdryair Dry air 1 KJ/(Kg ·K)Cvapour vapour 1.8 KJ/(Kg ·K)Cdryair Maltodextrin 1.5 KJ/(Kg ·K)Cwater water 4.2 KJ/(Kg ·K)λ latent heat of vaporisation 2.5 KJ/(Kg)

Qloss

Uloss heat transfer coefficient (chamber) 16.75 KJ/m2/hAChamber Surface area(chamber) 26.2 m2

Table B.1: The manipulated variables’ default operation values for test of themodels

121

B.2 Steady State Calculation

Steady State ResultsLoss Included TEST

Test TOutAir TOutAir

Description Temperature Temperature

Default System 86.1oC ≈ 86oCFfeed = 75 L/h 80.6oC ≈ 81oCTmain = 150 oC 79.9oC ≈ 79oCTmain = 170 oC 92.4oC ≈ 90oC

FMAIN = 2000 kg/h 90.9oC ≈ 89oCFMAIN = 1600 kg/h 80.6oCFSFB = 600 kg/h 86.2oC ≈ 83oCFSFB = 350 kg/h 85.9oC ≈ 84oCTSFB = 80 oC 84.4oC ≈ 82.5oCTSFB = 100 oC 87.9oC ≈ 85.6oCRHamb = 75 % 102 oC 86.7oCRHamb = 10 % 101.4 oC 85.9oC

Table B.2: Steady State Results for the drying air temperature TOutAir calculatedwith the variables and values as used in the real test on MSD-20. Cal-culated with a energi loss funtion included and without a loss function.These are compared with the results from the Test on MSD-20

122 Appendix B

Steady State Results for humidityLoss Included Loss Included TEST

Test Eq Moist. YOut Abs. HumDescription Content Abs. Hum Outlet Air

Default System 0.0033 0.0251 ≈ 0.010Ffeed = 75 L/h 0.0047 0.0277 ≈ 0.012Tmain = 150 oC 0.0045 0.0251 ≈ 0.011Tmain = 170 oC 0.0024 0.0251 ≈ 0.010

FMAIN = 2000 kg/h 0.0025 0.0237 ≈ 0.010FMAIN = 1600 kg/h 0.0047 0.0267FSFB = 600 kg/h 0.0032 0.0244 ≈ 0.0115FSFB = 350 kg/h 0.0035 0.0263 ≈ 0.012TSFB = 80 oC 0.0036 0.0251 ≈ 82.5oCTSFB = 100 oC 0.0030 0.0251 ≈ 85.6oCTamb = 50 oC 0.0051 0.0397Tamb = 10 oC 0.0026 0.0198RHamb = 75 % 0.0050 0.0386RHamb = 10 % 0.0026 0.0199

Table B.3: Steady State Results of absolute humidity and equlibrium moisturecontent calculated with the variables and values as used in the real teston MSD-20. Calculated with a energi loss funtion included. These arecompared with the results from the Test on MSD-20. The absolutehumidity is calculated from sensor 1616 and 1614.

123

B.3 Results from the Dynamic Model before mod-ification

B.3.1 Main inlet air temperature step up

1000 1500 2000 2500 3000 3500 4000145

150

155

160

165

170

175

180


=150−>170 oC

Time [sec]

Tem

pera

ture

[oC

]


1000 1500 2000 2500 3000 3500 400078

80

82

84

86

88

90

92


Time [sec]

Tem

pera

ture

[oC

]


Figure B.1: Dynamic step response of the TOutAir for increase in main inlet airtemperature from 1500C to 1700C . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

124 Appendix B

B.3.2 Feed Flow step down

900 950 1000 1050 1100 1150 1200 1250 130060

65

70

75

80

85


=75−>65 L/h

Time [sec]

Fee

d F

low

[L/h

our]

Model: No delayTEST 4 MSD−20

1000 1500 2000 2500 3000 3500 4000 4500 500080

81

82

83

84

85

86

87Temperature in Spray Dryer Chamber Spray Dryer for a Feed Step Change

Time [sec]

Tem

pera

ture

[oC

]

Model: No delayTEST 5 MSD−20

Figure B.2: Dynamic step response of the TOutAir for a decrease in feed flow ratefrom 75L/h to 65L/h. The top figure shows the applied step change.The bottom figure is the step response. Model results are comparedwith data from MSD-20(red)

125

B.3.3 Temperature SFB step down

1000 1500 2000 2500 3000 3500 400075

80

85

90

95

100

105

SFB Air Temperature step Tmain

=90−>80 oC

Time [sec]

Tem

pera

ture

[oC

]


1000 1500 2000 2500 3000 3500 400080

82

84

86

88Temperature in Spray Dryer Chamber Spray Dryer for SFB Inlet air Temperature change

Time [sec]

Tem

pera

ture

[oC

]


Figure B.3: Dynamic step response of the TOutAir for decrease in SFB inlet airtemperature from 900C to 800C . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

126 Appendix B

B.3.4 Temperature SFB step up

1000 1500 2000 2500 3000 3500 4000

80

85

90

95

100

SFB Air Temperature step Tmain

=80−>100 oC

Time [sec]

Tem

pera

ture

[oC

]


1000 1500 2000 2500 3000 3500 400080

82

84

86


Time [sec]

Tem

pera

ture

[oC

]


Figure B.4: Dynamic step response of the TOutAir for increase in SFB inlet airtemperature from 800C to 1000C . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

127

B.3.5 SFB air flow step down

1000 1500 2000 2500 3000 3500 4000 4500

480

500

520

540

560

580

600

620

SFB Air inlet flow step Fmain

=500−>350 kg/h

Time [sec]

Tem

pera

ture

[oC

]


1000 1500 2000 2500 3000 3500

82

83

84

85

86

Temperature in Spray Dryer Chamber Spray Dryer for SFB Inlet air Temperature change

Time [sec]

Tem

pera

ture

[oC

]


Figure B.5: Dynamic step response of the TOutAir for increase in SFB inlet airflow from 500kg/h to 600kg/h . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

