Schools of

Mechanical and Chemical Engineering

The University of Adelaide

Investigating the use

of Concentrated Solar Energy
to Thermally Decompose
Limestone
Richard Alexander Craig

Thesis Submitted for the

Degree of Doctorate of Philosophy
May 2010

Vtv|t|
Splendor Solis (1532-35)

iii

Abstract
The objectives of this research investigation are to answer fundamental questions regarding
the effectiveness of using concentrated solar energy as the sole heating source for the
thermo-chemical decomposition of limestone-marble, supplied by Penrice, Angaston.
Specifically, scientific analyses are used to investigate the energy requirements for the
efficient manufacture of quicklime using solar thermal energy. To achieve these aims, the
energy requirements for an industrial scale solar lime manufacturing system were first
evaluated. The main conclusion from this analysis is that the thermal efficiency of a solar
energy supplied lime manufacture system compares favourably with the best fossil fuelled
system. A good heat recovery system as well as a comprehensive preheating system is
recommended to minimise the energy losses from the system.
A zero dimensional model was then used to determine that the most energy efficient shape
for a travelling grate solar furnace is a triangular cross section. This shape maximise the
exposure of the limestone to the radiant energy while minimising structural heat losses. This
analytical evaluation also identified that the open area of entrance and exit openings, which
allow the process materials to flow through the kiln and for the exhaust gases to escape the
kiln, should be minimised. Thirty three times more heat flux is lost through these openings
than through the kiln structure. Minimising the openings area therefore improves kiln thermal
efficiency.
This investigation then evaluated the maximum bed thickness for the limestone when using a
grate bed system within the proposed solar furnace. Due to the nature of radiation it is
recommended that the limestone layer be no thicker than 2.5 times the nominal diameter of
the limestone in use.

This thickness optimises the exposure of the stone to the direct

radiation and increases the heat transfer to the stones lower within the bed and allows for the
unrestricted diffusion of CO2 away from these stones.
The investigation then experimentally quantified the effects of radiant heat flux intensity on
the calcination kinetics of the Penrice, Angaston marble as a function of stone size. This
experimental investigation involved comparing results from an electric muffle furnace, an
atmospherically open solar radiation furnace, and an enclosed triangular shaped solar
radiation furnace.

The muffle furnace provided a baseline values to which the solar

calcination rates could be compared.

iv

ABSTRACT

The open system solar calcination experiments showed that the preheating time of the stone
is directly proportional to the illuminated surface area of the stone and the intensity of the
heat flux to which it is exposed. Additionally, the reaction rate is directly proportional to the
radiant heat flux, and is independent of the stone size for heat fluxes greater than 430kW/m2.
The enclosed solar furnace experiments identified a 45% improvement in decomposition time
could be achieved by using the triangular shaped solar furnace compared to the open solar
system calcination. This benefit to the calcination time is best for the more intense heat
fluxes and for the larger stone sizes. The measured calcination times were similar to those
found for a conventional rotary kiln.

This demonstrates the practicalities of using solar

radiation technology for interchange with, or as a supplementary heating source to, a

combustion driven lime manufacturing industrial plant.
A multi-zone two dimensional mathematical model was then used to evaluate the radiant
heat exchange within the triangular solar furnace. The developed mathematical scheme
provides a comprehensive package with a validated base model for future evaluations of
solar furnace designs. A modified shrinking core calcination model was then developed,
which uses an energy balance approach to calculate the preheating times and calcination
rates for the Penrice marble exposed to various intensities of radiant heat flux. This version
of the heat transfer based shrinking core model was used after considering the one sided
heating of the stone from the point source radiation.

Declaration of Originality
This work contains no material that has been accepted for the award of any other degree or
diploma in any university or other tertiary institution and, to the best of my knowledge and
belief, contains no material previously published or written by another person, except where
due reference has been made in the text.
I give consent to this copy of my thesis, when deposited in the University Library, being made
available for loan and photocopying, subject to the provisions of the Copyright Act 1968.
I also give permission for the digital version of my thesis to be made available on the web,
via the Universitys digital research repository, the Library catalogue, the Australasian Digital
Theses Program (ADTP) and also through web search engines, unless permission has been
granted by the University to restrict access for a period of time.

Signed:
Richard Alexander Craig
on this 1st day of May, 2010

vi

Acknowledgments
It is with great thanks and the generosity of many people that I see the completion of this
research project. I would like to start by thanking Professor Gus Nathan and Associate
Professor Peter Mullinger for their generous support, advice and guidance throughout this
very rewarding process. Their academic and practical views provided significant balance to
this daunting task.
I would like to thank the academic and general staff from both the School of Mechanical
Engineering and School of Chemical Engineering for their help and support during my post
graduate studies. In particular A.Prof Bassam Dally for heat transfer advice, Mr Bill Finch
and Mr Silvio De Ieso for technical assistance with the experimental rig construction, A.Prof
Peter Ashman and A.Prof Richard Kelso for professional research advice and Billy
Constantine for his computer wizardry in code writing and saving my data on more than one
occasion.
To the friends that I made within the Department of Mechanical Engineering: Joshua Smith,
Ricky Morgans, Tonia Camporeale, Jackie Munn, Daniel Handley, Kelly Parish, Cris Birzer,
Eyad Hassan, Matthew Tetlow, Shahrooz Afshar, Grant England, Kimberly Clayfield and
David Thompson thanks to all of you for your advice, assistance, comic relief, creative
diversions and friendship over the years.
Parts of this project could not have been conducted without the help of colleagues and fellow
members of the Turbulence, Energy and Combustion (TEC) Group from The University of
Adelaide whom helped with data processing and theoretical modeling solutions that made
aspects of this research somewhat easier.

Special acknowledgment goes to Burkhard

Seifert whom spent considerable time assisting with the heat flux measurements.
Acknowledgment also goes to Dr Barry Jenkins for his modeling guidance and providing
assistance and access to his version of the Hottel zero dimensional model.
A big thank you goes to Graham Kelly from the Mechanical Engineering Thebarton Research
Laboratory whose technical support, interesting conversations and worldly advice will always
be remembered.

vii

ACKNOWLEDGMENTS

Thanks to Andrew Graetz at Penrice Quarry, Angaston and to Penrice Soda Holdings
Limited for the marble samples and allowing me exclusive access to the quarry. Thanks also
to Mark Joraslafsky and Northern Cement Limited for providing access to the Mataranka
limestone quarry.
This work was financially supported by the South Australian State Energy Research Advisory
Committee (SENRAC).

I would like to thank SENRAC for the valuable experience and

opportunities that I have gained from this project.

Most importantly, a million thanks to my lovely Alice. I could not have completed this work
without your wonderful love and support during the course of this project. Sorry it has taken
so long.
This Thesis is dedicated to my clever and beautiful daughters Tahlia and Charlotte. May it
inspire you to achieve your dreams also.

viii

Table of Contents
Page
List of Figures
List of Tables
Nomenclature

xiv
xxiv
xxxi

Chapter 1
Introduction
1.1
1.1.1
1.1.2
1.1.3
1.2
1.2.1
1.3
1.4
1.5
1.6
1.7
1.7.1

1
Current Environmental Issues
The Greenhouse Effect
Global Warming
Global Emissions of CO2
Carbon Sequestration
Carbon Sequestration via Mineral Carbonation
The Thermal Decomposition of Limestone
Conventional Lime Kilns
The Use of Alternative Energy for Lime Manufacture
CO2 Mitigation using Solar Lime Manufacture
Scope and Structure of Thesis
Thesis Structure

1
1
1
3
4
5
6
7
11
14
15
17

Chapter 2
Literature Review
2.1
2.2
2.2.1
2.2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.3.7
2.4
2.4.1
2.4.2
2.4.3
2.4.4
2.4.5

