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Injection phenomena and heat transfer in copper converters Bustos, Alejandro Alberto 1984

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INJECTION PHENOMENA AND HEAT TRANSFER IN COPPER CONVERTERS by ALEJANDRO ALBERTO BUSTOS Mining Eng., Universidad de Chile, 1972 M.Sc, Universidad de Chile, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Metallurgical Engineering) We accept this thesis as conforming to the_j^-quired standard THE UNIVERSITY OF BRITISH COLUMBIA December 1984 0 Alejandro Alberto Bustos, 1984 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Metallurgical Engineering The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date February 18, 1985 i i ABSTRACT The injection dynamics and related accretion build up, as well as bath motion and heat losses in copper converters, have been investigated. The studies involved physical and mathematical models coupled with plant t r i a l s at four copper smelters to examine gas discharge phenomena, bath slopping and heat transfer within the converter. th The laboratory work, performed on a 1|4 scale model of a converter, indicated significant tuyere interaction. Air discontinuously discharges into the bath with a frequency which increases with gas flow rate and is affected by the bath circulation velocity in the tuyere region. Measurements have delineated slopping behaviour in terms of tuyere sub-mergence and the buoyancy power input to the bath. The industrial t r i a l s were conducted in Peirce-Smith, Hoboken and Inspiration converters under normal conditions. A tuyerescope attached to the back of a tuyere permitted the direct observation of accretion growth and the sampling of accretions during blowing. The tests indicated that the copper converter operates under bubbling conditions. Pressure pulses from the tuyeres revealed that in non-ferrous submerged in-jection processes three regimes of gas-liquid interaction can be identified: bubbling, unstable envelope and channelling. i i i The relative dominance of each regime is affected by tuyere line erosion, viscosity of the bath and tuyere submergence. Analysis of the accretion samples revealed that accretions in the copper converter form mainly by the solidification of bath at the tuyere t i p . Oxygen enriched air does not prevent accretion formation, but seems to produce a softer, easy-to-punch accretion. The type of puncher as well as punching frequency affect conditions inside the tuyere pipe and this could have an influence on accretion formation. The mathematical heat transfer model indicated that when the converter is out of the stack, heat losses through the mouth of the converter cause the internal surface to cool rapidly which may lead to freezing at the tuyere line and tuyere blockage when blowing is resumed. The temperature gradient, localized to within 60-80 mm of the refractory inside wall, changes markedly within the f i r s t minutes of the converter being out of stack. This may generate thermal stresses in the converter wall and contribute to refractory erosion at the tuyere line. Covering the converter mouth during out-of-stack periods significantly reduces the change in temperature gradient at the inside wall as well as heat losses from the converter. iv TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS iv LIST OF TABLES v i i i LIST OF FIGURES x TABLE OF NOMENCLATURE xvi i ACKNOWLEDGEMENTS xx CHAPTER I INTRODUCTION: THE COPPER CONVERTING PROCESS 1 1.1 History of Copper Converting 2 1.2 Current Converting Practice 5 1.3 Problems in Copper Converting 9 CHAPTER II LITERATURE REVIEW: STUDIES IN GAS INJECTION 13 2.1 Studies in Side-Blown Injection 14 2.2 Bubble Formation During Submerged Injection 20 2.2.1 Bubble Formation in Low-Density, Inviscid Liquids 22 2.2.2 Bubble Formation in Liquid Metals 28 2.3 Pressure Fluctuations at the Tuyere .... 33 2.4 The Bubbling-Jetting Transition 44 2.5 Accretion Formation and Tuyere Blockage . 47 2.6 Bath Surface Movement. Splashing and Slopping 53 2.7 Summary 63 V CHAPTER III OBJECTIVES 66 CHAPTER IV EXPERIMENTAL TECHNIQUES 69 4.1 Laboratory Experimental Work 69 4.1.1 The isothermal Model ^ 4.1.2 Experimental Apparatus 77 4.1.2.1 Converter-Shaped Vessel 79 4.1.2.2 Tuyeres 82 4.1.2.3 Gas-Delivery System 85 4.1.2.4 Pressure Measurements 86 4.1.2.5 High-Speed Cinematography 86 4.1.3 Conditions for the Tests and General Procedure 88 4.2 Industrial Work 91 4.2.1 Smelters Selected for the Tests 92 4.2.2 Scope of the Industrial Tests 96 4.2.3 Equipment and Procedure 97 CHAPTER V EXPERIMENTAL RESULTS 103 5.1 Laboratory Results 103 5.1.1 Dynamic Pressure Measurements 103 5.1.1.1 Effect of the Air Flow Rate 104 5.1.1.2 Effect of Tuyere Spacing 110 5.1.1.3 Tuyere Interaction 113 5.1.1.4 Effect of Tuyere Submergence 115 5.1.2 High-Speed Cinematography 117 5.1.2.1 Observations at the Tuyere Line 117 5.1.2.2 Slopping Observations 120 5.1.3 Slopping Measurements 121 vi 5.2 Industrial Results 128 5.2.1 Dynamic Pressure in the Tuyeres 128 5.2.1.1 Effect of the State of the Refractory at the Tuyere Region 129 5.2.1.2 Effect of the Tuyere Submergence 132 5.2.1.3 Effect of Tuyere Blockage 132 5.2.2 Accretion Growth at the Tuyere Tip 136 5.2.2.1 Dynamics of Accretion Growth 136 5.2.2.2 Effect of Oxygen Enrichment of the Blast 138 5.2.2.3 Analysis of Accretion Samples 142 5.2.2.4 Influence of the 4B5 Punching System 144 5.2.2.5 Tuyere Pipes. Metallographic Work 148 5.2.3 Bath Surface Movement and Splashing 151 CHAPTER VI HEAT LOSSES FROM COPPER CONVERTERS. A MATHEMATICAL MODEL 154 6.1 Scope of the Heat Transfer Model 154 6.2 The Mathematical Model 155 6.2.1 Radiation Heat Transfer in Copper Converters 158 6.2.2 Transient Conduction in the Elements in the Model 162 6.2.3 Computer Program 166 6.2.4 Range of Variables Studied in the Model 168 6.3 Accuracy of the Heat Transfer Model 169 6.4 Influence of the Refractory Emissivity 171 6.5 Model Predictions 175 6.5.1 Effect of the Converter Mouth Position 175 6.5.2 Thermally Active Zone in the Refractory .... 179 6.5.3 Effect of the Converter Diameter 182 6.5.4 Effect of the Area of the Converter Mouth .. 184 6.5.5 Influence of the Coverage of the Mouth 187 v i i CHAPTER VII DISCUSSION 195 7.1 Injection Dynamics at the Tuyere Tip 195 7.2 Bath Movement and Slopping 209 7.3 Accretion Formation and Tuyere Blockage 213 7.4 Heat Losses from the Converter 218 CHAPTER VIII SUMMARY AND CONCLUSIONS 221 8.1 Summary 221 8.2 Suggestions for further Work 225 REFERENCES 228 APPENDIX I THE PLATE ORIFICE 240 APPENDIX II PRESSURE TRACES FOR DIFFERENT CHARGES OF THE COPPER CONVERTER 251 APPENDIX II RADIATION SHAPE FACTORS IN THE HEAT TRANSFER MODEL 253 APPENDIX IV THERMAL CONDUCTANCES FOR THE DIFFERENT NODES IN THE MODEL 257 APPENDIX V HEAT TRANSFER COEFFICIENT FOR THE EXTERNAL SURFACE OF THE CONVERTER 261 APPENDIX VI TEMPERATURE PROFILES IN THE CONVERTER WALL WITH VARIABLE THERMAL CONDUCTIVITY.. 267 APPENDIX VII HEAT TRANSFER MODEL PROGRAM 269 v i i i LIST OF TABLES Table 4.1 Physical Properties of Some Fluids 72 Table 4.1 Details of Copper Converter Practice in North America 80 Table 4.3 Characteristics of the Average 13 x 30 Converter and Three Other Plants 81 Table 4.4 Scaled-Down Characteristics for Different Models 89 Table 4.5 Range of Variables 90 Table 4.6 Conditions for the Industrial Trials 95 Table 6.1 Parameters in the Heat Transfer Model 170 Table 1.1 Characteristic Dimensions of Orifice and Comparison with Recommended Design Variables 241 Table 1.2 Values for Use in Equation (1.2) to Obtain Discharge Coefficients for 2-inch Plate Orifices 245 Table 1.3 Calibration of the Plate Orifice with a Diameter Ratio of 0.4 246 Table 1.4 Calibration of the Plate Orifice with a Diameter Ratio of 0.6 247 ix Table V.l Properties of Dry Air at Atmospheric Pressure 264 Table V.2 Heat Transfer Coefficient for Different Converter Diameters 265 Table V.3 Heat Losses by Convection and Radiation as Compared with Conductive Heat Flow Inside the Wall 266 X LIST OF FIGURES Figure 2.1 Bubbling Frequency versus Gas Flow Rate for Different Models. Number in Parenthesis Indicates Reference 27 Figure 2.2 Nozzle Pressure Fluctuation (from reference 77) (a) Discrete Bubble Formation (b) Bubble Coalescence (c) Orifice Jetting 37 Figure 2.3 Pressure Trace During Air Injection into Mercury. Note the Relationship between the Pressure and Stage of Bubble Growth (from reference 31) 40 Figure 2.4 Pressure Trace During Air Injection into a Nickel Converter with a New Refractory Lining (from reference 31) 41 Figure 2.5 Pressure Traces from the Slag Fuming Furnace (from reference 86) (a) Empty Furnace (b) Tuyere Submergence: 160 mm (c) Tuyere Submergence: 530 mm (d) Tuyere Submergence: 680 mm 43 Figure 2.6 Jet-Behaviour Diagram (from reference 31) . 45 Figure 2.7 Pipe-Shaped Accretion from a Tuyere of a Converter from Home Smelter . . . . 48 Figure 2.8 Air Injection Rate into a Copper Converter as a Function of Converter Volume (from reference 23) 55 Figure 4.1 Schematic of the Laboratory Apparatus .... 78 Figure 4.2 The Converter-Shaped Model (a) Frontal View (b) View Showing the Tuyere Assembly 83 Figure 4.3 The Tuyere Assembly 84 Figure 4.4 The Tuyere-Pressure Transducer System 87 xi Figure 4.5 The Tuyerescope 98 Figure 4.6 Apparatus to Measure Pressure Fluctuations in the Tuyeres of a Copper Converter 100 Figure 5.1 Bubbling Frequency versus Total Air Flow Rate in the Model with Five 16-mm Tuyeres .*.. 105 Figure 5.2 Bubbling Frequency versus Total Air Flow Rate In the Model with Five 12-mm Tuyeres .... 106 Figure 5.3 Bubbling Frequency versus Modified Tuyere Froude Number in the Model with Five Tuyeres 107 Figure 5.4 Pressure Traces in the Model as a Function of Gas Flow Rate. Five 16-mm Tuyeres, 40 pet. f i l l i n g . (a) 12,500 cm3/s (b) 33,700 cm3/s (c) 47,200 cm3/s Vertical Scale: 0.18 kPa/div Horizontal Scale:50 ms/div 109 Figure 5.5 Bubbling Frequency versus Total Air Flow Rate in the Model with Three 16-mm Tuyeres ... I l l Figure 5.6 Bubbling Frequency versus Modified Tuyere Froude Number in the Model with Three Tuyeres 112 Figure 5.7 Simultaneous Pressure Traces from Two Adjacent Tuyeres in the Model (a) Tuyeres are Interacting (b) Twenty Seconds Later, No Interaction is Observed 114 Figure 5.8 Pressure Traces in a Tuyere of the Model During Charging (a) Tuyere Submergence: 0 mm (b) Tuyere Submergence: 20 mm (c) Tuyere Submergence: 90 mm (d) Tuyere Submergence: 130 mm Horizontal Scale: 50 ms/div Vertical Scale: 0.18 kPa/div in Channel 1 Channel 2 Signal Filtered at 60 Hz 116 x i i Figure 5.9 High-Speed Film Photographs from the Tuyere Line of the Model (a) Left-Hand Side Tuyeres Covered by a Gas Envelope (b) Two Seconds Later, the Envelope Breaks Down 119 Figure 5.10 Model Under Non-Slopping Conditions (a) Tuyere Submergence: 130 mm Air Flow Rate: 3.7 l/s 40 pet. f i l l i n g (b) Pressure Trace from Central Tuyere Horizontal Scale: 0.5 s/div Vertical Scale: 0.18 kPa/div 122 Figure 5.11 Model Under Slopping Conditions (a) Tuyere Submergence: 130 mm Air Flow Rate: 20 l/s 40 pet. f i l l i n g (b) Pressure Trace from Central Tuyere Horizontal Scale: 0.5 s/div Vertical Scale: 0.18 kPa/div 123 Figure 5.12 C r i t i c a l Flow Data from Physical Model Experiments on Slopping-Behaviour Diagram . 126 Figure 5.13 Buoyancy Power Against Tuyere Submergence for Different Smelters. Solid Line is Extrapolation from Figure 5.12 Data-Points from reference 23 127 Figure 5.14 'Bubbling' Frequency from Different Copper and Nickel Converters versus Number of Charges in the Campaign 130 Figure 5.15 Tuyere Pipes in a Converter from Utah Smelter. (Courtesy of Dr.A.Weddick) (a) Pipes Protruding afeter Reline (b) Pipes after Third Charge .' 131 Figure 5.16 Pressure Traces during Charge 254 in a Copper Converter from Tacoma (a) Tuyere Submergence: 300 mm (b) Tuyere Submergence: 500 mm 133 x i i i Figure 5.17 Figure 5.18 Figure 5.19 Figure 5.20 Figure 5.21 Figure 5.22 Figure 5.23 Figure 5.24 Figure 6.1 Figure 6.2 Simultaneous Pressure Traces from Two Tuyeres in a Copper Converter. Tuyere No.6 in Channel 1 and Tuyere No.25 in Channel 2 (a) Both Tuyeres are Open (b) Seven Minutes Later, Tuyere No.6 is Blocked, Tuyere No.25 S t i l l Open (c) Three Minutes Later, both Tuyeres are Open Again. Vertical Scale: 4.8 kPa/div Horizontal Scale: 0.1 s/div 135 Dynamics of Accretion Formation in a Converter at Tacoma Smelter (a) Tuyere is Nearly Blocked (b) Accretion has Dislodged Spontaneously (c) -(f) Accretio Growth Resumes 137 Accretio Formation During First Slagmaking Blow in a Copper Converter at Home Smelter 139 Accretion Formation During Slagmaking Blow in a Converter at Utah Smelter 141 S.E.M. Photograph of the Accretion Sample from Slagmaking Blow in a Copper Converter at Home Smelter 143 Velocity Profiles Inside a Tuyere Pipe Showing the Effect of the Punching System 147 Longitudinal Sections of Tuyere Pipes from a Converter at Utah Smelter (a) End Tuyere (b) Central Tuyere 149 Metallographs of the Central Tuyere from a Converter at Utah Smelter (a) 5 mm from the Tuyere Tip (b) 18 mm from the Tuyere Tip (c) 25 mm from the Tuyere Tip (d) Back of the Tuyere. Virgin Pipe 150 (a) Schematic of the Peirce-Smith Converter (b) Schematic of the Hoboken Converter .. 156 Flow Chart of the Computer Program 167 xiv Figure 6.3 Average Error and Computing Cost Associated with the Number of Surface Elements into which the Converter Model is Subdivided 172 Figure 6.4 Temperature of a Central Tuyere in a Peirce-Smith Converter as a Function of Out-of-Stack Time for Different Values of Refractory Emissivity 174 Figure 6.5 Temperature Profiles along the Tuyere Line in a Peirce-Smith Converter for Different Out-of-Stack Times 176 Figure 6.6 Temperature Profiles along the Tuyere Line in an End Wall Mouth Converter for Different Out-of-Stack Times 177 Figure 6.7 Temperature Drop as a Function of Out-of-Stack Time for End and Central Tuyeres for both Central Mouth and End Wall Mouth Converters 178 Figure 6.8 Rate of Heat Losses and Total Heat Lost as a Function of Out-of-Stack Times for Central Mouth and End Wall Mouth Converters 180 Figure 6.9 Temperature Profiles inside the Refractory Wall at Different Out-of-Stack Times for an Element Facing the Mouth of a Peirce-Smith Converter 181 Figure 6.10 Surface Temperature as a Function of Out-of-Stack Time for Three Different Diameters of a Peirce-Smith Converter 183 Figure 6.11 Temperature Profiles along the Tuyere Line in a Peirce-Smith Converter for Two Converter Mouth Areas 185 Figure 6.12 Predicted Tuyere Line Temperature and Total Heat Losses in a Peirce-Smith Converter, Plotted against Out-of-Stack Time for Two Mouth Sizes 186 XV Figure 6.13 Tuyere Line Temperature and Total Heat Losses Plotted Against Out-of-Stack Time for a Peirce-Smith Converter with the Mouth Covered and Uncovered 188 Figure 6.14 Temperature Gradient Through the Refractory at the Inside Wall in a . Central-Mouth Converter Plotted Against Out-of-Stack Time 189 Figure 6.15 Temperature Gradient Through the Refractory at the Inside Wall in an End-Wall-Mouth Converter Plotted Against Out-of-Stack Time 190 Figure 6.16 Total Heat Losses from a Covered-Mouth Converter as a Function of Out-of-Stack Time for Three Different Temperatures of the Mouth Cover 192 Figure 6.17 Fuel-Oil Rate Consumption as a Function of Exit Gas Temperature for Uncovered and Covered-Mouth Converters 194 Figure 7.1 Idealized Tuyere Pressure Traces for Three Regimes of Gas Discharge from Horizontal, Closely Spaced Tuyeres 197 Figure 7.2 Summary of Injection Behaviour in the Full Slag Fuming Furnace, as Diagnosed from Dynamic Pressure Measurements in a Tuyere 201 Figure 7.3 Summary of Injection Behaviour in the Copper Converter with 254 Charges and 500 mm Tuyere Submergence, as Diagnosed from Dynamic Pressure Measurements in a Tuyere 202 Figure 7.4 Summary of Injection Behaviour in the Copper Converter with a New Refractory Lining, as Diagnosed from Dynamic Pressure Measurements in a Tuyere 204 Figure 7.5 Gas Channelling to the Surface of the Bath in the Copper Converter with 300 mm Tuyere Submergence, as Diagnosed from Dynamic Pressure Measurements in a Tuyere 208 Figure 1.1 Air Flow Rate versus Pressure Differential for the Plate Orifice with a Diameter ratio of 0.4 246 xvi Figure 1.2 Figure II.1 Figure II I . l Figure IV.1 Figure V.l Air Flow Rate versus Pressure Differential for the Plate Orifice with a Diameter Ratio of 0.6 247 Pressure Traces for Different Charges of a Peirce-Smith Copper Converter Vertical Scale 4.8 kPa/div (a) Charge 1 (b) Charge 3 (c) Charge 6 (d) Charge 12 (e) Old Converter 249 Geometric Arrangement to Calculate Radiation Shape Factors in the Heat Transfer Model 251 Geometric Configurations to Evaluate Thermal Conductances for the Different Nodes in the Model 255 Thermal Profile in the Cylindrical Shell of the Copper Converter 259 xvii TABLE OF NOMENCLATURE A c C C, CI d e e Fr Gr g G H h J K k M N Cross Sectional Area m' Specific Heat Thermal Conductance W K Added Mass Coefficient Drag Coefficient Diameter m Distance between Tuyeres m Associated Error in the Heat-Transfer Model as Defined by Equation (6.23) Blackbody Emissive Power W m Radiation Shape Factor from Surface ' i ' to Surface ' j ' Modified Froude Number Grashof Number Gravitational Acceleration m s" Irradiation or Radiation per Unit Time W m Incident on Unit Surface Area Tuyere Submergence m Heat Transfer Coefficient Radiosity Orifice Coefficient Thermal Conductivity Mass . kg Capacitance Group Pressure,gauge Pa J kg 1 K 1 -1 -2 -2 W m 2 K 1 -2 W m W m 1 K 1 p Pressure, absolute Pa Pr Prandtl Number Q Gas Flow Rate m s q Heat Transfer Rate W R Radius m Re Reynolds Number s Space m T Temperature K t Time s u Velocity m s~ 3 V Volume m Greek Symbols a Partition Factor of in Equation (7.1) g Bubbling Factor p Density kg m a Surface Tension N m~ u. Viscosity N s m x Reflectance E Emittance Kinetic Power per Unit Mass of Bath W kg-Buoyancy Power per Unit Mass of Bath W kg~ e g Stirring Power per Unit Mass of Bath W kg-e Wetting Angle degre xix Subscripts b Bubble c Chamber g Gas 1 Liquid M Model o At the Orifice P Prototype Surroundings XX ACKNOWLEDGEMENTS I would like to thank most sincerely my supervisor, Dr. Keith Brimacombe. His assistance, guidance and friendship made my stay at UBC one of the happiest periods in my lif e . Dr. John Grace was very kind lending us some of the equipment used in the experiments. I greatly appreciated the assistance of Dr. Neil Gray and Dr. Gregory Richards in some of the plant trials. Pat Wenman was an inexhaustible source of help and made life in the laboratory much easier for me. Thanks are due to Messrs. E. KLassen and H. Tump who built part of the equipment. My gratitude to those members of the Department of Metallurgy who helped me in many ways in my work. The generous support of Universidad Central de Venezuela-Proyecto UNESCOVEN 31, the Natural Sciences and Engineering Research Council of Canada, Noranda Mines, Kennecott Minerals, Union Carbide (Linde) and Inspiration Copper is gratefully acknowledged. I would also like to thank the co-operation of personnel from ASARCO, NORANDA, KENNECOTT and INSPIRATION in the performance of the industrial trials. Finally my gratitude to Camila, Alejandro and Pablo. Their help, understanding and patience constituted the strongest stimulus to initiate and complete this work. Indeed this thesis is also theirs. xx i El cobre ahi dormido. Son los cerros del Norte desolado. Desde arriba las cumbres del cobre, cicatrices huranas, mantos verdes, cupulas carcomidas por el impetu abrasador del tiempo, cerca de nosotros la mina: la mina es solo el hombre, no sale de la tierra el mineral, sale del pecho humano. Copper lies there resting. Amongst the desolated Northern heights. From above the copper hills, strange scars, green mantles, domes undermined by the ever embracing impetus of time, near us the mine: the mine is only man, minerals do not leave the earth, they leave the human heart. Es hora de dar el mineral a los tractores, a la fecundidad de la tierra futura, a la paz del sonido, a la herramienta a la maquina clara y a la vida. Es hore de dar la hurana mano abierta del cobre a todo ser humano. It is time to give the mineral to tractors, to the fertility of the future land, to the peace of sound, to tools, to the lucid machine and to life. It is time to give copper's shy and open hand to every human being. De los cerros abruptos, de la alture verde, saldra el cobre de Chile, la cosecha mas dura de mi pueblo, la corola incendiada, irradiando la vida y no la muerte, propagando la espiga y no la sangre, dando a todos los pueblos nuestro amor desenterrado, nuestra montafia verde que al contacto de la vida y el viento se transforma en corazon sangrante, en piedra roja. From the steep hills, from the green heights, copper will leave Chile, the hardest harvest of my people, the burning corolla, irradiating life denying death, giving life to the stem and not wounds, giving all peoples our unearthed love, our green mountain touched by life and wind transforming streams of blood, in red stone. PABLO NERUDA Translated by Dr. A. Urrello Dept. of Hispanic and Italian Studies The University of British Columbia 1 CHAPTER I INTRODUCTION: THE COPPER CONVERTING PROCESS The submerged injection of gas into molten baths has been practiced in both the ferrous and non-ferrous industries for a century. In steelmaking i t was f i r s t used as early as 1860 in the Bessemer bottom-blown acid process. Bottom-blown steelmaking is increasingly employed today due to the develop-ment of the concentric tuyere which allows injected oxygen to be shielded with another gas thus eliminating extremely high temperatures near the bottom refractories. Today in the non ferrous-industry processes that employ submerged injec-tion, such as the smelting of sulphide concentrates, the zinc slag fuming process, the treatment of t i n slags, and the pro-duction of copper and nickel are in operation or under study. The most important application of submerged gas injec-tion in the non-ferrous industry is the converting of copper mattes. The purpose of converting is to remove iron, sulphur and other impurities from matte, thereby producing liquid metallic copper in a crude blister form. This is achieved by oxidizing the molten matte with a i r . The converting reactions are exothermic and the process is autogeneous. 2 1.1 History of Copper Converting. Prior to the development of the converter, copper sulphide ores were smelted and processed into metallic copper by the use of the Welsh process for 'black copper1?" The Welsh process, from which reverberatory smelting sprung, was carried out in six separate operations involving the oxidation of some of the copper sulphide to copper oxide which then reacted with the remaining sulphides to produce copper, slag, and SC^. This operation was slow, tedious 2 3 and expensive ' . The primitive ancestor of the conversion of matte into copper through oxidizing the sulphur by means of a blast of air was the 'mabuki' method, practiced in Japan from early 2 times. Modern development had i t s inception when H. Bessemer pointed out that the removal of the carbon in pig iron could be accomplished by blowing air through the molten mass. The analogy of carbon in pig iron with sulphur in copper-iron sulphides suggested the idea of producing copper from matte in the Bessemer converter. Early experiments were unsuccessful because the liquid copper was cooled by the incoming a i r , to the extent that the liquid froze and choked the tuyeres. In 4 1879 J . Hollway made a series of experiments and pointed out that the heat generated by the oxidation of the iron and sulphur is sufficient to maintain the bath in a molten state 3 during operation and that the d i f f i c u l t i e s are lessened when the active mass is greater. He further pointed out that the SiC^ required to form a slag can either be derived from the siliceous lining of the converter or from siliceous material thrown into the converter during the progress of the operation. At the same time P. Manhes and P. David attacked 2 5 6 the problem at the Vedennes smelter ' ' . They soon discover-ed that the chief d i f f i c u l t y was the clogging of the tuyeres by the ch i l l i n g of the copper and hit on the expedient of placing the tuyeres horizontally, at such a height that the blast would not c h i l l the metallic copper as i t formed. After these t r i a l s the process was introduced on a larger scale , with two-3 ton Bessemer converters being used, in one of which the matte was concentrated up to about 607o copper, then trans-ferred and blown to blister copper in the second. By 1890 the advantages of the new method were generally recognized and upright type converters were in use or under construction in several places with the method of keeping the tuyeres free from copper by systematic punching being added to the operation. Nevertheless, soon i t was realized that there is a wide difference between the Bessemer process applied to iron and the same operation when employed for the treatment of copper mattes. In Bessemer steelmaking the bath is homogeneous during the entire process. On the contrary, during treatment 4 of copper mattes, as soon as the operation has proceeded so far that there is not sufficient sulphur l e f t three distinct 7 8 products are found ' : a slag floating on the surface, a mid-dle constantly decreasing zone of matte, and lowest of a l l , a constantly increasing layer of metallic copper. As a con-sequence, in the upright type of converter, i t frequently was found that the air was injected into slag, and the charge could not be blown to a f i n i s h , yielding copper. This d i f f i -culty soon led to the adoption by David and Manhes of a second form of converter, a horizontal cylindrical vessel, with lateral tuyeres, that could be turned around i t s central longitudinal axis. This cylindrical form of converter was f i r s t introduced at Livorno (Leghorn), Italy; in 1891 i t was 2 7 9 in operation at Jerez Lanteira, Spain ' ' . It was not until later that the horizontal converter was f i r s t employed in 2 North America at the Vivian plant at Sudbury, Ontario . The f i r s t converter of this type in the United States for treating 10 copper mattes was that of the Copper Queen Company Another problem was found during the treatment of copper mattes at this early age of copper converting. The oxidation of the iron formed large quantities of basic slags, which at once attacked the converter lining to satisfy their strong a f f i n i t y for s i l i c a . The necessity for frequent renewal of the li n i n g , typically after 12 blows^'^7, gave the driving 5 force for experiments with a lining which was not attacked chemically by the process. The use of an inactive lining in the form of magnesite brick, and the addition of SiC^ to slag the FeO formed, was carried out successfully by W. H. Peirce and E. A. C. Smith, in 1909, at the Baltimore Copper Smelting 11 12 and Rolling Co. ' . Although the basic character of the lining has nothing to do chemically with the process, the Peirce-Smith basic converter process was so eminently suc-cessful that i t replaced acid converting a l l over the world, and has remained an integral part of nearly a l l converting operations for three quarters of a century. 1.2 Current Converting Practice As has been described earlier copper converting is a batch process in which molten matte, predominantly a mixture of cuprous sulphide (CU2S) and ferrous sulphide (FeS), is artfully brewed with oxygen and s i l i c a to yield three end products: an iron silicate slag, sulphur dioxide, and molten copper. It takes place in two stages both of which involve blowing air into the liquid 8 13—15 matte ' : the slag-forming stage and the blister-forming or copper-making stage. At the start of the blowing the phases inside the convert-er are a bath of molten matte through which air is being blown and 6 upon which is floating a solid flux, mainly silica. The temperature is between 1100 and 1300 C. The main reaction occurring during the slag-form stage can be represented as follows: F e S( l ) + 7 °2(g) = F e 0( l ) + S 0 2(g) The matte is added to the converter in two or more steps, each step being followed by oxidation of much of the FeS from the charge. The resulting slag, liquid fayalite saturated with magnetite, is poured from the converter after each oxidation step and a new matte addition is made. Toward the end of the slag-forming stage the amount of copper in the converter has gradually increased so that there is sufficient for a final copper-making blow. At this point the FeS content of the matte is about 17o, and the formation of magnetite in the converter as indicated by the reaction: 3 FeQ0» / ^ + FeS,., = 10 FeO,.,, + S0O , , (1.2) 3 4(s) (l) ( l ; 2(g) becomes particularly severe. Although some magnetite is desirable to protect the refractories, an excessive amount leads to viscous slags and to the entrainment of large quantities of matte. A common practice to minimize magnetite formation is to maintain as high a concentration of FeS in 7 the matte as possible by only partially oxidizing the matte after each matte addition. This practice ensures that a considerable portion of the solid magnetite w i l l be reduced. During the blister-forming stage, metallic copper is formed in the converter and the remaining sulphur is oxidized to SC>2 by a combination of the reactions: 3 Cu2S( 1 ) + ? 02 ( g ) = Cu20( s ) + S02 ( g ) ( 1 < 3 ) CunSr i. + 2 Cuo0, , = 6 Cu,,. + S0o, . (1.4) 2(1) 2 ( s ) (1) 2(g) C u2S( l ) + °2(g) = 2 C u( l ) + S 02(g) ( 1'5 ) The process is carried out until the f i r s t trace of Cu20 appears. Great care is taken to ensure that the copper is not overoxidized, because there is no longer any Cu2S to reduce the Cu20 back to copper by reaction (1.4). The fin a l product is molten blister copper (98.5 - 99.57, Cu) containing about 0.057o S, 0.57> 0, and minor amounts of other impurities. Today the converting of copper mattes is almost univer-sally carried out in Peirce-Smith converters. In recent years, however, three novel types of converter have been developed : 16 the Hoboken or syphon type converter , the top-blown con-8 verter ' , and the Inspiration converter 1113 The Peirce-Smith converter ' is a horizontal cylinder, typically 4 m in diameter and 9 m long, constructed of a steel shell lined with burned magnesite or chrome-magnesite brick. Molten matte is charged to the converter through a large rectangular opening or 'mouth'. Air at low pressure (104 kPag, 8-12 Nm /s) is side blown into the converter through a single line of 4-6 cm diameter tuyeres, distributed along the length of the vessel. The tuyeres consist of steel pipes imbedded in the refractory and they are connected to a bustle pipe running the length of the converter. There are forty to f i f t y tuyeres per converter, depending upon their diameter and the size of the reactor. The converter is provided with a rotating mechanism which permits i t to be correctly positioned for charging, blowing, and pouring. The large volumes of hot, S O 2 - bearing gases produced during converting are collected by means of a loose-fitting hood above the converter. Recent concern over air pollution has led to the develop-ment of two types of converter, the Hoboken or syphon-type converter^, and the Inspiration converter^. Both reactors represent a method to improve the collection of the converter gases and to prevent their, dilution with a i r . In the Hoboken 9 converter the gases are drawn off through a flue connected axially to the converter, via a 'goose-neck' or syphon connection. In the Inspiration converter the gases are ex-tracted from the vessel via an 'off-gas mouth' in the mantle of the reactor. Both arrangements, though more complex than the Peirce-Smith configuration, have some useful features. The converters can run with a zero or slightly negative pressure at the charging mouth, preventing SC^ from escaping and minimizing dilution of the converter gases by i n f i l t r a t -ed a i r . In addition, charging can be carried out during the blow, reducing converting downtime and producing a more constant stream of gases. 