128 Appendix B

B.3.6 SFB air flow step up

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000300

350

400

450

500

550

600

650

SFB Air inlet flow step Fmain

=350−>500 kg/h

Time [sec]

Tem

pera

ture

[oC

]


800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 300082

83

84

85

86


Time [sec]

Tem

pera

ture

[oC

]


Figure B.6: Dynamic step response of the TOutAir for decrease in SFB inlet airflow from 600kg/h to 350kg/h . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

129

B.3.7 Main air flow step down

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 20001750

1800

1850

1900

1950

2000

2050


=2000−>1800 kg/h

Time [sec]

Tem

pera

ture

[oC

]


800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

84

86

88

90


Time [sec]

Tem

pera

ture

[oC

]


Figure B.7: Dynamic step response of the TOutAir for decrease in Main inlet airflow from 2000kg/h to 1800kg/h . The top figure shows the appliedstep change. Fan is a first order system τ = 40. The bottom figure isstep response. Model results are compared with data from MSD-20

130 Appendix B

B.4 Results from the Dynamic Model after mod-ification

B.4.1 Feed Flow step down with modefication

6900 7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 800060

65

70

75

80


=75−>65 L/h (modified)

Time [sec]

Fee

d F

low

[L/h

our]


7000 7500 8000 8500 9000 9500 10000 10500 11000

78

80

82

84

86

Temperature in Spray Dryer Chamber Spray Dryer for a Feed Step Change(Modified model)

Time [sec]

Tem

pera

ture

[oC

]

τevap

=1300 & τfast

=600

TEST 2 MSD−20

Figure B.8: Dynamic step response of the TOutAir for a decrease in feed flow ratefrom 75L/h to 65L/h. The top figure shows the applied step change.The bottom figure is the step response. Model results are comparedwith data from MSD-20(red)

B.4.2 Temperature MAIN step down with modification

6800 7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000140

145

150

155

160

165


=160−>150 oC

Time [sec]

Tem

pera

ture

[oC

]

Model: No delayModel: with delay τ=180

7000 7500 8000 8500 9000 9500 10000 10500 11000

78

80

82

84

86

Temperature in Spray Dryer Chamber Spray Dryer for a TMain

Step Change(Modified model)

Time [sec]

Tem

pera

ture

[oC

]

τevap

=1300 & τfast

=600

TEST 2 MSD−20

Figure B.9: Dynamic step response of the TOutAir for decrease in MAIN inlet airtemperature from 1600C to 1500C . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

131

B.4.3 Air flow MAIN step up with modification

6900 7000 7100 7200 7300 7400 7500 7600

1800

1850

1900

1950

2000


=1800−>2000 kg/h (modified)

Time [sec]

Air

flow

[Kg/

h]

Model: with delay τ=40MSD−20

7000 7500 8000 8500 9000 9500 10000 10500 11000

84

85

86

87

88

89

90

Temperature in Spray Dryer Chamber Spray Dryer for Main Inlet air flow change

Time [sec]

Tem

pera

ture

[oC

]

Model:with delay τ=40MSD−20

Figure B.10: Dynamic step response of the TOutAir for increase in MAIN inlet airflow from 1800kg/h to 2000kg/h . The top figure shows the appliedstep change. The bottom figure is step response. Model results arecompared with data from MSD-20

132 Appendix B

B.4.4 Absolute Humidity in Dryer For feed step up withmodification

7000 7500 8000 8500 9000 9500 10000 10500 110000.023

0.024

0.025

0.026

0.027

0.028

0.029

0.03Absolute humidity in Spray Dryer Chamber for a Feed Step Change (65−>75 l/h)(Modified model)

Time [sec]

Moi

stur

e co

nten

t [kg

wat

er/k

gdr

y ai

r]

τevap

=1000 & τfast

=500

τevap

=1300 & τfast

=600

τevap

=1000 & τfast

=100

τevap

=1000 & τfast

=1500

Figure B.11: Absolute Humidity in Dryer For feed step up with model modifica-tion. For various zero and pole in dry transfer function

B.4.5 Response for the system G(s)evap

7000 7500 8000 8500 9000 9500 10000 10500 110000.0105

0.011

0.0115

0.012

0.0125

0.013

Output of G(s)evap

for various zero and pole combination for feed step (65 −>75 l/h)

Time [sec]

Moi

stur

e ev

apor

atio

n ra

te (

kg /s

)

τevap

=1000 & τfast

=500

τevap

=1300 & τfast

=600

τevap

=1000 & τfast

=100

τevap

=1000 & τfast

=1500

Figure B.12: Response for the system G(s)evap. Evaporation rate (kg/s) as afunction of time

133

B.4.6 Simulink model

Figure B.13: Simulink implementation of the dynamic model. Left hand side:process inputs. Right hand Side: Drying chamber block, relativehumidity block and equilibrium moisture content block. red blockare subsystems

134 Appendix B

Appendix C

Appendix C

C.1 MSD-20 test 24-7-2009

Sensor Description1Sensor Name Description Value Unit

Input SensorsMAINKGH Main air flow into chamber PV Kg/hSFBKGH SFB air flow into chamber PV Kg/hT1702 Temperature of MAINKGH PV oCT1704 Temperature of SFBKGH PV oCF1626 Feed flow into chamber PV L/hP1706 Pressure difference of powder layer in SFB PV mmH2OT1624 Temperature of ambient temperature PV oCP1618 Relative humidity of ambient air PV %

Output SensorsT1709 Temperature of air flow out of chamber PV oCT1616 Temperature of air leaving system PV oCP1614 Relative humidity of air leaving system PV %

Calculated parametersINHUMABS Absolute humidity air IN PV Kg/Kg

based on sensor values (T1624 & P1618)OUTHUMABS Absolute humidity air OUT PV Kg/h

based on sensor values (T1616 & P1614)

Table C.1: PV:process value, Out: Controller Output value

136 Appendix C

C.2 Test Step & Responses

C.2.1 Test Program MSD-20 week 30 2009

Test Program MSD-20Time Test step Test Step Powder Sample

Description Value Interval(min)