Introduction
Limestone
Lime
Uses for Limestone and Lime
Mechanisms and Kinetics of Calcination
Mechanisms of Calcination
Kinetics of Calcination
The Effect of Carbon Dioxide Partial Pressure
Re-Carbonation
The Rate of Calcination
Effects of Heating Rate
Effects of Limestone Particle Size
Modelling the Calcination Reaction
Models Used For Non-Catalytic Gas-Solid Reactions
The Shrinking Core Model
The Uniform Conversion Model (Homogeneous Model)
The Grain Pellet Model
Calcination Modelling of Non Uniformly Heated Limestone

19
19
19
20
21
22
25
27
27
29
30
33
34
35
35
37
39
40
41

ix

TABLE OF CONTENTS

2.5
2.5.1
2.5.2
2.5.3
2.5.4
2.6
2.6.1
2.6.2
2.7
2.8
2.8.1
2.8.2
2.8.3
2.8.4
2.9
2.10

Controlling Parameters for Lime Kiln Design

Kiln Size and Production Rate
Stone Size Reduction
Optimising Furnace Shape for Radiant Heat Transfer
Basic Process Considerations
Solar Thermal Lime Manufacture
Solar Chemical Reactors Used For Lime Manufacture
Evaluation of Existing Reactor Designs
Economics of Commercial Scale Solar Lime Manufacture
Approaches to Modelling a Lime Kiln
Computational Fluid Dynamics
Flux Modelling
Zonal Modelling
Summary of Modelling Approaches
Conclusions from the Literature Review
Aims and Objectives of the Current Research

43
44
45
47
48
49
50
58
63
63
64
65
66
68
69
71

Chapter 3
Zero Dimensional Studies of a Solar Lime Furnace
3.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.2.6
3.2.7
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.3.6
3.3.7
3.3.8
3.3.9

Introduction
Theoretical Energy Requirements for Quicklime Production
System Requirements for Conventional Energy
Assumptions Used in the Energy Balance
Heat and Mass Balance for Conventional Lime Kilns
Heat and Mass Balance for Solar Lime Furnaces
Analysis of the Solar Furnace Heat and Mass Balances
Comparison of the Heat and Mass Balances
Conclusions from the Process Efficiency Analysis
Furnace Design Using a Zero Dimension Thermal Radiation
Hottel Zone Model
Application of the 0-D Zone Model
Assumptions used in the 0-D Zonal Model
Effect of Changing Kiln Length
Effect of Changing Kiln Shape
Effect of Varying Aspect Ratio
Effect of Varying Kiln Opening Size
Effect of Varying Kiln Structural Dimensions
Comparisons of Structural and Openings Heat Losses
Conclusions from the 0-D Zone Modelling

73
73
74
74
75
76
78
82
82
83
84
86
87
88
91
95
98
100
101
102

Chapter 4
Experimental Apparatus and Techniques
4.1

Introduction

104
104

TABLE OF CONTENTS

4.2
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.3.5
4.4
4.4.1
4.4.2
4.4.3
4.4.4
4.5
4.5.1
4.5.2
4.5.3
4.5.4
4.5.5
4.5.6
4.5.7
4.5.8
4.6
4.6.1
4.7
4.7.1
4.7.2

Temperature Measurement
Sample Collection and Preparation
Composition of Penrice Marble
Sample Preparation
Sieving
Mass Sizing
Drying
Muffle Furnace Experimental Apparatus
Electric Muffle Furnace
Crucible Bowl
Flat Bed Ceramic Fibre Refractory Board
Analytical Balance
Solar Simulation Experimental Apparatus
General Description of Apparatus
Xenon Short Arc Radiation Source
Cinemeccanica - Milano Lamphouse
Total Heat Flux Transducers
Beam Deflection Mirror
Calcination Platform
Equipment Frame
Data Collection and Analysis
Solar Calcination Experiments
Experimental Procedure
Experimental Solar Furnace
Temperature Measurements within the Furnace
Experimental Procedure

104
106
108
108
109
110
111
112
112
114
114
115
116
117
118
121
123
123
126
127
128
129
129
131
133
134

Chapter 5
Radiant Heat Flux Distribution Measurement
5.1
5.2
5.3
5.4
5.4.1
5.4.2
5.4.3
5.4.4
5.5
5.5.1
5.5.2
5.5.3
5.5.4
5.5.5

Introduction
Heat Flux from Electrical Power Supply
Surface Temperature Measurement
Heat Flux Transducer Measurement
Measurement Procedure
Data Collection and Analysis
Transducer Measurement Results
Error Analysis for Transducer Measurements
Heat Flux Measurement Using Digital Imagery
Experimental Arrangement for Digital Imagery
Image File Conversion
Background Light and Measurement Noise
Image Intensity Adjustment
Image Perspective Transformation

136
136
137
140
145
146
148
149
158
159
160
162
163
163
164

TABLE OF CONTENTS

5.5.6
5.5.7
5.5.8
5.5.9

Image Processing Program

Calibration of Image to Heat Flux
Calculation of Heat Flux at the Near Focal Region
Error Analysis for Digital Imagery

xi

165
166
168
173

Chapter 6
Muffle Furnace Calcination Experiments
6.1
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.2.5
6.3
6.4
6.5
6.6
6.7

Introduction
Experimental Methodology
Sample Preparation and Experimental Apparatus
Crucible Bowl Experiments
Constant Bed Diameter Experiments
Constant Mass Bed Experiments
Single Stone Calcination Experiments
Results
Analysis of Results
Conversion Rate and the Arrhenius Equation
Error Analysis for the Muffle Furnace Calcination Experiments
Conclusions from the Muffle Furnace Experiments

175
175
176
176
176
178
180
182
183
190
196
199
201

Chapter 7
Calcination Measurements of Penrice Marble Directly Exposed
to High Intensity Radiation
7.1
7.2
7.2.1
7.2.2
7.2.3
7.3
7.4
7.5
7.6

Introduction
Experimental Methodology
Experimental Apparatus
Single Stone Calcination Experiments
Measurement Accuracy
Results
Analysis of Results
Comparison of Results from Muffle Furnace Calcination and
Open System Radiation Calcination Experiments
Conclusions from Open System Radiation Calcination Measurements

203
203
204
204
204
205
209
212
217
218

Chapter 8
Calcination of Penrice Marble within a Solar Furnace
8.1
8.2
8.2.1
8.2.2
8.2.3
8.3
8.4

Introduction
Experimental Methodology
Experimental Apparatus
Single Stone Calcination Experiments
Measurement Accuracy
Results
Analysis of Results

220
220
221
221
221
224
226
232

TABLE OF CONTENTS

8.5
8.6

Comparison of Results from Enclosed Solar Furnace and

Open System Calcination Experiments
Conclusions from the Enclosed Solar Furnace Calcination
Measurements

xii

238
240

Chapter 9
Multi-Zone Two-Dimensional Studies of a Solar Lime Furnace
9.1
9.2
9.2.1
9.2.2
9.2.3
9.2.4
9.2.5
9.3
9.4
9.4.1
9.4.2
9.4.3
9.5
9.5.1
9.5.2
9.6
9.6.1
9.6.2
9.6.3
9.7

Introduction
Principles of the Zone Method
Direct Exchange Areas
Total Exchange Areas
Non-Grey Flux Exchange
Total Energy Balances
Monte Carlo Probability Distribution Technique
The RADEX Program
Calibration of the 2-D Multi-Zone Model
Details of the Modelling Parameters
Radiation Pseudo-Source Temperature
Sensitivity Analysis of the Calibration
Heat Flux Modelling of the Open Calcination System
Sensitivity Analysis of the Open System Modelling
Comparison of Calculated and Measured Heat Flux for the
Open System
Heat Flux Predictions for the Enclosed Triangular Solar
Furnace
Sensitivity Analysis for the Enclosed Triangular Solar
Furnace Modelling
Comparison of Calculated and Measured Heat Flux
for the Enclosed Triangular Solar Furnace
Comparison of Calculated Heat Flux between the
Enclosed Triangular Furnace and the Open System
Conclusions from the Multi-zone Modelling