1.3 Problems in Copper Converting In spite of i t s widespread use, gas injection in the Peirce-Smith converter (or any other submerged-injection-type of reactor) is not a technique free of operational d i f f i c u l t i e s . Since i t s inception the process has experienced several problems such as accretion formation, tuyeres block-age, refractory wear, tuyere erosion, splashing and slopping. During converting, a build up of solidified material or accretion takes place at the tuyere o r i f i c e . As a conse-quence the flow of air through the tuyere gradually becomes 10 blocked. Periodic clearing or 'punching' of the tuyere by forcing a steel bar through the tuyere, either manually or by a pneumatic/mechanical system, has therefore become a routine practice in every converting operation. Manual punch-ing has largely given way to mechanical/pneumatic punching devices. Two types of mechanical punchers most commonly are 21 used : the Kennecott (4B5) puncher, which is attached to each tuyere and the Gaspe puncher, which is mounted separate-ly from the converter and moves parallel to i t on r a i l s . Other innovations in tuyere punching include the development of silencers to reduce the considerable noise which accompanies 22 punching. A review of developments in tuyere punching and a tabulation of the type of punching systems in use in smelt-23 ers around the world have been published. The periodic clearing of the tuyeres, the high tempera-ture of operation, and the turbulent conditions of the bath constitute harsh conditions for the tuyeres and the adjacent refractory brick. Severe refractory erosion at the tuyere line usually appears in the form of a trench running from one tuyere to the next and is the limiting factor in the campaign l i f e of a converter. The lining l i f e today normally does not exceed 100 to 200 days or about 2.25 to 4.5 kg refractory per 13 tonne copper produced . Because of refractory wear and tuyere erosion, a converter is typically down one month in four such 11 that about 257o of the nominal converter capacity is lost. The energy of the injected air is not dissipated entire-ly in mixing the bath. Splashing occurs which causes particles of liquid to be carried out with the gas above the surface of the bath. This results in the build up of accretions at the converter mouth, and dust losses in the flue gas. A large amount of maintenance work to remove accretions resulting from splashing and to replace refractories i s required amount-13 ing to around 30% of the converter operating cost . Slopping also takes place in which a standing wave of the molten bath produces massive ejections of liquid through the mouth of the converter. The severity of splashing and slopping represents an ultimate limitation of the air flow rate through the 3 3 tuyeres. A limiting value of 0.14 Nm /s per m of converter 23 volume has been suggested Over the years numerous studies concerning the chemical reactions in copper converting have been conducted. In con-trast, remarkably l i t t l e is understood about the influence of the design and operation of the reactor on the numerous prob-lems underlined above, which have hampered the operation of the converter. From a general perspective, progress in design of the reactor or improvement in i t s operation w i l l not be achieved without process engineering knowledge. The present 12 thesis represents an effort to investigate some process engineering aspects of converter operation, such as: gas injection into the bath, accretion growth at the tuyere t i p , slopping of the bath and heat losses from the interior of the converter during out-of-stack periods. The study of these subjects has involved physical model laboratory experiments, plant measurements, and the formulation of a mathematical model. The following pages describe the work, its results and recommendations to extend refractory l i f e and to increase converter productivity. 13 CHAPTER II LITERATURE REVIEW: STUDIES IN GAS INJECTION The basic converting operation has remained esentially the same since i t s implementation. Fluid dynamics and heat flow of the process have not been studied in d e t a i l , and the design of reactors as well as the converting practice have been based mainly on operating experience. Such experience varies widely from plant to plant, as can be observed from 23 2^ \ 25 data reported during the last quarter century » ' . The effect of converting practice on bath movement, splashing } accretion formation at the tuyeres t i p , and the l i f e of tuyeres and refractory is not clearly understood. Operational improvements and the development of effective process control have been inhibited through the lack of such understanding. L i t t l e work has been done on the injection process in copper converters. Studies related to the subject have been performed under experimental conditions quite different from those prevailing during industrial converting. The relation-ship between the gas dispersion process and the bath move-ment and splashing, and the effect of adjacent tuyeres on bubble coalescence in the tuyere region have not been reported. 14 At present there are two main approaches used to de-scribe the process of gas injection into liquids. One is based on the similarity between the behaviour of a jet and its time-averaged shape; the other is concerned with the growth, separation and disintegration of the gas f i l l e d en-velopes that form at the tuyere. The links between them and the influence of the instantaneous conditions on the general behaviour of the process are not clear. 2.1 Studies on Side-Blown Injection When one flui d is discharged into another, a tangential unstable separation surface is created between the injected f l u i d and the surrounding medium. The instability of this surface leads to the entrainment of the surrounding medium and causes the jet to expand, forming a characteristic jet cone. 26 In 1969 Themelis et a l . , on the basis of mass and momentum balances, derived a dimensionless equation de-scribing the trajectory of a gas jet horizontally injected into a liquid, which was found to be a function of the modified Froude number for the gas-liquid system. Using a photographic technique the shape and trajectory of the jet 15 were measured for an air-water system. It was concluded that the cone angle is a function of the jet f l u i d properties, and that the increase of the jet diameter is proportional to the horizontal distance from the o r i f i c e . Agreement was obtained between the dimensionless equation and experimental results for the air-water system, with a liquid-gas density ratio of nearly nine hundred. Therefore i t was suggested that the jet trajectory equation should also be applicable to the case of an air jet injected into liquid matte or copper. 27 Later Engh and Bertheussen modified the model of Themelis et a l . by assuming the diameter of the cone to be proportional to the distance along the jet axis rather than the horizontal distance from the o r i f i c e . The results made clear that both models provide a satisfactory means of predicting the trajectory of air jets into water. 28 29 Spesivtsev et a l . ' published some data from tests made on both cold and hot models of converters. Their results showed that the penetration of the gas into the liquid is limited by the properties of the li q u i d , and that the inter-action between both fluids has a pulsating character. An equation was proposed describing the horizontal penetration of the jet as a function of the Froude number and the gas-liquid density ratio. It was concluded that to obtain a 16 longer service l i f e for the converter lining and stable blow-ing conditions the bath level should be kept constant. The existence of a certain permissible diameter for the converter was suggested. 3 In addition, experimental work by Oryall and Brimacombe 31 and by Hoefele and Brimacombe has called into question the validity of some of the assumptions upon which both models are based, and on the applicability of the models to the case of air injected into liquid-metal systems. The experimental results of Oryall and Brimacombe, obtained by horizontally injecting an inert gas into mercury, suggest that: a) the jet expands rapidly upon discharge from the nozzle, with an expansion angle of about 155 degrees, instead of 20 degrees as was found by Themelis et a l . for the air-water system. b) the jet expansion appears to be confined to the horizontal • region of i t s trajectory, the vertical sections do not show appreciable expansion. The general shape of the jet is more akin to a vertical column than to a cone. c) while the central streamline only penetrates 5 mm into the f l u i d , there is considerable backward penetration. The air penetrates a considerable distance behind the nozzle, and the jet looks as i f i t has been injected vertically upwards 17 rather than horizontally. 31 Hoefele and Brimacombe working in the laboratory, studied the injection of different gases from a submerged, horizontal tuyere, into water, a zinc-chloride solution, and a mercury bath. Working with actual industrial equipment, tests were performed involving pressure measurements in the tuyeres of a nickel converter under normal low-pressure blow-ing operation, and under higher pressure conditions. The re-sults of their studies can be summarized as follows: a) two regimes of flow can be distinguished. At normal low flow rates a bubbling regime predominates. In the indus-t r i a l tests the bubbling frequency was found to be about 10 to 12 s-"*". About half of the bubbling cycle is occupied by bubble growth, while for the other half, liquid sur-rounds the tuyere t i p . At higher flow rates a steady jet-ting regime predominates, in which gas flows from the tuyere continuously. Pressure changes in the tuyere have been correlated to the individual flow regimes. b) the flow regimes and the forward penetration of the gas depend on both the modified Froude number of the system and the gas-liquid density ratio. The latter result agrees with the findings of Spesivtsev et a l . c) a jet behaviour diagram was presented il l u s t r a t i n g the regimes of bubbling and jetting as a function of the 18 modified Froude number and the ratio of flu i d densities. d) the bubbling regime has two major disadvantages: the bubbles rise almost vertically from the tuyere tip and impinge on the back wall, contributing to refractory erosion, also between the formation of successive bubbles bath washes over the tuyere t i p , accelerating accretion formation and the need for punching. To avoid these problems Hoefele and Brimacombe suggested that the pres-sure be increased sufficiently to achieve choked flow 32 and steady jetting rather than bubbling conditions The concept of high-pressure air injection and punch-less converter operation was tested in-plant by Brimacombe 33 34 et a l . ' . Four standard tuyeres near the end wall of a converter were replaced by pipes with an I.D. of 19 mm, con-nected to a high pressure l i n e . Air at 60 psig was injected through the four high-pressure tuyeres at the same time as 15 psig air was blown through the remainder of the tuyeres in an otherwise normal converter campaign. The high-pressure tuyeres operated through eighty-eight charges over a period eighty-nine days without the need for punching. It was found through the test campaign that accretion formation around th periphery of the tuyere could be controlled by oxygen enrich ment. 19 Fruehan and Martonik , injecting air into water and glycerol-water solutions, found that the jets do not expand at a constant angle. The shape of the jet was shown to be dependent on the physical properties of the l i q u i d . It was also found that the horizontally injected air does not pen-etrate into the liquid as far as previously believed on the basis of model calculations. The experimental results were consistent with the interpretation that the gas jet breaks up into a swarm of small bubbles just above the tuyere t i p . The applicability of the models developed by Themelis et a l . , and Engh and Bertheussen, have also been called into question from the mathematical point of view. It was demon-strated that both models break down when applied to high liquid-gas density systems, or in other words, when the radius of curvature of the jet axis becomes equal to the radius of the jet. A general approach to model the flow f i e l d during the injection of gas into liquid has been outlined by 37 Mc.Kelliget et a l . 20 2.2 Bubble Formation During Submerged Injection The fact that air i n i t i a l l y discharges into the converter bath in the form of discrete bubbles is of fundamental importance to understanding converter operation. Most of the gas injection steelmaking processes work under jetting conditions. On the contrary, under normal operation, the copper converting process 31 is not a jetting system, but a bubbling system . Thus any successful comprehension of the process requires an understand-ing of the bubble formation mechanism during converting.Direct observations are obviously d i f f i c u l t due to the opacity of the melts, the elevated temperatures involved, and the highly turbulent characteristics of the bath. As a consequence, much data have been accumulated on bubble formation in aqueous or low-melting point metal systems. In almost a l l the published works the gas has been injected into the liquid bath through only one tuyere. Hence direct extrapolation to a metallurgical, multiple-tuyere process can be misleading and yield erroneous conclusions. When a gas is injected into a flu i d of greater density, three different flow regimes may be identified as a function of gas flow r a t e " ^-^ . At very low gas flow rates, of the order of 1 cm /s, a single bubble process exists, the bubbling 21 frequency is proportional to the gas flow rate, and the bubble size is almost constant. For higher gas flow rates, up to about 500 cm /s, the gas emerges as series of envel-opes or bubbles, characterized by liquid bridging of the o r i f i c e , the bubble volume increases with gas flow rate, while the frequency of formation remains almost constant. At very high gas flow rates a jetting regime is achieved, in which a continuous gas channel is formed through the liquid. During bubble format! on, the pressure within the bubble decreases due to upward displacement of i t s centroid, so that the gas flow rate may vary with time. If there is a high pres-sure drop between the gas reservoir and the o r i f i c e , the pres-sure fluctuation due to forming bubbles is much smaller than the pressure drop between the gas reservoir and the o r i f i c e , and in this case the gas flow rate can be considered as constant. If the volume of the reservoir, or chamber volume, is very large compared with the volume of the bubbles being formed, the pressure in the chamber wil l not significantly change. This corresponds to the other limiting case of bubble formation under constant pressure conditions. A general model applicable to the formation of bubbles under a l l kinds of conditions is not available. The many models proposed to describe bubble formation in liquids have been reviewed by C l i f t et al.^~* and Kumar and Kuloor^. A l l 22 are mechanistic and depend on some form of force balance for predicting one or more stages in the bubble growth. In the 'one-stage' models, bubbles originating at the ori f i c e are assumed to grow smoothly until detachment, which occurs when the rear of the bubble passes the o r i f i c e . In the 'multiple-stage' models i t is assumed that there is a basic change in the growth mechanism at one or more points in the process. From the metallurgical point of view, the more relevant bubbling processes are those under constant flow and constant bubbling frequency conditions. As the majority of the liquid melts into which a gas is injected exhibit small viscosities (except the treatment of metallurgical slags) the viscous forces are negligible compared with buoyancy and i n e r t i a l forces. 2.2.1 Bubble Formation in Low Density, Inviscid Liquids Many models have been proposed^-"'"' to describe bubble growth from a slow steady gas stream injected into a low density, inviscid liquid through only one tuyere or nozzle under stagnant bath and constant flow-rate conditions. The proposed models result in a relationship between bubble volume and gas flow rate of the form: 23 V b . . Q 6 / 5 g - 3 (2.1) where the bubbling factor 3 depends on the specific conditions of the gas injection process. a spherical bubble is assumed to be formed at a point source where the gas is supplied. The rising velocity is determined by a balance between the buoyancy force and the acceleration of the fluid around the bubble, which is carried along with i t . An 'added mass' or'virtual mass' contribution has to be included because acceleration of the bubble requires accel-eration of the li q u i d . The mass of the bubble is negligible compared with the mass of the liquid swept along with i t . As the flow rate is assumed constant, the final volume of the bubble at detachment can be expressed as: In the models developed by Davidson and coworkers 47-49 ( M - Mb) ( 2 . 2 ) ( 2 . 3 ) For a sphere moving parallel to a wall, the added mass coefficient has a value of 11/16; then the bubbling factor in 24 Equation (2.1) is 1.378, a solution given by Davidson and S c h u l e r ^ . For a nozzle protruding into a f l u i d Ca = ^, then the e coefficient becomes 1.13 , a result obtained by 49 Davidson and Harrison . An empirical expression similar to Equation ( 2 . 1 ) , with a bubbling factor of 1.725, had been previously developed by van Krevelen and Hoftijzer"*^ assuming the gas density to be negligible relative to the liquid density. 51 Kumar and Kuloor developed a model in which the bubble formation process was assumed to take place in two stages, the expansion stage and the detachment stage. During the expansion stage there is an in e r t i a l force due to the expansion rate. As the bubble grows the drag due to expansion decreases whereas the buoyancy force increases continuously. This stage termi-nates when the buoyancy force equals the downward ine r t i a l force. During the detachment stage the buoyancy force is high-er than the inertial force. The detachment takes place when the bubble base covers a distance equal to the radius of the bubble from the f i r s t stage. After some simplifications, and assuming a spherical bubble forming at a perforation in a f l a t plate, Kumar and Kuloor's model predicts a bubbling factor of 0.976. 53-55 Wraith and coworkers performed extensive observa-tions of submerged nozzle injection. A dispersion process was 25 observed, consisting of the successive expansion, movement and intermittent severance of bubbles from the source. At a higher level in the liquid the bubbles disintegrated, forming a column of foam rising to the surface. Visual observations when the gas source lies on a horizontal plate showed the growth of a hemispherical envelope pressed to the plate during an early stage of bubble expansion. The hemisphere evolves to-ward a spheroidal shape as the condition of tangential contact is approached. At the end of the expansion stage, the bubble formation process exhibits a 6 value of 1.09, thus the bubble volume is smaller than the volume predicted by the models of Davidson and coworkers. This result was verified for low ai r -injection rates into water. Following the tangential contact, the base of the bubble remains linked to the orifice by a gas-f i l l e d stem. The bubble volume grows continuously while i t moves upwards. At detachment the bubbling factor is 1.54, a value larger than that predicted by Davidson and coworkers. An isothermal study of submerged air lancing in water was also performed by Wraith"^. Coalescence was observed be-tween successive bubbles. When the lance immersion depth was greater than 2.5 times the lance radius, the bubble formation process was adequately described by Equation (2.1) and a B value of 1.138. For immersion depth lower than the above value, the bubble formation mechanism was different. Gas then chan-26 nelled directly to the surface through a series of incompletely formed envelopes. Under these conditions the relationship between bubble volume and gas flow rate is characterized by a bubbling factor of 1.453. 31 Hoefele and Brimacombe , working on a one tuyere model of a copper or nickel converter, indicated that the bubble-formation process can be adequately described by Equation (2.1) with bubbling factor values of 1.57 and 0.88 for mercury and aqueous baths respectively. However, when applied to a new, recently relined industrial converter, Equation (2.1) predicts a bubbling frequency 2 to 3 times lower than the measured value. Bubble volumes under high temperature conditions were also calculated. A comparison between the predictions of the above models 2 is shown in Figure 2.1, for a gas flow rates between 10 and 10 cm /s. The discrepancies are not so great, considering the various experimental conditions involved, and the different assumptions made to develop the models. When the ratio of gas momentum to buoyancy force acting on the system exceeds a c r i t i c a l value, the bubble formation process is significantly affected. Wraith and Chalkley"^ performed model experiments involving energetic gas injection. Gas flow rate (l/s) e 2.1 Bubbling Frequency versus Gas Flow Rate for Different Models. Number in Parenthesis Indicates Reference. 28 It was found that the effect of gas momentum i s to elongate the gas f i l l e d envelopes, producing continuous coalescence between successive bubbles. A jet like bubble-stem array was observed, which ultimately breaks down into foam due to basal intrusion. For submerged vertical injection, i f the in e r t i a l force is important compared with the buoyancy force, Equation (2.2) has to be transformed to: The results obtained by Nilmani and Robertson after the integration of Equation (2.4) were compared with the values from Davidson and Schuler's model for the different gas-liquid combinations. Good agreement between both models was observed when the gas-liquid density ratio is small. How-ever, for an air water system the predictions between the models differed significantly. 2.2.2 Bubble Formation in Liquid Metals (2.4) 57 As was mentioned, the previous models have been develop-ed to describe the bubble-formation process from a gas stream injected into a- water-like liquid. The predictions of the dif-29 ferent models are in reasonable agreement with experimental measurements. Nevertheless, the validation of such models for the case of gas injection into liquid metals is not conclusive. There are few studies involving bubble measure-ments in liquid metals, and the comparison between them is d i f f i c u l t due to the many different conditions used in the experiments. 5 8 Andreini et a l . discharged argon at low gas flow rates into copper, lead, and ti n baths. It was concluded that the bubble size generated for a particular orifice diameter was dependent upon the magnitudes of the orifice Froude and Weber numbers; therefore predictions of bubble size based on empirical regressions cannot be extrapolated from aqueous systems. As in aqueous systems, i t was found that the frequency of bubble formation increases with flow rate to some limiting value, above which a constant bubbling frequency occurs, confirming the weak dependence of bubbling frequency on gas flow rate. Similar results have been report-ed by Berdnikov et a l . ^ . The wetting characteristics of the liquid represents the principal difference between liquid metals and aqueous 43 44 59-61 systems regarding bubble formation ' ' . For a gas-bubble formation in aqueous or organic systems, when the 30 liquid wets the nozzle, the bubble forms at the tip of the o r i f i c e , that is at the internal nozzle diameter. In contrast, for non-wetting systems the bubble tends to form at the outer nozzle circumference. Mori and coworkers^-^ examined the nitrogen-mercury, nitrogen-silver, and argon-hydrogen- liquid iron systems. It was found that for intermediate flow rates, and small nozzle diameters, the bubble volume is well described by the equation 72 of Davidson and Amick db = 0.54 [Q d0-5]°-2 89 ( 2.6 ) or, in terms of the volume of the bubble: V. = 0.08 Q ° -8 7d0-4 4 (2.7) D O where d is the outer nozzle diameter, rather than the inner o ' diameter, as in the case of bubble formation from wetted nozzles in water and organic liquids. Although i t was found that the bubble volume is propor-tional to d^'^ for small nozzle diameters, there appeared to be no discernible effect of dQ for larger o r i f i c e s . The ap-parent transition occurred for nozzle diameters between 0.6 and 1.3 cm in the constant frequency regime. 31 It was also found^ that a gradual change from bubbling to jetting takes place in a transitional gas flow rate. The gas flow velocity at which the transition occurs was found to be independent of the orifice diameter, i t s value being very close to the sonic velocity. It is important to mention that the definition of jetting regime proposed by Mori and cowork-ers is somewhat different from the jetting regime described 31 by Hoefele and Brimacombe The weak dependence of bubbling frequency on gas flow rate was also pointed out by Irons and Guthrie ' . They proposed an equation to correlate their results and those of Sano and M o r i ^ and Andreini et a l . " ^ b 2 pi 8 c U P e C 3 6 g J 1 The effect of the chamber volume can be conveniently represented in terms of a dimensionless capacitance group, which for non-wetting systems is defined as: 4 p, g sine V Nc - ; d d. pKc ( 2-9 ) o i b the capacitance group has a pronounced effect on bubble volume, particularly under low gas flow rate conditions. 32 Equation (2.8) represents a combination of three separate experimental aspects governing bubbling behaviour in liquid metal systems. At low flow rates surface tension phenomena and chamber volume effects are dominant, i.e. the f i r s t two terms. At higher flow rates the i n e r t i a l , or third term,corre-sponding to the constant frequency regime, plays the dominant role in determining bubble size. 73 Sahai and Guthrie developed a mathematical model to predict bubble shapes at their moment of release in water and molten iron. It was found that argon bubbles forming in molten iron are about three times larger than air bubbles formed in water for the same gas flow rates and orifice diameters. 74 A mathematical model was developed to describe the dynamics of bubble formation at the tuyeres of a copper converter. The effect of heat transfer to the bubble, chemical reaction between the bubble and the bath, and coflowing bath circulation were studied. Temperature, volume and rise veloc-ity for the bubble were predicted as a function of time. The calculated bubble volumes showed discrepancies when compared with previous non-reactive, stagnant and isothermal bath bubble formation models. It was found that the heat transfer and bath circulation have a large influence on the bubble formation process. Heat transfer acts to decrease bubble frequency, while bath circulation has the opposite effect. 33 2.3 Pressure Fluctuations at the Tuyere The use of nozzle pressure to characterize submerged injection regimes is now a f a i r l y well stablished technique. A pressure trace technique has been used by Wraith and co-workers 75-76 ^ MQrj[ a n c j coworkers^^-^2, Hoefele and Brimacombe^ ''", 78 79 80 Richards and Brimacombe , Farias and Robertson , Gray et a l . , 83 and McNallan and King The theoretical basis for the link between tuyere pres-sure and bubble formation has been set out by Kupferberg and 81 82 Jameson and Pinczewski for vertical injection. The pres-sure inside a bubble growing in an i n f i n i t e , incompressible liquid is given by: P = P b rh [D d R 3,dRv*l 2c 4 u dR 1 * * A dP~+ 7 ^ J+R - + H T d T + 7pg uoc o s 6 ( 2'1 0 ) Where the terms on the right-hand side represent, re-spectively, the pressure head, liquid i n e r t i a , surface tension, viscous contribution and gas momentum. The bubble pressure can 81 be related to the chamber (tuyere system) pressure by P„ = P, + P K u2 (2.11) c b g o u , i i' 34 where K is the orifice coefficient. At the commencement of 2 2 bubble growth, R is small, and d R/dt and dR/dt are large, 2 79 (about 300-1000 m/s and 2-5 m/s, respectively ), so that the pressure inside the bubble and the tuyere is also very large from Equations (2.10) and (2.11). However, as bubble 2 2 growth continues, R increases, and d R/dt and dR/dt decrease resulting in a steady drop in pressure which takes longer than the rapid pressure r i s e . When the bubble becomes detached from the nozzle, the gas supply to i t is severed, a new bubble grows and the cycle of change in is repeated. A regular cyclic variation in bubble pressure results i f there is regular bubbling. Mori and coworkers^'^2 determined the size of argon bubbles in mercury, liquid silver and molten iron by measur-ing the frequency of bubble formation. For very low frequencies the measurements were made by observing the bubbles arriving at the liquid surface. At higher frequencies the pressure pulses in the gas-supply train were detected with a crystal earphone. The output from the earphone was fed to a synchro-scope. The bubble frequency was determined from the distance between two adjacent peaks. No studies were pursued on the shape and amplitude of the pulses. 79 Farias and Robertson measured the dynamic pressure in nozzles in N?-H9-water systems. The pressures were simultane-35 ously recorded in the bubble, in the liquid and in the supply l i n e . At low gas flow rates a very strong pulse associated with i n i t i a l growth was followed by a damped oscillation of pressure and an oscillating rate of growth during the early stages of bubble formation. For high flow rates, giving nominal Mach numbers up to 4, although the nozzle was nominal-ly choked the flow rate instantaneously decreased at the start of bubble growth due to the high inertial resistance to flow and the corresponding high pressure at the nozzle exit. It was found that the best transducer location is in the supply line i t s e l f , even i f away from the tuyere tip and that a general purpose transducer with a small dead volume is quite adequate. Wraith and coworkers^"*'^ have performed detailed studies of the shape of the tuyere pressure pulses during submerged gas injection in water and mercury. At relatively low gas flow rates (26 - 1,270 cm /s) three principal bubbling processes were observed, which in order of increasing injection rate are labelled triplet formation, bynary coa-lescence and stem coalescence?"* For high velocity gas injection (up to 0.03 m /s) "dif-ferent forms of bubble interaction may be distinguished^. Bubbles forming in a sequence are described as discrete i f a new bubble starts to grow only after the cut-off stage of the 36 previous bubble, as shown in Figure 2.2(a). The tuyere pres-sure is at i t s minimum at 'a' when the bubble starts to grow following the cut-off of a preceeding gas pocket from the o r i f i c e . Immediately the pressure rises sharply and almost linearly. With increasing bubble expansion the pressure f a l l s to ' j ' which corresponds to bubble detachment. Subsequent formation of a gas neck linking the detached rising bubble to the orifice gives rise to a secondary nozzle pressure pulse 'j-m'. The point 'm' represents the eventual cut-off of the bubble from the o r i f i c e . Coalescence occurs when a new bubble starts to grow at the orifice while the previous bubble is between the stages of detachment and cut-off, as shown in Figure 2.2(b). In the jetting regime, a subsequent bubble begins to form at the orifice before the detachment stage of an on-going bubble formation, as shown in Figure 2.2(c). Fol-lowing the gas pocket 'a-b', a submerged jet develops at the o r i f i c e . The pressure signals in the jetting regime lack the sharp peaks characteristic of bubble formation. This is a clear indication that the gas flows through the orifice as a jet column and not as individual bubbles. In general the pressure fluctuations in high-velocity gas injection are composed of the basic signals of bubbling, coalescence and jetting. Mixed dispersions can be observed up to near-sonic injection velocities with bubbling on the decline in favour of jetting with increasing velocity. T e 2.2 Nozzle Pressure Fluctuation (from reference 77) (a) Discrete Bubble Formation (b) Bubble Coalescence 39 The pressure trace techniques was also employed by 31 Hoefele and Brimacombe in the laboratory and in plant. The laboratory work involved the submerged injection of different gases into water, a zinc-chloride solution and a mercury bath. High speed cinematography and pressure measurements in the tuyere were carried out to study the gas discharge into the l i q u i d . The observations and pressure trace for the injection of air into mercury under bubbling conditions are shown in Figure 2.3. As can be seen a smooth decrease in pressure at the tip corresponds to the growth of a bubble while the mini-mum pressure occurs when the bubble necks off and rises from the tuyere. The minimum is followed by a sharp rise in pres-sure as the bath flows in around the nozzle to replace the rising gas bubble. The drop in pressure results from the i n i t i a t i o n and growth of the next bubble. On the other hand, the pressure oscillations under steady jet conditions were irregular with a smaller amplitude and could not be correlated with gas dynamics at the tuyere t i p . Hoefele and Brimacombe also investigated injection dynamics in an operating nickel converter, after reline, by measuring pressure fluctuations in several tuyeres with piezoelectric transducers. The pres-sure traces recorded during blowing were characterized by di s t i n c t , regular pulses separated by intervals of relatively constant, low pressure as can be observed in Figure 2.4^"^. Time (s ) Figure 2.3 Pressure Trace During Air Injection into Mercury. Note the Relationship between the Pressure and Stage of Bubble Growth, (from reference 31). o Nickel converter ( I 5 charge) 42 More recently Richards and Brimacombe measured the dynamic tuyere pressure in a slag zinc fuming furnace. A sequence of pressure traces obtained as the furnace was being f i l l e d is shown in Figure 2.5. In the empty furnace, Figure 2.5(a), the pressure trace is constant, at about 8 kPag. After 15 tonnes of liquid slag have been charged, Figure 2.5(b), which corresponds to a tuyere submergence of about 160 mm, the constant pressure signal is disturbed by pulses of short duration. With 39 tonnes charged (tuyere submergence of 530 mm), Figure 2.5(c), the pressure trace is characterized by pulses of longer duration which are not separated by lower pressure intervals. When the furnace is f u l l y charged such that the tuyere submergence is about 680 mm, the pressure pulses are slightly more regular with a frequency of 5 to 6 s-^. Most pulses are characterized by a rapid rise in pressure followed by a slower decline. The average back pressure in the tuyere with the furnace f u l l is about 33 kPag. Tests were performed with and without coal feeding to the tuyere; i t was found that the pulse frequency was unaffected but the average tuyere pressure increased by about 4 kPa with coal feeding. Presuma-bly this increase results from the greater pressure drop asso-ciated with blowing the air-coal mixture over the length of the tuyere. 43 (0 (d) Figure 2.5 Pressure Traces from the Slag Fuming Furnace (from Reference 86) (a) Empty Furnace (b) Tuyere Submergence: 160 mm (c) Tuyere Submergence: 530 mm (d) Tuyere Submergence: 680 mm Vertical Scale: 10 kPa/div Horizontal Scale: 200 ms/div 44 2.4 The Bubbling-Jetting Transition The criterion to be used for defining the transition between bubbling and steady jetting regimes has been a matter of some controversy amongst the researchers working in this area. The different definitions depend on the experimental technique employed, the gas-liquid system under study, the orientation of the nozzle and fi n a l l y on the objectives of the study under consideration. 