8.00 System Start Up9.00 Set Default System

Feed Flow 162610.00 1 Stable system:Test start 65 L/h 511.00 2 Feed Flow Step Up 75 L/h 512.30 3 Feed Flow Step Down 65 L/h 514.00 4 Feed Flow Step Up 75 L/h 515.30 5 Feed Flow Step down 65 L/h 5

Main Inlet Air Temperature 1702 (Default 160)17.00 6 Temperature Step down 150 oC 1018.30 7 Temperature Step Up 170 oC 1020.00 8 Temperature Step down 160 oC 10

Main Inlet Air Flow MAINKGH(Default 1800 Kg/h)21.30 9 MAINKGH Step Up 2000 Kg/h 1023.00 10 MAINKGH Step Down 1800 Kg/h 1000.30 11 MAINKGH Step Up 2000 Kg/h 10

(NO PI 1702)2.00 12 MAINKGH Step Down 1800 Kg/h 10

(NO PI 1702)SFB Inlet Air Flow SFBKGH(Default 500 Kg/h)

3.30 13 SFGKGH Step Up 600 Kg/h 104.30 14 SFBKGH Step Down 350 Kg/h 105.30 15 SFBKGH Step Up 500 Kg/h 10

SFB Inlet Air Flow Temperature(Default 90)6.30 16 Temperature Step down 80 oC 107.30 17 Temperature Step Up 100 oC 108.30 18 Temperature Step down 90 oC 10

VFB9.30 19 VFB Flow Step Up 400 kg/h 1010.30 20 VFB Flow Step Down 300 Kg/h 1011.30 21 VFB Temp Step Up 70 oC 1012.30 22 VFB Temp Step Down 60 oC 1013.30 END

Table C.2: Test Program for Test On MSD-20 week 30 2009. In total 22 TestSteps. Results are found on CD

C.2 Test Step & Responses 137

138

Appendix

C

C.2.2 Test Step & Results for the entire test on MSD-20

0 1 2 3 4 5 6 7 8 9 10

x 104

0

1000

2000

3000

Time [s]

Kg/

hour

TEST STEPS & RESULTS FROM MSD−20 (21/7−2009)−COMPARED

MAINKGHSFBKGH

1 2 3 4 5 6 7 8 9

x 104

50

100

150

Time [s]

T1702F1626T1704P1706T1709

0 1 2 3 4 5 6 7 8 9 10

x 104

0

0.005

0.01

0.015

Time [s]

Kg

wat

er/k

g dr

y ai

r

InHumAbsExHumAbs

DAYDAY NIGHT

Figure C.1: Test Step & Results for the entire test on MSD-20 to get a overview and quickly compare the results. For more detailedplots of test steps and responses see the following sections

C.2

Test

Step&

Resp

onses

139

C.2.3 Moisture content of the particle from the SFB discharge for the entire test on MSD-20

0 1 2 3 4 5 6 7 8 9 10

x 104

0.5

1

1.5

2

2.5

3

Time [s]

RM

%H

20/k

g po

wde

r

Powder RM VFBPowder RM SFB

Figure C.2: Moisture content of the particle from the SFB discharge for the entire test on MSD-20.

140

Appendix

C

C.2.4 Test Step & Results for change in feed rate on MSD-20

0 0.5 1 1.5 2 2.5 3

x 104

40

60

80

100Test: Feed rate 1626

Time [s]

Lite

r/ho

ur

Feed Flow 1626

0 0.5 1 1.5 2 2.5 3

x 104

80

82

84

86

88Time Respons Outlet Air Temperature 1709

Time [s]

Tem

pera

ture

(ce

lciu

s)

Outlet Air Temp. 1709

0 0.5 1 1.5 2 2.5 3

x 104

0.5

1

1.5

2

2.5Outlet Powder Moisture Content

Time [s]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Powder Moisture Content

Test1Test2 Test3

Test4Test5

Figure C.3: Test Step & Results for change in feed rate on MSD-20. Outlet air Temperature respons and mositure constent of thepowder taken from the SFB discharge.

C.2

Test

Step&

Resp

onses

141

C.2.5 Feed flow rate and Nozzle pressure results from test on MSD-20

1 2 3 4 5 6 7 8 9

x 104

60

65

70

75

80

Time [s]

Lite

r/ho

ur

Feed rate from MSD−20 test

Feed rate L/h

0 1 2 3 4 5 6 7 8 9 10

x 104

180

200

220

240

260

280

300

320Feed Nozzle Pressure (bar)

Time [s]

pres

sure

[bar

]

Nozzle pressure

Figure C.4: Feed flow rate and Nozzle pressure results from test on MSD-20. Feed flow is controlled by controlling the nozzle pressure.Increase in nozzle pressure increases feed rate and similarly for decreasing the pressure the feed rate decreases.

142

Appendix

C

C.2.6 Test Step & Results for change in Main inlet air temperature on MSD-20

0 2000 4000 6000 8000 10000 12000 14000 16000 18000140

150

160

170

180Test: Main Inlet Air Temperature

Time [s]

Tem

pera

ture

(ce

lciu

s)

Main Air Temp. 1702

0 2000 4000 6000 8000 10000 12000 14000 16000 1800075

80

85

90


Time [s]

Tem

pera

ture

(ce

lciu

s)


0 2000 4000 6000 8000 10000 12000 14000 16000 180000.5

1

1.5

2Time Respons Outlet Powder Moisture Content

Time [s]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)


Test 6Test 7 Test 8

Figure C.5: Test Step & Results for change in Main inlet air temperature on MSD-20. Outlet air Temperature respons and mositureconstent of the powder taken from the SFB discharge.

C.2

Test

Step&

Resp

onses

143

C.2.7 Test Step & Results for change in Main inlet air flow on MSD-20

0 0.5 1 1.5 2 2.5

x 104

1700

1800

1900

2000

2100Test: Main Inlet Air MAINKGH

Time [s]

Tem

pera

ture

(ce

lciu

s)

MainKGH

0 0.5 1 1.5 2 2.5

x 104

75

80

85


Time [s]

Tem

pera

ture

(ce

lciu

s)


0 0.5 1 1.5 2 2.5

x 104

1.4

1.6

1.8

2Time Respons Outlet Powder Moisture Content

Time [s]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)


Test 9 Test 10Test 11

Test 12

Figure C.6: Test Step & Results for change in Main inlet air flow on MSD-20. Outlet air Temperature respons and mositure constentof the powder taken from the SFB discharge.

