There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

I: Phenomena in the Blast Furnace.- 1 Dissection of Quenched Blast Furnaces.- 1.1 Introduction.- 1.1.1 Background to the present study.- 1.1.2 Methods of quenching and their effects.- 1.1.3 General in-furnace situations and peculiar phenomena.- 1.2 Relation Between Behavior of Descending Burden and State of Combustion Zone.- 1.2.1 Fundamental descent behavior of burden in the shaft.- 1.2.2 Asymmetrical descent of burden.- 1.3 Behavior of the Core.- 1.4 Situations in and Around the Combustion Zone.- 1.4.1 State in front of the tuyere nose.- 1.4.2 Formation of shell and movements at the lower part of the raceway.- 1.4.3 Conditions inside the furnace and the shape of the raceway.- 1.5 Shape of Cohesion Zone and Relation to Distribution and Movement of Burden.- 1.5.1 Formation of the cohesion zone.- 1.5.2 Relation between shape of the cohesion zone and operation conditions.- 1.6 Behavior of Circulating Elements.- 1.6.1 Effect of water quenching on the circulating elements.- 1.6.2 Behavior of circulating elements and amounts of circulation.- 1.7 Changes in Properties of Burden Materials.- 1.7.1 Macroscopic changes.- 1.7.2 Microscopic structural and composition changes.- 1.7.3 Effects of circulating elements on the behavior of the cohesion zone.- 1.8 Reactions in the Hearth.- 1.8.1 Slag formation reactions.- 1.8.2 Changes in the metal composition.- 1.9 Concluding Remarks.- 1.10 Addendum.- 1.10.1 Arrangement inside the furnace.- 1.10.2 Changes in properties of the burden.- 2 Measurements in Operating Blast Furnaces.- 2.1 Objectives of Blast Furnace Measurements.- 2.2 Development of Measurements for Clarification of Furnace Reactions.- 2.2.1 Standard instrumentation for blast furnaces a decade ago.- 2.2.2 Development of instrumentation since the introduction of blast furnace dissection.- 2.3 Relationship Between Furnace Measurement and Furnace Operation (Actual Examples).- 2.3.1 Relationship between measurements before blowing out of blast furnace and results of dissection.- 2.3.2 Measurements and estimations of the cohesive zone.- 2.3.3 Development and use of the latest sensors to study furnace interiors.- 2.4 Future Development of Blast Furnace Measurements.- II: Modelling of the Blast Furnace.- 3 Global Formulation.- 3.1 Review of Blast Furnace Models.- 3.1.1 Reichardt diagram.- 3.1.2 Operation diagram.- 3.1.3 Kinetic model.- 3.1.4 Control models.- 3.1.5 Models for estimating internal situations based on observed data.- 3.2 One-dimensional Static Model.- 3.2.1 Overall reaction rates.- 3.2.2 Overall material balance.- 3.2.3 Temperatures of gas and solid at the top of the furnace.- 3.2.4 Flow rate and composition of gas at tuyere level.- 3.2.5 Theoretical flame temperature.- 3.2.6 Temperature of gas and coke at tuyere level.- 3.2.7 One-dimensional mathematical formulation for internal state of blast furnace.- 3.2.8 Effect of various operating conditions on productivity and situation in blast furnace.- 3.2.9 Some applications of the model.- 3.3 Layered Structure Model.- 3.3.1 Radial distribution of flow rate of gas.- 3.3.2 Mathematical-kinetic model of blast furnace.- 3.3.3 Numerical analysis of blast furnace operation.- 3.3.4 Computed results.- 3.3.5 Steady-state two-dimensional modelling.- 3.3.6 Governing equations for cylindrical polar coordinates.- 3.3.7 Some auxiliary relations.- 3.3.8 Numerical solution of two-dimensional model.- 3.4 Two-dimensional Model for Gas Flow, Heat Transfer and Chemical Reactions.- 3.4.1 General concept of the radial distribution model.- 3.4.2 Momentum transfer.- 3.4.3 Mass transfer with chemical reactions.- 3.4.4 Heat transfer.- 3.4.5 Input conditions.- 3.4.6 Method of analysis.- 3.4.7 Simulation results.- 3.5 Two-dimensional Formulation by Finite Element Method.- 3.5.1 Flow analysis of gas.- 3.5.2 Computed results for gas flow.- 3.5.3 Simultaneous analysis of gas flow and heat transfer.- 3.5.4 Computed results on the simultaneous gas flow and heat transfer.- 3.6 Model for Estimating the Profile of the Cohesive Zone.- 3.6.1 General description of the mathematical model.- 3.6.2 Relation between indices estimated using the mathematical model and from blast furnace operation (cohesive zone analysis with 4000 m3 class blast furnace).