31 Hoefele and Brimacombe studied the behaviour of gas discharging into a liquid in the laboratory and in plant. Two regimes of flow, bubbling and jetting, were delineated on a jetting behaviour diagram, as observed in Figure 2.6, based on the modified Froude number of the jet and the ratio of the density of the gas to that of the l i q u i d . By interpretation of tuyere pressure traces and high speed films taken simulta-neously in the laboratory they distinguished two flow re-gimes: a 'pulsing' or bubbling regime and a 'steady jetting' regime. They defined a steady jet as essentially one in which there is a gas continuously at the tip of the tuyere and bubbling as the condition in which the gas necks off at the tuyere tip such that periodically liquid washes against the t i p . For systems with a low gas-to-liquid density ratio under-expanded flow in the tuyeres is a necessary condition for 45 Bubbling Matte converting 10 10 I d 4 10 10 r V P\ Figure 2.6 Jet Behaviour Diagram (from reference 31) 46 steady jetting. This is not the case for systems with greater gas-to-liquid density ratio in which steady jetting can be achieved under conditions of full y expanded flow in the tuyere. Mori and coworkers^'^'^ studied the injection of nitrogen into mercury and water. A high-speed camera was employed to measure the variation of the base diameter of the gas jet with time. At low gas flow rates they observed that the jets expanded immediately upon discharging, in a pulsating manner, forming bubbles the base diameter of which was much larger than the orifice diameter. They defined this phenomenon as bubbling. With increased gas flow rates they found that a continuous, non-pulsating jet of gas begins to form at the o r i f i c e . The base diameter of the gas jet and the orifice diameter coincide over various time ranges during which bubbles are not formed. Thus Mori and coworkers found that the bubbling-jetting tran-sition begins when the gas-flow velocity at the exit of the orifi c e exceeds the sonic velocity irrespective of the differences in the physical properties of liquids or orif i c e diameter. 83 McNallan and King employed high speed cinematography and the pressure-trace technique to study the injection of gas vertically upward into water and liquid metals. Two flow regimes of jet behaviour were observed: one in which unstable bubbles were produced at the jet nozzle, and one in which a 47 steady cone of gas emerged from the nozzle. The transition between both regimes was controlled by the mass flow of gas per unit area of nozzle o r i f i c e . The steady jet flow regime was predominant in jets where the mass flow per unit area was -2 -1 greater than 40 g cm s 2.5 Accretion Formation and Tuyere Blockage Although in use for over seventy years, the copper converter continues to be plagued with problems of tuyere blockage and low refractory l i f e particularly at the tuyere l i n e . The tuyere blockage is caused by the formation of accretions at the tuyere t i p . Accretions f a l l broadly into three categories. F i r s t l y they can be formed inside the pipe, close to the tuyere t i p . Secondly they may be pipe shaped (knurdles or horns) with gas flow channels predominantly through the centre. Thirdly they may be porous (mushrooms) with gas flow channels spreading radially outwards from the tuyere exit. The f i r s t two categories seem to be the most common during copper converting. An example of a pipe-shaped accretion, taken from an operating Peirce-Smith copper convert-er i s shown in Figure 2.7. Figure 2.7 Pipe-Shaped Accretion from a Tuyere of a Converter from Horne Smelter. 49 Tuyere blockage and accretion formation have been the subjects of some studies, but relatively l i t t l e work has been done directly on the copper converter. As was mentioned, 31 Hoefele and Brimacombe investigated injection dynamics in a nickel converter. They concluded that for normal operation the converter works under bubbling conditions which is unde-sirable because between the formation of successive bubbles, liquid washes against the tuyere t i p , contributing importantly to accretion build-up. Another process in which the link between gas flow conditions and tuyere blockage has been established is gaseous deoxidation of blister copper in the anode furnace. 80 In an industrial investigation Gray et a l . also used a pres-sure transducer to sense fluctuations just upstream from the tuyeres of two anode furnaces at Mt. Isa Mines. The pressure measurements indicated that the gas was discharging as bubbles. In order to reduce pressure fluctuations in the tuyere and the number of tuyere blockages, c r i t i c a l flow o r i f i c e s , designed to produce sonic velocity through the o r i f i c e , were installed upstream from each tuyere. No tuyere blockages occurred while c r i t i c a l flow conditions were maintained in the o r i f i c e . 50 Factors influencing accretion formation and tuyere blockage also have been investigated in the laboratory. Using a room-temperature model, Engh et a l . ^ ^ observed the pene-tration of droplets into a submerged tuyere. The number of droplets propelled into the tuyere was inversely related to the velocity of the gas and was a minimum for horizontal nozzles. Tuyere blockage during the horizontal injection of nitrogen at low flows into liquid cast iron was studied by Davis and Magny^"^. Cylinders of iron, consisting of succes-sive layers like an onion, were found lining the injection tubes. The blockage was considered to be associated with the periodic collapse of bubbles at the tuyere tip which caused droplets of iron to be propelled into the tube. The 'onion skin' appearence of the accretions also suggests that the liquid metal may penetrate as a thin layer around the pe-rimeter of the nozzle as has been observed in the tuyeres of the Bessemer process^"^. 108 Wood, Schoeberle and Pugh investigated the desulphuri-zation of blast furnace irons in torpedo ladles using pneumatic injection through a lance. Two types of blockage were found to occur. The f i r s t was characterized by a laminated build up of hot metal which extended a short distance into the lance. A second type was found to exist only at the nose of the lance and consisted of small metal droplets which built up until they covered, the whole of the bore of the lance. 51 109 Most recently Boxall et a l . reported a simple experi-mental technique to simulate knurdle formation and growth by injecting cooled gas into a transparent liquid such as water. Xu et a l . ^ " ^ ' ^ ^ also developed an aqueous model to study the formation of ice accretions by injecting supercooled helium into a bath of water. The accretion growth rate was found to be propotional to time, gas flowrate and gas 'supercool' temperature and inversely proportional to liquid 'superheat' temperature. Accretion formation in both nonferrous and ferrous injection processes also has been investigated mathematically, 112 Using the relaxation technique, Krivsky and Schuhmann predicted the temperature distribution in the refractory wall surrounding the tuyere pipe in a copper converter. They sug-gested that the cooling effect of the gas flow in the tuyere 109 was the cause of accretions. Boxall et a l . developed a mathematical model to predict the features of knurdles in their physical model and to allow the relevance of the model studies to real injection processes to be assessed. Pre-liminary results showed agreement between both models. Sahai 113 and Guthrie studied some pertinent factors governing the formation and growth of metallic mushrooms during shrouded gas injection operations in steelmaking. They carried out a thermal analysis of the accretion growth, in which the heat 52 removed by the protective gas equals the heat supplied by the hot metal and the heat required for the solidi f i c a t i o n of the metal. They found that 607o of the maximum cooling capa-b i l i t i e s of the shrouded gases are available for freezing a protective accretion around a tuyere. Ohguchi and Robertson carried out calculations to estimate the conditions under which pipe-shaped accretions''^ occur in steelmaking furnaces by considering heat transfer both in the refractory around the tuyere and in the molten metal. They also developed a porous-accretion model for heat transfer and accretion formation around a tuyere in order to calculate shapes of mushroom-like accretions^"*. For the pipe-shaped accretions i t was found that the thermal conductivity of refractory affects the bottom radius of the accretion, but does not affect i t s height. Accretion height has a maximum at a particular value of the heat-transfer coefficient between accretion and gas. The accretion grows in the form of a narrow tube increasing in height and rapidly reaches i t s maximum height; the pipe-shaped accretion then increases in radius, slowly reaching it s steady state shape. During accretion growth, the temperature distribution in the refractory changes significantly due to the cooling caused by the gas flow. This leads to considerable thermal stresses in the refractory. For both types of accretion a decrease of superheat or an increase 53 of gas flow rate increases the size of the accretion. It should be noted that in the ferrous injection processes accretion formation does not lead to tuyere blockage because the gas pressures employed are high; nonetheless, accretion build up around the tuyere exit is important because i t local-ly protects the refractory and extends lining l i f e . 2.6 Bath Surface Movement. Splashing and Slopping The submerged injection of gas into the bath of the copper converter imparts motion to the liquid which, depend-ing on conditions, may take the form of slopping and/or splashing. Bath slopping is an oscillatory motion of the liquid between the tuyere line and the breast of the converter (presumably the oscillation also could take place from end to end). Bath splashing is the phenomenon in which droplets of matte and slag are torn off the surface layers and ejected into the reactor atmosphere. Both phenomena are undesirable for several reasons: the ejection of bath from the converter and the build up of accretions at the mouth are accelerated and refractory erosion may increase due to thermal shock and wear. Past practice has endeavoured to control bath behaviour by employing tuyere air flow configurations that are optimum 54 according to operating experience. This has resulted in limited gas flow rates and hence, limited converter productivity. Studies of copper converter operating data have yielded few patterns; one of note is shown in Figure 2.8, where total air flow exhibits a linear dependence on 23 converter volume . Few investigation of the flu i d dynamics during gas injection have been reported, and descriptions of bath movement have been largely qualitative. In most of the studies conducted thus far, emphasis has centered on super-f i c i a l injection from lances during steelmaking. In 1948 Kootz and G i l l e ^ ^ studied converter shapes and blowing conditions for the production of air-refined steel low in nitrogen. During their search for links between blowing conditions and nitrogen in steel they found that the decisive factor is not the depth of the bath, but the relationship between the depth of the bath above the tuyeres and the bath volume. In order to conduct experiments on a large scale they con-structed a special converter, strikingly similar to a Peirce-Smith converter, which enabled the bath depth over the tuyeres to be easily changed. The horizontal converter had a length of 5m, an internal diameter of 2.5 m and held 5 to 10 tonne pig iron. Thus i t was found that the blowing properties of the converter were exceptiOnaly bad, especially at greater depths of bath. In order to avoid excessive slopping and 55 Figure 2.8 Air Injection Rate into a Copper Converter as a Function of Converter Volume. (Reprinted with the permission from 'Copper and Nickel Converters', edited by R.E. Johnson, The Metallurgical Society of AIME, 420 Commonwealth Drive, Warrendale, PA 15086, USA, 1979). 56 splashing Kootz and Gille pointed out that i t would be necessary to work with pressures of not more than 1 atm. They also indicated that the outbursts of slopping and splashing possibly occurred in cycles, associated with the turbulence of the bath of iron in the converter. To investigate the turbulence phenomena in the bath, Kootz and Gille constructed a vessel with glass end walls, f i l l e d with water, to simulate the horizontal converter. They noticed that during blowing the bath becomes strongly agitated at almost every position of the vessel. Two fun-damentally different types of bath movements were observed: one during which the whole bath is turbulent, and another during which standing waves are formed. Each type of motion started always at the same angle of immersion of the tuyeres, independently of the degree of f i l l i n g of the vessel and the volume of a i r . The bath remained free from strong agitation only when the tuyere line was submerged at a low angle, not exceeding */l2 rad (15°). For immersion angles of */l2 to */7 rad (15 to 25°) a very rapid movement sets in with a low amplitude,too small to give rise to slopping or splashing. When the tuyere line is allowed to be immersed in the range w/7 to 5*/l6 rad (25 - 50°) a slower but considerably strong-er bath motion of standing waves takes place, which would lead to slopping and splashing ocurring in the large converter. The 57 nature of the movement may be clearly recognized; in the mid-dle and on both sides of the vessel wave crests and wave throughs alternate with each other, and two nodal points can be observed. If the tuyere line is turned deeper than 5*/16 (5CT) then the slowest and strongest bath motion appears, whereby the whole bath moves to and fro. This type of bath motion is indeed the most significant for converter slopping and splashing. In an attempt to reduce splashing in an oxygen-blown open-hearth furnace L i * ^ studied the effect of lance angle, lance height, and jet flow rate on splashing. To this end he constructed a simple model of a fluidized air-water system and an impinging jet. Splash patterns were collected by a piece of f i l t e r paper exposed for a given length of time to the splashing, the results indicated that a foam layer present on the top of the liquid plays an important role, producing a damping effect on splashing. This may indicate that the condi-tions of slag may likewise affect splashing in an actual fur-nace. Lancing (that i s , injection of air with tha lance sub-merged in the bath) generally produces less splashing than jetting (with the lance above the surface). A sharp reduction in splashing occurs as the lance is lowered to touch the bath surface. 58 Holmes and Thring put forward three theories de-scribing the mechanism of splashing in the top-blown oxygen converter. The f i r s t is that splashing i s completely phys-ic a l and consequently the amount of splashing wi l l depend on the jet momentum. The second is that oxygen is absorbed into the steel and carbon monoxide is then formed explosively causing the splash. The last proposed mechanism is a compro-mise and claims that splashing is partly physical and partly chemical, the oxygen combining with carbon on the surface. They made some suggestions on how to modify certain similar-it y c r i t e r i a to account for any excess splashing taking place owing to chemical action. 119 Chatterjee and Bradshaw studied the variables affecting the onset of splashing when a subsonic jet i s directed v e r t i -cally on the surface of various liquids. Splash patterns were obtained by allowing water droplets containing a dye to im-pinge on a paper disk held above the liquid surface. The volume of liquid torn from the surface was measured by collect-ing the splashed liquid in a tray situated above the liquid surface. They concluded that for any liquid exposed to a gas jet impinging at i t s surface, splashing commences at a c r i t i -cal depth of depression of the bath. This c r i t i c a l depth almost solely depends on the liquid properties. An experimental relationship was obtained to predict the c r i t i c a l depth of 59 depression when the liquid properties are known. The onset of splashing was also related to jet parameters, such as jet momentum and lance height. An increase in the jet momentum or a decrease in the lance height causes the amount of splash-ing to rise to a maximum value. Further changes caused a de-crease in the volume of liquid splashed. A study to evaluate splashing in the nitrogen-water 1* system during submerged injection was performed by Igwe et al. Two modes of injection were considered, the horizontal nozzle and the submerged lance system involving one or more jets. High speed photographs were taken to qualitatively compare the splash severity under different conditions. At identical gas flow rates, the splashing from the top submerged lance is far less severe and more evenly distributed over the bath surface than the observed in horizontal nozzle injection. The vessel rocked vigorously during side injection, a situation which did not occur in the multiple-orifice top submerged injection. During top-submerged injection i t was also observed that as the number of nozzles is increased from one to four, the splash severity at a given total gas flow rate decreases. A slight worsening of the splash was observed as the depth of nozzle submergence increased. 60 In an air-water model study of bottom-blown converters 121 Etienne distinguished two types of factors which may influence splashing: geometric factors (design of the bottom, volume of the bath) and physicochemical factors (heating up of the gas, chemical reactions). Two types of models were investigated: an asymmetrical converter without tapping hole and tuyeres distributed in a half bottom, and a model of a symmetrical converter with tapping hole. Quantitative assess-ment of the amount of splashing was obtained by collecting the water splashes on thick absorbing papers hanging inside the converter. For the asymmetrical converters Etienne found that a calm blow is linked to an intense foaming of the bath. As the number of tuyeres or bath depth decrease the blow becomes rougher, tearing bundles of water away from the bath surface. An increase in the air flow rate enhances the amount of splashing but does not alter the type of behaviour of the bath. For symmetrical converters the motion of the bath depend-ed markedly on i t s depth and the number of tuyeres. When less than 10 tuyeres are employed heavy splashing is observed, which increases as the bath depth decreases. Blowing with more than 14 tuyeres produces a calm bath even with shallow bath depth. In this case the bath exhibits a tendency to o s c i l l a t e . The amplitude of these oscillations increases with bath depth. 61 Model studies on the bath motion and the amount of splashing produced in a sideblown vertical converter at high 122 gas flow rates were performed by Ericsson . A quantitative assessment of the amount of splashing produced was obtained by collecting the water splashes in a ring-formed reservoir placed in the upper part of the vessel. It was found that a number of factors influence bath movement. The projections may originate from mass oscillations that take place in the bath, generally as rotating waves. Another mechanism causing splashing at the greatest air flow rate is due to gas bubbles crossing the bath surface at high speed tearing bundles of water away from the surface. Splashing is increased markedly with increasing gas flow rates. When the tuyeres are inclined directed towards the surface the splashing seems to increase exponentially with gas flow rate. If the tuyeres are directed horizontally or downwards in the bath the importance of the gas flow rate decreases. An increase in bath depth increases splashing, this effect grows with increasing gas flow rates. An increase in tuyere diameter results in less splashing, especially when the tuyeres are directed upwards. In the latter case the amount of splashing even decreases at certain gas flow rates and tuyere diameter. 62 Robertson and Sabharwal , working with a water model of a transfer ladle into which air was injected by means of a scaled down lance identified two types of splashing. A 'pri-mary splashing' is caused directly by bubbles arriving at the liquid surface while 'secondary splashing' is a washing effect round the containing walls. Primary splashing wi l l result in accretion formation in the extraction hood over the ladle, while secondary splashing, i f vigorous, wi l l result in massive ejections onto the floor. Primary splashing was closely asso-ciated with the size of the gas bubbles arriving at the liquid surface in the water model. Secondary splashing is dependent on the interaction between the waves set up on the surface and the walls of the containing vessel, and also depends on the damping produced by the slag/metal medium. Robertson and Sabharwal adopted an ingenious electrical method to quantify primary splashing. A wire mesh was suspended horizontally around the injecting lance, so as to cover most of the liquid surface. An electrical circuit was made each time a splash impinged on the mesh, and was recorded as peaks on a chart recorder. For the assessment of secondary splashing the circuit was completed when splashes made contact with wire rings attached round the circumference of the vessel.Unfortu-nately due to possible commercial implications Robertson and Sabharwal did not discuss in detail the performance of spe-c i f i c lance designs in relation to splashing. 63 2.7 Summary Li t t l e is known about the fl u i d dynamics of submerged injection under actual metallurgical conditions. Although the proposed models of submerged gas jets compare well with air/ water experiments, they f a i l to predict r e a l i s t i c a l l y the behaviour of air injected into more dense mercury and other liquid metals. It is clear that the relationship between in-e r t i a l and buoyancy forces has a great effect on the submerged gas injection process. Also the physical properties of both the liquid and the injected gas are important to define jet cone angle, forward and backward penetration and the shape of the jet. There are two main flow regimes depending on the driving pressure of the gas. Three different ways have been proposed to define the bubbling-jetting transition. A l l of them are almost identical when applied to systems having a low gas-to-liquid density r a t i o , eg. gas-mercury and air-copper mattes. In this case the transition occurs for underexpanded flow conditions. For the case of aqueous systems Mori and coworkers and McNallan and King define the transition at sonic or near sonic velocities of the gas in the o r i f i c e , well above the transitional range reported by Hoefele and Brimacombe. Which of the definitions one adopts may depend largely on the 64 objective of the study under consideration. To investigate how injection conditions could affect nozzle blockage, the continuous-gas criterion may be more appropiate. But i f one were examining other aspects of jet behaviour, the no-pul-sation criterion may be better. Nevertheless whichever the definition to be adopted i t is clear from the operational point of view that the jetting regime is the best to avoid tuyere blockage and to obtain high mass transfer rates and lower refractory wear. The published models on bubble formation predict with sufficient accuracy the bubble volume for gas injection into liquid metals under low gas flow rates and non-reactive con-ditions. The relationship between bubble volume and gas flow rate defines two different bubbling regimes, a constant bubble volume regime for very low gas flow rates, and a constant frequency regime for higher flow rates. Nevertheless, when applied to a real industrial process, the models show large discrepancies with measured frequencies and bubble volumes. It seems that heat transfer to the bubble and bath circulation have a major effect on the bubble formation process under actual conditions. The measurement of tuyere pressure to characterize submerged injection regimes is now a f a i r l y well established 65 technique, at least when studying tuyere processes. By using this method the bubbling-jetting transition can be studied in de t a i l . Tuyere blockage and accretion formation have been the subjects of some studies, but relatively l i t t l e work has been done directly on the copper converter. It is clear that the non ferrous industry has many lessons to learn from i t s ferrous sister with respect to control of accretion growth for refractory protection. The high pressure injection of air in the copper converter appears as the most interesting devel-opment in this area. The mathematical models developed to grow accretions of different shapes work well under steady state, single tuyere, stagnant bath conditions. A l l the models coin-cide in that a decrease of superheat or an increase in gas flow rate increase the accretion formation process. Few investigations about bath movement during injection have been reported, and most of them have been largely quali-tatively with emphasis centered on superficial injection from lances during steelmaking . Slopping and splashing have been studied mainly from a physical-mechanical point of view, with almost no emphasis on the effect of gas expansion, and chemical reactions in the converter. The techniques employed to measure splashing are rather crude, while no quantitative technique at a l l as been proposed to study slopping. 66 CHAPTER III  OBJECTIVES Numerous thermodynamic i n v e s t i g a t i o n s of the chemical r e a c t i o n s i n copper c o n v e r t i n g have been conducted over the y e a r s . Thus much i s known of the e q u i l i b r i a amongst molten copper, s l a g and matte phases, and the i n f l u e n c e of oxygen p o t e n t i a l on copper l o s s e s i n s l a g . In c o n t r a s t to t h i s s t a t e of b a s i c knowledge of e q u i -l i b r i a , remarkably l i t t l e i s understood of the r a t e phenomena i n the copper c o n v e r t e r , p a r t i c u l a r l y as they are i n f l u e n c e d by the d e s i g n and o p e r a t i o n of the r e a c t o r . Aspects such as gas d i s c h a r g e dynamics, bath movement w i t h i n the c o n v e r t e r , s p l a s h i n g and heat t r a n s f e r have only begun to be t a c k l e d i n a concerted manner. Thus the t h r u s t of t h i s work was to i n v e s -tigate the following process engineering aspects of a c o n v e r t e r o p e r a t i o n : gas i n j e c t i o n i n t o the b a t h , a c c r e t i o n growth at the tuyere t i p , s l o p p i n g of the bath and heat l o s s e s from the i n t e r i o r of the converter during o u t - o f - s t a c k p e r i o d s . The study of these s u b j e c t s i n v o l v e d plant measurements, a p h y s i c a l l a b o r a t o r y model and the f o r m u l a t i o n of a mathematical model. 67 The main objectives expected to be f u l f i l l e d in the course of this work were the following: a) To study the effect of different injection parameters on bath motion, tuyere injection dynamics and slopping. Observations employing high-speed cinematography of the tuyere region and the bath, surface were to be performed in the physical model. The observed events were to be related to measurements of the dynamic gas pressure in the tuyeres. b) To study some characteristic features of converting under normal blowing conditions and to compare the converting operation and injection characteristics of the different reactors employed in industry (Peirce-Smith, Hoboken and Inspiration converters). c) To observe accretion build-up while a tuyere is operating. The task was accomplished with the aid of a 1tuyerescope' that facilitated direct observation, by eye or with cameras, of the dynamics of accretion growth at the tuyere tip. d) To gain knowledge on the effect of variables like bath properties, tuyere submergence, interaction of adjacent tuyeres, and state of the refractories at the tuyere line on injection dynamics. 68 e) To assess the relative importance of magnetite formation and freezing in the accretion growth process by taking samples of the accretion during operation. f) To link bath movement and events at the tuyere tip in order to minimize splashing and slopping in the copper converter. Thus, an attempt was to be made to study the influence of injection variables (gas flow rate, tuyere submergence) on bath movement, splashing and slopping. g) To quantify the influence of out-of-stack time and other converter variables on the temperature distribution in the refractory wall, especially at the tuyere line by means of a mathematical heat transfer model. h) Finally on the basis of the results from laboratory, industrial and computing work, to make suggestions that may lead to improvements in present gas injection practice in order to increase tuyere and refractory l i f e , and to decrease slopping and accretion build-up. 69 CHAPTER IV EXPERIMENTAL TECHNIQUES As discussed earlier, i t was of primary importance to obtain enough information to develop a definite set of operat-ing c r i t e r i a for copper converters. To accomplish this objec-tive laboratory experiments and industrial tests in four cop-per smelters were carried out, together with heat transfer calculations. The following sections describe the experimental techniques applied to the acquisition of industrial data and the laboratory work involved. 4.1 Laboratory Experimental Work The laboratory work was carried out to examine the relation between certain injection parameters and bath behav-iour. The high temperature system was simulated by means of a sectional 1/4 scale model of a copper converter. The iso-thermal model was considered to be the best means to simulate some aspects of the overall bath movement. 4.1.1 The Isothermal Model A major d i f f i c u l t y encountered in the physical modelling of a gas-liquid metal system lies in the number of physical 70 parameters involved in the process. It has been pointed out that a complete simulation of a process can be obtained by using 24 dimensionless groups, which evidently is impossible to accomplish from a practical point of view. To attain fluid flow similitude between two gas-liquid 59 88 systems, four conditions must be met ' : dynamic similarity, geometric similarity, kinematic similarity and thermal simi-l a r i t y . To meet thermal similarity requirements, the dimension-less numbers involving heat transfer or convective flow have to be equal in both systems. Thermal similarity appears to be unimportant in modelling copper converting processes since convective forces due to the thermal gradients are considered small relative to other forces acting on the system. The only important thermal effect to be considered is the expansion of the bubble due to heat transfer from the liquid metal to the gas phase. Kinematic similarity is ensured in a model that conforms to dynamic and geometric similarity. The principal forces to be considered in obtaining dynamic similarity in the converting system are i n e r t i a l , buoyancy (or gravitational), viscous, and surface tension forces. As indicated by Equation 2-8, the surface tension phenomena and ante-chamber volumes dominate at low flow rates. At higher flow rates, the inertial term plays the dominant 71 role in determining bubble sizes . Thus two dimensionless parameters which can be used in the modelling process are the modified Froude number, which relates i n e r t i a l and buoyancy forces, and the Reynolds number, relating inertial and viscous forces. In the investigation of gas-liquid metal systems, water is usually employed as the modelling liquid because i t is easy to handle, readly available, facilitates flow tracing, and i t s kinematic viscosity is close to that of liquid copper or copper mattes. Table 4.1 compares some physical properties of several fluids. However using water as the modelling liquid for copper mattes, i t is impossible to satisfy the two above mentioned dimensionless numbers simultaneously. The partial solution for such a problem lies in knowledge of the behaviour of the systems. It is known from a considerable body of ex-88 perience in the flow of fluids that the Reynolds number becomes relatively unimportant once ful l y turbulent flow, or a high value of Reynolds number, has been attained. In model experiments designed to simulate the bath motion in steel-89 making converters , useful results have been obtained by modelling to obtain similarity with respect to Froude number rather than to Reynolds number. TABLE 4.1 PHYSICAL PROPERTIES OF SOME FLUIDSiJ' DENSITV kg m VISCOSITY N s m~2 Helium (20 C) 0.177 1. 9 X 10"5 Air (20 C) 1.293 1. 8 X 10- 5 Air-He mixture (887. He) 0.315 1. 9 X lO"5 Air-He mixture (917=, He) 0.281 1. 9 X 10- 5 Air-He mixture (947. He) 0.248 1. 9 X lO"5 Water (20 C) 1000 1. 0 X 10- 3 Blister Copper (1200 C) 7800 3. 3 X 10- 3 Matte 307o Cu (1200 C) 4100 10. 0 X 10- 3 Matte 507, Cu (1200 C) 4600 10. 0 X lO"3 Matte 80% Cu (1200 C) 5200 10. 0 X 10- 3 73 To simulate some fluid dynamic aspects of a copper converter by means of an isothermal model, three characteris-tics of the process may be considered. The effect of the relationship between inertial and buoyancy forces has a great 26 31 56 influence on the dynamics of gas injection ' ' . Also during gas injection into a liq u i d , two regimes of flow can be distinguished, depending on both the modified Froude number 31 of the system and the gas-to-liquid density ratio . Therefore, similarity based on the modified Froude number criterion appears to be essential to simulate the process. Also the gas-to-liquid density ratio in the prototype and the model should be the same. Then the conditions of an air-matte system may be simulated by injecting a helium-air mixture into water. 