241
241
242
242
244
245
247
248
249
250
250
253
254
258
260
262
264
266
268
270
270

Chapter 10
Modelling the Calcination of Limestone
10.1
10.2
10.3
10.4
10.5
10.5.1
10.5.2
10.5.3
10.5.4

Introduction
Model Overview
Assumptions Used in the Modelling
Mass, Volume and Surface Area of the Marble Samples
The Energy Balance
Reflectivity, Absorptivity and Emissivity
Radiant Heat Transfer between the Sample and the Platform
Convective Heat Transfer
Conductive Heat Transfer

272
272
273
275
276
278
280
286
288
291

TABLE OF CONTENTS

10.6
10.7
10.7.1
10.7.2
10.7.3
10.7.4
10.8
10.8.1
10.8.2
10.9
10.10
10.11
10.12

Time to Heat the Marble to the Calcination Temperature

Calculation of Calcination Time
Energy Available for Calcination
Stone Surface Temperatures
Shrinking Core Calculation and Results
Analysis of Calculated Shrinking Core Results
Comparisons with the Experimental Results
Comparison of Measured and Calculated Calcination Times for
the Open Solar System
Comparison of Measured and Calculated Calcination Times for
the Enclosed Triangular Solar Furnace
Sensitivity Analysis of the Calcination Model
Calcination Rate Calculation
Validation of the Calcination Modelling
Conclusions from the Calcination Modelling

xiii

292
301
302
303
308
312
312
313
315
318
326
328
330

Chapter 11
Conclusions and Further Work
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.7.1
11.7.2
11.7.3
11.7.4
11.7.5

Zero Dimensional Studies of a Solar Lime Furnace

Multi-Zone Two Dimensional Studies of a Solar Lime Furnace
Muffle Furnace Calcination Experiments
Open System Calcination Experiments
Enclosed Solar Furnace Calcination Experiments
Modelling the Calcination of Limestone
Recommendations for Further Work
Process Modelling
Solar Furnace Design and Radiation Modelling
Mathematical Calcination Model
Experimental Investigations into the Calcination of Limestone
using Solar Radiation
The Road to Industrial Solar Lime Manufacture

332
332
333
333
334
335
336
337
337
337
338
338
339

Appendix A

341

Appendix B

342

Appendix C

345

Appendix D

347

Appendix E

355

Appendix F

357

Appendix G

358

Bibliography

359

xiv

List of Figures
Chapter 1

Page

Figure 1-1: Contribution to total CO2 equivalent emission by sector in 2004.

Figure 1-2: Cross-section of a continuous vertical shaft kiln.

Figure 1-3: Cross-section of a preheater short rotary kiln.

Figure 1-4: An early conceptual design of a flash calciner (floatation kiln).

10

Figure 1-5: A conceptual diagram of a rotating Calcimatic kiln.

11

Figure 1-6: Variation of concentrator type with concentration ratio

and equilibrium temperatures for earth and space.

14

Chapter 2
Figure 2-1: Energy required to produce 1 kg of lime as a function of initial
temperature based on Equation [2.2].

24

Figure 2-2: The range of dissociation pressure of CO2 for calcite for different authors.

25

Figure 2-3: Decomposition of a sphere of calcium carbonate (Shell or layer

model) under uniform heating.

26

Figure 2-4: Representation of a spherical particle undergoing decomposition,

showing pressure, gas density, temperature, molar fractions
and conversion gradients.

28

Figure 2-5: Representation of the (a.) standard concentric shrinking core model
and (b.) eccentric shrinking core model for a limestone sample
irradiated from one side.

42

Figure 2-6: Schematic diagram of a solar fluidised bed reactor.

50

Figure 2-7: Schematic diagram of an open ended inclined solar rotary furnace.

51

Figure 2-8: Diagram of the revised solar fluidised bed reactor, showing the
heat transfer wall.

53

Figure 2-9: Experimental apparatus for solar energy reactions.

54

Figure 2-10: Schematic diagram of the solar cyclone reactor.

55

Figure 2-11: The atmospheric open solar cyclone reactor combined with a
fluidised bed.

55

Figure 2-12: Schematic diagram of a proposed solar cement plant ~ Insert

shows details of the vertical cyclonic reactor.

55

Figure 2-13: Industrial solar reactor design. Insert shows simplified schematic
of the falling particle reactor for a proposed 1.5MW pilot plant.

56

Figure 2-14: Schematic diagram of the downward facing falling particle solar reactor.

57

Figure 2-15: Photo of the pilot scale solar rotary reactor system.

58

Figure 2-16: View of the solar reactor aperture.

58

LIST OF FIGURES

xv

Chapter 3
Figure 3-1: Energy and mass flow diagram for a typical fossil fuel burning limeproducing system.

74

Figure 3-2: Solar system evaluation case 1: Generic lime kiln with sufficient air
to fully preheat the limestone.

79

Figure 3-3: Solar system evaluation case 2: Evolved CO2 as sole preheating
medium, heat from hot lime product lost from system.

79

Figure 3-4: Solar system evaluation case 3: Heated air bypasses calcination zone.
Evolved CO2 used for preheating limestone within separate chamber.

80

Figure 3-5: Alternative case 3 solar system: Preheated CO2 bypasses calcination
zone and preheats the limestone feed.

81

Figure 3-6: Calculated comparative nett energy consumption for a typical lime
manufacturing process using different forms of energy based on
a constant mass of limestone.

83

Figure 3-7: Representation of the 0-D zone model.

84

Figure 3-8: A representation of a rotary kiln showing the total length and
characteristic diameter dimensions.

89

Figure 3-9: Predicted thermal efficiency of a 4m diameter rotary kiln, for increasing
kiln length and percentage of limestone fill within the kiln.

90

Figure 3-10: Kiln cross sectional shapes with the same cross sectional area.

91

Figure 3-11: Comparison of round, square, triangular and elliptical cross-section

kilns, with 95% of base bed area coverage.

92

Figure 3-12: Comparison of round, square, triangular and elliptical cross-section

kilns, with 25% bed area coverage.

93

Figure 3-13: Cross sectional diagrams of furnace shape for right angle triangle
with varying between 15 and 75.

94

Figure 3-14: Thermal efficiency of a right angled triangle cross-section kiln with
increasing length and change of roof angle from 15 to 75.

95

Figure 3-15: Cross-sectional view of a square kiln showing the change in

cross sectional shape as the kiln width is increased but the
cross-sectional area remains constant.

96

Figure 3-16: Effects of changing the kiln width on thermal efficiency while maintaining
a constant cross sectional area, but increasing kiln length.

97

Figure 3-17: Plot of heat loss from the kiln structure for kiln length for variations in
kiln width.

97

Figure 3-18: Characteristic dimensions and surface areas for changes in kiln width.
The differences between the square cross sectional kiln and 2x width
kiln cases are indicated.

98

Figure 3-19: Variation in kiln thermal efficiency as the floor area coverage
Is increased.

99

Figure 3-20: Variation in thermal efficiency as the area of openings is increased

with all other kiln parameters remaining constant.

100

Figure 3-21: Variation in kiln thermal efficiency as the characteristic dimensions

of the kiln are altered for constant opening area.

101

LIST OF FIGURES

Figure 3-22: Distribution of heat loss from a 3m high, 6m wide and is 75m long
kiln when changing the kilns height up to 6m.

xvi

102

Chapter 4
Figure 4-1: Mass loss from marble samples dried for varying lengths of time.