- 3.6.3 Analysis of operation with decrease in production.- 3.6.4 Future direction.- 3.7 One-dimensional Dynamic Model.- 3.7.1 Outline of mathematical simulation model.- 3.7.2 Applications to blast furnace operations.- 3.8 Notation.- 4 Flow of Gas, Liquid and Solid.- 4.1 Flow of Solids During Charging and Control of Burden Distribution.- 4.1.1 Burden distribution of bell top furnaces.- 4.1.2 Burden distribution of bell-less top furnaces.- 4.2 Flow of Solids in the Upper Part of the Furnace.- 4.2.1 Information from dissected blast furnaces.- 4.2.2 Burden descent model.- 4.2.3 Decrease in angle of layer inclination with burden descent.- 4.2.4 Influence of some other factors.- 4.3 Flow of Solids in the Lower Part of the Furnace.- 4.3.1 Basic phenomena.- 4.3.2 Formation of mixed zone in the peripheral region near the wall.- 4.3.3 Movement of coke to the raceway.- 4.3.4 Movement of coke in dead coke zone and hearth.- 4.4 Theoretical Approach to the Flow of Burden Material in the Furnace.- 4.4.1 Stress distribution in the blast furnace.- 4.4.2 Inclination of the dead coke zone boundary.- 4.4.3 Notation (Sections 4.3 and 4.4).- 4.5 Numerical Simulation of Radial Gas Flow Distribution.- 4.5.1 Burden distribution model.- 4.5.2 Two-dimensional gas flow in the blast furnace.- 4.5.3 Outline of results of calculation.- 4.5.4 Concluding remarks.- 4.5.5 Notation.- 4.6 Flow of Gas and Liquid in the Dropping Zone.- 4.6.1 Counter-current flow region.- 4.6.2 Cross flow region.- 4.6.3 Concluding remarks.- 4.7 Flow of Slag and Metal in the Hearth During Tapping.- 4.7.1 State of coke bed in the hearth.- 4.7.2 Flow of slag during tapping.- 4.7.3 Flow of metal during tapping.- 4.7.4 Mathematical simulation of hearth flow.- 4.7.5 Concluding remarks.- 5 High Temperature Properties of Iron Ore Agglomerates.- 5.1 Reduction Behavior in Lumpy Zone.- 5.1.1 Estimation of reducibility in lumpy zone.- 5.1.2 Determination of reaction rate constant of reduction and comparison with blast furnace operation.- 5.2 Change of Mineral Phases in Blast Furnace.- 5.2.1 Change of mineral phases during reduction.- 5.2.2 Mineral phases in reduced iron ore agglomerates.- 5.2.3 Change of gangue minerals.- 5.3 Flow Resistance of Gas Through the Fused Packed Bed.- 5.3.1 Measurement of pressure drop in fused packed bed.- 5.3.2 Numerical calculation of gas flow resistance through a fused packed bed by use of an orifice model.- 5.3.3 Equation of pressure drop in fused packed bed.- 5.3.4 Quantitative determination of softening properties.- 5.4 Effects of High Temperature Properties of Burden on Blast Furnace Operation.- 5.4.1 Factors for evaluating high temperature properties of burden.- 5.4.2 Relationship between high temperature properties of burden and blast furnace operating performance.- 5.5 High Temperature Properties of Burden with Cohesive Zone Model and Direct Measurement of Cohesive Zone.- 5.5.1 Estimation of cohesive zone with theoretical models.- 5.5.2 Effect of softening properties on gas permeability.- 5.5.3 Evaluation of softening properties of sinter.- 5.5.4 Direct measurement of cohesive zone.- 5.6 Notation.- 6 The Raceway.- 6.1 Measurement and Observation of the Blast Furnace Raceway.- 6.1.1 Movement of coke particles in the raceway.- 6.1.2 Condition near the raceway.- 6.1.3 Reactions in the raceway.- 6.2 Mathematical Model of the Raceway.- 6.2.1 One-dimensional model.- 6.2.2 Two-dimensional model.- 6.3 Notation.- 7 The Lower Region of the Blast Furnace and the Slag-Metal-Gas Reaction.- 7.1 Reaction of Silicon.- 7.1.1 Introduction.- 7.1.2 Behavior of silicon in the blast furnace.- 7.1.3 Kinetics of silicon transfer.- 7.2 Other Reactions.- 7.2.1 Manganese.- 7.2.2 Titanium.- 7.3 Application of Reaction Models of Silicon to Blast Furnace Operation.- 7.3.1 Review of silicon reaction models.- 7.3.2 Partition reactions of Si, S and Mn.- 7.3.3 Mathematical model of silicon reactions in the blast furnace.- 7.4 Notation.- III: Flexibility and Adaptability of Blast Furnace.- 8 Blast Furnace Ironmaking Technology in the Near Future.- 8.1 Flexible Operation.- 8.2 Increase of Furnace Life.- 8.3 Mechanization of Cast-house Operation.- 8.4 Technology Development Related to Innovative Steelmaking Process.- 8.5 Use of Blast Furnace for Producing Other Metals.