30 It has been suggested that the refractory wear observed in the area close to the tuyeres in a copper converter may be 31 due to the action of the rising bubbles.lt was also indicated that the bubbles forming at adjacent tuyeres overlap considera-bly; this interaction explains the uniformity of refractory wear observed along the back wall above the tuyere l i n e . There-fore, to simulate the fluid dynamic contribution to the re-fractory wear in a copper converter, the ratio between the bubble diameter at the tuyere tip and the distance between adjacent tuyeres should be the same in both the prototype and the model. 74 The above mentioned factors, coupled to geometric similarity with a selected scale factor, provide a useful frame of reference to develop relations to design an iso-thermal model of a copper converter. From the similarity of modified Froude numbers: 2 . 2 —*—-l -r—2—-i I P, - P d g P, - P d g 1 B O feJP L 1 g O 6 - ! (4.1) g "o 6 JP L" l ~ "g "o 6-lM If the gas-to-liquid density ratio is the same in both the prototype and the model: (4.2) M but, as PG < <P1 Eqs. (4.1) and (4.2) give: u M = u p (4.3) o,  o,P|dQ p As was mentioned, the ratio between bubble diameter at the tuyere tip and distance between adjacent tuyeres provides another similarity criterion: w. • m (4.4) M 75 The bubble diameter at the tuyere tip in the prototype can be given a value from the model developed by Ashman et al.^,the industrial values obtained by Hoefele^, and the industrial measurements to be carried out during the present work. A l l the bubble formation models in water-like liquids have been developed assuming stagnant bath conditions and have been tested under experimental conditions involving one tuyere only. It seems unlikely that the bubble diameter in the turbulent, multiple-tuyere water model could be described by Equation (2.1); then the bubble volume in the model has to be defined,from dynamic pressure measurements. The bubbling frequency to be measured is related to the gas flow rate as: or, in terms of the bubble diameter, the tuyere gas velocity and the tuyere diameter: Then, from Equations (4.3),(4.4) and (4.6) the tuyere diameter to be used in the model is defined by: b,M (4.5) (4.6) (4.7) 76 In Eq. (4.7) the tuyere diameter in the model is expressed as a function of the conditions existing in the prototype, the specific scale ratio to be used, and the bubbling frequency in the model. The tuyere submergence in the model can be defined by using the ratio between the bubble diameter at the tuyere tip and the tuyere submergence as an additional similarity crite-rion: (4.8) Then, from Eqs. (4.3), (4.6) and (4.8) the tuyere sub-mergence in the model can be expressed as: H . [ 3 uo , P l ^ 3 « P _ . d 5 / 6 ( 4 . 9 ) As was mentioned the gas-to-liquid density ratio should be the same in both the prototype and the model; then the a i r -matte system can be simulated by injecting helium into water. Unfortunately economic considerations owing to consumption of a large amount of gas in the laboratory work prevented the use of helium as the injected gas. Instead i t was decided to in-ject air through the tuyeres of the isothermal water model. 77 If an air-water system is used to simulate an air-matte system, Eq. (4.2) cannot be used, but the condition « P-^  is s t i l l v a l i d . Then Eq. (4.1) becomes: 0,P L<3 c P w P i r j ' L o,P g,M 1,PJ uQ M = u. „ - T ^ ' - T ^ I (4.10) Now, from Eqs. (4.10), (4.4) and (4.6) the tuyere diam-eter in the model i s : F ^ V P J L epJ L 0 , P p g , p pI,MJ B> P In the same way the tuyere submergence in the model can be expressed in terms of Eqs. (4.10). (4.6) and (4.8) „M . [3. V P Y ! 3 . ^ f ' 6 d ,4.1 2 ) L £M do,P J ^ L 8,M "l.PJ ° 'M 4.1.2 Experimental Apparatus The apparatus employed in the laboratory experiments is illustrated schematically in Figure 4.1. It consisted of a converter-shaped vessel, a gas-delivery system to supply air to the tuyeres and a fast-response piezoelectric transducer 2 ST 9m? UT l . 2. 3. 4. 5. 6 . 7. 8. 9. 10. I t . 12. Compressor Globe Valve Pressure Gage Plate Orifice Tuyere Manifold Tuyere Plexlglas Converter Pressure Transducer SLgnal Amplifier FY Tape Recorder Storage Oscilloscope High-Speed Camera Figure A.l Schematic of the Laboratory Apparatus. --J 00 79 coupled to a four-channel FM tape recorder and to a storage oscilloscope to measure and record the pressure along the tuyere. A high-speed camera to film events taking place in the tuyere region was also employed. 4.1.2.1 Converter-Shaped Vessel To obtain reliable information about the process, i t was decided to build a 1/4 scale, sectional Plexiglas model of a 13 x 30 Peirce-Smith copper converter. A smaller model could not be used because the tuyere diameter would be less than 10mm, and under these conditions the surface tension effect would become important with respect to buoyancy and in e r t i a l forces. A section containing five tuyeres was constructed. In North America there are seventeen plants using sixty-23 one 13 x 30 Peirce-Smith converters. From the data shown in Table 4.2 an 'average' converter can be defined, as one having 44 tuyeres with a diameter of 49mm. The average gas blowing 3 / 4 rate and blowing pressure are 9.1 Nm /s and 9.13 x 10 Pa, respectively. Table 4.3 shows other characteristics of the average converter and three plants which are of interest. TABLE 4.2 DETAILS OF COPPER CONVERTER PRACTICE IN NORTH AMERICA PLANT 13' x 30» Converters Number of Tuyeres Tuyere Diameter,mm Blowing Rate m3/s STP Blowing Pressure Pa x 10-4 * Tuyere Submergence, mm Falconbridge 4 - - 8.5 - 381 Gaspe 2 50 48 10.4 10.4 922 Hudson Bay 3 39* 50 8.5 9.7 762 Noranda 4 48 48 11.8 10.4 1041 Ajo 3 52 43 7.8 8.3 558 Douglas 5 47 43 7.8 9.7 304 Morenci 9 37* 59* 11.3 9.0 609 Hidalgo 3 52 48 8.5 6.9 457 White Pine 2 42 48 8.5 9.7 215 Ray 3 42 50 9.7 10.3 406 Nevada 1 43 50 9.0 9.7 457 Chi no 4 48 48 9.0 9.7 393 Utah 8 48* 50 8.5 10.3 533 Anaconda 2 48 43 10.2 11.0 584 El Paso 3 40 43 8.5 10.3 533 Hayden 1 49 43 11.3 10.3 508 Tacoma 3 42 40 8.3 10.3 457 * Averaged value. TABLE 4-3 CHARACTERISTICS OF THE AVERAGE 13 x 30 CONVERTER AND THREE OTHER PLANTS Average Tacoma Noranda Utah Number of tuyeres 44 42 48 48 Tuyere diameter, mn 49 41 48 50 Tuyere submergence, mm 540 457 1041 534 Gas flow rate, Nm /s 9.1 8.3 11.8 8.5 Tuyere gas velocity, m/s 109.7 149.7 135.9 87.4 Tuyere spacing, mm 195 205 179 179 Modified Froude number (1) 7.0 15.7 11.0 4.3 Reynolds number (1) 3.9 x 105 4.4 x 105 4.7 x 105 3.2 x 105 3 Converter bubble volume, m (2) 3.4 x 10"2 3.2 x 10"2 4.3 x 10~2 2.6 x 10~2 Bubble diameter @ tuyere, mm (2) 402 394 435 368 Bubble diameter Tuyere spacing 2.06 1.92 2.43 2.06 Tuyere submergence Bubble diameter 1.34 1.16 2.39 1.45 (1) Defined @ 25° C for a 50% Cu matte. (2) Calculated from Asham et a l .7 4 model. 82 As just described, a 1/4— scale Plexiglas model was constructed to simulate the Peirce-Smith prototype. The linear dimensions in the prototype were scaled down according to the scale factor, with the exception of the tuyere diameter, which has to be dimensioned as stated by Equation (4.7) i f a helium-water system is used, or by Equation (4.11) i f air is injected into water. The converter-shaped vessel was made from a Plexiglas plate 9.5 mm thick. The internal diameter of the model was 850 mm, and its length 270 mm. The end walls of the tank were also made from 9.5 mm thick transparent Plexiglas plate. The top of the vessel was provided with a 85 x 300 mm opening to discharge a i r . Figure 4.2 shows some views of the Plexiglas converter-shaped vessel employed during the laboratory work. 4.1.2.2 Tuyeres The five tuyeres in the model were held in place by means of an assembly as shown in Figure 4.3. The assembly consisted of a 58 x 70 x 248 mm Plexiglas rectangular block in which a 50 mm diameter hole was d r i l l e d . Into this hole was inserted a 330 mm long Plexiglas bar in which five threaded 7/8 NF holes, 52 mm apart had been d r i l l e d . The tuyeres then screwed into the threaded holes. The Plexiglas Figure 4.2 The Converter-Shaped Model (a) Frontal View (b) View Showing the Tuyere Assembly. 7/8 NF. H—52mm-H 50mm i 70mm 248mm 330mm H—58 mm—H Figure 4.3 The Tuyere Assembly. 85 bar could be rotated in order to change the inclination of the tuyeres in the model. Figure 4.2(b) shows a photograph of the tuyere assembly with the tuyeres in place. The tuyeres were made from 22.2-mm diameter brass rod in which a hole was d r i l l e d axially. The external surface was threaded with a 7/8 NF thread to allow the tuyeres to be screwed into the tuyere assembly. Two tuyere diameters, 16 mm and 12 mm, were used through the laboratory experiments. 4.1.2.3 Gas-Delivery System The source of air used in the current work was a Sutorbilt 4 MF air compressor, with a capacity of 0.08 m /s (165 CFM) at a gauge pressure of 48.3 kPa (7 psig). A globe valve was used to control the gas flow rate which was meas-ured using a plate o r i f i c e . Bourdon-type pressure gages placed at both the entrance and exit of the plate or i f i c e allowed the gas flow rate to be accurately determined, as indicated in Appendix I. At the exit from the plate orifice the air entered a 510 mm long cylindrical manifold 75 mm in diameter for distribution to the tuyeres in the vessel. To calculate the gas flow rate at the tuyere exit, both the atmospheric pressure and the static head of water were considered. 86 4.1.2.4 Pressure Measurements In order to measure the nozzle pressure oscillations, the back of the tuyere was fitted with a T-connection, as shown in Figure 4.4. The pressure was measured with a fast-response, National Semiconductor (LX 1810 GBZ) piezoelectric transducer. The output signal from the transducer was intermit-tently recorded on a Tektronik storage oscilloscope (Type 564), and continuously recorded on a four-channel FM tape recorder Tandberg (T1R-115). The signals from the recorder were subse-quently played back on the oscilloscope and a Honeywell Visicorder Oscillograph (Model 1508 A) via a Dual HI/LO Rockland f i l t e r (Model 442) to eliminate the ambient electric noise. The pressure traces observed on the oscilloscope were photographed with a Polaroid oscilloscope camera. 4.1.2.5 High-Speed Cinematography High-speed films of the tuyere line region were taken using a Hycam camera (Model K2054E). Most films were taken at a speed of 400 frames per second, but speeds of 800 frames per second were also used. Black-and-white 7277 Kodak film (320 ASA) and 4-X 7224 (400 ASA) Kodak film were used. I l l u -mination was provided by a PAMOTOR (Model 8500 C) lamp with a total power of 2400 W. The films were taken from below the Air from manifold 1/2 NPT 122mm i s \ s \ Figure 4.4 The Tuyere-Pressure Transducer System. 88 the tuyere region of the bath with the help of a mirror which can be observed in Figure 4.2. 4.1.3 Conditions for the Tests and General Procedure The tests were carried out under conditions that r e p l i -cated as closely as possible those prevailing in industrial converters. Table 4.4 shows the scaled-down values which should be used to simulate the injection process in the 'average' converter as well as in three other smelters in Canada and the U.S.. The values were calculated for the helium-water and the air-water systems. In a l l the experiments tap water was used. The calculations were performed assuming a bubbling frequency of 14 s for the aqueous system and a 50 pet. Cu matte in the industrial reactor. The following parameters were studied in the air-water tests: i) Tuyere diameter i i ) Tuyere submergence i i i ) Gas flow rate iv) Percent f i l l i n g v) Tuyere spacing (by varying the number of tuyeres in the model) The range of variables is summarized in Table 4.5. TABLE 4.4 SCALED-DOWN CHARACTERISTICS FOR DIFFERENT MODELS* AVERAGE TACOMA NORANDA UTAH Helium Air Helium Air Helium Air Helium Air Tuyere Diameter, mm 13 18 11 15 13 18 13 17 Tuyere Submergence, mm 135 175 114 147 260 336 134 172 Tuyere Velocity, m/s 56.5 30.7 76.8 41.7 70.7 38.5 44.0 23.9 Tuyere Gas Flow Rate, Nl/s 7.5 7.6 7.0 7.0 9.4 9.5 5.8 5.7 Tuyere Spacing, mm 49 52 45 45 * Calculated assuming a bubbling frequency of 14 s in the model. Scaled-down values for a 50 °L Cu matte. TABLE 4.5 RANGE OF VARIABLES Tuyere Diameter, mm 12 16 Gas Flow Rate, l/s 0 to 50 30 Pet. F i l l i n g 35 40 45 Tuyere Submergence, mm 60 to 200 Number of Tuyeres 1 3 5 91 The general procedure to carry out the tests was as follows. First a set of injection conditions was chosen. The gas was turned on and when steady state conditions were reached (it usually took a few seconds) the pressure was measured in the three pressure gages in the system for further calculation of the air flow rate. Then the tuyere pressure oscillations were recorded with the FM tape recorder as well as with the storage oscilloscope and Polaroid photographs. If a movie picture was desired the vessel was illuminated and high-speed films were taken. To simulate the effect of tuyere line erosion on fl u i d dynamic events in the tuyere region two 60 mm deflectors were used in some of the experiments, as can be seen in Figure 4.2 (b). The deflectors were placed at right angles to the inside wall of the model along the entire lenght of the tuyere l i n e , 35 mm above and 25 mm below the tuyere centerline. 4.2 Industrial Work The injection of air into water carried out during the present laboratory experimental work, differs from industrial practice in many ways. Firstly, the air injected in the laboratory was approximately at the same temperature as that of the bath (room temperature). This is not the case in a copper converter in which air is injected at room tempera-ture into a liquid at about 1200 C. Thus industrial jets are non isothermal 92 and considerable expansion of the gas close to the tuyere region must be expected. Secondly, the air injected during the laboratory work did not react with the water. On the other hand the objective of injecting air into the bath in a copper converter is to produce chemical reactions between the injected gas and the melt. These reactions are exothermic and change the volume and composition of the injected gas and the bath. Finally, the laboratory work involved a single-phase, homoge-neous liq u i d . In contrast during copper converting, three distinct liquids can be found: slag floating on txhe surface, a middle zone of matte, and metallic copper at the bottom. Therefore different flow patterns can be generated in the melt, which in turn may affect the jet behaviour. Owing to these differences between the air-water and the copper converting systems, several industrial tests under normal operating conditions were considered desirable in order to link the laboratory results with metallurgical processes. 4.2.1 Smelters Selected for the Tests The industrial studies were undertaken to check the con-clusions reached in the laboratory work and to further the understanding of gas discharge dynamics and accretion growth in an operating converter. To achieve this, an agreement was 93 made with four copper smelters in North America to perform industrial tests under normal operating conditions: the ASARCO Smelter in Tacoma, Washington; the NORANDA Smelter in Noranda, Quebec; the KENNECOTT Utah Smelter in Salt Lake City, Utah; and the INSPIRATION Smelter, in Miami, Arizona. The experiments at the Tacoma smelter were performed on a 13 x 30 Peirce-Smith converter. At the time of the tests the refractory lining of the converter had endured 254 charges. The tuyeres selected for study in the converter were No. 5 and No.6 near one end of the reactor. At the Noranda Home smelter the study was carried out on the tuyeres of both Peirce-Smith converters and the Noranda reactor. Two converters were monitored: a relatively old con-verter (Converter No.6) almost at the end of i t s working pe-riod and a 'middle-aged' converter (Converter No.4). On each a f u l l converter cycle was studied. For the Noranda reactor, which is esentially continuous, the test period was about four hours. The tests at the Utah smelter were performed on the tuyeres of two 13 x 30 Peirce-Smith converters: a relatively old converter (Converter No.2) and a newly relined converter' (Converter No.3). On Converter No.2 almost a f u l l converter cycle was studied. With the new converter, four cycles were 94 followed (Charges 1, 3, 6, and 12). In both reactors two tuyeres were monitored, most of the time simultaneously, Tuyere No. 25 at the centre of the converter, and Tuyeres No. 6 or 7, close to the end of the tuyere l i n e . The Inspiration smelter work involved two sets of t r i a l s . During the f i r s t t r i a l , cinematographic observations of the bath movement were performed at two copper converters, a Hoboken-type (Converter No. 4) and the Inspiration con-verter. For the second set of t r i a l s studies were performed at the tuyeres of the Inspiration converter during Charges 17 and 18 and at the Hoboken converter (Converter No2) during charge 22. In both converters f u l l converter cycles were studied. Two tuyeres were monitored, most of the time simultaneously, one near the mouth of the converter (Tuyeres No. 5 in the Hoboken converter and No. 7 in the Inspiration converter) and the other at the middle of the tuyere line (tuyere No. 21 in converter No. 2 and Tuyere No. 27 for the Inspiration converter). Tables 4.2 and 4.3 show operating 23 data, as compiled by Johnson et a l . , for the 13 x 30 Peirce-Smith copper converters monitored in the course of the present work. Table 4.6 compares other converter characteris-tics in the four smelters under consideration. TABLE 4.6 CONDITIONS FOR THE INDUSTRIAL TRIALS SMELTER TYPE OF CONVERTER CHARGE MONITORED OXYGEN ENRICHMENT PUNCHING EQUIPMENT TACOMA 13 x 30 PEIRCE-SMITH 254 YES GASPE HORNE 13 x 30 PEIRCE-SMITH 64 and 195 NO GASPE UTAH 13 x 30 PEIRCE-SMITH 1, 3, 6, 12 and 60 YES KENNECOTT 4B5 INSPIRATION HOBOKEN INSPIRATION 22 17 and 18 NO KENNECOTT 4B5 96 4.2.2 Scope of the Industrial Tests As was mentioned, a major objective in the industrial investigation was to observe accretion build-up while a tuyere was operating. The task was accomplished with the aid of a "tuyerescope" that during operation was attached to the back of the tuyere under study. The use of such a device is not new since "endoscopes" have been employed to investigate movement and combustion of coke in the raceway of blast 90-94 furnaces ; however their use to study tuyere phenomena in the copper converting process is believed to be novel. In order to gain knowledge on the effect of some operating variables on injection dynamics the tuyere pressure measurement technique, f i r s t developed by Hoefele and 31 Brimacombe in a nickel converter, was extended to the copper converter. In addition, samples of accretion were sought during operation to assess the relative importance of magnetite formation and freezing in the accretion growth process. Finally, i t was also intended to perform cinematographic observations of the bath surface inside the converter; for this advantage was taken of the particular features of the syphon-type reactors operating in the inspiration smelter. 97 4.2.3 Equipment and Procedure The tuyerescope used to observe tuyere phenomena in the copper converter is shown in Figure 4.5. It was constructed of a 130-mm length of 33-mm diameter stainless steel pipe one end of which was covered by a removable Plexiglas window. This tuyerescope was designed to be inserted quickly into the tuyere immediatly after punching and to be removed once the tuyere had blocked. Insertion of the tuyerescope into the back of the tuyere, as in the case of punching, forced the ball valve up into the ball race in the tuyere body as shown in Figure 4.5. A simple lock-fit device was employed to secure the tuyerescope in place and to prevent air leakage. Thus the tuyerescope facilitated direct observation, by eye or with cameras, of the dynamics of accretion growth at the tuyere tip while blowing proceeded. Focusing on the tip of the tuyere, photographs were taken with cameras individually mounted at the back of the tuyerescope. In the Tacoma smelter tests, motion pictures were taken with a standard Super 8 camera at 25 fps using 25 ASA Kodachrome 40 color film. For the t r i a l s in the other smelters, a 16 mm Beaulieu R16 movie camera, to which a Sony TV zoom lens (f = 20-80 mm, 1:25) was attached, was employed. Both color (Ektachrome 7256,64 ASA) and black and white 99 (Kodak 4-X 7277, 400 ASA) film were u t i l i z e d . The most detail was obtained with the 64 ASA film. S t i l l shots were also made with a motor driven 35 mm camera, usually at f5.0 and 1/4 to 1/125 s (depending on the coverage of the tuyere tip by accretions) using 64 or 400 ASA color film. The 64 ASA film was found to give the finest d e t a i l . No f i l t e r s were used, and exposure settings were determined with a Pentax spot light meter. Samples of accretion growing at the tuyere tip were taken. For this purpose a 9.5 mm hole was d r i l l e d in the Plexiglas window of the tuyerescope and a probe, consisting of a 1.3 m length of 64 mm rod, was inserted. The last 15 mm of the rod was bent at a right angle to form a hook. With the probe inserted through the window i t was possible to observe the hook and manipulate i t to take accretion samples. Pressure fluctuations at the tuyere tip in the copper converter were measured by inserting a 9.5 mm o.d. pipe through the Plexiglas window of the tuyerescope. Pressure in the pipe was sensed with the same pressure transducer of the laboratory work, which was connected via an amplifier to a storage oscilloscope and an FM tape recorder as shown in Figure 4.6. M tape recorder Signal amplifier Pressure transducer / Tuyerescope Peirce - Smith converter Oscilloscope Figure 4.6 Apparatus to Measure Pressure Fluctuations in the Tuyeres of a Copper Converter. 101 To study the bath surface movement inside the converter, cinematographic observations were performed during two sets of t r i a l s at the Inspiration smelter. Two converters were monitored, a Hoboken-type and the Inspiration converter. In both cases the observations were carried out during the slag making blow. With the Inspiration converter the air flow rate into the reactor was about 12.3 - 13.7 Nm /s, the tuyere air 4 pressure 11.0 x 10 Pa (16 psig) and the bath temperature about 1180 - 1230°C. The operating conditions at the Hoboken con-verter were 8.0 - 10.4 Nm3/s, 10.3 - 11.0 x 104 Pa and 1150 - 1210°C, respectively. The cinematographic work was performed with the 16 mm Beaulieu camera, to which a Sony TV zoom lens was attached. Daylight Ektachrome 7256 (64 ASA) film was used. During the f i r s t set of t r i a l s the movie pictures were obtained with the camera placed on the sampling platform close to the converter, in such a way that i t was possible to observe events taking place mainly in the non-spout single-phase region of the bath. No changes in the operating variables (tuyere submergence, rate of gas flow) were at-tempted. For the second t r i a l i t was intended to carry out observations of the spout or two-phase region in the converter l i n e . To perform this study i t was necessary to have an appropriate view port through which motion and s t i l l pictures 102 could be taken. A possible location for this view port was the opening in the side wall of the Inspiration converter, through which burners were formerly held in place but now are mudded over. Two attempts were carried out to implement a view port by mudding a glass window about 200 mm in diameter over the opening. The f i r s t glass was put in place during a con-verter turn-around. Nevertheless, about 5 minutes after blowing was started the window became covered with droplets of liquid which adhered to i t , making visualization of the bath surface practically impossible. A second attempt was made to i n s t a l l a second glass during an interval between blowing in order to try to make observations immediately after blowing was resumed. Unfortunately this time the glass f e l l and broke after which no further t r i a l s were pursued. 103 CHAPTER V EXPERIMENTAL RESULTS 5.1 Laboratory Results This section presents the results obtained with the th sectional 1/4— -scale model of the copper converter. The air-water system was employed to study a number of variables such as tuyere diameter, gas flow rate, pet. f i l l i n g , tuyere submergence, and tuyere spacing. Table 4.5 summarizes the range of the variables under consideration. The experimental procedure followed to carry out the tests is described in section 4.1.3. 5.1.1 Dynamic Pressure Measurements The pressure pulses from the tuyeres in the model were tape recorded or photographed directly from the screen of a storage oscilloscope. Two characteristics of the pressure signals were examined and compared: the frequency of the pulses and the shape of the traces. To calculate the value of the pulse frequency and i t s standard deviation the recorded signals were played back on the oscilloscope to measure the pulse frequency. About 50 to 100 counts were performed'for each set of blowing conditions. Following the frequency 104 measurements, a representative trace of the pressure signals was photographed by means of the oscilloscope camera. 5.1.1.1 Effect of the Air Flow Rate The frequency of the pressure pulses changes with the total flow rate of the injected air as can be observed in Figures 5.1 and 5.2 showing measurements in the laboratory converter model with fiv e , 16-mm and 12-mm diameter tuyeres, respectively. When no deflectors are positioned close to the tuyere line in the model, the frequency of the pulses at low 3 rates (5,000 to 9,000 cm /s, or Froude numbers of about 0.4 —1 to 2.5) is about 13 to 14 s for both tuyere diameters. An increase in the gas flow rate produces an almost linear increase in the pulse frequency in both cases. With 16-mm tuyeres in place the frequency is about 20 s~* for air flow 3 rates and Froude numbers of the order of 40,000 cm /s and 13, respectively. For the case of smaller tuyeres, the frequency -1 3 of 20 s is reached at flow rates of about 24,000 cm /s,or Froude numbers in the range of 14. The overall effect of placing the two deflectors along the tuyere line in the model is a reduction in the frequency of the pressure signals. Figure 5.3 shows this frequency as a function of the modified Froude number of the system, with 22 I 8 J2 14 > » o c o - I 0 0) No deflectors I- — o -n : Two deflectors Tuyere diameter : 16 mm ~ u submergence : 170mm " spacing : 50 mm 42% fill 10 20 30 4 0 Total air flow ( l / s ) Figure 5.1 Bubbling Frequency versus Total Air Flow Rate in the Model with Five 16-mm Tuyeres Bands indicate Standard Deviation. 50 o 24 -20 I 6 o £ I 2 £ 8 T Tuyere diameter : 12mm Tuyere submergence : 170mm Tuyere spacing : 50mm 4 2 % fill No deflectors Two deflectors 10 15 20 2 5 Total air flow rate ( l/s ) Figure 5.2 Bubbling Frequency versus Total Air Flow Rate in the Model with Five 12-mm Tuyeres Bands Indicate Standard Deviation. o ON 107 24 2 0 ~ 16 8 .O-A-A A Tuyere spacing : 50mm o 16 mm , no deflector • " ,two " A 12 mm, no deflector A " , two " 10 I 4 18 22 Fr = />gu 0 /g(^-^> g )d 0 Figure 5.3 Bubbling Frequency versus Modified Tuyere Froude Number in the Model with Five Tuyeres. 108 and without deflectors in place, for both tuyere diameters. With a low Froude number the decline in frequency is about 6 to 7 pulses per second, a much more pronounced reduction than for the case of higher values of the Froude number, in which case the frequency declines no more than 4 pulses per second. The shape of the pressure pulses is also influenced by the air flow rate. The effect of gas flow rate on pressure pulses is shown in Figure 5.4 for the discharge of air through 3 five 16-mm dia. tuyeres. At a flow rate of 12,500 cm /s, or a Froude number of 1.27,(Figure 5.4 (a)), the pulses are characterized by a relatively sharp increase in pressure until a maximum is reached, immediately followed by a more gentle decline. The amplitude of the oscillations is about 2.4 - 2.8 kPa. At a flow rate of 33,700 cm3/s, or a Froude number of 9.25, Figure 5.4(b), the traces are more symmetrical, and the amplitude of the pressure pulses becomes more irregular varying between 2.8 and 6.0 kPa. At a higher flow rate of 3 45,200 cm /s (Froude number 16.6), Figure 5.4(c), the pressure pulses are even sharper and more symmetrical than before, and are now spaced by intervals of constant low pressure signals. The amplitude of the oscillations varies from 2.8 to 5.2 kPa. (a) (b) Figure 5.4 Pressure Traces in the Model as a Function of Gas Five 16-nrm Tuyeres, 40 pet. f i l l i n g , (a) 12.5 1/s, (b) 33.7 1/s, (c) 47.2 1/s. Vertical Scale: 0.18 kPa/div Horizontal Scale: 50 ms/div 110 5.1.1.2 Effect of Tuyere Spacing To study the effect of the distance between tuyeres, several experiments were carried out injecting air through three tuyeres in the laboratory model, instead of using five tuyeres as before. This results in an increase in the tuyere spacing from 50 mm for the five-tuyere situation to 100 mm when air is injected through three tuyeres only. The effect of tuyere spacing can be observed by com-paring Figure 5.1 with Figure 5.5 which shows measurements in the model using three 16-mm tuyeres.For a tuyere spacing of 100 mm the frequency of the pressure pulses is much less affected by gas flow rate than in the five-tuyere configura-tion. In the case of the former the frequency changes from —1 3 —1 14 s at an air flow rate of 7,000 cm /s to 18 s when the flow rate is increased to 43,000 cm /s. The same variation in total gas flow rate when the tuyeres are closer together produces changes in frequency from 13 to about 21 s-^". Figure 5.6 shows the variation in the frequency of the pulses in terms of the modified Froude number for the three-tuyere configuration. Again the frequency is much less sensitive to Froude number in this case than for a tuyere spacing of 50 mm, as shown in Figure 5.3. For a 100 mm spacing, changes in the modified Froude number from 2 to 40 produce an increase in the pulse frequency of less than 4 pulses per second. No deflectors -r TT T I I -ttH-i--11 1 1 11 T i r , i -- f - i Two deflectors Tuyere diameter: 16mm — M submergence :170 mm II spacing : lOOmm 42%f i l l 10 15 20 25 30 35 4 0 45 Total air flow rate ( l /s) Figure 5.5 Bubbling Frequency versus Total Air Flow Rate in the Model with Three 16-mm Tuyeres. Bands Indicate Standard Deviation. L7T i — Z O A -Tuyere spacing 100mm o 16mm , no deflector • II two " A 12 mm no deflector A II two " " A — I 0 14 18 22 26 30 34 38 42 Fr=/DgUoVg(/),-^g)d0 Figure 5.6 Bubbling Frequency versus Modified Tuyere Froude Number in the Model with Three Tuyeres. 113 5.1.1.3 Tuyere Interaction To ascertain whether tuyere interaction takes place or not, two tuyeres were monitored simultaneously in the converter model. Figure 5.7 shows representative traces from piezoelectric transducers placed in the central tuyere of the model (Channel 1) and in an adjacent tuyere (Channel 2), 50 mm apart from the central tuyere. In Figure 5.7(a) an almost complete correspondence between the two signals is observed. Each pressure peak in the central tuyere is mirrored in the traces from the adjacent tuyere, therefore the tuyeres are interacting. This indicates that the same type of fluid dynamic events are taking place in the central and the immediately adjacent tuyere. Twenty seconds later, Figure 5.7(b), the signals from both tuyeres are somewhat different from each other. Only a slight correspondence is observed during the i n i t i a l 200 ms of the signals, after which the events taking place in the central tuyere are clearly different from those occurring in the lateral tuyere. No interaction is found; and the tuyeres are working independently. 0.5s J\ |« 0.5 s (a ) ( b ) Figure 5.7 Simultaneous Pressure Traces from Two Adjacent Tuyeres in the Mode (a) Tuyeres are Interacting (b) Twenty Seconds Later, No Interaction is Observed. 115 5.1.1.4 Effect of Tuyere Submergence A sequence of pressure traces obtained as the labora-tory converter model was being f i l l e d with water is shown in Figure 5.8. In this way i t was possible to study the effect of tuyere submergence on the injection dynamics in the tuyere region. The Plexiglas model was placed with i t s tuyere line 180 mm from the bottom of the model and the air flow rate was kept constant at 22 l/s during the complete measuring sequence. Thus as long as the water level is below the tuyere line in the model the pressure trace is constant, Figure 5.8(a), as expected for the homogeneous discharge of air into a i r . For a tuyere submergence of about 20 mm or 21 pet. f i l l , Figure 5.8(b), the pressure signals are charac-terized by irregular pulses of relatively short duration spaced by intervals of low pressure. For a tuyere submergence of 90 mm (30 pet. f i l l ) , Figure 5.8(c), the pulses become more symmetrical and less disorganized as compared with the previous signals. For a tuyere submergence of 130 mm (37 pet. f i l l ) the pulses occupy longer time periods although intervals of low pressure can s t i l l be observed, Figure 5.8 (d). 116 (c) (d) Figure 5.8 Pressure Traces in a Tuyere of the Model During Charging. (a) Tuyere Submergence: 0 mm (b) Tuyere Submergence: 20 mm (c) Tuyere Submergence: 90 mm (d) Tuyere Submergence: 130 mm Horizontal Scale: 50 ms/div Vertical Scale: 0.18 kPa/div in Channel 1 Signal in Channel 2 Filtered at 60 Hz. 117 5.1.2 High-Speed Cinematography Two different aspects of the injection of air in the water model were studied with the aid of high-speed cinema-tography. During blowing, the air-matte interaction in the tuyere region influences the state of the refractory and the formation of accretions at the tuyere t i p . Therefore i t was considered important to observe events taking place in the tuyere region of the model and relate them to the dy-namic pressure measurements in the tuyeres of both the lab-oratory model and operating copper converters. The high-speed cinematographic work technique was also employed to investi-gate the conditions under which slopping takes place in the _ 102,103 copper converter ' In both cases frame-by-frame analysis of the high-speed films was conducted using a film analyzer and d i g i t i z e r . Also, individual photographs from the films were obtained to i l l u s -trate the different events taking place during the injection of air into water. 