112

Figure 4-2: a). Photo of the electric Carbolite muffle furnace used for the muffle furnace
experiments. b). schematic showing location of the temperature
measurement points within the muffle furnace.
113
Figure 4-3: Photograph of the solar simulator apparatus showing the lamphouse,
the solar furnace, the mirror mounting, the analytical balance platform
and the camera traverse.

118

Figure 4-4: Photo of a HLR Osram 3kW Xenon short-arc lamp.

119

Figure 4-5: Spectral intensity of a Xenon arc lamp compared with extraterrestrial
and ground level solar irradiance.

120

Figure 4-6: Orthographic drawing of a Zenith X6500H lamphouse.

121

Figure 4-7: Calculated beam diameter as a function of distance from the rear of
the lamphouses reflector.

122

Figure 4-8: Reflectance of stainless steel, aluminium and silver between 0.3m
and 2.5m.

124

Figure 4-9: Solar reflectance from an aluminium mirror as the surface anodises
over time.

125

Figure 4-10: A pictorial view of the calcination platform showing the locations of
the analytical balance, isolation tube, heat shield and calcination
platform.

127

Figure 4-11: An isometric view of the equipment frame showing the lamphouse,
mirror mounting and analytical balance rest.

128

Figure 4-12: Photograph of one gram marble samples placed on the calcination
platform ready for exposure to the simulated solar radiation.

130

Figure 4-13: Sectional drawing of the solar furnace in front of the lamphouse with
side wall removed for clarity.

131

Figure 4-14: Photograph of the solar furnace with the rear wall removed, showing
the calcination platform system.

132

Figure 4 15: Pictorial representation of the walls of the solar furnace showing the
locations of the permanent (solid) and transitional (white) temperature
measurement points.

134

Chapter 5
Figure 5-1: Dimensional parameters used to characterise the radiation beam
emitting from the lamphouse.

136

Figure 5-2: Calculated beam diameter Db, and average heat flux qelec, as a function
of distance S, from focal point for 49% conversion efficiency.

139

Figure 5-3: Diagram showing the temperature measurement locations on the

ceramic board target illuminated by the radiation beam.

142

LIST OF FIGURES

xvii

Figure 5-4: Heat flux transducer distances from the focal point for the no mirror
measurements.

147

Figure 5-5: Transducer measurement distances for the two mirror positions.

148

Figure 5-6: Transducer (92242) measurement of the heat flux at an axial distance
S4 = 1040mm from the focal point.

150

Figure 5-7: Transducer (92242) measurement of the heat flux at an axial distance
S3 = 790mm from the focal point.

150

Figure 5-8: Transducer (92242) measurement of the heat flux at an axial distance
S2 = 690mm from the focal point.

150

Figure 5-9: Transducer (92242) measurement of the heat flux at an axial distance
S1 = 540mm from the focal point.

150

Figure 5-10: Comparison of measured ( ) and calculated ( ) using Eq [5.3]

maximum heat flux for axial distances from the focal point.

152

Figure 5-11: Normalised rms heat flux profile of the radiation beam, without a mirror.

153

Figure 5-12: Heat flux measurements for S7 = 790mm, with the 45 aluminium
mirror located at 90mm from the focal point.

154

Figure 5-13: Heat flux measurements for S6 = 690mm, with the 45 aluminium
mirror located at 90mm from the focal point.

154

Figure 5-14: Heat flux measurements for S5 = 540mm, with the 45 aluminium
mirror located at 90mm from the focal point.

154

Figure 5-15: Comparison of measured ( ) and calculated ( ) using Eq [5.5]

maximum heat flux for axial distances from the focal point when
the mirror was located 90mm from the focal point.

155

Figure 5-16: Heat flux measurements for S8 = 540mm with the 45 aluminium
mirror located before the focal point.

156

Figure 5-17: Pictorial diagram of the experimental setup used for the heat flux
measurements using digital imagery.

161

Figure 5-18: Diagram showing observed intensity from a Lambertian surface for
a normal and off-normal observer.

164

Figure 5-19: Calibration pixel gradient of illumination at 525mm from focal point
using 1/60 shutter speed and 22 aperture stop.

167

Figure 5-20: Calibration pixel gradient of illumination at 525mm from focal point
using 1/90 shutter speed and 22 aperture stop.

167

Figure 5-21: Plot of the calculated heat fluxes for distances of 100mm to 30mm
from the focal point using two different camera shutter speeds.

170

Figure 5-22: Measured heat flux distribution at S = 100mm from the focal
point using a shutter speed of 1/60.

171

Figure 5-23: Calculated isorad contour image at S = 100mm from the focal
point using a shutter speed of 1/60.

171

Figure 5-24: Measured heat flux distribution at S = 50mm from the focal
point using a shutter speed of 1/90.

172

Figure 5-25: Calculated isorad contour image at S = 50mm from the focal
point using a shutter speed of 1/90.

172

LIST OF FIGURES

xviii

Chapter 6
Figure 6-1: Photo of the crucible bowl inside the preheated muffle furnace.

177

Figure 6-2: Photo of a 1.000 gram (dc = 9.44mm) Penrice marble sample
placed in the muffle furnace set at TF = 1000C.

183

Figure 6-3: Calcination profiles of Penrice marble at TF = 900C and TF = 1000C

conducted on 100g samples of four different diameters placed in
a crucible in the muffle furnace.

184

Figure 6-4: Calcination profiles of 40 gram Penrice marble at TF = 900C and

TF = 1000C conducted on four different nominal diameters spread
evenly over an area of 80mm diameter in the muffle furnace.

184

Figure 6-5: Calcination profiles of Penrice marble at TF = 900C and TF = 1000C

conducted on four different particle size ranges spread evenly over an
area of 80mm diameter with a bed thickness of 1.5 times the particle
diameter in the muffle furnace.

185

Figure 6-6: Calcination profiles of 100g samples of 3mm nominal diameter

Penrice marble spread to form five different bed thicknesses at
at TF = 1000C in the muffle furnace.

185

Figure 6-7: Calcination profiles of 200g samples of 10mm nominal diameter

Penrice marble spread to form five different bed thicknesses at
TF = 1000C in the muffle furnace.

186

Figure 6-8: Calcination profiles of Penrice Marble at TF = 900C and TF = 1000C

conducted on single marble samples of three different dc in the
muffle furnace.

186

Figure 6-9: Calcination profiles for 1.000g (dc = 9.44mm) Penrice marble for
varying muffle furnace temperatures.

187

Figure 6-10: Photographs taken after calcination showing the heights of the
20mm and 27mm thick beds of the 10mm nominal diameter
Penrice marble.

192

Figure 6-11: Measured calcination rate verses bed thickness for the 3mm and
10mm nominal diameter Penrice marble. Also showing the fit with
Equations [6.4] and [6.5] with 95% confidence limits.

193

Figure 6-12: Relationship between particle diameter (dc) and calcination rate for
various bed thicknesses and muffle furnace temperatures (TF).

194

Figure 6-13: Measured calcination rates verses muffle furnace temperature for
dc = 9.44mm Penrice marble. Also showing the fit with
Equation [6.6] with 95% confidence limits.

195

Figure 6-14: Arrhenius plot of the calcination of Penrice marble from the
100 gram crucible experiments for the four different particle size
ranges for TF = 900C and TF = 1000C. Slopes of CaCO3
conversion taken for X=50%.

197

LIST OF FIGURES

xix

Chapter 7
Figure 7-1: Calcination profiles of four single 6.54mm nominal Penrice marble
stones exposed to a radiant heat flux of 28020 kW/m2 at S = 75mm
in the open atmosphere solar calcination system.

206

Figure 7-2: Calcination profiles of four single 6.54mm nominal Penrice marble
stones exposed to a radiant heat flux of 43030 kW/m2 at S = 50mm
in the open atmosphere solar calcination system.