144

Appendix

C

C.2.8 Test Step & Results for change in SFB inlet air temperature on MSD-20

0 2000 4000 6000 8000 10000 1200070

80

90

100

110Test: SFB Inlet Air Temperature

Time [s]

Tem

pera

ture

(ce

lciu

s)

SFB Air Temp. 1704

0 2000 4000 6000 8000 10000 1200080

82

84


Time [s]

Tem

pera

ture

(ce

lciu

s)


0 2000 4000 6000 8000 10000 120000.5

1

1.5

2

2.5Time Respons Outlet Powder Moisture Content

Time [s]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)


Figure C.7: Test Step & Results for change in SFB inlet air temperature on MSD-20. Outlet air Temperature respons and mositureconstent of the powder taken from the SFB discharge.

C.2

Test

Step&

Resp

onses

145

C.2.9 Test Step & Results for change in SFB inlet air flow on MSD-20

0 2000 4000 6000 8000 10000 12000300

400

500

600

700Test: SFB Inlet Air SFBKGH

Time [s]

Tem

pera

ture

(ce

lciu

s)

SFBKGH

0 2000 4000 6000 8000 10000 1200082

83

84


Time [s]

Tem

pera

ture

(ce

lciu

s)


0 2000 4000 6000 8000 10000 120001

1.5

2

2.5Time Respons Outlet Powder Moisture Content

Time [s]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)


Figure C.8: Test Step & Results for change in SFB inlet air flow on MSD-20. Outlet air Temperature respons and mositure constent ofthe powder taken from the SFB discharge.

146

Appendix

C C.2.10 Ambient Air Conditons At AIR intake (21/7-2009)

0 1 2 3 4 5 6 7 8 9 10

x 104

15

20

25

30

35

40

Time [s]

Rel

ativ

e hu

mid

ity%

Relative Humidity at AIR intake (Sensor 1618)

Rel. Humidity

0 1 2 3 4 5 6 7 8 9 10

x 104

24

26

28

30

32

34Temperature of AIR at Intake (sensor 1624)

Time [s]

Tem

pera

ture

oC

Temperature oC

NightDAY DAY

Figure C.9: Ambient Air Condition at Intake during the test

C.3 Logbook for MSD-20 test 24-7-2009 147

C.3 Logbook for MSD-20 test 24-7-2009

Figure C.10: Logbook From Test on MSD-20 week 30 2009

148 Appendix C

Figure C.11: Logbook From Test on MSD-20 week 30 2009

C.3 Logbook for MSD-20 test 24-7-2009 149

150 Appendix C

Appendix D

Appendix D

D.1 Humidity Calculation

Ideal Gas Law

PV = nRT (D.1)

P = pressure(Pa)

V = V olume

T = Temperature(kelvin)

R = Universal Gas Constant(J/K ·mol)

n = number of moles(mole)n = m/M

M = Molar mas(Kg/Kmol)

m = amount of substance(Kg)

Molar Mass Water

Mw = 18.01(g/mol) (D.2)

(D.3)

Molar Mass dry air

MdryAir = 28.96(g/mol) (D.4)

152 Appendix D

Density

n

V=m/M

Vm/M

V=m

V

1

M

ρ =m

V(Kg

m3) (D.5)

Pressure

Ptotal = PDry + PV apour (D.6)

n

V=

P

RT

ρ =MP

RTρtotal = ρDry + ρV apour (D.7)

=MdryAirPdry

RT+Mw

Pvapour

RT(D.8)

=MdryAirP − Pvapour

RT+Mw

Pvapour

RT

Volume of Chamber

V =π

4Dchamber

2Hchamber (D.9)

+ πDchamber

3

24(

1

TAN( π180

ACone

2 )+

1

TAN( π180 (90−ACeiling))

)

Dchamber = Diameter of Chamber

Hchamber = Height of Chamber

Acone = Chamber cone angle

Aceiling = Chamber ceiling angle

D.2 Droplet calculations

Surface Area of Sphere

Adrop = 4πr2 = d2π (D.10)

r = radius of sphere

d = diameterofdroplet

D.3 Thermal Conductivity Air 153

Volume of Sphere

Vdrop = 4/3 · π · r3 (D.11)

r = radius of sphere

Diameter change of particle during evaporation (Xparticle > Xc)

VdropChange = VdropInit − Vdrop (D.12)

VdropChange = 4/3 · π ·DdropInit

2

3

− 4/3 · π ·Ddrop

2

3

Ms(X0 −Xparticle)

ρwater=

(

4

3

1

23π(DdropInit

3 −Ddrop3)

)

(D.13)

Ddrop =

(

DdropInit3 −

6Ms(X0 −Xparticle)

πρwater

)1/3

(D.14)

Diameter change of particle during evaporation (Xparticle < Xc)

Ddrop =

(

DdropInit3 −

6Ms(X0 −XC)

πρwater

)1/3

(D.15)

Number of drops

Ndrops =Ffeed

Vdrop(D.16)

Mass of a single drop

Massdrop =FfeedρfeedVdrop

Masssolid =MassdropSconcSconc = Solid concentration in feed

(D.17)

D.3 Thermal Conductivity Air

Air Prperties table http://www.engineeringtoolbox.com/air-properties-d_156.html Coefficients:



154 Appendix D

Figure D.1: Thermal Conductivity of Air vs. Temperature in kelvin. http://

users.wpi.edu/~ierardi/PDF/air_k_plot.PDF

kair = p1kair ∗ T4gas + p2kair ∗ T

3gas + p3kair ∗ T

2gas + p4kair ∗ Tgas + p5kair

(D.18)

p1kair = −2.3572e − 013

p2kair = 1.3447e − 010

p3kair = −3.3402e − 008

p4kair = 7.5159e − 005

p5kair = 0.024159

D.4 Thermal Diffusivity Air

D.5 Kinematic Viscosity Air

Kinematic viscosity from absolute viscosity

ν =µ

ρ(D.19)

http://users.wpi.edu/~ierardi/PDF/air_k_plot.PDF

http://users.wpi.edu/~ierardi/PDF/air_k_plot.PDF

D.6 Mean Residense Time for the particle in the Spray dryer 155

Figure D.2: Thermal Diffusivity of Air vs. Temperature in kelvin. http://

users.wpi.edu/~ierardi/PDF/air_alpha_plot.PDF

Reynolds number Inertial forces are characterized by the product of thedensity r times the velocity V times the gradient of the velocity dV/dx.The viscous forces are characterized by the dynamic viscosity coefficient mutimes the second gradient of the velocity d2V/dx2. http://www.grc.nasa.gov/WWW/BGH/reynolds.html

Re =Inertia force

Viscous force(D.20)

Re =ρV dV

dx

µd2Vdx2

(D.21)

Re =ρV L

µ(D.22)

D.6 Mean Residense Time for the particle in theSpray dryer

Mean particle residence time The mean residense time for the powderin the spray dryer can be calculated by the amount of powder in the SFB

http://users.wpi.edu/~ierardi/PDF/air_alpha_plot.PDF

http://users.wpi.edu/~ierardi/PDF/air_alpha_plot.PDF



156 Appendix D

Figure D.3: Kinematic Viscosity of Air vs. Temperature in Kelvin. http://

users.wpi.edu/~ierardi/PDF/air_nu_plot.PDF

divided by the amount of powder leaving(either per second or per hour).The mass of powder in the SFB is calculated from the size of the SFB, theheight of the powder layer in SFB and the density of the of the agglomeratedpowder(V olume · density). The time from the powder enter the dryer anduntil it ends in the SFB is very small compared to the residence time in theSFB and the therefore neglected in the calculations.

SFBarea = 0.1886m2

powderlayerSFB = 0.35 ( Height of the powder layer in SFB)

ρpowder = 300kg

m3(agglomerated Maltodextrin powder density)

Xout = 0.03kgwater

kgpowder(mositure content in particle at equilibrium)

powderSFB = SFBarea ∗ pulverlag ∗ denspowderkg powder in SFB

Fsolid = Feedf lows ∗ 1 ∗ SolidamountDry solids feed flow per sec

mpowder = Fsolid ∗ (1 +Xout) ∗ 3600mass powder leaving the chamber per hour

residenstMEAN = powderSFB/mpowder ∗ 3600Mean residense time in hours

residenstMEAN = 0.59hours ≈ 36min (D.23)

The mean particle residense time in MSD-20 spray dryer during the experi-ment was ≈ 36 min.

http://users.wpi.edu/~ierardi/PDF/air_nu_plot.PDF

http://users.wpi.edu/~ierardi/PDF/air_nu_plot.PDF

D.6 Mean Residense Time for the particle in the Spray dryer 157

Bv1

1Simulink regards disturbance v as in input to the system.Bv is therefore a part of the

determined matrix B. 6.1 is then B

[

δu(t)δv(t)

]

158 Appendix D

Appendix E

Appendix E

160 Appendix E

E.1 Air and Particle Trajectory in Chamber

Figure E.1: Air Stream and particle trajectory in chamber. Particles follows theair stream.CFD simulation GEA NIRO

Appendix F

Appendix F

F.1 Mass transfer and Drying time appendix

F.1.1 Default state operation condtion

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−9

−8

−7

−6

−5

−4

−3

−2

−1

0x 10

−12 Mass evaporated at default steady state Operation for particles of different size

Time [sec]

Mas

s ev

apor

ated

(Kg

H2O

)

Particle Ddrop

= 57 µ m

Particle Ddrop

= 76 µ m

Particle Ddrop

= 114 µ m

Particle Ddrop

= 152 µ m

Particle Ddrop

= 228 µ m

Particle Ddrop

= 304 µ m

Figure F.1: Mass evaporated for various particles sizes at default state operationconditions vs. time

F.1.2 TOut varied

162 Appendix F

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 52

2.5

3

3.5

4

4.5

5

5.5

6

6.5Mass Transfer coefficients at default operation for different particle sizes

Time [sec]

Km

ass(m

/s)

Particle Ddrop

= 57 µ m

Particle Ddrop

= 76 µ m

Particle Ddrop

= 114 µ m

Particle Ddrop

= 152 µ m

Particle Ddrop

= 228 µ m

Particle Ddrop

= 304 µ m

Figure F.2: Mass Transfer coefficient for various particles sizes at default state

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−150

−100

−50

0

50

100

150Resistance ’f’ in crust in mass tranfer rate equation

Time [sec]

f res

ista

nce

Particle Ddrop

= 57 µ m

Particle Ddrop

= 76 µ m

Particle Ddrop

= 114 µ m

Particle Ddrop

= 152 µ m

Particle Ddrop

= 228 µ m

Particle Ddrop

= 304 µ m

Figure F.3: Crust resistance f in mass transfer rate equation for various particlesizes

F.1 Mass transfer and Drying time appendix 163

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

0.05

0.1

0.15

0.2

0.25

Drying Time for Particle at various Drying Temperature by changing Feed rate

Time [sec]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Feed rate = 65 L/hFeed rate = 75 L/hFeed rate = 105 L/hFeed rate = 35 L/h

Figure F.4: Drying time for particle at various feed flow rate, thus varying outletair temperature. Moisture content vs. time

0 0.1 0.2 0.3 0.4 0.5

10

20

30

40

50

60

70

f resistance in crust in mass tranfer rate equation at changing feed rate

Time [sec]

f res

ista

nce

Feed rate = 65 L/hFeed rate = 75 L/hFeed rate = 105 L/hFeed rate = 35 L/h

Figure F.5: Crust resistance f for various feed flow rates, thus varying outlet airtemperature. Moisture content vs. time. f resistance in crust takeslonger to increase for higher feed rates.