5.1.2.1 Observations at the Tuyere Line Analysis of the high-speed films showed that the tuyeres 118 may work independently or may interact. Figure 5.9 shows two photographs taken from a high-speed film of air injected into water at a flow rate of 11.5 l / s , equivalent to a modified Froude number of 1.1. In Figure 5.9(a) the three tuyeres at the lef t of the tuyere line are seen to produce large bubbles, each tuyere acting independently from the others. In this case i t is easy to identify which tuyere is discharging gas; the tips of the other two tuyeres in the model are covered by a gas packet or envelope, which makes impossible to discern the formation of bubbles in those tuyeres. In this case there is a gas path connecting the exit of the tuyeres. Twenty seconds later, Figure 5.9(b), the situation has almost com-pletely reversed. Now the l e f t region of the tuyere line is covered by a large envelope of gas. On the other side, the tuyeres are generating bubbles more independently with less interaction than before. Thus the injection process at the tuyere line is characterized by the generation of an unstable gas-filled packet or envelope, which at certain instants may cover several tuyeres simultaneously, making possible the interaction between them. This unstable envelope breaks down in a matter of seconds, so that the tuyeres which were inter-acting an instant before start to operate as independent tuyeres and viceversa. 119 (b) Figure 5.9 High-Speed Film Photographs from the Tuyere Line of the Model (a) Left-Hand Side Tuyeres Covered by a Gas Envelope (b) Two Seconds Later, the Envelope Breaks Down. 120 5.1.2.2 Slopping Observations As stated .earlier the injection of gas into the bath imparts motion to the liquid which, depending on conditions, may take the form of slopping. High-speed cinematographic observations and tuyere pressure measurements were carried out to study bath movement and fluid dynamic events close to the tuyere region. The high-speed cinematographic work showed that during horizontal submerged injection two regions can be discerned at the surface level of the bath, as can be observed in Figure 4.2. Above the tuyere line a spout or two-phase region exists, covering about 20-40 "L of the surface level of the bath, characterized by a strong agitation of the surface, as the air bubbles disengage from the tuyere t i p . This region is thought to be the primary source of splashing and build-up of accretions at the converter mouth. The remainder of the bath surface consists of a single-phase region with much less agitation which contributes l i t t l e to splashing, except for the case of shallow tuyere submergence; then injection is accompanied by slopping of the bath and enhanced entrainment and splashing. As described in Section 5.2.3, in the single-phase zone in an operating copper converter the bath surface moves mainly from the region above the tuyere line toward the opposite wall. Superimposed on this bath movement, there is evidence of a strong splashing toward the mouth of the reactor 121 5.1.3 Slopping Measurements Bath slopping is an oscillatory motion of the liquid between the tuyere line and the breast of the converter. To investigate the influence of variables such as air injection rate, tuyere submergence and pet. f i l l i n g of the converter 103 on slopping Jorgensen et a l . carried out slopping meas-t h urements in the sectional 1/4 scale model of the copper converter. Slopping and non-slopping of the bath were deter-mined under various injection conditions by visual observa-tion, high-speed cinematography and by measuring the dynamic pressure in the central tuyere with the piezoelectric transducer described earlier. Typical observations of non-slopping and slopping are shown in Figures 5.10(a) and 5.11(a) respectively. As expected when the bath is not slopping, the liquid surface is horizon-tal with waves moving between the jet spout and the opposite wall. However under slopping conditions, the bath surface moves back and forth with a frequency of about 1 Hz, and some of the injected gas moves to the opposite wall. During slopping, periodic pulses of sound could be heard from the air jet, in concert with the rise and f a l l of liquid above the tuyere l i n e . The pressure traces recorded on the screen (a) Figure 5.10 ( b ) Model Under Non-Slopping Conditions. (a) Tuyere Submergence: 130 mm Air Flow Rate: 3.7 1/s 40 pet. f i l l i n g (b) Pressure Trace from Central Tuyere Horizontal Scale: 0.5 s/div Vertical Scale: 0.18 kPa/div (a) (b) Figure 5.11 Model Under Slopping Conditions (a) Tuyere Submergence: 130 mm Air Flow Rate: 20 l/s 40 pet. f i l l i n g (b) Pressure Trace from Central Tuyere Horizontal Scale: 0.5 s/div Vertical Scale: 0.18 kPa/div 124 of the oscilloscope. Figures 5.10(b) and 5.11(b), also clearly reveal the state of bath slopping. Under non-slopping condi-tions the pressure fluctuates, due to the formation of bubbles, about a constant mean value whereas bath slopping causes a 1 Hz oscillation to be superimposed on the signal. The pressure signals were particularly helpful in delineating the transi-tion from non-slopping to slopping. 103 Jorgensen et a l . conducted experiments with varying pet. f i l l i n g and tuyere submergence to determine the c r i t i c a l air flow rate, above which bath slopping prevailed, for each set of conditions. An attempt was then made to correlate the c r i t i c a l air flow rates in terms of kinetic and buoyancy power into the bath from the injected a i r . In a physical-model study conducted earlier by Haida and Brimacombe , the mixing time in hot-metal ladles and torpedo cars has been correlated, and scaled-up to f u l l size, successfully with buoyancy power while kinetic power was found to have a minor influence. Thus the kinetic power and buoyancy power per unit mass of bath were calculated from the following ! u- 104 respective relationships : (5.1) (5.2) Eb = bath 125 for the c r i t i c a l flow rates determined in the experiments. It was found that the c r i t i c a l flow could not be correlated with the kinetic power, but a good correlation was obtained in terms of buoyancy power input. Indeed the critical-flow data from a l l the experiments can be represented on a plot of buoyancy power per unit mass of bath against tuyere 102 submergence as shown in Figure 5.12 . The least-squares f i t line passing through the data delineates regions of slopping and non-slopping so that Figure 5.12 is effectively a 1slopping-behaviour' diagram. It is sten that more buoyancy energy, e.g. greater air flow rate, can be imparted to the bath without slopping when the tuyere submergence is large. To relate these physical model results to converter operation, data on operating converters have been taken from 23 the world-wide survey conducted by Johnson et a l . ; the buoyancy power (calculated at standard conditions) and tuyere submergence for the different smelters has been determined and plotted on the slopping-behaviour diagram shown in Figure 5.13. The c r i t i c a l slopping l i n e , shown in Figure 5.12, has been extrapolated to converter tuyere submergences and also is presented in Figure 5.13. It is seen that most of the converter operations are reasonably close to the c r i t i c a l slopping line. — % F i l l 30 • — 35 A 4 0 O — 45 • l — I — i — I — i — I — i — i — i I I r Slopping No slopping L J I i l l ! I | _ | I L 40 80 120 160 2 0 0 Tuyere submergence (mm) 2 4 0 Figure 5.12 C r i t i c a l Flow Data from Physical Model Experiments on Slopping Behaviour Diagram, 327 i i i m—i—i Empress Morenci Chuquicamoto I Colelones I* / Noranda Ajo Hayden Douglas • Tacoma' El Paso • • Gaspe • Inspiration # Palabora Ronnskar Kosaka Chi no* White Pine* Tamano ^Hidalgo* Port Kembla Utah Anaconda * # •Saganoseki Onahama • y * San Manuel Ventanas / N a o s h i m a - / » Copper Hill B o r « / * K h e t r i 1 i I I I I I I I I L 2 0 0 400 6 0 0 800 1000 Tuyere submergence (mm) Figure 5.13 Buoyancy Power Against Tuyere Submergence for Different Smelters. Solid Line is Extrapolation from Figure 5.12 (Data-points from reference 23) 128 5.2 Industrial Results The results obtained during the t r i a l s at the four smelters studied in this work are presented in this section. The conditions for the tests are summarized in Tables 4.2, 4.3 and 4.6. The number of tests was limited r e a l i s t i c a l l y by the duration of a copper converter cycle and the d i f f i c u l t conditions that are typical of a smelter. However the results obtained at each smelter were consistent with the results from the others and also with what was expected from the results of the laboratory work. 5.2.1 Dynamic Pressure in the Tuyeres Compared to the pressure traces obtained in the labora-tory experiments, the pressure signals recorded during the industrial tests were noisier, mainly due to the rest of the electrical equipment operating in the converter a i s l e . To eliminate part of this ambient noise, most of the signals from the tape recorder were analyzed after being filtered as described in Section 4.1.2.4. 129 5.2.1.1 Effect of the State of the Refractory  at the Tuyere Region Tuyere pressure measurements commencing with the f i r s t charge of a freshly relined converter revealed an interesting change of pulse frequency with increasing number of charges processed by the converter, as shown in Figure 5.14. During the f i r s t charge, the pulse frequency was about 14 s~\ a value close to the frequency measured by Hoefele and 31 Brimacombe at the tuyeres of a Peirce-Smith nickel converter during the f i r s t charge of its campaign. By the third charge of the copper converter the pulse frequency dropped to 8 s-"*" _ i and to about 7 s for Charges 6 and 12 respectively; and thereafter there was a slow decline to a steady value of 4 to 6 pulses per second. It is important to mention that in the smelter in which most of these measurements were made, the tuyere pipes are protruding into the converter 150 mm or more beyond the lining after new refractory has been installed, as can be observed in Figure 5.15. The same situation prevails at the Thompson Smelter. Coincidentally within about three charges the pipes burn back to become flush with the inside wall, but no visible erosion (or damage) of the refractory is observed. Appendix II shows the shape of the pressure pulses during different charges of the converter being monitored. i—i—i—i—i n 1—i—i—i—r r 14 to o c 3 cr 10 • Utah smelter O Tacoma smelter • Home smelter A Thompson smelter A Inspiration converter • Hoboken converter L 31 • O -J L 15 25 J I I I 60 140 2 2 0 Number of charges Figure 5.14 'Bubbling' Frequency from Different Copper and Nickel Converters versus Number of Charges in the Campaign. o 131 ( b ) Figure 5.15 Tuyere Pipes in a Converter from Utah Smelter. (Photographs courtesy of Dr.A. Weddick) (a) Pipes Protruding after Reline (b) Pipes after Third Charge 132 5.2.1.2 Effect of the Tuyere Submergence A typical pressure trace measured at the tuyere tip in the copper converter at Tacoma is shown in Figure 5.16, for two tuyere submergences: 300 mm (normal practice) and 500 mm. The measurements were made during the second slagmaking blow of Charge 254. Thus, with the shallow tuyere submergence, Figure 5.16 (a), a relatively constant, low-pressure signal interrupted periodically by pulses of short duration is observed. The pulse frequency is close to 4 s ^. With the deeper tuyere submergence of 500 mm, Figure 5.16 (b), pulses of greater duration but the same frequency are observed. Again, the pulses are separated by intervals of constant lower pressure. 5.2.1.3 Effect of Tuyere Blockage As was mentioned, the tests at the Utah smelter were performed at the tuyeres of two Peirce-Smith converters. In both reactors two tuyeres were monitored, most of the time simultaneously. During the bulk of the observation period the tuyeres under study remained open. Nevertheless, when tuyere blockage took place the pressure pulses from the tuyeres being monitored showed some interesting features, as can be observed in Figure 5.17, which shows pressure pulses from Tuyeres No. 6 (a) (b) Figure 5.16 Pressure Traces During Charge 254 in a Copper Converter from Tacoma. (a) Tuyere Submergence: 300 mm (b) Tuyere Submergence: 500 mm Vertical Scale: 14 kPa/div Horizontal Scale: 100 ms/div 134 and No. 25 (Channels 1 and 2, respectively) of Utah Converter No. 2. In Figure 5.17 (a) the pulses are coming from tuyeres totally open, as could be observed through the Plexiglas window of the tuyerescope. The pressure traces are character-ized by pulses with an amplitude of about 7 to 14 kPa and a frequency of 4 to 5 s-^". Seven minutes later Tuyere No. 6 was observed to be blocked, while Tuyere No. 25 remained open. The tuyere pressure traces under these conditions can be observed in Figure 5.17 (b). For the open tuyere the pressure traces remain essentially the same as before, while the signals from the blocked tuyere change drastically to a f l a t trace, without pulses. Three minutes later the accretions blocking tuyere No. 6 dislodged by themselves, and again the signals from both tuyeres are characterized by regular pulses, as can be ob-served in Figure 5.17 (c). This suggests that the pressure signals from individual tuyeres may be used to detect tuyere blockage. It is also important to mention the effect of the tuyere punching on the amplitude of the pressure pulses. Immediately after punching the pressure traces had a greater amplitude, which then decreases as the next punching cycle was approached. Similar results were obtained previously by Hoefele and 31 Brimacombe in a nickel converter. (a) ( b ) (c) Figure 5.17 Simultaneous Pressure Traces from Two Tuyeres in a Copper Converter. Tuyere No.6 in Channel 1 and Tuyere No.25 in Channel 2. (a) Both Tuyeres are Open (b) Seven Minutes Later, Tuyere No.6 is Blocked, Tuyere No.25 is Open (c) Three Minutes Later, Both Tuyeres are Open Again. Vertical Scale: 4.8 kPa/div Horizontal Scale: 100 ms/div LO Ln 136 5.2.2 Accretion Growth at the Tuyere Tip As stated earlier the tuyerescope provided an excellent view of the bath and the growth of accretions, and made pos-sible the sampling of the material forming the accretion while i t was growing at the tuyere t i p . 5.2.2.1 Dynamics of Accretion Growth Typical accretion growth in the copper converter, de-picted by a sequence of photographs taken with the 35 mm camera, is shown in Figure 5.18. These photographs were taken during the second slagmaking blow of Charge 254 of a converter from the Tacoma Smelter. The oxygen content of the enriched air was 26 pet and the matte grade was 43 pet Cu.Figure 5.18 (a) shows the tuyere nearly covered with an accretion which within seconds of the photograph being taken, spontaneously dislodged. The ensuing photographs in the sequence reveal the growth of the next accretion over a time span of about 180 seconds whereupon the tuyere again was nearly covered. Typi-c a l l y , the time for complete coverage of the tuyere was 60 to 180 seconds at this stage of the converter cycle. In Figures 5.18 (b) to (f) the accretion can be seen to grow primarily from the bottom of the horizontal tuyere. I n i t i a l l y , the accretion is crescent-shaped extending from the 3 to 9 o'clock 137 (e) 10mm (f ) i 1 Figure 5.18 Dynamics of Accretion Formation in a Converter at Tacoma Smelter. (a) Tuyere is Nearly Blocked (b) Accretion Dislodged Spontaneously (c) -(f) Accretion Growth Resumes 138 position of the tuyere; the accretion continues to grow upward u n t i l , as seen in Figure 5.18 (a) and ( f ) , the uncovered region of the tuyere tip has been reduced to a small area at the 1 o'clock position. In Figures 5.18 (e) and (f) the upper region of the accretion is seen to be brighter, i.e., hotter, than that near the bottom of the tuyere; in addition, s t r i -ations which are roughly concentric with the circular tuyere are v i s i b l e . Visual observation and the cinematography con-firmed these general features of accretion formation and also showed that, from time to time, protruding parts of an accre-tion would disappear then reappear suddenly. At f i r s t i t was thought that this phenomenon was caused by rapid melting and freezing, but i t is more like l y a result of temporary immersion of the protuberances as bath washes briefly against the accretion. 5.2.2.2 Effect of Oxygen Enrichment of the Blast The photographic work in the tuyeres of the different converters indicated that the mechanism of accretion growth is affected by the oxygen enrichment of the blast. Figure 5.19 shows accretion formation during the f i r s t slagmaking blow in a converter at the Noranda Smelter, where oxygen enrichment of the air is not used. As can be observed, early in the cycle the accretion tends to build up gradually, mainly 139 Figure 5.19 Accretion Formation During First Slagmaking Blow in a Copper Converter at Home Smelter. 140 upward from the bottom of the tuyere without remelting of the solidified material. Late in the converter cycle the build-up of accretions is faster, but with some remelting back to the bath. In Figure 5.19 (a) the tuyere is about half-blocked with solidified material growing from the bottom and the upper part of the tuyere t i p . Ten and twenty seconds later, Figures 5.19 (b) and 5.9 (c), some remelting of the accretion material back to the bath is observed. Sixty seconds later, Figure 5.19 (d), the accretion growth process has started again and about 70 pet. of the tuyere tip area is blocked. During the entire cycle at Noranda the accretions were observed to be more dense and stable, as compared with the accretions formed at Tacoma which are porous and can be removed easily by punching. The effect of oxygen-enrichment can be further eluci-dated by referring to the accretion formation process at Utah smelter, where oxygen-enriched air is used. Figure 5.20 de-picts a sequence of photographs taken during the slagmaking blow of Charge 1 of a converter from the Utah smelter. As in Tacoma the oxygen content of the enriched air was 26 pet. The time between each photograph was 20 seconds. It is seen that the accretion grows primarily from the bottom of the tuyere. As in Tacoma the accretion is i n i t i a l l y crescent shaped and continues to grow until the uncovered region of the tuyere (a) (b) Figure 5.20 Accretion Formation During Slagmaking Blow in a Converter at Utah Smelter. 142 tip is reduced to a small area in the upper region of the tuyere. As in the case of the Tacoma smelter, the accretions were porous and could be removed easily by punching. 5.2.2.3 Analysis of the Accretion Samples Samples of accretion, which were obtained with some d i f f i c u l t y , were studied by X-Ray Diffraction and Scanning Electron Microscopy. Samples of accretion formation taken during the f i r s t slagmaking blow at Tacoma, during the third slagmaking blow at Noranda, and at the end of the slagmaking blow, and during the coppermaking blow at the Utah smelter were analyzed. For a l l the samples obtained during slagmaking blows, the major constituent of the accretion was found to be Cu^ ggSj a high-temperature phase which is metastable at room temperature. Other compounds in the samples were identified as various copper-iron sulphides (FeS2, Cu^FeS^, Cu^FeS^, etc). No magnetite was found even though special care was taken to detect i t s presence. This suggests a freezing mechanism of the bath for the accretion growth, rather than a magnetite precip-itation mechanism due to local over oxidation of the bath. Figure 5.21 shows a S.E.M. photograph of the material from the third slagmaking blow at Noranda. The analysis of the copper-making accretions from the Utah Smelter indicated that the major components of the sample were metallic copper and Cu1 QfiS. It 143 Figure 5.21 S.E.M. Photograph of the Accretion Sample from Slagmaking Blow in a Copper Converter at Home Smelter. 144 should be mentioned that during the sampling of this last specimen i t was not possible to perceive clearly i f this sample represented accretions growing at the end of the tuyere or simply liquid bath freezing at the tip of the sampling probe. 5.2.2.4 Influence of the 4B5 Punching System The Utah smelter and the Inspiration smelter employ 4B5 Kennecott mechanical punchers to clear a blocked tuyere by forcing a steel rod through i t . The 4B5 puncher is attached to each tuyere, with its punch rod inserted half-way through the tuyere pipe during injection. Therefore to carry out the dynamic pressure measurements at the tuyeres of .the two smelters i t was necessary to remove the 4B5 punchers in order to attach the tuyerescopes to the back of the tuyeres to be monitored. In the course of these measurements i t was suspected that the punching system plays a role in the accretion growth at the tuyere t i p . During most of the observation period at the Utah and Inspiration smelters, the tuyeres under study (with the tuyerescope attached to them) remained open. Accretion formation was observed mainly during the f i r s t period of the slagmaking stage, wherein a fast build up of accretions 145 occurred. Later in the cycle, only occasionally some accretion growth was observed during short intervals, after which the solidified material dislodged by i t s e l f from the tuyere t i p , perhaps due to remelting effects. Nevertheless the rest of the tuyeres in the converter (with the 4B5 puncher at their back) were intermittently blocked, as evidenced by the drop in total gas flow rate into the converter. The fact that the tuyeres being monitored showed almost no accretion build-up for considerable lenghts of time, while for the other tuyeres blockage did take place, indicates that the 4B5 punching system affects in some way the mechanism of accretion growth by influencing the fluid-dynamic conditions inside the tuyere pipe. To test this hypothesis some laboratory tests were carried out. Using a pitot static tube, the velocity profile across a 600 mm (51 mm I.D.) pipe positioned in a tuyere body from the Utah smelter was measured. Working under gas flow rate conditions close to normal operation three different situations were studied, namely: a) no punch bar inserted through the back of the tuyere b) a 25-mm punch bar inserted 600 mm through the back of the tuyere body and touching the bottom of the tuyere pipe 146 c) same as in b) but now with the punch rod touching the top of the tuyere t i p . The velocity profiles measured under these three conditions can be observed in Figure 5.22. When no punch bar is inserted the velocity profile is non-symmetrical, which is a consequence of the off-axis injection of air through the tuyere body and the short length of the tuyere pipe which makes i t d i f f i c u l t to obtain fully developed flow conditions. Nevertheless, although non-symmetrical, the velocity profile is relatively flat as expected for the flow of air under tur-bulent conditions (the Reynolds number throughout the measure-ments was about 6 x 10^). When the bar was inserted touching the bottom of the tuyere pipe the velocity profile was observed to be relatively symmetrical and parabolic, with a maximum velocity close to the tuyere centerline and decreasing rapidly toward the wall of the pipe. Finally, when the inserted punch rod was touching the upper part of the tuyere pipe wall the velocity profile was observed to be significantly non-symmetrical, with the lowest velocities near the bottom of the pipe wall and gradually increasing to reach a maximum value close to the top of the tuyere pipe wall. Thus i t is clear that the punching system affects the flow regime at the tuyere pipe and therefore possibly also the process of accretion growth. Distance from tuyere pipe centreline (mm) Figure 5.22 Velocity Profile Inside a Tuyere Pipe Showing the Effect of the Punching System. 148 5.2.2.5 Tuyere Pipes. Metallographic Work Two tuyere pipes from a converter out of service for relining were obtained; a short (25 cm) pipe and a longer (50 cm) pipe supposedly coming from the centre and the end of the tuyere line respectively. These tuyeres were examined and compared with high pressure tuyeres from the t r i a l s at ASARCO 3 A Tacoma . The end tuyere (Figure 5.23 (a)) exhibits what appears to be a neck 15 mm from the tip of the tuyere presuma-bly due to the tensile strains caused by the punch bar. There is evidence of damage by the punch bar because the tip of the tuyere has been bent back at right angles to its axis on one side. The outside of this tuyere tapers down somewhat presuma-bly due to the oxidation and spalling. The central tuyere, Figure 5.23 (b) in contrast shows no evidence of necking or tapering of the outside. The tuyere seems to be wearing away on the inside presumably due to the punching action and thermal and chemical attack. This tuyere obviously was shorter than the end tuyere; therefore its tip was farther removed from the bath, making i t colder and less prone to necking under the influence of the punch bar. Metallographs of the central tuyere at 5 mm, 18"mm,arid 25 mm from the tuyere tip are presented in Figure 5.24 (a) to (c) respectively; Figure 5.24 (d) shows a metallograph from the back of the tuyere pipe (virgin pipe). 149 Figure 5.23 Longitudinal Sections of Tuyere Pipes from a Converter at Utah Smelter (a) End Tuyere, (b) Central Tuyere (a) (b) ( c ) (d) Figure 5.24 Metallographs of the Central Tuyere from a Converter at Utah Smelter (a) 5 mm from the Tuyere Tip (b) 18 mm from the Tuyere Tip (c) 25 mm from the Tuyere Tip (d) Back of the Tuyere. Virgin Pipe 151 Neither of the tuyeres exhibit significant internal oxidation of the steel pipe in contrast to the high pressure 34 tuyere which exhibits internal oxidation running back 120 mm from the t i p . This could also indicate that the tip of the high pressure pipe is significantly closer to the bath and is running much hotter. 5.2.3 Bath Surface Movement and Splashing As described previously, to study the bath surface movement inside the converter, two set of observations at the Inspiration Smelter were carried out. During the f i r s t set of t r i a l s movie pictures were obtained with the camera placed on the sampling platform of the Hoboken and the Inspiration converters, in such a way that i t was possible to observe events taking place mainly in the non-spout region of the bath. The results obtained from this preliminary t r i a l indicated that i t is possible to observe with some detail the bath surface movement of a syphon-type converter while blowing. The movie pictures indicate that in the single-phase zone the bath surface moves mainly from the region above the tuyere line toward the opposite wall. Some axial movement of the bath was also observed, as evidenced by solids floating on the bath surface. It is not clear whether this axial movement takes place over the entire converter length or not. 152 Superimposed on this bath movement, there is evidence of a strong splashing taking place from the spout region toward the mouth of the converter. Unfortunately i t was not possible to film the core of the spout region, in which the gas bursts through the bath surface. During the second set of t r i a l s i t was attempted to carry out observations of both the two-phase spout and the remainder of the bath surface. A major objective of these t r i a l s was to link bath movements and events at the tuyere tip to define optimum conditions to minimize build-up in the converter. Thus, an attempt was made to study the influence of several injection variables on splashing and build-up at the mouth and off-take regions of the converter and relate them to injection behaviour. Unfortunately, as was mentioned, two attempts to implement an appropriate view port fai l e d , after which no further t r i a l s were pursued. Therefore, i t was not possible to make direct observations of bath surface movement at the spout region nor to link these observations with some injection parameters. Nevertheless i t was possible to observe the amount of liquid material ejected from the charging mouth of the converter and to relate i t to tuyere submergence. These observations, although rather crude, indicated that for the Inspiration converter a 153 tuyere submergence of less than 70 cm tends to generate severe splashing. On the other hand no splashing could be observed for tuyere submergences deeper than 90-100 cm. 154 CHAPTER VI HEAT LOSSES FROM COPPER CONVERTERS.  A MATHEMATICAL MODEL. 6.1. Scope of the Heat T r a n s f e r Model In Chapter I several, o p e r a t i n g problems which a f f e c t o p e r a t i n g p r a c t i c e , such as tuyere blockage due to a c c r e t i o n growth at the tuyere t i p , r e f r a c t o r y wear at the tuyere l i n e , and tuyere e r o s i o n , were d e s c r i b e d . Many of these problems are r e l a t e d to the i n j e c t i o n dynamics i n the tuyere r e g i o n as w e l l as to heat l o s s e s from the con v e r t e r while the r e a c t o r i s out of the s t a c k . Because a c c r e t i o n formation i n v o l v e s s o l i d i f i c a t i o n of bath at the tuyere t i p , the temperature of the r e f r a c t o r i e s near the tuyere l i n e , p a r t i c u l a r l y j u s t as the c o n v e r t e r i s r o l l e d i n t o the s t a c k , can i n f l u e n c e tuyere blockage and a l s o punching frequency. I f , while the converter i s out of the s t a c k , s u f f i c i e n t heat i s l o s t through the mouth to c o o l the i n s i d e w a l l below the s o l i d u s temperature of the ba t h , some m a t e r i a l w i l l f r e e z e against the r e f r a c t o r i e s when the con v e r t e r i s r o l l e d back i n t o the stack to commence blowing. 155 To quantify the influence of out-of-stack time and other converter variables on the temperature distribution in the refractory wall, especially at the tuyere l i n e , a mathematical model has been formulated. Factors such as diameter of the converter, size and position of the converter mouth and the use of a mouth cover have been studied with the model, in order to relate converting practice to operating problems. 6.2 The Mathematical Model The model calculates the radiative heat exchange between a given surface element and the rest of the elements in the mantle and the end walls of the converter as well as the mouth of the reactor. The convective and radiative heat losses from the external surface of the vessel and conduction through the refractory wall also are included in the calculations. The model is flexible in that i t allows variation in the size and position of the converter mouth. Therefore i t is possible to simulate heat-transfer conditions for both Peirce-Smith (central mouth) and Hoboken (end-wall mouth)converters. Figure 6.1 schematically depicts both types of reactors. 156 Tuyere 77777" Mouth fflmmiTy^^^J))iiniiinj Tuyeres 7 7 7 * 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 " (a) Tuyere t / / n ~ r n n u Mouth / Tuyeres /}///////////////// /\ / / / / / / / (b) Figure 6.1 (a) Schematic of the Peirce-Smith Converter (b) Schematic of the Hoboken Converter 157 To develop the heat transfer mathematical model, the following assumptions were made: a) The converter is empty during out-of-stack periods. b) The convective heat transfer inside the internal volume of the converter is negligible. c) The heat exchange by conduction between the different elements into which the converter wall is divided is negligible. d) The refractory is considered as a gray body. e) The gas inside the converter is a non-absorbing and non-transmitting medium. f) The mouth of the converter is considered as a black body at constant temperature. g) The converter radius is large enough such that each element into which the converter internal surface is subdivided can be considered as a plane surface. h) The size of the elements into which the converter surface is subdivided is small enough such that the shape factor angles can be considered as constants for each element. i) The thermal conductivity of the refractory is a linear function of temperature. 1 6.2.1 Radiation Heat Transfer in Copper Converters The radiation heat transfer taking place amongst the different surface elements in the copper converter can be treated conveniently in terms of the radiosity J^~ >i^^ >i which is defined as the rate at which radiation leaves a given surface per unit area. J . = x.G. + e.E, . (6.1) I i i I b,i The net rate of heat transfer from a surface * i ' by radiation is the difference between the radiosity and the irradiation. qi = Ai( Ji ~ Gi} ( 6*2 ) In the model the refractory and the gas inside the converter are considered as a gray surface with constant emissivity and as a non-absorbing and non-transmitting medium, respectively. For gray bodies, *t = 1 - e (6.3) then: (6.4) 159 The incident radiation ( i r r a d i a t i o n ) consists of the portions of radiation which impinge on from a l l the ele-ments, and can be expressed compactly i n the form N A.'G. = V A.•J . «F. . (6.5) j = l J ' J Substituting Equation (6.5) for G^ i n Equation (6.2) yie l d s [JI - |JJ -FI . J ] ( 6 - 6 ) To calculate the radiation heat transfer from any one of the N elements into which the converter i s subdivided i t i s necessary to solve N equations i n N unknowns. These equations are obtained by evaluating the emittances of the surfaces and the radiation shape factors between them and writing Equations (6.4) and (6.6) for each element. Then, in a general form: q. £ . r "I N A. 1 - e . |_ b,l i j 1 ^ j 1, j (6.7) with 1 < i< N Equation (6.7) can be recast i n the more convenient form: a. 1. + a. „ J0 + a. JK 7 = C. (6.8) i , l l i , 2 2 i , N N l 160 Where the coefficients a. . and C. i , J i are a. . = 1 - F. . + -a i - (6.9) 1,1 1,1 1 -e. l a. . = - F. . (i 4 j) (6.10) and E, . • £ . C. = - (6.11) 1 1 - e . 