207

Figure 7-3: Calcination profiles of single Penrice marble stones exposed to a

radiant heat flux of 17510 kW/m2 in an open atmosphere
solar system.

209

Figure 7-4: Calcination profiles of single Penrice marble stones exposed to a

radiant heat flux of 28020 kW/m2 in an open atmosphere
solar system.

210

Figure 7-5: Calcination profiles of single Penrice marble stones exposed to a

radiant heat flux of 43030 kW/m2 in an open atmosphere
solar system.

210

Figure 7-6: Calcination rate (dm/dt50) verses radiant heat flux for dc = 6.54mm,
dc = 9.44mm and dc = 13.62mm.

214

Figure 7-7: Photo of the 13.62mm nominal diameter stone before calcination.

215

Figure 7-8: Photo of the 13.62mm nominal diameter stone after calcination at
430 kW/m2.

215

Figure 7-9: Preheat time verses radiant heat flux for dc = 6.54mm, dc = 9.44mm,
and dc = 13.62mm calcined at 17515kW/m2, 28020kW/m2, and
43030kW/m2.

215

Figure 7-10: Plot showing relationship between the preheat time and projected
area, for each stone size exposed to 17515kW/m2, 28020kW/m2,
and 43030kW/m2.

216

Figure 7-11: Calcination completion time verses radiant heat flux for dc = 6.54mm,
dc = 9.44mm and dc = 13.62mm exposed to 17515kW/m2,
28020kW/m2, and 43030kW/m2 in the open solar system.

217

Figure 7-12: Comparison between open solar system and muffle furnace
measurements of calcination rate for dc = 6.54mm, dc = 9.44mm,
and dc = 13.62mm.

218

Chapter 8
Figure 8-1: Photo of the solar furnace enclosure with the rear wall removed
showing the calcination platform on which the marble is placed.

222

Figure 8-2: Heat flux measurement of the preheated calcination platform prior to
marble placement, for S = 100mm.

223

Figure 8-3: Heat flux measurement with isorad contours showing placement
of the dc = 6.54mm (0.333g) Penrice marble in the beam, for
S = 100mm.

223

Figure 8-4: Heat flux measurement with isorad contours showing placement
of the dc = 9.44mm (1.000g) Penrice marble in the beam, for
S = 100mm.

223

LIST OF FIGURES

xx

Figure 8-5: Heat flux measurement with isorad contours showing placement
of the 13.62mm (3.000g) Penrice marble in the beam, for
S = 100mm.

223

Figure 8-6: Calcination profiles of five single dc = 6.54mm Penrice marble

stones exposed to a radiant heat flux of 30025 kW/m2 at
S = 75mm in the enclosed solar furnace.

225

Figure 8-7: Calcination profiles of five single dc = 6.54mm nominal Penrice marble
stones exposed to a radiant heat flux of 45030 kW/m2 at
S = 50mm in the enclosed solar furnace.

225

Figure 8-8: Calcination profiles of single Penrice marble stones placed at

S = 100mm and exposed to a radiant heat flux of 20015 kW/m2
in the enclosed solar furnace.

227

Figure 8-9: Calcination profiles of single Penrice marble stones placed at

S = 75mm and exposed to a radiant heat flux of 30025 kW/m2
in the enclosed solar furnace.

227

Figure 8-10: Calcination profiles of single Penrice marble stones placed at

S = 50mm and exposed to a radiant heat flux of 45030 kW/m2
in the enclosed solar furnace.

228

Figure 8-11: Calcination profile for dc = 11.90mm (2.000 gram) single Penrice marble
stones placed at S = 70mm and exposed to a radiant heat flux
of 32525 kW/m2 in the enclosed solar furnace.

228

Figure 8-12: Calcination profiles for dc = 13.62mm (3.000 gram) and dc =16.15mm
(5.000 gram) single Penrice marble stones placed at S = 60mm
and exposed to a radiant heat flux of 38525 kW/m2 in the
enclosed solar furnace.

229

Figure 8-13: Completion time verses radiant heat flux for dc = 6.54mm, dc = 9.44mm,
dc = 11.90mm, dc = 13.62mm and dc = 16.15mm Penrice
marble calcined in the enclosed solar furnace.

233

Figure 8-14: Preheat time verses radiant heat flux for dc = 6.54mm,
dc = 9.44mm, dc = 11.90mm, dc = 13.62mm and dc = 16.15mm
Penrice marble in the enclosed solar furnace.

234

Figure 8-15: Plot showing relationship between the preheat time and illuminated
surface area, for each stone size exposed to 20015kW/m2,
30025kW/m2, and 45030kW/m2.

235

Figure 8-16: Calcination rate (dm/dt50) verses radiant heat flux for dc = 6.54mm,
dc = 9.44mm, dc = 11.90mm, dc = 13.62mm and dc = 16.15mm
Penrice marble calcined within the solar furnace.

235

Figure 8-17: Measured wall temperatures on the internal surface of the solar
furnace at the thermocouple locations presented in Figure 4-15
when the calcination platform is positioned at S = 100mm, S = 75mm,
S = 70mm, S = 60mm and S = 50mm and therefore exposed to
radiant heat fluxes of 20015kW/m2, 30025kW/m2, 32525kW/m2,
38525kW/m2 and 45030kW/m2 respectively.

237

LIST OF FIGURES

Figure 8-18: Comparison of conversion rates for the Enclosed Triangular Solar
Furnace (ETSF) measurements, the Open Solar System (OSS)
measurements and the muffle furnace (MF) measurements for
dc = 6.54mm, dc = 9.44mm and dc = 13.62mm.

xxi

238

Chapter 9
Figure 9-1: Incident, emitted and reflected radiant fluxes at a surface element.

245

Figure 9-2: Experimental apparatus used for radiation source measurement.

251

Figure 9-3: Representation of the experimental apparatus used in RADEX

for the source temperature calculations.

252

Figure 9-4: Calculated heat flux received at the transducer location for
variations in pseudo-source temperature.

254

Figure 9-5: Representation of the open solar system (OSS) experimental

apparatus used in RADEX.

258

Figure 9-6: Calculated heat flux on the surface of the calcination platform at
various distances S, from the focal point for the OSS.

259

Figure 9-7: Comparison of modelling results and measured heat flux at the
calcination platform for the OSS.

263

Figure 9-8: Representation of the Enclosed Triangular Solar Furnace (ETSF)

experimental apparatus used in RADEX.

264

Figure 9-9: Calculated heat flux on the surface of the calcination platform at
various distances S, from the focal point for the ETSF.

266

Figure 9-10: Comparison of calculated and measured heat flux on the calcination
platform for the ETSF.

269

Figure 9-11: Comparison of calculated heat fluxes on the calcination platform for
the ETSF and OSS for various distances S from the focal point.

270

Chapter 10
Figure 10-1: Representation of the marble sample on the platform irradiated by
radiation.

274

Figure 10-2: Heat flux exchange between the radiation source, the marble sample
and the calcination platform.

279

Figure 10-3: Representation of the view factor: sphere to coaxial disk in a parallel
plane.

286

Figure 10-4: Representation of the view factor: rectangle to coaxial disk in a

parallel plane.

287

Figure 10-5: Representation of the contact area between the marble sample and
the platform.

291

LIST OF FIGURES

xxii

Figure 10-6: Plot showing the calculated energy absorbed into the sample as a
function of heat flux from the radiation source received by the three
marble samples for the triangular furnace (solid line) and the
open system (broken line).

294

Figure 10-7: Calculated radiative heat transfer between the platform and the
9.44mm (1.00g) marble sample for a fixed direct heat flux of
200kW/m2 in the Open Solar System (OSS).

295

Figure 10-8: Calculated radiative heat transfer between the platform and the
9.44mm (1.00g) marble sample for a fixed direct heat flux of
200kW/m2 in the Enclosed Triangular Solar Furnace (ETSF).