164 Appendix F

0.1 0.15 0.2 0.25 0.3 0.35 0.4

0.05

0.1

0.15

0.2

0.25

Drying Time for Particle at various Drying Temperature by MAINinlet

Time [sec]

Moi

ostu

re C

onte

nt (

Kg

H2O

/Kg

solid

)

Main Inlet air= 1800 Kg/hMain Inlet air= 2500 Kg/hMain Inlet air= 1000 Kg/h

Figure F.6: Drying time for particle at various Main inlet air flow, thus varyingoutlet air temperature. Moisture content vs. time

Appendix G

Appendix G

G.1 1st order system

1. Order system

G(s) =1

τs+ 1(G.1)

Step response

y(t) = (1− e−t/τ )hstep + h0 (G.2)

Figure G.1: Control variable as a first order system. The gain is equal to 1/τ

166 Appendix G

Appendix H

Appendix H

168 Appendix H

H.1 System Identification

Linear difference equation for the BEST ARX model(10th order)

A(q)y(t) = B(q)u(t) + e(t)

A(q) = 1− 1.899(+ − 0.01379)q−1 + 0.8909(+ − 0.02959)q−2

+ 0.0004731(+ − 0.03204)q−3 + 0.0001774(+ − 0.03204)q−4

− 0.0003988(+ − 0.03204)q−5 + 0.01811(+ − 0.03204)q−6

− 0.01516(+ − 0.03204)q−7− 0.0005041(+ − 0.03204)q−8

+ 0.02059(+ − 0.02961)q−9− 0.01521(+ − 0.01382)q−10

B1(q) = −1.939e − 006(+ − 1.846e − 006)q−8

B2(q) = −8.505e − 005(+ − 4.977e − 005)q−8

B3(q) = 1.792e − 006(+ − 1.318e − 006)q−8

B4(q) = −3.227e − 005(+ − 1.647e − 005)q−8

B5(q) = 4.07e − 005(+ − 3.612e − 005)q−8

B6(q) = −0.1174(+ − 0.1623)q−8

B7(q) = −7.449e − 006(+ − 1.87e − 005)q−8

B8(q) = 0.0001645(+ − 0.000102)q−8

B9(q) = 0.3597(+ − 0.3024)q−8

Estimated using ARX with focus from data set data

Loss function 0.00105043 and FPE 0.00105798

Sampling interval: 10

H.2 ARMAX models

ARMAX modelsna nb nc nk Loss FPE Best

10 5 8 8 0.0010 0.0010 298 7 8 8 0.000171 0.000176 246 7 2 8 0.000169 0.000174 365 7 8 8 0.000168 0.000178 332 7 8 8 0.00022 0.00023 -4910 2 8 8 0.00025 0.00025 -482 2 2 1 0.00242 0.00224 -3910 5 8 1 0.00020 0.000213 -45

Table H.1: ARMAX model with number of coeffiecients in polynomial A (na), B(nb), C (nc), and delays (nk). The quality parameters Loss function,Final Prediction Error, and Best fit for the given model.

Plots of the ARMAX model listed in H.1. The figures show the simulated

H.1 System Identification 169

H.1.1 Model Misfit Vs Number parameters for ARX model

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x 10−3

Number of parameters

Une

xpla

ined

out

put v

aria

nce

(in %

)

Model Misfit vs number of parameters in the ARX model (9 inputs 1 output)

best fit 19 parametersna =10, nb=1, nk=8

Figure H.1: Model Misfit Vs Number parameters for ARX model. Test range1:10 for all coefficients. Model order of 10 with a total number ofparameters of 19 seems to be the best with lowest Unexplained out-put variance (in %), which is the ratio between the prediction errorvariance and the output variance in percent. The final predictionerror is also the lowest for this model.

output compared to the measured output (moisture content) from the vali-dation data.The coefficient of the model is given in the title of the figure.

170 Appendix H

H.1.2 Zero Pole plot for the ARX model

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1Poles (x) and Zeros (o) for the ARX model of 10th order

Figure H.2: SZero-Pole plot for the 10th order ARX model. There is a zero polecancellation in 0.


H.2.1 ARMAX simulations

Plots of the ARMAX model listed in H.1. The figures show the simulatedoutput compared to the measured output (moisture content) from thevalidation data.The coefficient of the model is given in the title of the

figure. Low values for the A and B polynomial and small delay results inbad estimations.

0 1 2 3 4 5 6 7 8 9 10

x 104

−1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time

Measured and simulated model output (10,5,8,1)

Figure H.3: ARMAX model with the coefficients given in the title.(na, nb, nc,nk)

172 Appendix H

0 1 2 3 4 5 6 7 8 9 10

x 104

−1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time



0 1 2 3 4 5 6 7 8 9

x 104

0.5

1

1.5

2

Time




0 1 2 3 4 5 6 7 8 9 10

x 104

0

0.5

1

1.5

2

2.5

Time

Measured and simulated model output(5,7,8,8)


0 1 2 3 4 5 6 7 8 9 10

x 104

−1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time

Measured and simulated model output(2,7,8,8)


174 Appendix H

H.2.2 ARMAX Zero-pole plot for 6th order model

−1 −0.5 0 0.5 1

−1

−0.5

0

0.5

1

Poles (x) and Zeros (o) for the 6th order ARMAX model

Figure H.8: Zero-Pole plot for ARMAX 6th model decribed in the report. Themodel is table since all the poles lies within the unit circle.


−0.01 −0.005 0 0.005 0.01

−0.015

−0.01

−0.005

0

0.005

0.01


Figure H.9: Zero-Pole plot for ARMAX 6th model decribed in the report. Themodel is table since all the poles lies within the unit circle. Zoomedin origo

176 Appendix H

0.99 0.992 0.994 0.996 0.998 1 1.002 1.004

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02


Figure H.10: Zero-Pole plot for ARMAX 6th model decribed in the report. Themodel is table since all the poles lies within the unit circle. Zoomedin around +1 on the x axis


−1 −0.5 0 0.5 1 1.5−2

−1.5

−1

−0.5

0

0.5

1

1.5

2Poles (x) and Zeros (o)

Figure H.11: Zero-Pole plot for State space model 4th order.Discrete time. plot-ted with confidence interval. Thus there is no zero pole cancellation.

