List of Tables

vii

List of Figures

viii

Nomenclature

xvii

Acknowledgements

xxiii

1.

Introduction

1

1.0

Scope

1

1.1

Circulating Fluidized Bed (CFB) System

2

1.1.1

Basic CFB Systems

2

1.1.2

CFB Applications in Various Technologies

3

1.2

Motivation

5

1.2.1

Approach

7

1.3

Objectives

8

1.4

Report Organization

9

2.

Background

11

2.0

Scope

11

2.1

Review of Solids Flow Measurements in CFBs

12

2.1.1

Solids Dynamics

12

2.1.1a

Solids Velocity

15

2.1.1b

Solids Concentration

19

2.1.1c

Solids Mass Flux

23

2.1.2

Solids Mixing

25

2.2

Solids Flow Modeling in Gas-Solid Risers

28

2.2.1

Modeling of Solids Mixing

28

2.2.2

Modeling of Two Phase Fluid Dynamics

29

2.3

Summary

31

3.

CARPT and CT Reconstruction Algorithms

32

3.0

Scope

32

3.1

Introduction

33

3.2

CARPT Position Rendition

37

3.2.1

Available Position Reconstruction Methods

38

3.2.2

Cross-Correlation Based Algorithm

41

3.2.3

Algorithm Validation

49

3.3

CT Image Reconstruction

53

3.3.1

Introduction

53

3.3.2

Alternating Minimization Algorithm

54

3.3.3

Algorithm Validation

56

3.4

Summary

59

4.

CFB System and Overall Solids Mass Flux Measurements

60

4.0

Scope

60

4.1

CFB Setup

61

4.1.1

Modifications Needed to Achieve Stable Operation of the CFB Loop

61

4.2

Tracer Studies

66

4.2.1

Overall Solids Mass Flux Measurements – Literature Survey

66

4.2.2

Measurement Technique

70

4.2.3

Densitometry Experiments

71

4.2.4

Time-of-flight Experiments

74

4.3

Results and Discussion

76

4.3.1

Solids Holdup Measurements

76

4.3.2

Time-of-flight Measurements

81

4.4

Flow Regimes

91

4.5

Summary

93

5.

Solids RTD Measurements

95

5.0

Scope

95

5.1

Introduction

96

5.2

Measurement Technique

97

5.3

Results and Discussion

101

5.3.1

Reproducibility and Occurrence Independence

105

5.3.2

FF and DPT Regimes

105

5.3.3

RTD, FPTD and Response Function of Conventional Injection-Detection

108

5.3.4

RTDs at High and Low Fluxes

113

5.3.5

Axial Dispersion Coefficients

121

5.3.6

Core-Annulus Interchange Model

123

5.4

Summary

124

6.

Solids Velocity Field and Holdup Measurements

126

6.0

Scope

126

6.1

CARPT Technique

127

6.1.1

Challenges in Implementing CARPT on Gas-Solid Risers

128

6.1.2

Experimental Setup

137

6.1.3

CARPT at Sandia National Laboratory

138

6.2

CT Setup on Gas-Solid Riser

138

6.3

Results and Discussion

140

6.3.1

Solids Velocity Field

140

6.3.1a

Instantaneous Positions and Velocity Calculations

140

6.3.1b

Post Facto Validation

144

6.3.1c

FF versus DPT Regimes

154

6.3.2

Solids Holdup Measurements

182

6.3.3

Comparison of CT versus CARPT Derived Holdup Profiles

195

6.4

Summary

196

7.

Further Analysis of Solids Flow and Mixing:  Effect of Operating Conditions

198

7.0

Scope

198

7.1

Introduction

199

7.2

Effect of Operating Conditions

199

7.2.1

Solids Velocity Fields

199

7.2.2

Mean Radial Velocity Profiles

204

7.2.3

Radial Profiles of Turbulent Parameters

208

7.3

Solids Backmixing

213

7.3.1

Residence Time Distributions

213

7.3.2

Circulation Time Distributions

218

7.3.3

Evaluation of Eddy Diffusivities

223

7.4

Solids Eddy Diffusivities

227

7.5

Overall Continuity Problem

234

7.6

Summary

236

8.

Summary, Conclusions, and Recommendations

239

8.1

Recommendations for Future Research

244

9.

Appendices

248

9.1

Appendix A:  Flowchart of the Cross-Correlation Based Search for Position Rendition from CARPT Data

248

9.2

Appendix B:  Phenomenological Model of Solids RTD in Risers

250

9.3

Appendix C:  Time-Averaged Axial Differential Pressure Profiles

255

10.

References

257

11.

List of Publications

276