295

Figure 10-9: Calculated conductive heat transfer between the platform and the
three marble samples for a fixed direct heat flux of 200kW/m2
in the OSS.

296

Figure 10-10: Calculated conductive heat transfer between the platform and the
three marble samples for a fixed direct heat flux of 200kW/m2
in the ETSF.

296

Figure 10-11: Calculated convective heat transfer between the boundary layer air
and the three marble samples for a fixed direct heat flux of 200kW/m2
in the OSS.

297

Figure 10-12: Calculated convective heat transfer between the boundary layer air
and the three marble samples for a fixed direct heat flux of 200kW/m2
in the ETSF.

297

Figure 10-13: Calculated radiative heat transfer between the three marble samples
and the surrounding atmosphere for a fixed direct heat flux of
200kW/m2 in the OSS.

298

Figure 10-14: Calculated radiative heat transfer between the three marble samples
and the surrounding atmosphere for a fixed direct heat flux of
200kW/m2 in the ETSF.

298

Figure 10-15: Calculated energy available for heating the three marble samples
for a fixed direct heat flux of 200kW/m2 in the OSS.

299

Figure 10-16: Calculated energy available for heating the three marble samples
for a fixed direct heat flux of 200kW/m2 in the ETSF.

299

Figure 10-17: Plot showing the calculated times to heat the marble samples
to 1173K when exposed to heat fluxes between 100kW/m2 and
600kW/m2.

301

Figure 10-18: Plot showing the calculated net energy available for calcination as the
temperature of the marble sample increases for an incident radiant
heat flux of 175kW/m2 for the OSS.

303

Figure 10-19: Temperature / time and fractional calcination / time curves for a
44.45mm (1 inch) cube of marble calcined at 1100C.

306

Figure 10-20: Representation of the calcination time against sample surface

temperature for the three surface temperature scenarios for
qincident = 200kW/m2.

307

LIST OF FIGURES

xxiii

Figure 10-21: Comparison of calculated and measured calcination times for the
dc = 6.54mm, dc = 9.44mm and dc = 13.62mm Penrice marble
exposed to radiant heat fluxes of 175kW/m2, 280kW/m2 and
430kW/m2 in an OSS.

315

Figure 10-22: Comparison of calculated and measured completion times for the
Dc = 6.54mm, dc = 9.44mm and dc = 13.62mm Penrice marble
exposed to radiant heat fluxes of 200kW/m2, 300kW/m2 and
450kW/m2 in an ETSF.

317

Figure 10-23: Comparison of calculated calcination times with error bars for the
three nominal diameter Penrice marble for the OSS and the ETSF.

326

Figure 10-24: Calculated fractional calcination verses normalised calcination time

using the modified shrinking core mathematical model.

327

Appendix D
Figure D-1: Photo of dc = 2.855mm marble spread over refractory board to form
80mm diameter circle, before calcination.

349

Figure D-2: Photo of dc = 0.375mm marble spread over refractory board to form
80mm diameter circle, before calcination.

349

Figure D-3: Calcination profiles of 40 gram samples of four different sized

Penrice marble exposed to radiation with an average heat flux of
approximately 115 kW/m2.

351

Figure D-4: Calcination profiles of four different sized Penrice marble spread to
form a bed 1.5 times the marbles nominal diameter, and exposed
radiation with an average heat flux of approximately 115 kW/m2.

351

Figure D-5: Photo of dc = 2.855mm marble spread over refractory board to form
80mm circle, after calcination.

353

Figure D-6: Photo of dc = 0.375mm marble spread over refractory board to form
80mm circle, after calcination.

353

Appendix G
Figure G.1: Calculated radiative heat transfer between the platform and the
dc = 6.54mm (0.333g) marble sample for a fixed direct heat flux of
200kW/m2 in the OSS.

358

Figure G.2: Calculated radiative heat transfer between the platform and the
dc = 6.54mm (0.333g) marble sample for a fixed direct heat flux of
200kW/m2 in the ETSF.

358

Figure G.3: Calculated radiative heat transfer between the platform and the
dc = 13.62mm (3.000g) marble sample for a fixed direct heat flux of
200kW/m2 in the OSS.

358

Figure G.4: Calculated radiative heat transfer between the platform and the
dc = 13.62mm (3.000g) marble sample for a fixed direct heat flux of
200kW/m2 in the ETSF.

358

xxiv

List of Tables
Chapter 2

Page

Table 2-1: Operating output and range of stone sizes for various commercial
lime kilns.

44

Table 2-2: Specifications for four types of crushers used on limestone.

46

Table 2-3: Advantages and disadvantages of the fluidise bed and cyclone
solar furnaces.

59

Table 2-4: Advantages and disadvantages of the rotary kiln and flat bed
solar furnaces.

60

Table 2-5: Comparison of the advantages and disadvantages of thermal

radiation modelling techniques for solar furnaces.

69

Chapter 3
Table 3-1: Calculated results from energy balances using various fossil fuels
as the heating source for lime furnaces.

77

Table 3-2: Results from energy balance analysis of three solar lime furnaces
with 100% and 80% effective heat transfer.

81

Chapter 4
Table 4-1: Measured thermocouple temperature for iced and boiling water for
both before and after (in parentheses) use within the experiments.

106

Table 4-2: Screen Sizes at Penrice quarry, Angaston.

107

Table 4-3: Marble size ranges stockpiled at the Penrice quarry, Angaston.

107

Table 4-4: Component weight % dry basis, of some South Australian limestone.

108

Table 4-5: Selected sieve sizes and resulting nominal diameter of marble particle.

109

Table 4-6: Mass sizes of marble and nominal characteristic diameter.

110

Table 4-7: Furnace temperatures measured using thermocouple D.

114

Table 4-8: Specifications for the Xenon XBO 5000W / HBM OFR lamp.

120

Chapter 5
Table 5-1: Percentage of the total radiant energy emitted within the UV, Visible
and IR spectral bands from a xenon-arc bulb. Note: total = 100.2%
(Source: Oriel Instruments,1998).

138

Table 5-2: Conversion of electrical energy into radiation from xenon arc lamps.
Note: total = 49%.

138

Table 5-3: Measurement of temperatures in centigrade taken at 30mm intervals

with the board positioned normal to the beam at S = 150mm.

142

xxv

LIST OF TABLES

le 5-4: Measurement of temperatures in centigrade taken at 22.5mm intervals

with the board positioned normal to the beam at S = 100mm.

142

Table 5-5: Measurement of temperatures in centigrade taken at 20mm intervals

with the board positioned normal to the beam at S = 90mm.

143

Table 5-6: Calculated average heat flux (W/m ) within the radiation beam at
S =150mm.

144

Table 5-7: Calculated average heat flux (W/m ) within the radiation beam at
S = 100mm.

144

Table 5-8: Calculated average heat flux (W/m2) within the radiation beam at
S = 90mm.

144

Table 5-9: The total power within the radiation beam calculated from the
temperature measurements.

145

Table 5-10: Maximum heat flux measured for the no mirror case at four axial
Distances S, from the focal point.

151

Table 5-11: Maximum measured heat flux for the first mirror case at three axial
distances, S, from the focal point and comparison to the no mirror
measurement.

155

Table 5-12: Maximum measured heat flux for the second mirror case at an axial
distances of S = 540mm from the focal point and comparison with
theno mirror and 1st mirror measurements.

157

Table 5-13: Error in the heat flux intensity measurement due to path length
accuracy.

159

Table 5-14: Maximum error in the heat flux intensity measurement due to all
sources of error.

159

Table 5-15: Camera settings used for the calibration and measurement of the
heat flux intensity.

166

Table 5-16: Calculated heat flux between S = 100mm and S = 30mm using two
different camera shutter speeds.

169

Table 5-17: Maximum possible variation in the digital imagery heat flux
measurements.