178

Appendix

H

H.2.3 State Space- continous time zero-pole plot

−0.1 −0.05 0 0.05 0.1

−0.1

−0.05

0

0.05

0.1

From u1

To

y1

−0.1 −0.05 0 0.05 0.1

−0.1

−0.05

0

0.05

0.1

From u2

−0.05 0 0.05 0.1

−0.1

−0.05

0

0.05

0.1

From u3

−0.1 −0.05 0 0.05 0.1

−0.1

−0.05

0

0.05

0.1

From u4

−0.1 0 0.1 0.2−0.2

−0.1

0

0.1

0.2From u5

−0.1 0 0.1 0.2−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

From u6

−0.1 0 0.1

−0.2

−0.1

0

0.1

0.2

−0.1 −0.05 0 0.05 0.1

−0.1

−0.05

0

0.05

0.1

From u8

−0.1 −0.05 0 0.05 0.1

−0.1

−0.05

0

0.05

0.1

From u9

Figure H.12: Zero-Pole plot for State space model 4th order.Continuous time. There are no zero-pole cancellation.

Appendix I

Appendix I

I.1.1 Linearized model- State Space(Jacobians)

A

-0.0250 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 -0.0063 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 -0.0056 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 -0.0020 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 -0.2000 0.0000 0.0000 0.0000

0.0007 -0.0009 0.0413 0.0115 0.0021 -0.0676 -12.2654 0.0000

-0.0000 -0.0000 0.0000 0.0000 0.0001 0.0000 -0.0563 0.0004

0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 -0.0001 -0.0008

B

0.0250 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0063 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0056 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0020 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.2000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 -0.4735 0.0672

0.0000 0.0000 0.0000 0.0000 0.0000 -0.0101 -0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 -0.0219 -0.0000

C 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000

180 Appendix I

I.1 Linearization of the dynamic Model - openloop

Operating Point for LinearizationVariable Name Description Value Unit

Input u0u01 Main air flow IN 1800 Kg/hu02 SFB air flow IN 500 Kg/hu03 Temperature of MAIN 160 oCu04 Temperature of SFB 90 oCu05 Feed flow IN 65 L/h

Disturbance input v0 (mean)v01 solids of total feed 50 %v02 Temperature of ambient air 30 oCv03 Rel. humidity ambient air 28 %v04 Temperature of feed 50 oC

State x0x01 Tout 85.44 oCx02 Main air flow IN 1800 Kg/hx03 SFB air flow IN 500 Kg/hx04 Temperature of MAIN 160 oCx05 Temperature of SFB 90 oCx06 Feed flow IN 65 L/hx07 evaporation rate 0.0108 Kg/sx08 Vapour in chamber 0.1933 Kg

output y0y01 Tout 85.44 oC

Table I.1: Operating Point for linearization: Stationary state

D

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Transfer function from input 1 to output:

1.75e − 005

s2 + 0.0926s + 0.00169(I.1)


−5.67e − 006

s2 + 0.0739s + 0.0004259(I.2)


0.0002313

s2 + 0.0732s + 0.0003786(I.3)

181

I.1.2 Frequency response - from inputs to output

10−5

100

−180

−90

0

90

180

To:

Out

(1)

From: In(2)

10−5

100

From: In(3)

10−5

100

From: In(4)

10−5

100

From: In(5)

10−5

100

Bode Diagram− process inputs (u) to output

Frequency (Hz)

Mag

nitu

de (

dB)

; Pha

se (

deg)

−200

−150

−100

−50

0From: In(1)

To:

Out

(1)

Figure I.1: Frequency response of the linearized model from each process input u to output.

182

Appendix

I

−80

−60

−40

−20

0From: In(5)

To:

Out

(1)

10−5

10−4

10−3

10−2

10−1

100

101

−180

−135

−90

−45

0

45

90

135

180

To:

Out

(1)

Bode Diagram− feed flow input to output

Frequency (rad/sec)

Mag

nitu

de (

dB)

; Pha

se (

deg)

Figure I.2: Frequency response of the linearized model from each feed flow input to output.

183

−60

−40

−20

0

20

40

System: sysI/O: In(6) to Out(1)Frequency (rad/sec): 0.442Magnitude (dB): 1.28

From: In(6)

To:

Out

(1)

10−5

10−4

10−3

10−2

10−1

100

101

102

90

180

270

360

To:

Out

(1)

Bode Diagram− solids content disturbance input to output

Frequency (rad/sec)

Mag

nitu

de (

dB)

; Pha

se (

deg)

Figure I.3: Frequency response of the linearized model from each disturbance input (Solids content) v1 to output.

184

Appendix

I

−50

−40

−30

−20

−10

0

From: In(7)

To:

Out

(1)

10−5

10−4

10−3

10−2

10−1

100

−180

−135

−90

−45

0

45

90

To:

Out

(1)

Bode Diagram− disturbance inputs Ambient Relative Humidity (v) to output

Frequency (Hz)

Mag

nitu

de (

dB)

; Pha

se (

deg)

Figure I.4: Frequency response of the linearized model from each disturbance input(Ambient Relative humidity) v2 to output.

185

I.1.3 Zero-Pole plot for the transfer functions - from each inputs to output

−0.08 −0.06 −0.04 −0.02 0−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1From: In(1)

−0.08 −0.06 −0.04 −0.02 0

From: In(2)

−0.08 −0.06 −0.04 −0.02 0

From: In(3)

−0.08 −0.06 −0.04 −0.02 0

From: In(4)

−0.2 0 0.2 0.4

From: In(5)

Pole−Zero Map− For the transfer function from each process input u to output

Real Axis

Imag

inar

y A

xis

Figure I.5: Zero-Pole plot for the transfer functions - from each process inputs to output. All poles and zeros are in left half plane forthe first 4 process inputs. feed flow transfer function has a zero in RHP

186

Appendix

I

−0.1 0 0.1 0.2 0.3−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1From: In(6)

Pole−Zero Map: for the transfer functions from each disturbance input v to output

Real Axis

Imag

inar

y A

xis

−0.08 −0.06 −0.04 −0.02 0

From: In(7)

Figure I.6: Zero-Pole plot for the transfer functions - from each disturbance inputs to output. All poles are in left half plane . Distur-bances (Solids content, Ambient temperature, and Relative humidity amibient air) inputs have zeros in Right half plane.