1 In the model the mouth of the converter is considered as a black surface at constant temperature. For any black surface at temperature T in the converter enclosure, the radiosity must equal o T4 and is no longer an unknown. To simplify the calculation procedure, the following matrix representation is defined A = al l a12 l21 d22 NI N2 IN NN 161 C = and J = J N The set of equations to be solved can be written then as: (6.12) If £AJ ^ represents the inverse of matrix £AJ , the solution for the radiosities is given by: H - H_1[c] (6.13) Once the radiosities are known, the rate of heat flow can be obtained from Equation (6.4) for each element. To take into account the fact that the mouth of the converter is being considered as a black surface, the elements a., and C. in the converter mouth are arbitrarily defined as: a. . = h + , L_ 1 x 10 1 1 L ^ T J x 10 162 In order to calculate the rate of heat flow from each element in the model i t is necessary to evaluate the fraction of the total diffuse radiation leaving one surface which is intercepted by another surface and vice versa. The fraction of diffusely distributed radiation leaving a surface Ag that reaches surface A„ is called the radiation shape factor F„ ~ R v E,R. The technique employed to calculate the radiation shape factor in the model is given in Appendix III. 6.2.2 Transient Conduction in the Elements of the Model Once the rate of heat flow from each element of the model has been calculated, i t is possible to evaluate the variation in temperature that takes place within each element An implicit one-dimensional fin i t e difference method was considered suitable to carry out the calculations. The sim-plest implicit formula for node 'm' in any of the elements into which the converter has been subdivided, in the absence 97 of heat generation, is : [ T (j + l ) - T ( j ) l = T C IV (j+D -T (j + l ) l (6.14) t |_ m J m J J ^ n,ra[ n J m J J where 'n' denotes the nodes bordering node 'm'; Tm(j) and Tm(j+1) are the temperatures of node 'm' at times ' j ' and 'j+1', respectively, and C^ ^ is the thermal conductance between nodes 'n' and 'm', defined as: 163 C - Conductivit x i A"r e a Transverse to Conduction Path n,m ~~ ^ Length ot Conduction Path In general K x S (6.15) n n ,m The thermal conductance expressions for the different types of nodes in the one-dimensional calculations are presented in Appendix IV. Rearrangement of Equation (6.14) yields: T N C t "I N C t Tm(j) = Tm( j+i ) | i + ^ rWrl- 2 T n ( J + 1 ) ( 6 - 1 6 ) L n=| mJ n = | m Therefore, the method requires the simultaneous solution of a set of equations at every time step. For a general interior node, Equation (6.16), after some simplifications, can be expressed in a matrix compatible notation as: B. = T. ..(j + 1) A. . 1 + T. (j + 1) A. . + T. . ( j + 1) A. . , l l - l J isi - l i 1,1 i+l i,i+l (6.17) where: c p V. Bi ~K7~t~ Ti ^ J ^  c P V A. . = —rs •r— + S . . ., + S . . 1,1 t l j l - 1 1,1+1 164 A. . = - S. . and A. . ., = - S. . A i , i - l i , i - l i,i+l i,i+l For node i= l , i.e. the node at the internal surface of one element, i t is necessary to take into account the rate of radiative heat flow at each surface node. In this case the heat balance, in matrix compatible notation, is expressed as Bl = Ti(J+ 1 ) Al 1 + T2 Al 2 (6.18) where: c P V. r i A1 B l = - T 7 - t - i T l ( J ) "A *KT c P V±  Al , l = K1 t + Sl , 2 Al , 2 " Sl , 2 The radiative heat flow, q/A, is calculated according to the method outlined in Section 6.2.1. For node i=N, i.e. the node at the external surface of one element, i t is necessary to take into account the heat losses by convection and radiation from the surface to the surroundings. In this case the heat balance in matrix compatible notation is expressed as: 165 BN = Tn - l(J+ 1 ) AN,N-1 + TN(J+ 1 ) AN,N (6.19) where: c P V AN,N ~ KN t + SN,N-1 AN,N-1 = SN,N-1 The convective heat transfer coefficient from the external surface, hN, is calculated by the method outlined in Appendix V. Equations (6.17),(6.18) and (6.19) represent a set of equations for the 'future' temperature of each nodal point and the future temperatures at neighboring points. There wil l be as many equations as there are unknown future temperatures, and once this set of equations is solved the resulting future temperatures become the i n i t i a l temperatures for the next time increment. The coefficients are always positive and the implicit technique will therefore be stable with any time increment step. In essence, the implicit technique reduces to the solution of a set of simultaneous algebraic equations at each time increment; a matrix inversion method can be used for solution by means of a digital computer. 166 To solve the set of equations, i t is necessary to know the temperature profile under steady state conditions, that is when the converter is charged and air is being injected into the melt, as an i n i t i a l condition. Also i t is necessary to take into account the variation of the refractory thermal conductivity with temperature. Appendix VI outlines the pro-cedure employed to calculate both the steady state temperature profile and the variation of thermal conductivity with temperature. 6.2.3 Computer Program The mathematical heat-transfer model described in the previous sections was solved by using the program reproduced in Appendix VII. A flow chart illustrating the sequence of operations for the computer solution of the model is shown in Figure 6.2. Two double-precision subroutines developed by the UBC Computing Centre were used; the subroutine DSLIMP to obtain, and improve iteratively, the solution of Equation (6.12) and the subroutine SLE to solve the system of linear Equations (6.17),(6.18) and (6.19). As was mentioned, in the case of the one-dimensional, finite-difference method, the coefficients are always positive and the implicit technique wil l therefore be stable with any 167 S T A R T EVALUATE PARAMETERS AND CONSTANTS NO CALCULATE RADIOSITIES SOLVE EQ. (6.12) WITH SUBROUTINE DSLIMP-UBC COMPUTE INITI/ PROFILE IN H *L TE1MPERATURE IE REFRACTORY COMPUTE RAD1 FACTOR FOR 1 IN THE CONVE ATION SHAPE HE ELEMENTS IRTER MODEL EVALUATE HE EACH CONVEF AT FLOW FROM ITER ELEMENT EVALUATE TEMPERATURE PROFILES SOLVE EQS.(6.17),(6.18),(6.19) WITH SUBROUTINE SLE-UBC t = t + At P R I N T OUT OF STACK TIME-HEAT FLOW RATES REFRACTORY TEMPERATURES YES ( S T O P j F i g u r e 6.2 Flow Chart o f the Computer Program 168 time increment step. However, i t has been pointed out that there is an optimum combination of the size increment step 99 Ax, and the time increment step at. Thomas et a l . indicated that this optimum occurs at smaller time steps with finer meshes and that the dimensionless parameter K At P C AX 2 appears to remain constant with a value of roughly 0.1 at the optimum of three meshes under study. Therefore, with the values for density and specific heat of the refractory given in Table 6.1 and assuming an average refractory temperature of 800 °C, the optimum combination of size and time increment steps would be: 18.65 That i s , i f a time step of 100 s is chosen, the size increment step has to be about 2.3 cm. 6.2.4 Range of Variables Studied in the Model The following variables dealing with geometric and oper-ating characteristics of the copper converting process were studied: 169 i) Diameter of the Converter i i ) Size of the Converter Mouth i i i ) Position of the Converter Mouth iv) Temperature of the Converter Mouth v) Use of a Mouth Cover By changing the position of the mouth i t was possible to calculate the thermal conditions prevailing in both, central mouth,or Peirce-Smith converters, and end wall mouth, or Hoboken or Inspiration converters. The values of the varia-bles employed in the solution of the heat-transfer model were selected to reproduce the conditions prevailing in industrial converters. Table 6.1 shows the levels of the variables as well as some constant values employed in the solution of the model. 6.3 Accuracy of the Heat-Transfer Model As was mentioned, for purposes of modelling, the inside wall of the converter was subdivided into a number of surface elements. The accuracy of the model was calculated based on the value of the radiation shape factor of the elements. Since for an enclosure, such as that formed by the internal surface of the converter and its mouth, the radiant energy leaving the surface ' i ' must impinge on the N surfaces forming the enclosure: (6.20) TABLE 6.1 PARAMETERS IN THE HEAT TRANSFER MODEL Converter Diameter, m 4.0 4.6 5.2 Converter Length, m 9.1 Converter Mouth Temperatute, °C 30 400 600 2 Area of the Mouth, m 4.50 6.24 Emissivity of Refractory Surface 0.4 0.6 0.8 Refractory Thermal Conductivity, W|m K 1.16 @ 199 C 1.47 @ 649 C 1.73 @1316 C 101 1 Refractory Density , kg/m 2930 Refractory Specific Heat, J/kg K 960 External Surface Temperature, °C 190 Heat Transfer Coefficient, W/m2 K 7.2 171 The error associated with the model calculation can therefore be defined as: N N 1 I N I N = l - i l Y F . - (6.21) I j J Figure 6.3 shows the average error, and the computing cost associated with the number of surface elements into which the converter model is divided. As a compromise between the accuracy of the model and i t s computing cost, the converter was therefore divided into about 200 elements for a l l the computer runs performed during the calculations. Under these circumstances the estimated error in the calculations was always less than 4 %. 6.4 Influence of the Refractory Emissivity The emissivity of most bodies is a function of the wavelength of the radiation and of some properties of the emitting surface such as type of material, roughness and temperature. The value of emissivity ranges from zero to unity and may be regarded as a 'correction' factor repre-senting the deviation of the actual emissive power of a surface from that of a blackbody at the same temperature. The reported emissivities of some materials show considerable • f - 123,124 variation even over a narrow range or temperatures ' 100 2 0 0 300 4 0 0 Number of elements Figure 6.3 Average Error and Computing Cost Associated with the Number of Surface Elements into Which the Converter Model is Subdivided 173 Caution therefore should be exercised in using emissivity values and i t is necessary to study the sensitivity of the model to such an important'parameter as the emissivity of the refractory surface. For purposes of this analysis three values of the refractory emissivity were used (0.4,0.6 and 0.8) to calculate the temperature of the refractory at the central tuyere of a converter as a function of out-of-stack times. The results are presented in Figure 6.4, for the case of a Peirce-Smith converter 4 m in diameter and 9.1 m in length. As can be observed, the temperature at the central tuyere is almost negligibly affected by the value of the emissivity employed in the calculations. This result is not surprising i f one looks at the geometry of the converter which is strik-ingly similar to the laboratory approximation of a blackbody, i.e. a cavity whose interior walls are maintained at a uni-form temperature. The irradiation in such a cavity is equal to the emissive power of a blackbody at the same temperature (indeed this is the definition of a blackbody in practical terms). A small hole in the wall (and the converter mouth is a small hole as compared with the other dimensions of the converter) of this cavity will not disturb this condition appreciably, and the radiation escaping from the converter therefore will have blackbody characteristics dependent only on i t s temperature. 174 1200 l — I — I I I I ,n—r Dc= 400cm L c =910 cm A M= 4.50 m 2 I 150 o I 100 O £ 1050 1000 h = 7 . 2 X I 0 ~ 4 W / m 2 K 9 5 0 I L 1 J I I I L 4 0 0 Out 800 of stack 1200 time (s) 1600 Figure 6 . 4 Temperature of a Central Tuyere in a Peirce-Smith Converter as a Function of Out-of-Stack Time for Different Values of Refractory Emissivity. 175 6.5 Model Predictions The model was utilized to study the effect of changes in different variables and the implications for the copper converting operation. 6.5.1 Effect of the Converter Mouth Position The temperature profiles calculated along the tuyere line for different out-of-stack times are relatively f l a t . Figure 6.5 shows the temperature of the refractory surface at the tuyere line as a function of the distance from the centre of a Peirce-Smith converter for different out-of-stack times. As can be observed, for a l l times being considered, the temperature difference between a tuyere facing the mouth of the converter and one close to the end wall of the reactor is less than 30 °C. Similar results are obtained for end-wall mouth vessels, Hoboken or Inspiration converters, as indicated in Figure 6.6, which shows the temperature at the tuyeres as a function of the distance from the end wall. In this case the difference in temperature between an end-wall tuyere and a tuyere facing the converter mouth is about 60 °C. Figure 6.7 compares the drop in temperature . as a function of out-of-stack times for tuyeres close to the end wall of the converter and tuyeres facing the mouth of the reactor for both central-mouth and end-wall mouth converters. If one considers that the melting 200 F T l r 1—=1 I 150 I 100 1050 1000 9 5 0 9 0 0 I L T m = 3 0 ° C h = 7.2XlO*W/cm2 K 1 1 1 1 Dc =400cm = 9IOcm Am = 4.5 n>2 4 0 0 200 2 0 0 4 0 0 Distance from centre of the converter (cm) Figure 6.5 Temperature Profiles along the Tuyere Line in a Peirce-Smith Converter for Different Out-of-Stack Times. i — r t= 100s 300s 600 s Am=4.5 m 2 T m = 3 0 ° C h =7.2XI0"4W/cm2K 1 200 400 600 800 Figure 6 . 6 Distance from the end wall (cm) Temperature Profiles Along the Tuyere Line in an End Wall Mouth Converter for Different Out-of-Stack Times. o o a) a> a. E <D 1200 50 0 0 0 5 0 1000 950 D c = 400cm L c =9IOcm A m = 4.5 m T m =30*C h = 7.2 XlO 4W/cm 2K Central tuyeres End wall mouth converter Central mouth converter 200 600 000 4 0 0 1800 Figure 6.7 Out-of-stack time(s) Temperature Drop as a Function of Out-of-Stack Time for End and Central Tuyeres for both Central Mouth and End Wall Mouth Converters. 00 179 point of copper mattes is about 1050 to 1100 C, for the case of central-mouth or Peirce-Smith converters, out-of-stack times of more than about 10 minutes would generate massive accretion formation along the entire length of the tuyere line when blowing is resumed. On the other hand for end-wall mouth converters, out-of-stack times of 10 minutes would tend to produce accretion formation mainly in the region facing the mouth of the reactor. The position of the mouth has almost no effect with respect to heat losses from the converter. Figure 6.8 shows the rate of heat losses and the total heat losses through the converter mouth as a function of out-of-stack times for both central-mouth and end-wall mouth converters. As can be seen, converters with the same geometric and operating characteris-t i c s , other than the position of the converter mouth, behave almost identically from the point of view of heat losses from the converter mouth while the reactor is out of the stack. 6.5.2 Thermally Active Zone in the Refractory The temperature changes inside the refractory wall at different out-of-stack times can be observed in Figure 6.9. Changes in temperature are restricted to a penetration of about 6 to 8 cm, even for out-of-stack times as long as one hour. This means that for practical purposes the refractory wall of the copper converter may be considered as composed by 6 0 0 9 0 0 1200 Out of stack time (s) 5 0 0 1800 Figure6.8 Rate of Heat Losses and Total Heat Lost as a Function of Out-of-Stack Times for Central Mouth and End Wall Mouth Converters. 00 o 181 Penetration in the refractory (cm) Figure 6.9 Temperature Profiles Inside the Refractory Wall at Different Out-of-Stack Times for an Element Facing the Mouth of a Peirce-Smith Converter. V 182 two regions. One, the zone 6 to 8 cm thick mentioned above, is subjected to a thermal cycle of temperature decrease during the out-of-stack periods followed by a rise in temperature as blowing is resumed. The other zone, beyond this internal unsteady state zone, is characterized by a refractory temper-ature that does not change with changes during the converting cycle. Once the temperature profile inside the refractory wall has developed, this external region of the refractory maintains this temperature profile during the rest of the converter campaign. 6.5.3 Effect of the Converter Diameter Changes in the diameter of the copper converter do not affect significantly the thermal response of the reactor. Figure 6.10 depicts the surface temperature of a tuyere facing the mouth of a Peirce-Smith converter as a function of the out-of-stack time. In the calculations three different con-verter diameters -400 cm, 460 cm and 520 cm- have been consid-ered. Perhaps the most interesting effect of an increase in the converter diameter is the consequent increase of the time for accretion formation upon resumption of blowing. For the 400-cm diameter case the temperature at the central tuyere of the converter drops to 1050 °C after about 12 minutes of the converter being out of the stack. For a converter with a diameter of 460 cm the temperature at the tuyere line of the 1200 I 150 I 100 1050 000 950r -L T Lc=910 cm A m = 4.5 m 2 Tm = 30°C h =7.2XI0"4W/cm2K Dc= 520cm 400cm 460 cm 1 400 800 1200 1600 Out of stack time (s) Figure 6.10 Surface Temperature as a Function of Out-of-Stack Time for Three Different Diameters of a Peirce-Smith Converter. 184 reactor is above the temperature of accretion formation for out-of-stack times of up to 17 minutes. For the largest diameter considered in the calculations, blowing could be resumed after about 20 minutes without extensive accretion formation at the tuyere l i n e . 6.5.4 Effect of the Area of the Converter Mouth An increase in the area of the mouth of the converter does not affect the shape of the temperature profiles along the tuyere line as shown in Figure 6.11 for the case of a Peirce-Smith converter. In the calculations two converter mouth areas have been considered to calculate thermal pro-f i l e s for out-of-stack times of 300 s and 1800 s. Although i t does not significantly change the shape of the temperature profiles, an increase in the area of the mouth obviously increases the total heat losses from the reactor as well as the drop in temperature at the refractory surface. Figure 6.12 indicates that a mouth area of 4.5 m decreases the temper-ature at a central tuyere in the converter down to 1050 °C in about 12 minutes. The same reduction in temperature for a 2 mouth area of 6.24 m takes place in a matter of 8 minutes. Obviously, large converter mouth areas will tend to generate formation of accretion at the tip of the tuyere faster than smaller mouth areas. I 2 0 0 F H r I 1 5 0 -I 1 0 0 -1 0 5 0 -1 0 0 0 -9 5 0 -9 0 0 -A m = 6.24 m' A m =4.50 m : = 910cm T m = 30°C h = 7.2 W/cm2K D c = 400cm 4 0 0 Figure 6.11 2 0 0 2 0 0 4 0 0 Distance from centre of converter (m) Temperature Profiles along the Tuyere Line in a Peirce-Smith Converter for Two Converter Mouth Areas, 0 600 1200 1800 Out-of-stack time(s) Figure 6.12 Predicted Tuyere Line Temperature and Total Heat Losses in a Peirce-Smith Converter Plotted Against Out-of-Stack Time for Two Mouth Sizes. 187 6.5.5 Influence of the Coverage of the Mouth The most important factor affecting the heat exchange in the converter is whether the mouth of the converter is covered or not while i t is out of the stack. Figure 6.13 shows the influence of placing a cover over the mouth of the converter while i t is out of the stack. Both the tuyere line temperature drop and total heat losses are dramatically re-duced by covering the converter mouth. After half an hour out of the stack with the mouth covered, the tuyere line remains well above 1050 °C as compared with the case of an uncovered mouth where the temperature drops to 1050 °C in about 10 min. The effect of covering the mouth is even more impressive from the standpoint of total heat losses from the converter, which with the mouth covered, are decreased by a factor of four, as can be observed in Figure 6.13. The coverage of the mouth not only reduces the drop in temperature of the refractory surface and the total heat losses from the reactor. Possibly i t s most important effect is the reduction in thermal gradients through the refractory at the inside wall as shown in Figures 6.14 and 6.15 for the Peirce-Smith and Hoboken converters respectively. In both cases, with the converter mouth uncovered, the temperature gradient at the inside wall swings from negative to positive by 40-50 °C/cm during an out-of-stack period of about 10 min. Mouth open Mouth covered 1 1 I 0 300 600 900 1200 1500 1800 Out-of-stack time (s) gure 6.13 Tuyere Line Temperature and Total Heat Losses Plotted Against Out-of-Stack Time for a Peirce-Smith Converter with the Mouth Covered and Uncovered. 1 1 1 L Central tuyere J | 4 — End tuyere — Central tuyere \i / ' 1 // T r 1 f D c =400cm L C = 9I0 cm A m = 4.5 m 2 h =7.2 XI0" 4W/cm 2 K — ( Mouth - Mouth i i open covered i I 1 1 I I i 3 4 0 0 8 0 0 1200 1600 Out-of-stack time (s) Figure 6.14 Temperature Gradient Through the Refractory at thelnside Wall in a Central Mouth Converter Plotted Against Out-of-Stack Time. Figure 6.15 Temperature Gradient Through the Refractory at the Inside Wall in an End-Wall-Mouth Converter Plotted Against Out-of-Stack Time. 191 On the other hand, coverage of the mouth halves the change in temperature gradient which remains negative. The large change in thermal gradient generates stresses in the refrac-tory, as mentioned earlier, which could contribute to tuyere line refractory erosion. It may be noted that in the Hoboken converter, the through-thickness temperature gradient at the tuyere line remote to the mouth, Figure 6.15, is considerably less than that in the Peirce-Smith converter, Figure 6.14. If thermal cycling is a significant factor in tuyere line erosion, refractory wear would be greater in the mouth region of a Hoboken converter than near the opposite end when the mouth is uncovered while out of stack. In the Peirce-Smith converter the wear would be more uniform along the tuyere l i n e . In the calculations carried out to evaluate tuyere line temperature and total converter heat losses with the mouth covered while out of the stack, Figure 6.13, the panel covering the mouth of the converter was assumed to be i n i t i a l l y at room temperature. In the model the temperature of the panel subsequently increases as the refractories in the mouth cover are heated by the radiation from the inside wall of the reactor. Figure 6.16 shows the total heat losses from the reactor while out of the stack for three different i n i t i a l temperatures of the panel covering the mouth of the converter, namely room temperature, 400°C and 600°C. Out of stack time (s) igure 6.16 Total Heat Losses from a Covered-Mouth Converter as a Function of Out-of-Stack Time for Three Different Temperatures of the Mouth Cover. 193 As can be observed in Figure 6.16, an increase in the temper-ature of the mouth to 600 °C reduces the total heat losses by a factor of two as compared to the case of the mouth cover at room temperature as previously assumed. The coverage of the mouth of the converter is also beneficial from the standpoint of savings in energy of the burners employed to keep the converter at working temperature while out of the stack. Figure 6.17 compares the fue l - o i l consumption rate for the cases of converters with and without mouth covers. Again three temperatures are considered for the refractories in the panel covering the mouth. The results are expressed in kg/hr of fuel-oil necessary to compensate for the total heat losses from the converter as a function of the exit gas temperature. When the mouth of the converter is not covered while out of the stack, the fue l - o i l consumption is about 140 kg/hr i f the exit gas temperature is assumed to be 1000 °C. This consumption of fuel-oil can be reduced by a factor of three to four when the converter mouth is covered. 2 4 0 ~ 2 0 0 JZ \ 5 160 D c=400cm L c = 9IOcm Am= 4.5 m 2 h = 7.2XI0" 4 W/cm 2 K Mouth open Mouth covered I 2 0 3 8 0 4 0 0 T m = 3 0 ° C -— ~ ~~~ Jm_=±Q9!C-~ "Tm=600°C U-i 1 1 8 0 0 1000 1200 Exit gas temperature (°C) 1400 Figure 6.17 Fuel-Oil Rate Consumption as a Function of Exit Gas Temperature for Uncovered and Covered-Mouth Converters. •P> 195 CHAPTER VII  DISCUSSION 7.1 Injection Dynamics at the Tuyere Tip The pressure traces obtained from the tuyeres of the laboratory model and the operating copper converters were carefully studied because i t was believed that hitherto unknown differences in injection behaviour could be discerned. It was also considered important to learn to 'read* the pressure traces in a diagnostic sense, so that in future, the pressure measurements could be used as a quick and easy check on injection behaviour which could influence process perfor-mance . In the pursuit of these goals, three aspects of the pressure traces were examined and compared: i) the shape of the pressure pulses i i ) the frequency of pulses, and i i i ) the duration of the constant-pressure intervals separat-ing pulses. Looking f i r s t at pulse shape, the measurements of Hoefele and 31 Brimacombe showed that a sharp rise in pressure at the tuyere tip occurs when liquid washes against the tuyere, while 196 a decline in pressure corresponds to the growth of a bubble at the tuyere t i p . As was mentioned in Section 2.3 the theoretical basis for the link between tuyere pressure and 81 82 bubble formation has been set out elsewhere * . In summary, a classical bubbling regime is characterized by a pressure trace in which a sudden pressure rise is followed by a slower decline as shown schematically in Figure 7.1. No intervals of constant low pressure are observed in this classical bubbling regime. The second aspect of the pressure traces to be con-sidered, i.e. the frequency of the pressure pulses, is important because i t affects the size of the bubbles. Bubble volume and equivalent radius must be considered for the copper converter because the horizontal tuyeres are separated by only about 200 mm (Table 4.3). Thus, as Hoefele and 31 Brimacombe have suggested earlier, interaction among bubbles growing at adjacent tuyeres is possible. The third characteristic of the pressure traces, the periods of constant, low pressure between pulses, is likely caused by such interaction among adjacent tuyeres. These periods of low pressure are not caused by jetting because the tuyere pressure and air velocity are too low. I Classic Bubble growth Detachment 2 Unstable envelope Growth Detachment 3 Channelling ^ _ J L _ J L _ J LA ' Interruption Figure 7.1 Idealized Tuyere Pressure Traces for Three Regimes of Gas Discharge from Horizontal, Closely Spaced Tuyeres. 198 The interaction among adjacent tuyeres was confirmed by the high-speed observations carried out in the water model. As can be observed in Figure 5.9 the coalescence of bubbles discharging from several adjacent tuyeres creates a horizontal unstable gas envelope covering several tuyeres simultaneously; at the same instant other tuyeres are working more independent-l y . Thus for part of the time a given tuyere feeds this unstable envelope with l i t t l e resistance from surrounding liquid, and the tuyere pressure remains low until the envelope locally collapses. At this point the pressure sharply rises then drops as a gas bubble begins to form again. The bubble continues growing until i t either detaches from the tuyere t i p , in which case a new bubble starts to grow, or until i t coa-lesces with an adjacent bubble whereupon the pressure drops to the previous low level. Thus, with such tuyere interaction the duration of the bubble growth period is reduced and the pressure pulse becomes more symmetrical than is found with classical bubble growth from non-interacting tuyeres. An idealized pressure trace resulting from tuyere interaction is shown in Figure 7.1. The interaction between tuyeres can also be ascertained by studying pressure traces coming from adjacent tuyeres, as indicated by Figure 5.7. The rapid change from interactive to non-interactive injection conditions is also an indication of the instability of the gas-envelope covering several tuyeres simultaneously making interaction between them possible. 199 In addition, the question of bubble size relative to tuyere submergence has to be considered since gas channeling to the surface of the bath is a possibility. If the tuyere submergence is shallow, relative to the bubble size, bubbles may break through to the surface of the bath before disengag-ing from the tuyere tip so that for most of the time there is l i t t l e resistance to gas flow and the tuyere pressure is primarily low. Periodically, this gas channel to the surface collapses and causes a pressure pulse; but due to the proximity of the tuyere to the bath surface, the channel is reopened quickly so that the pulse is symmetrical and of short duration, as depicted in Figure 7.1. Comparison of Figure 2.5(d), from the slag fuming 78 furnace measurements carried out by Richards and Brimacombe , and Figure 7.1 reveals that in the f u l l slag fuming furnace (deep tuyere submergence, viscous bath), the air discharges in the form of bubbles from the individual tuyeres. This is confirmed by the single-nozzle bubble model of Davidson and 48 128 —1 coworkers ' which predicts a frequency of 6 s for the slag-fuming injection conditions. This is in excellent agreement with the measured value of 5 to 6 bubbles per 85 second . Thus although closely spaced, each tuyere operates independently like the single tuyere employed by Hoefele and 31 Brimacombe to inject gases into mercury which gave rise to the 200 bubbling behaviour shown in Figure 2.3. The lack of inter-action among adjacent tuyeres is perhaps surprising since with a bubbling frequency of 5 at a gas flow rate of 3 86 3.6 to 4.4 Nm /min per tuyere the radius of an equivalent spherical bubble at ambient temperature is 150 mm which is larger than the half-spacing between tuyeres of 100 mm. The apparent lack of coalescence may be due to the bubbles being elongated ve r t i c a l l y , but more importantly may be related to -2 the high viscosity of the slag which is about 0.5 N s m (5 poise). The high viscosity retards drainage of the liquid film separating adjacent tuyeres. An injection diagnosis for the f u l l slag fuming furnace is summarized in Figure 7.2. Turning to the copper converter, comparison of Figures 5.16(b) and 7.1 suggests that bubbles growing from adjacent tuyeres submerged 500 mm are coalescing to form an unstable gas envelope as depicted schematically in Figure 7.3. For the time interval of one second shown in Figure 5.16(b), tuyere discharge into the unstable gas envelope (constant low pres-sure part of the trace) occupies about 0.8 second. There are several reasons to expect this injection behaviour. F i r s t l y , i f classical bubbling occurred at each tuyere with a frequency -1 3 of 4 s while blowing at 11.8 Nm per minute, the radius of an equivalent spherical bubble at ambient temperature would be 230 mm which is more than double the tuyere half-spacing Zinc fuming furnace O / i O i - O / i O O ; High viscosity liquid No wall erosion Little tuyere interaction Figure 7.2 Summary of Injection Behaviour in the Full Slag Fuming Furnace, as Diagnosed from Dynamic Pressure Measurements in a Tuyere. 202 Copper converter (254 charges) > TO in CL CVJ a CL Is O O O O O » ^ ^ — - — . • ' Low viscosity liquid Tuyere line erosion Strong tuyere interaction Figure 7.3 Summary of Injection Behaviour in the Copper Converter with 254 Charges and 500 mm Tuyere Submergence, as Diagnosed from Dynamic Pressure Measurements in a Tuyere. 203 of 100 mm. This bubble size is considerably larger than that calculated for the slag fuming furnace. Secondly, the viscos--2 -2 ity of the bath in the converter is only 10 N s m , f i f t y - f o l d less than that of the fuming furnace slag, so that coalescence of bubbles at adjacent tuyeres is more favorable. Thirdly, the converter had already processed 254 charges with the result that the refractory at the tuyere line had eroded to form a typical V-shaped notch. This tends to act as a horizontal cavity providing a measure of stability for the gas envelope. Such a stabilizing notch is not found in the slag fuming furnace because, being water-jacketed, refracto-ries are not required as a lin i n g . A summary of the injection behaviour diagnosed for the 'middle-aged' copper converter with 500 mm tuyere submergence is given in Figure 7.3. Further evidence of the influence of the state of the tuyere pipe and the refractory at the tuyere line on injection dynamics may be gained by comparing the pulse frequency of about 4 s ^ measured in the middle-aged copper converter with -1 -1 the values of 14 s and 10 to 12 s measured in the tuyeres 31 of freshly relined copper and nickel converters, respective-l y . Pressure traces from freshly relined nickel and copper converters are strikingly similar as can be compared from Figures 2.4 and 7.4, respectively. In both cases the diameter of an equivalent spherical bubble forming at the tuyere tip 204 Copper converter ( l 8 t charge) h 0.5s H •ov:o:;o"; o « . . . * , ; Low Viscosity Liquid Tuyere Pipes Protruding Less Tuyere Interaction Figure 7 . 