174

Chapter 6
Table 6-1: Bed depth for the 40g marble samples placed to form an 80mm
diameter bed.

179

Table 6-2: Bed depth and measured mass to obtain a bed thickness of 1.5 x dc.

180

Table 6-3: Measured and calculated bed depth for variations in bed diameter
for the 100g, dc = 3mm and 200g, dc = 10mm marble samples.

181

Table 6-4: Mass of marble and the calculated nominal characteristic diameter
dc, using Eq [6.3].

182

Table 6-5: Calcination rates for the 100g crucible muffle furnace experiments.

187

LIST OF TABLES

xxvi

Table 6-6: Calcination rates for the 40g flat bed muffle furnace experiments.

188

Table 6-7: Calcination rates for the bed thickness of 1.5 x dc muffle furnace
experiments.

188

Table 6-8: Calcination rates for 100g samples of dc = 3mm Penrice marble at
TF = 1000C in the muffle furnace.

188

Table 6-9: Calcination rates for 200g samples of dc = 10mm Penrice marble at
TF = 1000C in the muffle furnace.

189

Table 6-10: Calcination rates and time to complete calcination for dc = 6.54mm,
dc =9.44mm and dc = 13.62mm marble for muffle furnace temperature
of TF = 900C and TF = 1000C.

189

Table 6-11: Calcination rates for dc = 9.44mm (1.000g) marble for muffle furnace
temperatures between TF = 850C and TF = 1000C.

189

Table 6-12: Arrhenius parameters for the calcination of Penrice Marble

for the 100 gram crucible experiments with 900C < TF < 1000C,
for chemical conversion dm/dt50.

197

Table 6-13: Variation in Arrhenius parameters from all muffle furnace calcination
experiments using 900C < TF < 1000C and dm/dt50.

198

Chapter 7
Table 7-1: Comparison of preheating time, calcination rate and time to complete
calcination for dc = 6.54mm Penrice marble exposed to either
28020kW/m2 or 43030 kW/m2 for the open atmosphere solar
calcination system.

208

Table7- 2: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 17515kW/m2
in an open atmosphere solar system.

211

Table 7-3: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 28020kW/m2
in an open atmosphere solar system.

211

Table 7-4: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 43030kW/m2
in an open atmosphere solar system.

212

Table 7-5: Average CO2 release rate for Penrice marble exposed to radiant heat
flux of 17515kW/m2, 28020kW/m2 or 43030kW/m2.

213

Chapter 8
Table 8-1: Average measured heat flux on the projected surface area of
stone at various distance (S) from the focal point.

223

Table 8-2: Comparison of preheating time, calcination rate and time to complete
calcination for dc = 6.54mm Penrice marble exposed to either
30025kW/m2 or 45030 kW/m2.

226

LIST OF TABLES

xxvii

Table 8-3: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 20015kW/m2
in an enclosed solar furnace.

230

Table 8-4: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 30025kW/m2
in an enclosed solar furnace.

230

Table 8-5: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 45030kW/m2
in an enclosed solar furnace.

230

Table 8-6: Preheating time, calcination rate and time to complete calcination for
11.90mm (2.000g) Penrice marble exposed to a radiant heat flux of
32525kW/m2 in an enclosed solar furnace.

231

Table 8-7: Preheating time, calcination rate and time to complete calcination for
single Penrice marble exposed to a radiant heat flux of 38525kW/m2
in an enclosed solar furnace.

231

Table 8-8: Summary of measured wall temperatures on the internal surface of

the solar furnace at the permanent thermocouple locations presented
in Figure 4-15 when the calcination platform is positioned at S = 100mm,
S = 75mm, S = 70mm, S = 60mm and S = 50mm from the focal
point and therefore exposed to radiant heat fluxes of 20015kW/m2,
30025kW/m2,32525kW/m2, 38525kW/m2 and45030kW/m2
respectively.
232

Chapter 9
Table 9-1: Median wavelength of emitting and absorbing spectral bands for H2O
and CO2.

246

Table 9-2: Grey gas parameters used in mixed grey gas correlations for CO2
and H2O mixtures.

247

Table 9-3: Specifications for reflectivity, emissivity and temperature used for model
calibration.

251

Table 9-4: Simulated radiation pseudo-source temperature variation and the

resulting received heat flux at the transducer measurement location.

253

Table 9-5: Variation in pseudo-source temperature to achieve the measured

heat flux tolerances.

256

Table 9-6: Comparison of calculated heat flux by changing various modelling

parameters.

256

Table 9-7: Calculated heat flux on the calcination platform for various distances S
from the focal point for the open solar system (OSS).

259

Table 9-8: Comparison of calculated heat flux at the simulated calcination platform,
after changing various modelling parameters in the OSS model.

261

Table 9-9: Variation in error for the calculated heat flux received at the surface
of the calcination platform in the OSS model.

262

LIST OF TABLES

xxviii

Table 9-10: Comparison of calculated and measured heat flux on the calcination
platform for the OSS.

263

Table 9-11: Calculated heat flux on the calcination platform for S = 100, S = 75 and
S = 50 for the ETSF.

265

Table 9-12: Comparison of calculated heat flux at the simulated calcination platform,
after changing various modelling parameters in the ETSF model.

267

Table 9-13: Variation in error for the calculated heat flux received at the surface
of the calcination platform in the ETSF model.

268

Table 9-14: Comparison of calculated and measured heat flux on the calcination
platform for the ETSF.

269

Chapter 10
Table 10-1: Calculated number of moles, volume, total surface area, characteristic
diameter and projected area of the Penrice marble samples.

278

Table 10-2: Solar absorptivity for marble and limestone.

282

Table 10-3: Solar absorptivity of lime.

283

Table 10-4: Emissivity of lime.

285

Table 10-5: Reflectivity from the surface of the marble for solar and infrared
radiation.

285

Table 10-6: View factors for stone to platform radiation exchange.

287

Table 10-7: View factors for platform to stone radiation exchange.

288

Table 10-8: Calculated air temperature of the natural convection boundary layer
using the measured platform temperatures.

290

Table 10-9: Calculated contact area between the marble sample and the platform.

292

Table 10-10: Energy distribution of 200kW/m direct radiation received by

the three marble sample sizes.

293

Table 10-11: Average, maximum, minimum and standard deviation of the

measured wall temperatures for the furnace enclosure for variations
in distance S between the calcination platform and focal point.

297

Table 10-12: Calculated time (in seconds) to heat the marble samples from 298K
to 1173K using heat fluxes between 100kW/m2 and 500kW/m2
in the OSS or ETSF.

300

Table 10-13: Calculated maximum temperature of the marble samples when

exposed to various incident heat fluxes in the OSS and ETSF.

303

Table 10-14: Proposed surface temperatures for the three sizes of Penrice marble.

305

Table 10-15: Calculated additional heating time (in seconds) to heat the three
marble samples from 1173K to the proposed surface temperature
for the three surface temperature scenarios for all the qincident
of interest in the OSS and ETSF.

308

LIST OF TABLES

xxix

Table 10-16: Time (in minutes) to complete calcination of the three nominal
diameter Penrice marble for the three sample surface temperature
scenarios for the OSS and ETSF assuming a concentric shrinking
core model.

311

Table 10-17: Time (in minutes) to complete calcination of the three nominal
diameter Penrice marble for the three sample surface temperature
scenarios for the OSS and ETSF assuming an eccentric shrinking
core model.

311

Table 10-18: Comparison of calculated (using eccentric model) and measured

preheating times and calcination times for dc = 6.54mm, dc = 9.44mm
and dc = 13.62mm Penrice marble exposed to 175kW/m2
280kW/m2 and 430kW/m2 in the OSS.