I.2 Comparison of linear and Non linear model 187


2.3e − 005

s2 + 0.0696s + 0.0001352(I.4)


0.00042s2 − 0.0002213s − 3.736e − 007

s4 + 0.3247s3 + 0.02885s2 + 0.0007841s + 6.095e − 007(I.5)


−0.4735s2 + 0.09684s + 0.0001852

s3 + 0.1247s2 + 0.003905s + 3.047e − 006(I.6)


0.0672

s+ 0.0676(I.7)

Eigenvalues for system matrix A- poles for the linearized system

-0.0676 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.0000 -0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.00000.0000 0.0000 -0.0563 0.0000 0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000 -0.0250 0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.0000 -0.0063 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.0000 -0.0056 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2000

Eigenvector for the system matrix A

0.0000 0.0000 0.0000 0.9999 0.0000 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.9999 0.0000 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.8323 0.0000 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9850 0.00000.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.99681.0000 -0.7978 -1.0000 0.0164 -0.0147 0.5544 0.1727 -0.07980.0000 0.0043 0.0009 0.0000 0.0000 0.0000 0.0000 -0.00070.0000 0.6029 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0010

I.2 Comparison of linear and Non linear model

Linear and nonlinear model is compared by applying a various steps on theprocess and disturbance input. The step value shown in the plots are isdeviation from the linearised operating point.

188 Appendix I

• Process inputs

– Feed

– Main inlet air flow

– Main inlet air temperature

• Disturbance inputs

– solids content

– Relative humidity of ambient air

I.2.1 Feed flow

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

84.4

84.6

84.8

85

85.2

85.4

85.6

85.8

Tout

outlet air temperature Linear model compared to Non linear model Feed flowrate step Ffeed

Time [sec]

Tem

pera

ture

[oC

]


=2

Nonlinear model

Figure I.7: Comparison of linear and Non linear model


1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

72

74

76

78

80

82

84

Tout

outlet air temperature Linear model compared to Non linear model: Feed flowrate step Ffeed

Time [sec]

Tem

pera

ture

[oC

]


=25

Nonlinear model


1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

80

81

82

83

84

85

86

Tout

outlet air temperature Linear model compared to Non linear Feed flowrate step Ffeed

Time [sec]

Tem

pera

ture

[oC

]


=10

Nonlinear model


190 Appendix I

I.2.2 Main inlet air flow

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

85

86

87

88

89

90

91

Tout

outlet air temperature Linear model compared to Non linear model: main air flowrate step Fmain

Time [sec]

Tem

pera

ture

[oC

]

Linear model: ∆ Fmain

=200

Nonlinear model



1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

85.3

85.4

85.5

85.6

85.7

85.8

85.9

Tout


Time [sec]

Tem

pera

ture

[oC

]


=20

Nonlinear model


192 Appendix I

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

x 104

85.4

85.6

85.8

86

86.2

86.4

86.6

86.8

87

Tout


Time [sec]

Tem

pera

ture

[oC

]


=50

Nonlinear model



I.2.3 Main inlet air temperature

0.95 1 1.05 1.1

x 104

79

80

81

82

83

84

85

86

Tout


Time [sec]

Tem

pera

ture

[oC

]


=−10

Nonlinear model

Figure I.13: Comparison of linear and Non linear model: Main inlet air temper-ature

194 Appendix I

2 4 6 8 10 12 14

x 104

90

100

110

120

130

140

Tout


Time [sec]

Tem

pera

ture

[oC

]

Linear model: ∆ T

main =10


=30


=50


=100


0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

x 104

86

88

90

92

94

96

98

Tout


Time [sec]

Tem

pera

ture

[oC

]


=20

Nonlinear model



0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

x 104

85

90

95

100

105

110

out outlet air temperature Linear model compared to Non linear model: main air temperature step T

Time [sec]

Tem

pera

ture

[oC

]


=40

Nonlinear model


196 Appendix I

I.2.4 Solids Content

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

x 104

85

86

87

88

89

90

91

92

Tout


Time [sec]

Tem

pera

ture

[oC

]


=0.1

Nonlinear model

Figure I.17: Comparison of linear and Non linear model: Solids content

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

x 104

85

90

95

100

105

Tout


Time [sec]

Tem

pera

ture

[oC

]


=0.3

Nonlinear model

1.3 1.4 1.5 1.6 1.7 1.8 1.9

x 104

103.5

104

104.5

105

Zoomed in

Time [sec]

Tem

pera

ture

[oC

]


=0.3

Nonlinear model

Figure I.18: Comparison of linear and Non linear model: Solids content


I.2.5 Relative Humidity of Ambient air

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

x 104

85.44

85.46

85.48

85.5

85.52

85.54

85.56

Tout

outlet air temperature Linear model compared to Non linear model:ambient Relative humidity RHamb

Time [sec]

Tem

pera

ture

[oC

]

Linear model: ∆ RHamb

=0.1

Nonlinear model

Figure I.19: Comparison of linear and Non linear model: Relative humidity ofambient air

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

x 104

85.5

85.6

85.7

85.8

85.9

86

Tout

outlet air temperature Linear model compared to Non linear model:ambient Relative humidity RHamb

Time [sec]

Tem

pera

ture

[oC

]


=0.5

Nonlinear model

1 1.002 1.004 1.006 1.008 1.01 1.012 1.014

x 104

85.5

85.6

85.7

85.8

85.9

86Zoomed in

Time [sec]

Tem

pera

ture

[oC

]


=0.5

Nonlinear model

Figure I.20: Comparison of linear and Non linear model: Relative humidity ofambient air

198 Appendix I

www.elektro.dtu.dk

Department of Electrical EngineeringAutomation and ControlTechnical University of DenmarkElektrovejBuilding 326DK-2800 Kgs. LyngbyDenmarkTel: (+45) 45 25 35 50Fax: (+45) 45 93 12 95

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