4 Summary of Injection Behaviour in a Copper Converter with New Refractory Lining, as Diagnosed from Dynamic Pressure Measurements in a Tuyere 205 is over 200 mm, again double that of the tuyere half-spacing so that coalescence of bubbles at adjacent tuyeres is l i k e l y . But the overall duration of low-pressure intervals, indicative of multiple tuyere interaction, is only about 50 to 60 pet of the time studied as compared to 80 pet in the middle-aged copper converter. This is because in the new converters the tuyere pipes protrude 150 mm or more beyond the refractory l i n i n g , so that there is no notch to provide s t a b i l i t y to the horizontal envelope. A summary of the injection behaviour in a freshly relined converter is presented in Figure 7.4. It may be that gas bubbles discharging from the protrud-ing tips of adjacent tuyeres tend to coalesce less readily so that the horizontal gas envelope is not well established and tuyeres operate more independently. Thus the intervals of low pressure are reduced and the pulse frequency is high as bubbles subjected to the influence of both buoyancy and bath motion^4 discharge from the tuyere. After the tuyeres burn back to the wall, the refractory i t s e l f may play a role in enhancing tuyere interaction through surface tension effects. If in the early l i f e of the li n i n g , the refractory is not wetted by the bath, bubbles discharging from a given tuyere can easily spread laterally along the wall to link up with adjacent bubbles and form the horizontal envelope. This has the effect of reducing the resistance to gas flow for longer time 206 periods which lengthens the intervals of low pressure and decreases the pulse frequency measured in the tuyere. Later on as the notch at the tuyere line deepens due to refractory erosion, the horizontal envelope is stabilized further. Thus surface tension effects also may strongly influence injection behaviour in the copper converter. The V-shaped notch which forms in the refractory along the tuyere line after several charges also may have the effect of reducing the bath circulation velocity over the tuyere t i p . If this reduction in velocity takes place a reduction in bub-bling frequency should be expected as Ashman et a l . ^4 have shown from the results of a mathematical model developed to describe bubble formation at the tuyeres of a copper converter. The reduction in bath circulation velocity induced by the notch was simulated in the laboratory model. Two deflectors were placed along the tuyere line in the model, the effect of which was to locally reduce the bath circulation velocity over the tuyere tip and also to confine the discharging gas. As can be observed from figures 5.1 to 5.3 for a low gas flow rate , the effect of the deflector is to reduce the frequency of pressure pulses by 6 to 7 pulses per seconds. At higher air flow rates this reduction is less pronounced. 207 Finally, examining Figures 2.5 (b), 5.8 (b), and 5.16 (a) obtained with shallow tuyere submergences in the 85 86 fuming furnace ' , the laboratory water model and the copper converter, respectively, the relatively constant pres-sure trace interrupted periodically by pressure bursts is indicative of gas channeling, as described earlier. In this case the gas channeling lik e l y prevents either bubble forma-tion or multiple tuyere interaction. A summary of these results is shown in Figure 7.5. Gas channeling is lik e l y to be detrimental to productivity at least from the standpoint of decreased oxygen ut i l i z a t i o n because the residence time of the air in the bath and the bath/gas contact area both may be reduced. Indeed the Tacoma Smelter, where a shallow tuyere submergence of about 300 mm is standard practice, has reported one of the lowest oxygen efficiencies, 63 pet, in the world 23 wide compilation of converter practice by Johnson et a l . However other factors also must have an influence because a good correlation between tuyere submergence and oxygen ef-ficiency could not be found from the compilation. 208 Copper converter (254 charges) Shallow tuyere submergence Low viscosity liquid Channeling Figure 7.5 Gas Channelling to the Surface "of the Bath in the Copper Converter with 300 mm Tuyere Submergence, as Diagnosed from Dynamic Pressure Measurements in a Tuyere. 209 7.2 Bath Movement and Slopping The laboratory work indicated that a shallow tuyere submergence has the disadvantage of leading to bath slopping at lower levels of buoyancy power (gas flow rates) as well as the disadvantage of causing gas channeling described earlier. The extrapolation of the model results to operational conditions also indicated that most converters are being operated at the maximum air flow rate close to the point of bath slopping. Bath slopping correlates well with buoyancy power per unit mass of bath and not with the kinetic power, which numerically is more important, or with the total power per 130 unit mass being incorporated into the system. Abramovich has pointed out that the kinetic energy is rapidly d i s s i -pated in the immediate vicinity of the tuyere and thus does not contribute significantly to the stirring energy of the bath. As a consequence during submerged injection the stirring power per unit mass of bath can be expressed as: e = e + ae (7.1) s b k in which the factor a'varies from 0.04 as proposed by 130 * 131 Abramovich , to 0.06 as reported by Lehrer and to 0.15 according to Haida and Brimacombe'*"^ 210 It has been pointed out that Equation (7.1) is useful as a scale-up criterion, because i t incorporates the important energy terms that are responsible for fluid flow and mixing. The results of the present work provide support-ing evidence to this idea, because a good correlation is obtained between buoyancy power and tuyere submergence, with-out taking into account the kinetic power contribution. This, in addition, suggests that the factor a in Equation (7.1) is relatively unimportant for horizontal submerged injection. Further evidence of the usefulness of Equation (7.1) as a scaling criterion is found when the extrapolation of the c r i t -i c a l slopping line obtained in the laboratory agrees well with data from industrial converter operations. At this point however i t is necessary to emphasize the fact that to extrapolate the c r i t i c a l slopping line to indus-t r i a l operations the buoyancy power in the converter was calculated under standard conditions. This means that the work done by the thermal expansion of the air when contacted with the molten matte is being neglected. Also for the evaluation of the buoyancy power per unit mass of bath (assumed to be blister copper) a 40 pet. f i l l i n g of the converter was con-sidered. Therefore, i t is clear that more work has to be performed to further clarify the effect of parameters such as bath temperature, tuyere diameter, tuyere angle and other 211 variables on bath slopping in the laboratory. Once these effects have been elucidated i t will be possible to delineate a comprehensive blowing practice for an industrial operation. It is also necessary to consider the definition of the modified Froude number, which since the pioneering work by 26 Themelis et al has been widely used to describe the injection of gas into a liquid. The modified Froude number, described as the ratio of gas kinetic energy to gas potential energy due to buoyancy force has a clear meaning when i t is used to describe the trajectory of side blown gas injection where the former and the latter energies rule the horizontal and the vertical motion of the gas, respectively. For the case when the volume change of the gas is negligible small, i.e. P > > p - i g h, the buoyancy energy is given by: The buoyancy energy can be expressed as: (7.2) (7.3) On the other hand, the kinetic energy i s : 1 2 k 2 o g o (7.4) 212 And the modified Froude number i s : Fr = (7.5) Eb By introducing Equations (7.3) and (7.4) into Equation (7.5): u 2 The modified Froude number defined by Equation (7.6) is similar to the modified Froude number defined in Equation (4.1) with the difference that the nozzle diameter has been replaced by the tuyere submergence as the characteristic lenght. Both definitions become equivalent as far as the dimensional similarity of d and h is maintained. J o On the other hand, the liquid disturbances that can generate splashing depend on the ratio between the inertial force of the jet disturbing the surface and the force of 118 gravity tending to flatten i t out . Therefore i t seems more appropriate to study this phenomenon in terms of the Froude number of the system instead of using the modified Froude number as before. 213 7.3 Accretion Formation and Tuyere Blockage The observations of accretion growth as well as the X-ray diffraction analysis of the accretion samples indicate that the mechanism of accretion formation is basically the solidification of bath around the tuyere t i p , rather than, say, the generation by chemical reaction of a solid phase like magnetite. That the accretion commences to grow mainly in the lower region of the tuyere can be explained simply by buoyancy effects. Liquid, which in the vi c i n i t y of the tuyere is driven upward by the ascending bubbles, presses in on the discharging gas at the bottom of the tuyere and is solidified by the cold gas. At the same time, owing to the low value of the modified Froude number, the upper area of the tuyere is surrounded predominantly by rising gas which also is directed upward by the growing accretion. Whether the accretion grows inside the tuyere or commences to build up just at the tip and grow outward is not clear. However, the latter is most likel y based on observations through the converter mouth of the tuyere line after i t had been rolled up out of the bath. An example of a pipe-shaped accretion, taken from a converter from Noranda, is shown in Figure 2.7. 214 The bright, hotter areas in the upper part of the accretion, seen in Figures 5.18 (e) and ( f ) , are consistent with a solidification mechanism. Being the last to freeze, they are thinner and able to conduct more heat to the cooling inside surface of the accretion from the bath than the thicker region at the base of the accretion. The striations observed in the accretions may have similar origins as the 'onion' layered structure observed by Davis and Magny^^ in their cast-iron accretions. It seems most likely that this structure arises from the solidification of successive layers of material as the bath periodically washes against the accretion, and is not due to droplets of liquid being propelled into the tuyere as suggested by Davis and Magny. The role of tuyere punching in the formation of accre-tions is very important. Factors such as the punching system being employed, the punching frequency, and the shape of the puncher head could profoundly influence the dynamics of fluid flow at the tuyere t i p . From the results in Figure 5.23 i t is clear that the punching system employed affects the flow regime at the tuyere pipe and therefore possibly also the process of accretion growth. 215 The punching frequency may also affect the rate of accretion growth. During punching, depending on i t s shape, the puncher head virtually may f i l l the tuyere cross-section blocking the flow of air and allowing bath to wash against the tuyere t i p . Then as the punch rod is withdrawn i t may suck liquid a short distance into the tuyere providing an anchor for subsequent accretion growth. Presently in every smelter the punching of tuyeres is a non-selective operation, that is a l l the tuyeres are punched whenever a drop in total gas flow rate into the converter is observed. Under these circumstances some of the tuyeres indeed are blocked while the rest are open. Then, the indiscriminate punching practice implies that in some cases the punch rod is being inserted into open, unblocked tuyeres, generating unnecessarily in this way the washing/sucking process above mentioned which w i l l contribute to the acceleration of the accretion formation process. A selective tuyere punching operation then seems to offer an advantageous alternative. This selective punching can be easily developed taking advantage of the differences in the pressure signals from the tuyeres when they are blocked, Figure 5.17 (b), as compared to the case when the tuyeres show no accretion formation. 216 The shape of the puncher head also could profoundly affect the dynamics of flu i d flow at the tuyere tip at the instant of punching and thereafter as the punch rod is with-drawn, via the blocking/sucking mechanism explained above. Since the puncher head used in a l l the converters under study were round with a diameter close to the inside diameter of the tuyere, punching practice could have contributed to the i n i t i a l stages of accretion formation. Alternative designs of puncher heads such as a chisel shape, therefore, may offer 132 certain advantages 8 5 The growth of accretions in the slag fuming furnace takes about 200 seconds for complete coverage, similar to the coverage time in the copper converter. However i t must be emphasized that this time is not meaningful for normal slag fuming operations because the coal to the tuyere had been turned off in order to visualize the tuyere t i p . With coal feeding, tuyere blockage is relatively infrequent, possibly because the pulverized coal abrades the accretion or the coal partially combusts generating sufficient heat to prevent local bath freezing. The possibility that solids injection could prevent tuyere blockage at least for part of the converting cycle warrants further investigation. It may be that siliceous flux currently added to the bath surface with a flux gun could be injected through the tuyeres and thereby prevent tuyere blockage in the slagmaking stage of converting. Analysis of 217 the accretion samples from the fuming furnace indicated that, as in the case of the copper converter, the accretion and bath had similar compositions. Thus, the accretion also forms by a freezing mechanism. At the oxygen levels normally employed in copper convert-ing, the enrichment of the blast does not prevent accretion growth. Nevertheless, oxygen-enrichment affects the accretion formation process. In converters in which oxygen-enriched air is used the accretions are porous and can be easily removed by punching. In contrast, in converters without oxygen enriched a i r , the accretions are more dense and stable. This may indi-cate that enriched air produces a more intensive oxidation at the region close to the tip of the tuyeres. Therefore a greater heat generation may be expected in this zone, with higher bath temperatures and thinner and more porous accretions, as com-pared with the case of no-oxygen enrichment of the blast. This suggests that the formation of accretion around the tuyeres of the copper converter may be controlled by adjusting the oxygen level in the blast, as is currently practiced in the steel industry. Indeed control of oxygen enrichment of the 33 34 blast, coupled with injection at higher pressures * offers an alternative to conventional low-pressure injection practice so that conditions can be adjusted, depending on matte grade and other variables of the process, to build up accretions around the tuyeres to protect the adjacent refractory and thereby prolong lining l i f e . 218 7.4 Heat Losses from the Converter The excessive wear observed at the tuyere line of the copper converter and the region facing the charging mouth, is related to the charging-blowing practice of the operation under consideration. At most smelters i t is not uncommon for a converter to be out of the stack for periods of about sixty minutes or longer; typical turnaround times are also quite prolonged. Under these circumstances large heat losses by radiation through the mouth of the converter occur, as the heat transfer model developed in the present work clearly shows. These heat losses through the mouth of the converter cause the inside wall to cool rapidly which leads to freezing at the tuyere line and tuyere blockage when blowing is resumed. The rapid change in temperature, localized within 60 to 80 mm of the inside wall, may generate severe thermal stresses which contribute to the refractory wear at the tuyere l i n e . In order to solve, or at least reduce, the problem of excessive refractory wear at the tuyere region, three major aspects of the converting operation should be considered. F i r s t l y , i t is obvious that out-of-stack times as well as turnaround times should be kept at minimum levels. In this way the thermal cycling at the inside surface of the refrac-tory would be less frequent with the consequent reduction of thermal stresses and refractory wear. 219 To reach this goal the complete operation at the con-verter aisle has to be optimized in order to maximize crane utilization and reduce the dead times in a converter. When i t is unavoidable to keep a converter out of the stack burners, big enough to compensate the converter heat losses, should be used even for out of stack times as short as ten minutes. Secondly, i t is extremely advisable to implement the coverage of the mouth as a routine practice when the converter is out of the stack, during turnaround times, and even during the start-up period of a recently relined converter. If this practice is implemented the thermal gradients at the inside wall can be reduced by a factor of two and therefore the wear of the refractory at the tuyere line also can be reduced. Moreover, the coverage of the mouth makes unnecessary the use of burners inside the converter even for long out-of-stack times. It is entirely possible that the savings in fuel o i l alone would pay for any modification made to the converter in order to implement the practice of mouth coverage. Finally, the reaming practice in use at some smelters has to be considered from the point of view of thermal stress in the refractory wall while the converter is out of the stack. In some smelter the tuyeres are reamed ('dressed') between converter cycles in order to keep the tuyere pipes clean and to obtain high air flow rates during blowing. This 220 practice, although i t may be helpful to meet the design blast air setpoint, could be extremely detrimental to the operation, at least from the standpoint of refractory l i f e . In one of the smelters visited during the present work massive damage of the refractory during reaming was observed. Pieces of, or complete bricks were observed to break off as a consequence of the reaming bar being inserted through the tuyeres. Without doubt reaming is more deleterious when applied to a converter after a long out-of-stack period due to the thermal stresses induced at the inside surface of the refractory wall. If the reaming practice is to be pursued i t should be performed immediately after blowing or after a burner has generated an even thermal f i e l d in the refractory surrounding the tuyere pipe. CHAPTER VIII 221 SUMMARY AND CONCLUSIONS 8.1 Summary The i n j e c t i o n dynamics and r e l a t e d a c c r e t i o n b u i l d up as w e l l as bath motion and heat l o s s e s i n the copper converter have been i n v e s t i g a t e d . The s t u d i e s have i n v o l v e d p h y s i c a l and mathematical models coupled with p l a n t t r i a l s at four copper smelters to examine gas dis c h a r g e dynamics, bath s l o p -p i n g and heat t r a n s f e r w i t h i n the c o n v e r t e r . The l a b o r a t o r y work, c a r r i e d out i n a 1 1 s c a l e model of a Pie r c e - S m i t h converter has shown that there i s significant i n t e r a c t i o n amongst adjacent tuyeres such that an unstable envelope of gas e x i s t s at the tuyere l i n e , c o v e r i n g s e v e r a l tuyeres s i m u l t a n e o u s l y . Each tuyere feeds i n t o the envelope which breaks down p e r i o d i c a l l y to r e l e a s e gas bubbles. The frequency of the discontinuous d i s c h a r g e of a i r i n t o the bath i n c r e a s e s with gas flow r a t e and i s a f f e c t e d by the bath c i r c u l a t i o n v e l o c i t y c l o s e to the tuyere l i n e . Bath s l o p p i n g measurements have i n d i c a t e d that s l o p p i n g i s dependent on tuyere submergence and the buoyancy power input to the bath from the r i s i n g gas bubbles. Shallow tuyere submergence gives r i s e to s l o p p i n g at lower l e v e l s of buoyancy power per u n i t 222 mass of bath and therefore is undesirable. Slopping conditions can be delineated on a 'slopping-behaviour' diagram and i t is useful to examine industrial converter operations in this lig h t . The industrial t r i a l s investigated the injection dynamics and related accretion build-up at the tuyeres of operating Peirce-Smith, Hoboken and Inspiration converters. A tuyerescope attached to the back of a tuyere has permitted the direct observation of accretion formation and the sampling of accre-tions during blowing. Dynamic pressure fluctuations in the tuyere due to injection behaviour have been measured with a piezoelectric transducer. The t r i a l s indicated that, under normal conditions, the Peirce-Smith, the Hoboken and the Inspiration converters operate in the bubbling regime. Careful examination of the shape and frequency of the pressure pulses and the duration of periods of low pressure in the tuyere, sensed by the piezoelectric transducer, revealed that in non-ferrous submerged injection processes the interaction between tuyeres depends on the bath viscosity, state of the refractory at the tuyere l i n e , and tuyere submergence. In high viscosity baths, such as that in the slag fuming furnace, individual tuyeres act independently and the gas discharges in the clas-sical bubbling regime. In the copper converter with relatively deep tuyere submergences there are long periods in which the 223 tuyere discharges into a horizontal unstable envelope formed by the coalescence of bubbles at adjacent tuyeres. This behaviour is enhanced by the relatively low viscosity of the bath, and for the case of middle-aged converters, the V-shaped notch at the tuyere line resulting from refractory erosion that stabilizes the horizontal gas envelope. If the tuyere submergence is shallow, such as 300 mm in the copper converter, bubbles may break through the bath surface before detatching from the tuyere so that the gas forms a vertical channel. This may lead to poor oxygen ut i l i z a t i o n in the copper con-verter. The piezoelectric measurements also indicated that the pressure traces from individual tuyeres provide a method to ascertain whether the tuyere is blocked or not. This could be used to develop a selective punching operation, and elimi-nate the indiscriminate punching practice employed nowadays in every smelter which accelerates the accretion formation process. The tuyere pressure measurements also revealed a decrease of the pulse frequency with increasing number of charges processed by the converter. This is related to the converter relining practice and again to the V-shaped notch which forms at the tuyere line after several charges. 224 Analysis of the accretion samples revealed that the accretions in the copper converter form by a solidification mechanism. The accretions were observed to grow upward from the bottom of the horizontal tuyere and to cover the tip within 60 to 200 seconds. Protruding parts of the accretion sometimes disappeared then reappeared suddenly as the bath washed over the accretion then receded. Striations visible on the accretions may be caused by successive layers of bath freezing onto the accretion due to the periodic washing of the tuyere t i p . The role of tuyere punching in the early stages of accretion formation could not be determined but could be important i f the puncher head blocks the air flow during punching or sucks liquid back into the tuyere during with-drawal. The type of puncher used in the converter affects f l u i d flow conditions inside the tuyere pipe and this could have an influence on accretion formation at the tuyere t i p . It is possible that the formation of accretion around the tuyeres of the copper converter may be controlled by adjust-ing the oxygen level in the blast, as is currently practiced in the steel industry, in order to protect the adjacent refractory and thereby prolong lining l i f e . The fact that accretion build-up is not a problem with coal feeding in the slag fuming furnace may indicate that tuyere blockage in the copper converter could be prevented, at least for part of the converting cycle, by injecting powdered siliceous flux through the tuyeres. 225 The mathematical heat-transfer model has indicated that when the converter is out of the stack, heat losses through the mouth of the converter cause the inside wall to cool rapidly which may lead to freezing at the tuyere line and tuyere blockage when blowing is resumed. The temperature gradient into the refractory at the inside wall can change by up to 50 °C/cm within the f i r s t 10 minutes of the converter being out of the stack. The rapid temperature change is local-ized to within 60-80 mm of the inside wall and may contribute to the refractory wear at the tuyere line. Covering the con-verter mouth during out-of-stack periods markedly reduces the change in through-thickness temperature gradient at the inside wall. Moreover, the coverage of the mouth makes unnecessary the use of burners inside the converter even for long out- of-stack times. 8.2 Suggestions for Further Work It is hoped that the present thesis has shed light on many aspects of the copper converter practice. From the results obtained throughout the work some ideas have emerged that merit further research and development. In the laboratory model i t is necessary to conduct a more complete study on the effect of several injection 226 variables on bath motion. A possible correlation between the oscillatory disturbances of the bath surface and the Froude number of the system should be investigated. This would help to develop a definite criterion to control slopping and splashing in the copper converter. It is also necessary to carry out a set of in-plant t r i a l in which the minimum air pressure required for the punchless operation of tuyeres in a copper converter can be determined for different levels of oxygen enrichment of the blast and different tuyere diameters. For a given tuyere diameter, the t r i a l would likely proceed as follows. Normal air at say 60 psig would be injected i n i t i a l l y to ensure that the tuyere does not block. This pressure would be lowered steadily until accretions begin to form. The pressure would be raised until no accretions were formed. Next the air would be enriched in oxygen and again the minimum pressure at which accretions are prevented would be defined. The air enrichment would be increased and the procedure repeated, and so on. The plant t r i a l s should also help to verify the heat transfer mathematical model before a further modelling work is done. 227 The heat transfer mathematical model should be further developed in two main areas. F i r s t l y , i t is necessary to obtain a more quantitative information about thermal stresses being generated at the tuyere line of the copper converter. Secondly, the model should be able to predict the shape and size of the accretions which will form at the tuyere line once the converter is turned back to the stack and blowing is resumed. 228 REFERENCES 1. H.K. Picard; 'Copper from the Ore to the Metal', Sir Isaac Pitman and Sons, Ltd. London, 1916, 89-96. 2. T.T. Read, and H. Haas; 'Recent Copper Smelting1, T.T. Read ed., Mining and Scientific Press, San Francisco, 1914, 213-222. 3. T.M. Morris; J. Metals, 1968, 20 (7), 73-75. 4. J. Hollway; in'Recent Copper Smelting', T.T. Read ed., Mining and Scientific Press, San Francisco, 1914, 201-212. Extracts from a paper presented before the Society of Arts (London), February 14, 1879. 5. E.D. Peters;'Modem American Methods of Copper Smelting', Scientific Publishing Co., New York, 1887, 330-335. 6. E.D. Peters; 'Modern Copper Smelting', 7— Ed. Hill Publishing Co., New York, 1907, 528-575. 7. H.O. Hofman, 'Metallurgy of Copper', McGraw-Hill Book Co., New York, 1914, 298-358. 8. E.A. Peretti, Discuss. Faraday Soc., 1948, 4, 179-184. 9. J. Massia, Eng. Min., 1891, 52, 307. 10. Douglas; Tr. Inst. Min. Met., 1899-90, 8, 2; also Trans. AIME, 1899, 24, 538. 11. U.S. Patents, N. 942346 and 942621, Dec. 7, 1909; N. 942973 and 9432.80, Dec. 14, 1909. 12. Anonymous, Eng. Min. J., 1911, 91, 944. 229 13. A.K. Biswas, and W.G. Davenport; 'Extractive Metallurgy of Copper', 2— Ed., 1980, Pergamon Press. 14. E.A. Peretti, in 'Copper', Chapter 7, A. Butts, ed., Reinhold Pub. Corp., N. York, 1954. 15. A.A. Tseidler ; Metallurgy of Copper and Nickel, 1964, Jerusalem, S. Monson ed. 16. P.J. Lenoir, J. Thiriar, and C. Coekelbergs; in 'Advances in Extrac- tive Metallurgy' , M.J. Jones, Editor, The Institution of Mining and Metallurgy, London, 1971, 373-86. 17. F. Sehnalek, J. Holeczy and J. Schmiedl; J. Metals 1964, 165, (5), 416-420. 18. R.A. Daniele, and L.H. Jaquay; TMS-AIME, Paper Number A72-101, 1972. 19. G. Rottman and W. Wuth; in 'Copper Metallurgy: Practice and Theory| M.J. Jones, Editor, The Institution of Mining and Metallurgy, London, 1975, 49-52. 20. 0. Christophersen, D. Alvarez and J. More; Inspiration Consolidated Copper Company. Internal Report PESMCV 8301, 1983. 21. F.M. Aimone, J. Metals, September 1968, 33-37. 22. F.M. Aimone, and K.A. Fern; in 'Gas Injection into Liquid Metals', A.E. Wraith, ed., University of Newcastle-upon-Tyne, 1979, L1-L21. 23. R.E. Johnson, N.J. Themelis and G.A. Eltringham; in 'Copper and  Nickel Coverters', R.E. Johnson, ed. The Met. Soc. of AIME, New York, N.Y., 1979, 1-32. 230 24. F.E. Lathe, and L. Hcdnett; Trans. TMS-AIME, 1958, 212 , 603-17. 25. C. L. Milliken and F.F. Hofinger; J. Metals, 1968, 20 , 39-45. 26. N. J. Themelis, P. Tarassoff and J. Szekely; Trans TMS-AIME, 1969, 245, 2425-33. 27. T. A. Engh and H. Bertheussen ; Scand. J. of Metall., 4 , 241-49. 28. A. V. Spesivtsev, V.V. Mechev, G. B. Strekalcvskii and A.V. Vanyukov; Tsvet. Metall., 1973, 14, (2), 10-12. 29. A. V. Spesivtsev, V. V. Mechev and A. Vanyukov; Tsevet. Metall., 1973, 14 , (7), 17-18. 30. G. N. Oryall and J. K. Brimacombe; Metall. Trans., 1976, 7B , 391-403. 31. E.O. Hoefele, and J. K. Brimacombe; Metall. Trans., 1979, 10B , 631-48. 32. J. K. Brimacombe and H. 0. Hoefele; U.S. Patent N°- 4,238,228, December 9, 1980. 33. J. K. Brimacombe, S.E. Meredith and R.G. Lee; Proc. of 1983 Int. Sulf. Smelting Symp., ed. H. Y. Sohn, D.B. George and A.D. Zunkel, TMS-AIME, 1983, 839-854. 34. J. K. Brimacombe, S. E. Meredith and R. G. Lee; Metall. Trans., 1984, 15B, 243-50. 35. R. J. Fruehan, and L. J. Martonik; Third Int. Iron and Steel Congress, 1979, ASM, Ohio, U.S.A. 229-38. 36. J. W. McKelliget, M. Cross, and R.D. Gibson; Iromak. and Steelmaking., 1978, 6 ,282-84. 231 37. J.W. McKelliget, M. Cross, and J.K.Brimacombe; in "Gas Injection in Liquid Metals". Univ. of Newcastle-upon-Tyne, April 1979. 38. I. Leibson, E.G. Holcomb, A.G. Cacoso, and J.J.Jamie; AlCHE J.> September 1956, 296-306. 39. R.L. Muller, and R.G.H. Prince; Chem Engrng. Sci., 1972, 27, 1583-92. 40 V.I. Berdnikov, A.M. Levin, and K.M. Shakirov; Izvest.VUZ Chern. Metall., 1974, 10 , 15-22. 41. G.N. Oryall; M.A.Sc. Thesis, Dept. of Metallurgicall Engineering. The University of British Columbia, 1975. 42. G.J. Payne, and R.G.H. Prince; Trans. Instn. Chem. Engrs., 1975, 53, 209-23. 43. G.A. Irons, and R.I.L. Guthrie; Metall. Trans., 1978, 9B , 101-10. 44. G. A. Irons, and R.I.L. Guthrie; Can. Metall. Quart., 1980, 19, (4), 381-87. 45. R. Clift J.R. Grace, and M.E. Weber; "Bubbles,Drops, and Particles", 1978, Academic Press, N. York. 46. R. Kumar, and N. R. Kuloor; Adv. Chem. Engng., 1970, 8 , 225-368. 47. J.F. Davidson , and B.O.G. Schuler; Trans. Instn. Chem. Engrs., 1960, 38, 144-54. 48. J.F. Davidson, and B.O.G. Schuler; Trans. Inst. Chem. Engrs., 1960, 38, 335-42. 232 49. J.F. Davidson, and H. Harrison; "Fluidized Particles", 1963, Cambridge University Press, Cambridge. 50. D.W. van Krevelen, and P.J. Hoftijzer; Chem. Eng. Prog., 1950, 46, 29-35. 51. R. Kumar, and N.R. Kuloor; Chem. Tech., 1967, 19, 733-41. 52. A.E. Wraith; Chem. Engng. Sci., 1971, 26, 1659-71. 53. R.T. Baxter, and A.E. Wraith; Chem. Engng. Sci., 1970, 25, 1244-47. 54. A.E.Wraith, and T. Kakutani; Chem. Engng. Sci., 1974, 29 ,1-12. 55. A.E. Wraith; in "Advances in Extractive Metallurgy and Refining", 1972, IMM, London, 303-16. 56. A.E. Wraith, and M.E. Chalkley; in "Advances in Extractive Metallurgy". 1977, IMM, London, 27-33. 57. M. Nilmani, and D.G.C. Robertson; Trans. IMM, 1980, 89, C42-C53. 58. R.J. Andreini, J.S. Foster, and R.W. Callen; Metall. Trans., 1977, 8B, 625-31. 59. J. Szekely; "Fluid Flow Phenomena in Metals Processing"r 1979, Acade-mic Press, N. York. 60. M. Sano, and K. Mori; Trans. JIM (Japan), 1976, 17, 344-52. 61. M. Sano, Y. Fujita, and K. Mori; Metall. Trans., 1976, 7B, 300-1 62. K. Mori, M. Sano, and T. Sato; Trans. ISIJ, 1979, 19, 553-58. 233 63. K. Mori, and M. Sano; in SCANINJECT I, International Conference on Injection Metallurgy, Lulea, Sweden, 1977. 64. M. Sano, and K. Mori; Trans. ISIJ, 1980, 20, 668-74. 65. M. Sano, and K. Mori; Trans. ISIJ, 1980, 20, 675-81. 66. K. Mori, Y. Ozawa, and M. Sano; Metall. Trans., 1979, 10B, 678-80. 67. Y. Ozawa, and K. Mori; 99th ISIJ Meeting, April 1980, Japan. 68. Y. Ozawa, K. Mori, and M. Sano; 99th ISIJ Meeting, April 1980, Japan. 69. Y. Ozawa, K. Mori, and M. Sano; Trans. ISIJ, 20, 1980, 312. nd 70. M. Sano, and K. Mori; 2— Japan-Sweden Joint Symposium on Ferrous Metallurgy, Tokyo, Japan, December 1978. 71. K. Mori, Y. Ozawa, and M. Sano; Trans. ISIJ, 1982, 22, 377-84. 72. J.F. Davidson, and E.H. Amick; AICHEJ, 1956, 2, 337-41. 73. YiSahai, and R.I.L. Guthrie; Metall. Trans., 1982, 13B, 193-202. 74. D.W. Ashman, J.W. McKelliget, and J.K. Brimacombe; Can. Met. Quart., 1981, 20, (4), 387-95. 75. M.E. Chalkley, and A.E. Wraith; Trans. IMM, December 1978, c266-c271. 76. P. Collins, and A.E. Wraith; in "Injection Phenomena in Extraction and  Refining", A.E. WRAITH ed., University of Newcastle-upon-Tyne, April 1982. 2 34 77. P.E. Anagbo, and A.E. Wraith; in 'Injection Phenomena in Extraction  and Refining' . A.E. Wraith, ed., University of Newcastle- upon-Tyne, April 1982. 78. G.G. Richards, and J.K. Brimacombe; unpublished work, The University of British Columbia. 79. L. Farias, and D.G.C. Robertson; in'Injection Phenomena in Extraction  and Refining', A.E. Wraith, ed., University of Newcastle-upon-Tyne, April 1982. 