313

Table 10-19: Comparison of calculated (using eccentric model) and measured

preheating times and calcination times for dc = 6.54mm, dc = 9.44mm
and dc = 13.62mm Penrice marble exposed to 200kW/m2,
300kW/m2 and 450kW/m2 in the ETSF.

316

Table 10-20: Changes in the calculated calcination time for variation of emissivity
of CaO for dc = 6.54mm and dc = 13.62mm Penrice marble in the
OSS and ETSF.

319

Table 10-21: Changes in the calculated calcination time for variation of absorptivity
of CaO for dc = 6.54mm and dc = 13.62mm Penrice marble in the
OSS and ETSF.

320

Table 10-22: Changes in the calculated calcination time for variation of thermal
conductivity of the CaO layer on dc = 6.54mm and dc = 13.62mm
Penrice marble in the OSS and ETSF.

321

Table 10-23: Comparison of calculated calcination time by varying the

illuminating radiant heat flux for both dc = 6.54mm and
dc = 13.62mm Penrice marble in the OSS and ETSF.

322

Table 10-24: Maximum variation in calculated calcination time for dc = 6.54mm,

dc = 9.44mm and dc = 13.62mm Penrice marble in the OSS
and ETSF.

324

Table 10-25: Calculated calcination times with maximum and minimum tolerances
for dc = 6.54mm, dc = 9.44mm and dc = 13.62mm Penrice marble
Penrice marble using the heat fluxes from the OSS and ETSF
investigations.

325

Table 10-26: Calculated rates of calcination for dc = 6.54mm, dc = 9.44mm,

and dc = 13.62mm Penrice marble exposed to the heat
fluxes from the OSS and ETSF investigations.

328

Table 10-27: Measured heat fluxes and platform temperatures used for the
calculation of calcination times for dc = 1 1.90mm, dc = 13.62mm
and dc = 16.15mm Penrice marble.

329

Table 10-28: Comparison of calculated and measured preheating and calcination

times for dc = 11.90mm, dc = 13.62mm and dc = 16.15mm
Penrice marble exposed to 325kW/m2 and 385kW/m2.

329

LIST OF TABLES

xxx

Chapter 11
Table 11-1: Calcination rates and completion times for single stone marble
in a muffle furnace at either TF = 900C or TF = 1000C.

334

Appendix A
Table A-1: Enthalpy analysis for four fuels and two solar energy furnaces.

341

Appendix D
Table D-1: Bed depth for the 40g marble samples placed to form an 80mm
diameter bed exposed to the radiation beam.
`

348

Table D-2: Mass and measured bed depth of samples to obtain a bed thickness
of 1.5 times the particle diameter.

349

Table D-3: Calcination rates for the 40 gram flat bed experiments exposed to an
average 115kW/m2.

352

Table D-4: Calcination rates for the bed thickness of 1.5 x dc exposed to an
average 115kW/m2.

352

Appendix E
Table E-1: Measured wall temperatures on the internal surface of the solar
furnace at the thermocouple locations presented in Figure 4-15
for various calcination platform distances S from the focal point
and the associated radiant heat fluxes.

355

Table E-2: Measured wall temperatures on the external surface of the triangular
solar furnace at the thermocouple locations presented in Figure 4-15
when the calcination platform is positioned at S = 100mm from the focal
point and therefore exposed to a radiant heat flux of 20015kW/m2.

356

Appendix F
Table F-1: Average characteristic specifications for air surrounding the heated
platform.

357

xxxi

Nomenclature
Abbreviations and Constants
C
CaCO 3
CaO
CMOS
CO2
ETSF
g
K
kg
kW
m
MJ
mm
N2
0-D
OSS
SCM
TGA
TIFF

Degrees centigrade
Calcium Carbonate, Limestone, Marble
Calcium Oxide, Lime, Quicklime
Complementary Metal Oxide Semiconductor
Carbon Dioxide
Enclosed Triangular Solar Furnace
grams
Kelvin
kilograms
kilowatt
metre
megajoule
millimetre
Nitrogen
Zero-Dimensional
Open Solar System
Shrinking Core Model
Thermogravimetric Analyser
Tagged Image Files Format (also TIF)

Roman Symbols
bd
CA
dc
D
D'
De
Deq
Db
dm
Ea
gg, GG
gs, GS
(GS1)R
g
h
H
HF
Imeasured
In
k
K
Kp
ks
L

limestone bed depth (mm)

reactant gas concentration
marble / limestone nominal diameter (mm)
furnace/kiln diameter (m or mm)
dimensionless firing density
effective diffusivity through the product layer (mm-1)
furnace/kiln characteristic equivalent diameter (mm)
radiation beam diameter (mm)
conversion gradient of CaCO3 to CaO
activation energy of the reaction (kJ/kg or kJ/mol)
gas to gas heat exchange
gas to surface heat exchange
total exchange area with allowance for effect of surface zones in radiative
equilibrium
gas phase (Italic)
enthalpy (J)
kiln height (m or mm)
enthalpy flux in the feed stream entering the chamber per hour
bit level of each pixel within the image
irradiation normal to the surface
Arrhenius rate constant (sec-1)
attenuation factor (extinction coefficient) (m-1)
equilibrium constant
reaction rate constant
kiln length (m or mm)

NOMENCLATURE

Roman Symbols (Cont)

L
MB
M
mo
mt
m3
m50
m75
m100
Ng
P
PCO2
Pv
q
Q
Q
Qout
R
R2
r
rc
ro
S
Ss, SS
sg, SG
T
t
t50
t75
t100
TAF
Tambient
Tboard
To
TPlatform
TF
W
X
XCO2
Xls
XN2
y1

number of volume elements

molecular weight of the solid reactant (g/mol)
number of surface elements
initial mass of limestone (g)
mass of calcining sample at any time (t)
mass of calcining sample equal to 3% of the stones final mass (g)
mass of calcining sample equal to 50% of the stones final mass (g)
mass of calcining sample equal to 75% of the stones final mass (g)
final mass of calcining sample at 100% calcination (g)
number of gray gases
total resistance pressure (pa)
partial pressure of CO2 (pa)
vapour pressure (pa)
radiant heat flux (W/m2)
heat (or power), (W)
dimensionless furnace efficiency
energy leaving a surface or gas zone (J/s)
Universal Gas Constant = 8.314 J/ K. mol
coefficient of determination
distance between each zone (m)
radius of the un-reacted limestone core at any time (mm)
initial radius of the solid limestone (mm)
distance from the focal point along radiation beam (m)
surface to surface heat exchange
surface to gas heat exchange
temperature (K)
time (s or min)
time to achieve 50% calcination (s or min)
time to achieve 75% calcination (s or min)
time to complete (100%) calcination (s or min)
adiabatic flame temperature (K)
ambient temperature (K)
measured board temperature (K)
base temperature (K)
temperature of calcination platform (K)
muffle furnace temperature (K)
kiln width (m or mm)
fractional calcination
molar fraction of carbon dioxide
rate of conversion of limestone used in Arrhenius equation
molar fraction of nitrogen
constant mole fraction of CO2

Greek Symbols

absorptivity
emissivity
bulk density of the reacting particle
reflectivity
Stefan-Boltzmann constant = 5.67x10-8 W/m2.K4

xxxii

NOMENCLATURE

Greek Symbols (Cont)

Change in Parameter
Roof angle for triangular shaped furnace (deg)
transmissivity factor

Subscripts
Air
B
b
beam
d,c
d,m
elec
Ex
g
Lime
LS
m1
m2
max
os
React
s
temp
TSF

ambient air
bulk phase
stoichiometric coefficient
within the radiation beam
calculated bed depth
measured bed depth
calculated from electrical power
exhaust gases
gas phase
quicklime
limestone
mirror position 1
mirror position 2
maximum
open system
calcination reaction
solid phase
calculated from temperature measurement
triangular solar furnace

Superscripts
e
i

equilibrium
interfacial

xxxiii