80. N.B. Gray, M.J. Hollitt, R.G. Henley, and J. Pritchard; Trans. IMM, 1983, 91, C54-C63. 81. A. Kupferberg, and G.J. Jameson; Trans. Instn. Chem. Engrs., 1969, 47, T241-T250. 82. W.V. Pinczewski; Chem. Engn. Sci., 1981, 36, 405-11. 83. M.J. Mcnallan, and T.B. King, Metall. Trans., 1982, 13B, 165-173. 84. E.O. Hoefele; M.A. Sc. Thesis, Dept. of Metallurgical Engineering, The University of British Columbia, 1978. 85. G.G. Richards; Ph. D. Thesis, Dept. of Metallurgical Engineering, The University of British Columbia, 1983. 86. A.A. Bustos, G.G. Richards, N.B. Gray, and J.K. Brimacombe; Metall. Trans., 1984, 15B, 77-89. 87. A. Ferreti, V. Giordano, and M. Podrini; Boll. Finsider, February 1977, (360), 120-33. 235 88. R. E. Johnstone, and M. W. Thring; 'Pilot Plants, Models,  and Scale-Up Methods in Chemical Engineering', McGraw-H i l l , 1957 89. W.O. Philbrook; J . of Metals, October 1957, 1353-58 90. F. W. Hillnhiitter, H. Kister, and B. Kruger; Ironmaking P r o c , Iron and Steel Society of AIME, Toronto, 1975, 34, 368-80. 91. W. Sabella, and C. Matysik; Hutnik (Katowice), 1980, 47, 301-05. 92. H. Suzuki, and J . Ohno; Trans. ISIJ, 1979, 19, 440-44. 93. M. Tate, Y. Kuwano, K. Suzuki, M. Matsuzaki, E. Tsuji, T. S. Chan, and K. Honda; Trans. ISIJ, 1976, 16, 447-52. 94. M. J . McCarthy, and J . M. Burgess; BHP Tech. Bull., 1981, 25, 76-80. 95. F. Kreith; 'Principles of Heat Transfer', 3r d Ed., Harper and Row, Pub. Inc., N.York, 1973. 96. J . P. Holman; 'Heat Transfer', 5t h Ed., McGraw-Hill, 1975 97. 'Heat Transfer Data Book', General Electric Co., Corpo-rate Research and Development, Schenectady, N. York, 1977. nd 98. G. Keramidas; 2 International Conference on Numerical Methods in Thermal Problems, Venice, Italy, July 7-10, 1981, R. Lewis et al.,Eds., Pineridge Press Ltd., Swansea, 1981. 236 99. B.G. Thomas, I.V. Samarasekera, and J.K. Brimacombe; Metall. Trans., 1984, 15B, 307-18. 100. J . Szekely, and N.J. Themelis; 'Rate Phenomena in  Process Metallurgy', Wiley-Interscience, N. York, 1971. 101. G.H. Geiger, and D.R. Poirier; 'Transport Phenomena  in Metallurgy', Addison-Wesley Pub. Co., Ma., 1973. 102. J.K. Brimacombe, A.A. Bustos, D. Jorgensen, and G.G. Richards; 'The Herbert H. Kellog Symposium on Extractive  Metallurgy'' , AIME Annual Meeting, New York, 1985. 103. D. Jorgensen, A.A. Bustos, J.K. Brimacombe, and G.G. Richards; unpublished work, The University of British Columbia. 104. 0. Haida, and J.K. Brimacombe; Proc. SCANINJECT-III, MEFOS/Jernkontoret, Lulea, 1984, 5:1-5:17. 105. T. Robertson, and A.K. Sabharwal; in 'Gas Injection into  Liquid Metals', A.E. Wraith Ed., University of Newcastle-upon-Tyne, 1979, 11-129. 106. T.A. Engh, H. Tveit, H. Bertheussen, P. Stromnes, K. Venas, and T.M. Svartas; Scand. J . Metall., 1976, 5_, 21-26. 107. K.G. Davis, and J.G. Magny; Metals Tech., 1979, 6, 1-7. 108. J.K. Wood, G.E. Schoeberle, and R.W. Pugh; 'Simposium on  External Desulphurisation of Hot Metal', W.K. Lu, Ed., 3r McMaster Symposium on Iron and Steelmaking, Hamilton, Ontario, May 22-23, 1975. 237 109. G. Boxall, A.K. Subharwal, T. Robertson, and R.J. Hawkins, in 'Injection Phenomena in Extraction and Refining', A. E. Wraith, Ed., University of Newcastle-upon-Tyne, 1982, B1-B18. 110. C. Xu, Y. Sahai, and R.I.L. Guthrie; in 'Injection  Phenomena in Extraction and Refining', A.E. Wraith, Ed., University of Newcastle-upon-Tyne, 1982, K1-K27. 111. C. Xu, Y. Sahai, and R.I.L. Guthrie; Ironmak. and Steelmak., 1984,11, (2), 101-07. 112. W.A. Krivsky, and R. Schuhmann; Trans. TMS-AIME, 1959, 82-86. 113. Y. Sahai, and R.I.L. Guthrie; Iron and Steelmaker; April 1984, 34-38. 114. S. Ohguchi, and D.G.C. Robertson; in 'Injection Phenomena  in Extraction and Refining', A.E. Wraith, Ed., University of Newcastle-upon-Tyne, 1982, J1-J37. 115. S. Ohguchi, and D.G.C. Robertson; Ironmak. and Steelmak., 1983, 10, (1), 15-23. 116. T. Kootz, and G. Gi l l e ; Stahl und Eisen, 1948, 68, N° 17/18 287-94. 117. K. L i , J.I.S.I., November 1960, 275-80. 118. B.S. Holmes, and M.W. Thring; J.I.S.I., November 1960, 259-61. 238 119. A. Chatterjee, and A.V. Bradshaw; J.I.S.I., March 1972, 179-87. 120. B.U. Igwe, S. Ramachandran, and J.C. Fulton; Metall. Trans., 4, August 1973, 1887-94. 121. A. Etienne, C.R.M., June 1975, (4), 13-21. 122. E.O. Ericsson; Proc. 2nc* Japan-Sweden Joint Symposium on Ferrous Metallurgy. Tokyo, Japan. December 1978, 43-49. 123. E.M. Sparrow, and R.D. Ces; 'Radiation Heat Transfer', Brooks-Cole, 1967. 124. H.C. Hottel, and A.F. Sarofim; 'Radiative Heat Transfer', McGraw-Hill, N. York, 1967. 125. L.K. Spink; 'Principles and Practice of Flow Meter  Engineering', 8C Ed., Foxboro Co., Foxboro, Ma., 1958. 126. A.S.M.E., 'Fluid-Meters, their Theory and Application', Report of the A.S.M.E. Research Comitte on Fluid Meters, 6t h ed., H.S. Bean, Ed., N. York, 1971. 127. J.W. Murdock; A.S.M.E. Paper 64-WA/FM-6. 128. J.K. Walters, and J.F. Davidson; J . Fluid Mech., 1962, 408-16. 129. K. Mori, and M. Sano; Tetsu-to-Hagane, 1981, 67, 672. 130. G.N. Abramovich; 'Theory of Turbulent Jets',1963, MIT Press, Cambridge, Mass. 239 131. L.H. Leherer; Ind. Eng. Che., Process Design and Develop., 7, 1968,226-38. 132. A. Pelletier; private communication, Noranda Mines, Home Smelter. 133. 'Tables of Thermal Properties of Gases', National Bureau of Standards, Circular 564, U.S.Government Printing Off. November 1955. 240 APPENDIX I THE PLATE ORIFICE A thin-plate square-edged orifice was used to measure the air flow rate into the system. The orifice was designated two inches, corresponding to the nominal I.D. of the pipe in which i t was installed. Corner taps were used, as suggested 125 by Spink for pipe diameters less than 51 mm. For other tap locations there is the possibility that the low-pressure tap will be downstream from the vena contracta, in a highly turbu-lent region where the standard discharge coefficients would not apply. The most important orifice dimensions are discussed in 126 detail in the A.S.M.E. report on fluid meters . In the f o l -lowing paragraphs the recommendations of this report are considered and related to the design of the orifice used. The actual dimensions of the device are listed in Table 1.1. Two different diameter ratios, defined as the ratio between the orifice diameter and the inside diameter of the pipe, were used. A diameter ratio of 0.6 was employed when measuring relatively high gas flow rates, whereas a diameter ratio of 0.4 was used for lower rates. 241 TABLE 1-1 CHARACTERISTIC DIMENSIONS OF ORIFICE AND COMPARISON WITH RECOMMENDED DESIGN VARIABLES ..Inside Diameter of Pipe, D , mm 50.4 Orifice Diameter ( ^  =' 0.4) Dq, mm 20.2 Orifice Diameter (ft = 0.6) Dq, mm 30.2 Length of Hole in Plate, LQ, mm 1.50 0.030 VDo < £ = 0 . 4 > 0.074 L /(D -D v o p o) 0.050 Width of S l i t , D , mm ' s' 1.02 D /D s P 0.020 Recommended Ratio, D /D s p 0.02 Exit Length, L^, mm 1346.2 Ll/°p 26.71 Recommended Minimum L./D 1 P 25 Entrance Length, L2S mm 914.4 L2/ Dp 18.14 Recommended Minimum L0/D 2 P 8 Plate Thickness, L , mm P 3.18 Thickness Ratio, L /D ' P P 0.063 242 The upstream orifice edge was made as sharp as possible in order to render i t s effect on the discharge coefficient negligibly small. The plate thickness selected was 3 mm. The location of the pressure tap holes was fixed by specifying corner taps. For the case of corner taps, i t is the width of the s l i t between the orifice plate and the end of the pipe that is important, rather than the tap hole diameter. The A.S.M.E. report recommends that the s l i t be made the same size as flow nozzles, namely less than or equal to 0.02 D^. This later specification was used. The roughness of the pipe wall, according to the report, is not an important factor i f the pipe wall is smooth, as was the case for the copper pipes employed in the present work. Since the standard orifice coefficient, which includes the effect of jet contraction, would increase i f the edge-width ratio (LQ/D ) was too large, i t is necessary to specify an upper limit•to i t . According to the A.S.M.E. report, the edge-width ratio has no appreciable effect on the discharge coefficient i f LQ does not exceed any of the following values: Lo 1 ^o . 1 Lo , 1 p o p o 243 The actual size of Lq used in the plate is listed in Table 1.1. This is seen to be smaller than the corresponding recommended maxima. However, the plate thickness was greater than Lq, and so following the recommendations of the A.S.M.E, report the downstream face of the plate was bevelled at 4 5 ° . The theoretical rate of flow of a compressible f l u i d , according to the A.S.M.E. report i s : 2/Y _ ( Y + 1 ) / Y ^ J > ("2 Y P L P (r ' - rv )• m. , . = A i i , , I (1.1) l d e a l °L (Y-1) (1- r YB ) J where: r: static pressure ratio (pQ/p^) Y: ratio of specific heats (c /c ) r p v A : cross sectional area of the orifice o p^: density of the fl u i d upstream the or i f i c e p^; absolute static pressure upstream the or i f i c e 6: diameter ratio (D /D ) o p The actual rate of flow i s : * - CD-*ideal ( I - 2 ' 244 To calculate C^, the discharge c o e f f i c i e n t , the equation 127 presented by Murdock was used: (1.3) where Cq and AC represent the discharge c o e f f i c i e n t when the throat Reynolds number R^"*"0 and the increase i n the discharge 4 c o e f f i c i e n t for the arbitrary Reynolds number change from 10 to i n f i n i t y , r e s p e c t i v e l y . The exponent 'a' i n Equation (1.3) takes the value of one for flange and pipe taps. Values for Cq and AC are l i s t e d i n Table 1.2 for o r i f i c e s with flange taps, inside diameter of 50.8 mm, and diameter r a t i o s of 0.4 and 0.6. Tables 1.3 and 1.4 show the results for the c a l i -bration of the plate o r i f i c e used i n the present work, for diameter ra t i o s of 0.4 and 0.6, res p e c t i v e l y . The relat i o n s h i p of gas flow rate and pressure drop at the o r i f i c e plate can be expressed as an exponential curve. If the a i r flow rate i s expressed i n Nl/s and the pressure drop i n mm R^ O the relationship for the case of a diameter r a t i o of 0.4 i s : 2.45 ( A P )0'4 8 5 (1.4) with a correlation c o e f f i c i e n t of 99.97 "L. 245 TABLE 1-2 VALUES FOR USE IN EQUATION 1-2 TO OBTAIN DISCHARGE COEFFICIENTS FOR 2 INCH PLATE ORIFICES J8 Co A C 0.30 0.59784 0.01440 0.32 0.59852 0.01489 0.34 0.59923 0.01549 0.36 0.59995 0.01621 0.38 0.60066 0.01707 0.40 0.60139 0.01809 0.42 0.60212 0.01928 0.44 0.60286 0.02066 0.46 0.60360 0.02223 0.48 0.60434 0.02401 0.50 0.60504 0.02600 0.52 0.60568 0.02821 0.54 0.60632 0.03063 0.56 0.60694 0.03328 0.58 0.60751 0.03614 0.60 0.60799 0.03920 0.62 0.60833 0.04250 0.64 0.60846 0.04596 246 TABLE 1.3 CALIBRATION OF THE PLATE ORIFICE WITH A DIAMETER RATIO OF 0.4 AP mm H2O Pl _5 Pa x 10 p° -5 Pa x 10 D CD Air Flow Rate Nl/s 23.5 1.016 1.014 0.61747 3.75 33.5 1.018 1.014 0.61517 4.37 45.5 1.019 1.014 0.61338 5.03 44.0 1.019 1.015 0.61323 5.09 56.5 1.020 1.015 0.61204 5.66 86.5 1.023 1.015 0.61007 6.94 92.0 1.024 1.015 0.60971 7.25 97.5 1.025 1.015 0.60945 7.48 102.0 1.025 1.015 0.60934 7.59 111.5 1.026 1.016 0.60905 7.87 121.5 1.028 1.016 0.60880 8.25 127.0 1.028 1.016 0.60856 8.41 127.0 1.028 1.016 0.60853 8.40 136.0 1.029 1.016 0.60832 8.70 156.0 1.032 1.016 0.60785 9.33 176.0 1.034 1.017 0.60750 9.87 178.0 1.034 1.017 0.60745 9.95 205.0 1.037 1.017 0.60707 10.61 210.0 1.038 1.017 0.60701 10.73 237.5 1.041 1.018 0.60667 11.41 246.0 1.042 1.018 0.60661 11.55 260.5 1.043 1.018 0.60643 11.95 284.5 1.046 1.018 0.60622 12.49 299.5 1.048 1.019 0.60611 12.77 304.0 1.048 1.019 0.60611 12.77 323.5 1.051 1.019 0.60593 13.27 333.5 1.052 1.019 0.60588 13.43 247 TABLE 1.4 CALIBRATION OF THE PLATE ORIFICE WITH A DIAMETER RATIO OF 0.6 p mm H20 Pl _5 Pa x 10 J P ° - 5 Pa x 10 CD Air Flow Rate Nl/s 31.3 1.022 1.019 0.61965 11.21 57.1 1.029 1.023 0.61734 13.98 81.6 1.035 1.027 0.61566 17.04 134.6 1.050 1.036 0.61403 21.63 153.7 1.054 1.039 0.61376 22.65 197.2 1.062 1.043 0.61312 25.49 254.3 1.084 1.059 0.61241 29.55 274.7 1.088 1.062 0.61231 30.27 349.5 1.108 1.075 0.61187 33.71 427.0 1.130 1.088 0.61149 37.35 457.0 1.139 1.094 0.61134 39.03 516.8 1.154 1.104 0.61121 40.63 557.6 1.170 1.112 0.61099 43.58 571.2 1.167 1.112 0.61105 42.65 580.7 1.176 1.119 0.61099 43.61 646.0 1.194 1.130 0.61084 45.89 665.0 1.203 1.136 0.61078 46.77 738.5 1.222 1.150 0.61068 48.52 775.2 1.239 1.163 0.61062 49.75 788.8 1.239 1.162 0.61060 50.12 For a diameter r a t i o of 0.6 the relationship i s : Q = 2.10 ( A P )W' ^ ' - ' (1.5) with a correlation c o e f f i c i e n t of 99.89 "L. Figures 1.1 and 1.2 show the experimental results of the c a l i b r a t i o n s for both diameter ratios as well as for the curves representing Equations (1.4) and (1.5). 160 200 240 280 A P (mm H 20) 320 360 Figure 1.1 Air Flow Rate versus Pressure Differential for the Plate Orifice with a Diameter Ratio of 0.4 ro Figure 1.2 Air Flow Rate versus Pressure Differential for the Plate Orifice with a Diameter Ratio of 0.6 251 APPENDIX II PRESSURE TRACES FOR DIFFERENT CHARGES  OF THE COPPER CONVERTER Pressure o s c i l l a t i o n s for di f f e r e n t charges of the copper converter are shown i n Figure II.1.The measurements were performed at the tuyeres of two converters from the Utah smelter. In a l l the photographs the pressure pulses as coming from the pie z o e l e c t r i c transducer are shown i n Channel 2 of the oscilloscope (bottom part of the screen). Channel 1 (upper part of the screen) shows the same signal as i n Channel 2 after f i l t e r i n g a l l the ambient e l e c t r i c a l noise with a frequency greater than 30 Hz. In a l l the photographs the v e r t i c a l scale i s set at a value of 4.8 kPa/div. 0.5s H h 1.0s-( Q ) ( b ) gure II.1 Pressure Traces for Different Charges of a Peirce-Smith Copper Converter. Vertical Scale: 4.8 kPa/div (a) Charge 1, (b) Charge 3 (c) Charge 6, (d) Charge 12 (e) Old Converter. 253 APPENDIX III RADIATION SHAPE FACTORS IN THE HEAT TRANSFER MODEL In order to calculate the rate of heat exchange from each element in the model i t is necessary to evaluate the fraction of the total diffuse radiation leaving one surface which is intercepted by another surface and vice versa. The fraction of diffusely distributed radiation leaving a given surface A that reaches surface A is called the radiation e r shape factor F , which evaluated on the basis of the area e j r of the emissive surface i s : Ae lA l/ cosa .dA •cosa • dA e.r A , . , . 6 ! „ i ! r r « " • * > A ir-D e r The different terms in Equation (III.l) are defined according to the geometric arrangement notation sketched in Figure I I I . l . In the model the converter radius is assumed large enough such that each element into which the converter internal surface is subdivided can be considered as a plane surface. Also i t is assumed that the areas of the elements in the model are small enough so that both angles in Equation (III.l) can be considered as constant for each element. By virtue of R (Xp , YZ ,ZR ) E ( XE, YE ZE) Figure III.l Geometric Arrangement to Calculate Radiation Shape Factors in the Heat Transfer Model. ro Ln these two assumptions Equation (III.l) can be expressed as cosa cosa F = ^ ,—I A (III.2) e> r To2 r Also cosa^ and cosa^ can be expressed as: 2 2 2 c o s ae= - i - ^ - q ( I I I-3 ) e and = 2 D 0 2 2 2 V + 0 - S cosa_ = — ^ * (III.4) ^r Substituting Equations (III.3) and (III.4) for cosa^ and cos«r in Equation (III.2) yields: ? ? ? ? ? ? (Dz + Q - SZ)(DZ + Q - SZ) Fe r = " S ^-1 — A (III.5) 'r 4 if 0 Q D r e ^r It is possible to express D, Qg, Q^ _, and S^ in Equation (III.5) as: D = (X -X )2 + (Y -Y )2 + (Z -Z )2\2 ( I I I .6 ) | _ e r e r e r j = (X -X )2 + (Y -Y )2 + (Z -Z )2P (III.7) |_ e oe e oe e oe J = (X -X )2 + (Y -Y ) 2 + (Z -Z ) 2 P (III.8) r [_ r or r or r or J Q 256 S = | ( X - X ) 2 + (Y - Y ) 2 + (Z - Z ) 2 p e I r oe r oe r oe J S = | ( X - X )2 + (Y - Y )2 + (Z - Z ) 2 P r I e or e or e oe J Equations (III.5) to (III.10) provide a method to n u m e r i c a l l y c a l c u l a t e the r a d i a t i o n shape f a c t o r s i n the h e a t - t r a n s f e r model. (III.9) (III.10) 257 APPENDIX IV THERMAL CONDUCTANCES FOR THE DIFFERENT NODES IN THE MODEL The thermal conductances d e f i n e d by Equation (6.15) depend on the s p e c i f i c geometry and p o s i t i o n of the node under c o n s i d e r a t i o n . This appendix i n d i c a t e s the expressions used f o r the i n t e r i o r and boundary nodes i n the mantle and the end wa l l s of the c o n v e r t e r . Mantle of the Converter i ) For an i n t e r i o r node as shown i n Figu r e I V . 1 ( a ) , the thermal conductances can be expressed as: i , i + 1 i , i - l and the volume of the node i s : V. l = Y-z-r.' i r l 258 ( c ) (d) Figure IV.1 Geometric Configurations to Evaluate Thermal Conductances for the Different Nodes in the Model. 259 i i ) For a node at the internal surface of the converter, Figure IV.Kb), the thermal conductance i s expressed as : Cl , 2 = Kl ^ [l + T ] = K1" S1 ,2 and the volume of the node i s V1 = I ^ . U r2 + h r± Ar) i i i ) For a node at the external surface of the converter, Figure IV.1(c), the thermal conductance i s expressed as: CN,N-1 ~ KN"AT [ RN 2~~] ~ KN'SN,N-1 and the volume of the node i s VN = - i r -( 4 RN A R - A R 2 ) End Wall Nodes In this case there i s a plane wall to be considered, as shown i n Figure IV.1(d). 260 i ) Therefore for an i n t e r i o r node C. . . = K. R 2 t a n ( Y / 2 ) = K. s i , i + l 1 Ar l i s 1- + 1 V± = R2 tan(v/2) A r i i ) For a node at the internal surface of the converter end wall 2 r v R " tan( Y/2 ). „ c  C'l,2 ~ 4 *r kl Sl , 2 V, = R2 tan(Y/2) A r 1 - o » v . / - / 2 i i i ) For a node at the external surface of the converter end wall 2 r v R tan(Y/2) _ „ c N,N-1 " N IT K "N,N-1 VM = R2 tan(Y/2) IN1 ^ 261 APPENDIX V HEAT TRANSFER COEFFICIENT FOR THE  EXTERNAL SURFACE OF THE CONVERTER During i t s operation, the external surface of the con-verter is losing heat to the surroundings by convection and radiation. If the thermal conductivity of the refractory is a linear function of temperature, the heat flow by conduction through the cylindrical shell of the converter, Figure V . l , can be expressed as: q„ , = - 2 nr L k(l+k1T )4 I (V.l) ^cond o  dr Rearranging and integrating, the heat flow per unit length of converter is obtained, «cond= ^ - l £ T ^ [ V T . - £ < T ^ > ] ( V ' 2 ' The heat flow by conduction has to be equal to the heat losses by convection and radiation Q • , = 2 TT R |h(T -T ) + a(T4-T4)| cond el e 00 e » I (V.3) igure V.l Thermal Profile in the Cylindrical Shell of the Copper Converter. 263 To evaluate the heat-transfer coefficient the following 101 equation has been proposed for horizontal cylinders under natural convection Nu = 0.13 (Gr P r )1 / 3 (V.4) 9 12 in the turbulent range 10 < Gr Pr < 10 . To evaluate the properties of the ambient air a film temperature, 0.5(Te+Too) was used. It is necessary to emphasize that Tg in Equations 133 (V.2) and (V.3) is unknown. Table V.l shows values of some properties of air at atmospheric pressure as a function of film temperature. Table V.2 shows the calculated values of the heat-transfer coefficients as a function of T , for converter e' diameters of 400, 460 and 520 cm. The thickness of the refrac-tory was taken as 40 cm, and the ambient temperature 30 °C. Once the heat-transfer coefficient is known for a given temperature of the external surface of the converter the heat losses by convection can be evaluated. Table V.3 shows the values of the heat flow by conduction through the wall as well as the heat losses by convection and radiation, as a function of T , for different converter diameters. The heat-balance, e' Equation (V.3) is satisfied in a l l cases with an external sur-face temperature of about 190 °C and a heat-transfer coefficient of about 7.15 W m~2 K. TABLE V.l PROPERTIES OF DRY AIR AT ATMOSPHERIC PRESSURE Temperature C Density kg m Viscosity N s m~2 x 105 e -1 2 K x 10 Conductivity W m'hC1 x 102 Pr 82 0.995 2.097 2.817 3.043 0.696 87 0.980 2.118 2.778 3.079 0.695 92 0.968 2.139 2.740 3.115 0.694 97 0.953 2.161 2.703 3.150 0.693 102 0.942 2.180 2.667 3.186 0.692 107 0.929 2.201 2.632 3.227 0.691 112 0.916 2.223 2.597 3.259 0.690 117 0.905 2.244 2.564 3.295 0.690 122 0.895 2.265 2.532 3.332 0.689 127 0.883 2.286 2.500 3.366 0.689 265 TABLE V.2 HEAT TRANSFER COEFFICIENT FOR DIFFERENT CONVERTER DIAMETERS D = 400 cm T, C Gr x 10"11 Nu x 10 3 h -2 -1 W m ZK 1 179 184 189 194 7.807 7.834 7.844 7.849 1.058 1.059 1.059 1.061 7.06 7.11 7.15 7.20 D = 460 cm •T, C Gr x 10 1 2 Nu x 10 3 h W m~2K_:L 179 184 189 194 1.112 1.115 1.117 1.118 1.191 1.192 1.192 1.192 7.07 7.11 7.15 7.19 D = 520 cm T, C Gr x 10 1 2 Nu x 10 3 h W m~2K_1 179 184 189 194 1.525 1.530 1.532 1.533 1.323 1.324 1.324 1.325 7.07 7.11 7.15 7.19 266 TABLE V.3 HEAT LOSSES BY CONVECTION AND RADIATION AS COMPARED WITH CONDUCTIVE HEAT FLOW INSIDE THE WALL D = 400 cm T, C ^cond W/m x 10~4 Q conv W/m x IO"4 Qrad , W/m x IO"4 Q + Q A conv rad W/m x 10~4 179 184 189 194 5.06 5.04 5.02 5.00 1.59 1.65 1.71 1.78 2.85 3.01 3.18 3.35 4.44 4.66 4.89 5.13 D = 460 cm T, C ^cond . W/m x 10"* Q conv , W/m x 10 * Qrad , W/m x 10~4 Q + Q A conv ^rad W/m x 10~4 179 184 189 194 5.75 5.73 5.71 5.68 1.79 1.85 1.93 2.00 3.21 3.39 3.57 3.77 5.00 5.24 5.50 5.77 D = 520 cm rp /-i ^cond Q conv Qrad Q + Q A conv rad T, C W/m x IO- 4 W/m x 10~4 W/m x 10~4 W/m x 10~4 179 6.44 1.98 3.56 5.54 184 6.42 2.07 3.76 5.83 189 6.39 2.14 3.97 6.11 194 6.37 2.22 4.18 6.40 267 APPENDIX VI TEMPERATURE PROFILES IN THE CONVERTER WALL  WITH VARIABLE THERMAL CONDUCTIVITY From data presented by Szekely and T h e m e l i s , the thermal conductivity of a chrome-magnesite refractory brick as a function of temperature can be expressed as: k = 1.08(1 + 4.5 x 10 4T) = k (l+k-T) (VI.l) o 1 1 1 o where k and T are expressed in W m_ C~ and C, respectively, for the range 200 to 1300 °C. For the cylindrical wall of the converter (extending from R. to R ), under steady-state conditions and in the I e J absence of heat generation the energy balance equation i s : • 4 [ k o , 1 + k i T ) r S ] = 0 ( v i - 2 ) Integration of Equation (VI.2) twice with the boundary conditions: T(r=R.) = T± T(r=R ) = T e e 268 gives the temperature profile for the cylindrical wall 1 2 2 T " Ti + 7 kl( T Ti) 1 2 2 T.- T + i k i(TT - T ) l e 2 1 l e ln(r/R.) ln(R./R ) l e (VI.3) Similarly for the end walls of the converter the steady state energy equation i s : t i [ k o( 1 + kiT ) i i] - 0 , V I - 4 ) Again integrating Equation (VI.4) twice with the boundary conditions: and T(z=z.) = T. l I T(z=z ) = T e e gives the temperature profile for the end walls T - T. + i L t T2 - T?) z - z. 1 i i \- = T ^ r <VI-5> Ti- Te + j k1(T^ - zi ze APPENDIX VII HEAT TRANSFER MODEL PROGRAM 270 c_ _ ******************************************************* C THIS PROGRAM CALCULATES HEAT EXCHANGE C BETWEEN ALL THE ELEMENTS OF THE CONVERTER C ASSUMING CONSTANT HEAT TRANSFER COEFFICIENT C AND TAKING INTO ACCOUNT THE END WALLS Q ** * * * * * * *t* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * IMPLICIT REAL*8(A-H,0-Z) DIMENSION TI(240,26).FER(240),0(240) DIMENSION DA(240,240),DT(240,240),DX(240),DB(240),IPERM(480) DIMENSION DA 1 (26,26 ) ,DT1(26,26).DX1(26 ) ,DB1(26).I PERM 1 (52 ) DIMENSION F(240,240),DRZ(240) C0MM0N/ZZ1/XE,YE,ZE,XR.YR,ZR,OE,OR,D,SE,SR COMMON/ZZ2/GAMMA,THETE,THETR,AR,0.OT,OL,QTL • • COMMON/ZZ3/TR,TM,TI,TF,F,DA,DB,DX,FER,TIME,DTIME,TE,DH C0MM0N/ZZ4/R,DR,CL,W1,W2,Z.E,NSL,NSEC,ISM,LSM,NSM,NCS,N.M COMMON/ZZ5/TC0ND.DIF.PENT,PI,SIGMA,HCAP.DENST,HTRAN COMMON/ZZ6/Y,DB1.DX1,DA 1,C1,C2,C3 Q T _ **************************************** C R=CONVERTER RADIUS(CM) C DR=REFRACTORY THICKNESS(CM) C CL=CONVERTER LENGTH(CM) C W1=M0UTH WIDTH(CM) C W2=M0UTH LENGTH(CM) C Z=WIDTH OF ONE SLICE(CM) C E=REFRACTORY EMISSIVITY C DTIME=DELTA TIME(S) C TIME=OUT OF STACK TIME(S) C DH=SIZE INCREMENT(CM) C TM=MOUTH TEMPERATURE(C) C TR=INITIAL REFRACTORY TEMPERATURE(C) C TE=EXTERNAL SURFACE TEMPERATURE(C) C TI(I)=INITIAL TEMPERATURE OF ZONE 1(C) C TF(I)=FINAL TEMPERATURE OF ZONE 1(C) C 0(I)=HEAT LOSSES FROM ZONE I (W/CM2) C OL=HEAT LOSSES THROUGH THE MOTH (W/CM2) C HTRAN=HEAT TRANSFER COEFFICIENT (W/CM2 K) C M=SLICES IN THE REFRACTORY C NSL=NUMBER OF SLICES (NSL=CL/Z) C NSEC=NUMBER OF SECTIONS C NCS=NUMBER OF CENTRAL SLICE C ISM=INITIAL SLICE IN MOUTH C LSM=LAST SLICE IN MOUTH C NSM=NUMBER OF SLICES IN THE MOUTH C TCOND=THERMAL CONDUCTIVITY (W/CM K) C Y=PENETRATION IN THE REFRACTORY (CM) C SIGMA=STEFAN-BOLTZMANN CONSTANT (W/CM2 K4) C HCAP=REFRACTORY SPECIFIC HEAT(W/GR C) C DENST=REFRACTPRY DENSITY(GR/CM3) Q _ **************************************** READ(5,5)R,DR,CL,Z.E,TIME.DTIME,DH,NSEC,ISM,LSM 5 F0RMAT(8F7.2,3I3) NSL=CL/Z NDIMAT=240 N=NSEC*(NSL+2) NRHS=1 ITMAX=7 NDIMA=26 ND I M T » 2 6 NDMIBX=26 NS0L=1 271 M=(DR/DH)+1.DO TR=1200.DO TM=600.D0 TE=190.D0 C 1 = 1.DO C2=4.5892D-4 C3=1.0919D-2 HCAP=0.9GD0 DENST=2.9D0 HTRAN=7.20D-4 SIGMA=5.672D-12 NCS=(NSL+1+(NSEC*2))/2 W2=(LSM-ISM+1)*Z NSM=W2/Z PI=3.141592654D0 GAMMA=(2.DO*PI)/(DFLOAT(NSEC)) W1=4.DO*R*DTAN(GAMMA/2.DO) WRITE(6,10)R,DR.CL,W1,W2,Z,E,TIME.DTIME,DH,TM,TR,TE,NSL,NCS, 1NSM,ISM,LSM,NSEC,DENST.HCAP,HTRAN,M 10 FORMAT(' ',T10.'CONVERTER RADIUS='.F7.2./, 1T10,'REFRACTORY THICKNESS=',F5.2./, ITIO,'CONVERTER LENGTH1',F8.2,/. 1T10,'MOUTH WIDTH=',F7.2,/,T10,'MOUTH LENGTH3'.F7.2,/, 1T10, 'SLICE SIZE"',F5.1,/,T10, 'REFRACTORY EMI SSI VITY='.F4.2,/, 1T10,'0UT OF STACK TIME='.F8.2./,T10, 'TIME STEP=',F8 . 2,/, 1T10,'SIZE INCREMENT=',F4.2,/, 1T10,'MOUTH TEMPERATURE=',F8.2./, 1T10,'INITIAL REFRACTORY TEMPERATURE3',F8.2,/, 1T10,'EXTERNAL SURFACE TEMPERATURE=',F8.2,/, 1T10, 'NUMBER OF SLICES=',13,/,T10. 'CENTRAL SLICE= ' ,13,/, 1T10,'SLICES IN THE MOUTH=',13./, 1T10.'INITIAL SLICE IN MOUTH='.13,/, 1T10.'LAST SLICE IN MOUTH=',13,/, 1T10,'NUMBER OF SECTIONS3',13,/, IT 10, 'REFRACTORY DENSITY3',F6.3,/, 1T10.'REFRACTORY SPECIFIC HEAT=',F6.3./, 1T10,'HEAT TRANSFER COEFFICIENT='.F12.10,/. 1T10.'SECTIONS IN THE REFRACTORY3',13,/) CALL TEMP1(I,J) K=NSEC+1 PRINT 11 11 FORMAT(T4, ' I' ,T8, 'T1' ,T 14, 'T2',T20. 'T3' ,T26, ' T4 ' ,T32, 'T5' , 1T38, 'T6' ,T44. 'T7' ,T50. 'T8' ,T56, 'T9' ,TG 1 , 'T10' ,T67. ' T 1 1 ' ) WRITE(6.16)K.TI(K,1).TI(K,2).TI(K,3),TI(K.4),TI(K,5), 1TI(K,6),TI(K,7),TI(K,8),TI(K,9).TI(K,10).TI(K,11) CALL SFER(NE.NR) NTIME=TIME NDTIME=DTIME DO 30 K=NDTIME.NTIME.NDTIME DO 12 1=1,N DB(I)3SIGMA*((TI(I,1)+273.D0)**4) 12 CONTINUE DEPS=1 .D-8 CALL DSLIMP(DA.DT,DB.DX.DRZ,IPERM,N,NDIMAT,DEPS,NRHS,ITMAX) CALL HEAT(I ) DO 14 I=1,N CALL MATRA(I.d) CALL SLE(M,NDIMA,DA 1,NSOL,NDIMBX,DB1,DX1,I PERM 1,NDIMT,DT1, 1DDET,JEXP) DO 13 L=1,M 272 IF(I.GE.ISM.AND.I.LE.LSM)G0 TO 20 IF(I.GE.ISM+NSLMNSEC-1).AND.I.LE.LSM+NSL*(NSEC-1))G0 TO 20 TI(I.L)=DX1(L) GO TO 13 20 TI(I.L)=TM 13 CONTINUE 14 CONTINUE WRITE(G,19)K,QT,QL.QTL N1=NSEC+((NSEC/2)-1)*NSL+1 N2=N1+NSL-1 PRINT 11 DO 17 I=N1,N2 WRITE(6,16)I,TI(I,1).TI(I,2),TI(I,3),TI(I,4).TI(I.5). 1TI(I.6).TI(I.7).TI(I,8).TI(I,9),TI(I,10),TI(I,11) 16 FORMAT(T2.I3,T6.F5.0,T12,F5.0,T18,F5.0.T24,F5.0.T30,F5.0, 1T36,F5.0,T42,F5.0,T48,F5.0.T54,F5.0.T60.F5.0,T66,F5.0) •17 CONTINUE 19 FORMAT(/,T5,'TIME=',I5,T19,'0I = ' ,E12.3.T40. 'QL=' ,E 1 2.3, 1T60,'OTL=',E12.3) 30 CONTINUE STOP END SUBROUTINE SFER(NE.NR) IMPLICIT REAL*8(A-H,0-Z) DIMENSION TI(240.26),FER(240),0(240) DIMENSION DA(240.240),DT(240.240).OX(240),DB(240),I PERM(480) DIMENSION DA1(26.26).DT1(26,26 ) ,0X1(26),DB1(26).IPERM 1(52) DIMENSION F(240,240),DRZ(240) COMMON/ZZ1/XE,YE,ZE,XR,YR,ZR.OE.OR.0,SE.SR C0MM0N/ZZ2/GAMMA.THETE,THETR,AR,Q,QT,QL,QTL COMMON/ZZ3/TR,TM,TI,TF,F,DA,DB,DX,FER.TIME.DTI ME.TE,DH COMMON/ZZ4/R,DR.CL,W1,W2,Z,E,NSL,NSEC,ISM,LSM,NSM,NCS,N.M C0MM0N/ZZ5/TC0ND.DIF.PENT.PI,SIGMA.HCAP.DENST,HTRAN DO 117 NE=1,N DO 116 NR=1,N IF(NE.GT.NSEC)GO TO 103 THETE = (GAMMA/2.DO) + (NE-1)*GAMMA XE=R*DCOS(THETE)/DSQRT(2.DO) YE=R*DSIN(THETE)/DSQRT(2.DO) ZE=CL/2.D0 XOE=XE YOE=YE IF(NR.LE.NSEC)GO TO 101 IF(NR.GT.NSEC*(NSL+1))G0 TO 102 ZOE = ((NCS-NR) + ((NR-NSEC- 1 )/NSL ) *NSL)*Z GO TO 105 101 Z0E=CL/2.D0 GO TO 105 102 Z0E=-CL/2.DO GO TO 105 103 IF(NE.GT.NSEC*(NSL+1))GO TO 104 THETE = ((NE-NSEC-1)/NSL ) *GAMMA+(GAMMA/2.DO) XE = R*DCOS(THETE ) YE=R*DSIN(THETE ) ZE=((NCS-NE)+((NE-NSEC-1)/NSL)*NSL)*Z X0E=O.DO Y0E=O.DO ZOE-ZE 273 GO TO 105 104 THETE=(GAMMA/2.DO)+(NE-1-NSEC*(NSL+1))*GAMMA XE=R*DC0S(THETE)/DSQRT(2.DO) YE=R*DSIN(THETE)/DSQRT(2.DO) ZE=-CL/2.DO XOE=XE YOE=YE IF(NR.GT,NSEC*(NSL+1))G0 TO 102 IF(NR.LE.NSEC)GO TO 101 Z0E=((NCS-NR)+((NR-NSEC-1)/NSL)*NSL)*Z 105 IF(NR.GT.NSEC)GO TO 108 THETR=(GAMMA/2.DO)+(NR-1)*GAMMA AR=R*R*DTAN(GAMMA/2.DO) XR=R*DC0S(THETR)/DSQRT(2.DO) . ,YR = R*DSIN(THETR)/DSQRT(2 . DO) ZR=CL/2.DO XOR=XR YOR=YR IF(NE.LE.NSEC)GO TO 106 IF(NE.GT.NSEC*(NSL+1))G0 TO 107 ZOR=((NCS-NE)+((NE-NSEC-1)/NSL)*NSL)*Z GO TO 110 106 Z0R=CL/2.D0 GO TO 1 10 107 Z0R=-CL/2.DO GO TO 1 10 108 IF(NR.GT.NSEC*(NSL+1))G0 TO 109 THETR=((NR-NSEC-1)/NSL)*GAMMA+(GAMMA/2.DO) AR=2.D0*Z*R*DTAN(GAMMA/2.DO) XR=R*DCOS(THETR) YR=R*DSIN(THETR) ZR=((NCS-NR)+((NR-NSEC-1)/NSL)*NSL)*Z X0R=O.DO Y0R=O.DO ZOR=ZR GO TO 110 109 THETR=(GAMMA/2.DO)+(NR-1-NSEC*(NSL+1))*GAMMA AR=R*R*DTAN(GAMMA/2.DO) XR=R*DCOS(THETR)/DSORT(2.DO) YR=R*DSIN(THETR)/DSQRT(2.DO) ZR=-CL/2.D0 XOR=XR YOR=YR ' IF(NE.LE.NSEC)G0 TO 106 IF(NE.GT.NSEC*(NSL+1))G0 TO 107 ZOR=((NCS-NE)+((NE-NSEC-1)/NSL)*NSL)*Z 110 IF(NE . LE .NSEC .AND.NR . LE .NSEOGO TO 111 IF(NE.GT.N-NSEC.AND.NR.GT.N-NSEC)G0 TO 111 IF(NE.EO.NR)GO TO 111 QE=DSQRT((XE-X0E)**2+(YE-YOE)**2+(ZE-Z0E)**2) 0R = DS0RT((XR-XOR)**2+(YR-YOR)**2+(ZR-ZOR)**2 ) D = DSORT((XE-XR)**2+(YE -YR)*'2 +(ZE-ZR ) •*2 ) SE=DSORT((XR-XOE)**2+(YR-YOE)**2+(ZR-ZOE)**2) SR = DS0RT((XE-X0R)**2+(YE -YOR)**2+(ZE-ZOR)•* 2 ) IF(OE.EO.O.OR.OR.EOO)GO TO 111 F1=D**2+0E**2-SE**2 F2=D**2+0R**2-SR**2 F3=4.D0*PI*0E*0R*D**4 F4=F1*F2/F3 F(NE,NR)=F4 *AR 274 GO TO 112 111 F(NE,NR)=O.DO 112 FER(NE)=FER(NE)+F(NE,NR) 116 CONTINUE 117 CONTINUE D0125 NE=1 ,N DO 124 NR=1,N IF(NE.GE.ISM.AND.NE.LE.L5M)GO TO 114 IF(NE.GE.ISM+NSL*(NSEC-1).AND.NE.LE.LSM+NSL*(NSEC- 1))GO TO 114 IF(NE.EQ.NR)GO TO 113 DA(NE,NR)=-((1.DO-E)/E)*F(NE.NR) GO TO 124 113 DA(NE,NR)=1.DO+FER(NE)•(1.DO-E)/E GO TO 124 114 IF(NE.EO.NR)GO TO 115 • DA(NE,NR)=O.DO GO TO 124 115 DA(NE,NR)=1.DO 124 CONTINUE 125 CONTINUE RETURN END Q _ **********************************+*+***************** SUBROUTINE TEMPI(I.J) Q ****************************************************** IMPLICIT REAL*8(A-H,0-Z) DIMENSION TI(240.26),FER(240),0(240) DIMENSION DA(240,240),DT(240,240),DX(240).DB(240),IPERM(480) DIMENSION DA 1(26,26) ,DT1(26,26 ) ,DX 1(26),DB 1(26) .I PERM 1(52) DIMENSION F(240,240),DRZ(240) COMMON/ZZ3/TR,TM,TI,TF,F,DA,DB,DX,FER,TIME,DTI ME,TE.DH C0MM0N/ZZ4/R,DR,CL,W1.W2,Z,E.NSL.NSEC,ISM,LSM,NSM,NCS.N.M C0MM0N/ZZ6/Y.DB1,DX1.DA 1,C1.C2,C3 DO 209 I=1.N DO 208 0=1,M F1=DH*(DFLOAT(J - 1)) IF( I . LE .NSEC .OR . I .GT .N-NSEOGO TO 201 Y=R+F1 IF(I.GE.ISM.AND.I.LE.LSM)GO TO 207 IF(I.GE.ISM+NSL*(NSEC-1).AND.1.LE.LSM+NSL*(NSEC-1) )G0 TO 207 F2=DL0G(Y/R)/DLOG(R/(R+DR) ) F3 = C1*(TR-TE)+0.5D0*C2*((TR**2 )-(TE**2) ) F4=F2*F3 F5 = C1*TR+0.5DO*C2*(TR**2 ) F6=-(F4+F5) F7 = DSQRT((C1**2)-(2 .D0*C2*F6) ) F8 = F7-C 1 TI(I,J)=F8/C2 GO TO 208 201 IF(I .GT.N-NSEOGO TO 202 Y=CL/2.D0+F1 F9=(CL/2.DO-Y)/DR GO TO 203 202 Y=-CL/2,00-F1 F9=(Y+CL/2.D0)/DR 203 F10=C1*(TR-TE)+0.5D0*C2*((TR**2 ) -(TE**2 ) ) F11=F9*F10 F12=C1*TR+0.5DO*C2*(TR**2 ) F 1 3 - - ( F 11+F12) F 1 4 » D S 0 R T ( ( C 1 * * 2 ) - ( 2 D0*F13*C2)) 275 F15=F14-C1 TI(I,J)=F15/C2 GO TO 208 207 TI(I,U)=TM 208 CONTINUE 209 CONTINUE RETURN END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE HEAT(I ) 0 _ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * IMPLICIT REAL*8(A-H,0-Z) DIMENSION TI(240.2G),FER(240),0(240) OIMENSION DA(240,240),DT(240,240),0X(24O),DB(240),IPERM(480) DIMENSION DA 1(26,26),DT1(26,26),DX1(26),DB1(26),IPERM 1(52) DIMENSION F(240,240),DRZ(240) COMMON/ZZ2/GAMMA,THETE,THETR,AR,0,QT,OL,QTL . COMMON/ZZ3/TR,TM,TI,TF,F,DA,DB,DX,FER,TIME,DTIME,TE,DH COMMON/ZZ4/R,DR.CL.W1,W2,Z,E,NSL,NSEC,ISM,LSM,NSM.NCS,N,M 01=0.DO QT=O.DO 0L=0.DO DO 300 I=1.N 0(I)=0.D0 . . 300 CONTINUE DO 302 I=1,N DO 301 J=1,N 0 ( I ) = 0 ( I ) + F ( I . J ) » ( D X ( I ) - D X ( J ) ) / F E R ( I ) 301 CONTINUE 302 CONTINUE DO 304 I=1,N IF(I.GT.NSEC.AND.I.LE.N-NSEC)G0 TO 303 A=R*R*DTAN(GAMMA/2.DO) QT=QT+Q( I )*A • i-GO TO 304 -303 A=GAMMA*R*Z 0T=0T+Q(I)*A 304 CONTINUE DO 305 I=ISM,LSM A=GAMMA*R*Z 01=01+0(I)*A 305 CONTINUE QL=2.D0*01 QTL=QTL+QL*DTIME RETURN END C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * SUBROUTINE MATRA(I.J) Q *************************************************** IMPLICIT REAL*8(A-H,0-Z) DIMENSION TI(240.26),FER(240).0(240) DIMENSION DA(240,240),DT(240,240),DX(240),DB(240),IPERM(480) DIMENSION DA1(26,26),DT1(26,26),DX1(26),DB1(26),IPERMK52) DIMENSION F(24O,240).DRZ(24O) COMMON/ZZ2/GAMMA,THETE,THETR,AR,0,QT,OL,OTL COMMON/ZZ3/TR,TM,TI,TF,F,DA,DB,DX.FER,TIME.DTIME,TE . DH COMMON/ZZ4/R,OR.CL,W1,W2,Z,E,NSL.NSEC,ISM,LSM.NSM,NCS.N,M COMMON/ZZ5/TC0ND,DIF,PENT,PI,SIGMA,HCAP,DENST,HTRAN C0MM0N/ZZ6/Y,DB1,DX1.DA 1,C1,C2,C3 DO 470 J=1,M 276 TC0ND=C3*(C1+C2*TI(I,J)) HEAT=HCAP*DENST/(TCOND*DTIME) IF(I.GT.NSEC.AND.I.LE.N-NSEC)GO TO 403 A=R*R*DTAN(GAMMA/2.DO) V=0.5D0*DH*A IF(d.GT.1)G0 TO 401 DA1(d,d)=HEAT*V+A/DH DA 1 (<J , J+ 1 ) = -A/DH DB1(d)=HEAT*V*TI(I,d)-Q(I)*A/TCOND GO TO 470 401. IF(I.E0.M)G0 TO 402 DA1(d,d-1)=-A/0H DA1(d,d)=2.DO*(HEAT*V+A/DH) DA 1(J,J+1 ) = -A/DH DB1(d)=2.D0*HEAT*V*TI(I, d) GO TO 470 402 DA1(J,J-1)=-1/DH DA 1(J,J)=HEAT*V+A/DH F1=SIGMA*((TI(I,J)+273.DO)**4-(TM+273.DO)**4) F2=HTRAN*(TI(I,d)-TM) DB1(J)=HEAT*V*TI(I,J)-(A/TCOND)*(F1+F2) GO TO 470 403 Y = R+DH*(DFLOAT(J-1 ) ) IF(J.GT.1)G0 TO 404 SP=(GAMMA*Z/DH)*(Y+0.5D0*DH) V=GAMMA*Z*(DH* *2+4.DO*Y*DH)/8.DO DA1(d,d)=HEAT*V+SP DA1(J,J+1 ) = -SP DB1(0)=HEAT*V*TI(I,J)-0(I)*GAMMA*Y*Z/TCOND GO TO 470 404 IF(J.EQ.M)G0 TO 405 SN=(GAMMA*Z/DH)*(Y-0.5D0*DH) SP=(GAMMA * Z/DH)*(Y+0.5D0*DH) V=GAMMA*Z*Y*DH DA 1(J,J-1) = -SN DA 1(0,J)=HEAT*V+SN+SP DA 1(J,J+1 ) = -SP DB1(d)=HEAT*V*TI(I,J) GO TO 470 405 SN=(GAMMA*Z/DH)*(Y-0.5D0*DH) V=GAMMA*Z*(4.DO*Y*DH-DH**2) DA1(d,d-1 ) = -SN DA1(d,d)=HEAT*V+SN F1=SIGMA*((TI(I,d)+273.DO)**4-(TM+273.D0)**4) F 2 = HTRAN*(TI(I,J)-TM) DB1(d)=HEAT*V*TI(I,d)-(GAMMA*Z*Y/TCOND)*(F1+F2) 470 CONTINUE RETURN END 

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