Blast furnace phenomena and modelling

Since the hot metal silicon content simultaneously reflects the product quality and the thermal state of the blast furnace, its modeling is crucial and representative. In order to facilitate the realization of control, this paper proposes a Bayesian block structure sparse based Takagi–Sugeno (T–S) fuzzy modeling method, with which the main important fuzzy rules and the corresponding pivotal consequent parameters can be selected automatically to obtain a compact fuzzy model with good generalization performance. For being conjugate to the Gaussian likelihood that would lead to the associated Bayesian inference to be performed in closed form, a hierarchy of block structure sparse priori is adopted, and the variational Bayesian inference is used to solve it. The screening of model inputs and data processing appropriately consider the characteristics of the blast furnace process. The applicability and performance of the proposed method are demonstrated on no. 2 blast furnace of Liuzhou Steel in China.

Bayesian Block Structure Sparse Based T–S Fuzzy Modeling for Dynamic Prediction of Hot Metal Silicon Content in the Blast Furnace

Since the hot metal silicon content simultaneously reflects the product quality and the thermal state of the blast furnace, accurately predicting the development tendency of hot metal silicon content has the immensely guiding role for blast furnace operators. This paper focuses on fuzzy classifier design for the development tendency of hot metal silicon content based on blast furnace operation data. The cross characteristic of binary classification problem was found via embedding high-dimensional blast furnace data into a two-dimensional space. Then, presented a nonparallel hyperplanes based fuzzy classifier, which conquered the cross classification still holding the interpretability advantage as fuzzy classifier. The proposed method was tested on No.2 blast furnace of Liuzhou Steel in China, that demonstrated the excellent performance compared with some other classifier algorithms.

Fuzzy Classifier Design for Development Tendency of Hot Metal Silicon Content in Blast Furnace

Coke reaction behavior in the blast furnace hearth has yet to be fully understood due to limited access to the high temperature zone. The graphitization of coke and its interaction with slag in the hearth of blast furnace were investigated with samples obtained from the center of the deadman of a blast furnace during its overhaul period. All hearth coke samples from fines to lumps were confirmed to be highly graphitized, and the graphitization of coke in the high temperature zone was convinced to start from the coke surface and lead to the formation of coke fines. It will be essential to perform further comprehensive investigations on graphite formation and its evolution in a coke as well as its multi-effect on blast furnace performance. The porous hearth cokes were found to be filled up with final slag. Further research is required about the capability of coke to fill final slag and the attack of final slag on the hearth bottom refractories since this might be a new degradation mechanism of refractories located in the hearth bottom.

Graphitization of Coke and Its Interaction with Slag in the Hearth of a Blast Furnace

Phosphorus removal in basic oxygen steelmaking is a significant problem for integrated steelmakers. Phosphorus removal is required due to its deleterious effect on the mechanical properties of stee...

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A review of phosphorus partition relations for use in basic oxygen steelmaking

Phosphorus generally has a negative effect on the mechanical properties of steel.1–3) Phosphorous levels in iron ore are expected to increase4,5) and may cause difficulties in achieving steel specification using current processing methods and conditions. Against this background of increasing phosphorous in the ore, an improved understanding of steel dephosphorisation fundamentals will underpin any adjustments steelmakers need to make to the steelmaking process to continue to meet steel specification. Phosphorus removal in basic oxygen steelmaking (BOS) is typically described by the ionic reaction given in Eq. (1). It may also be represented by the simple molecular reaction, given in Eq. (2),

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Phosphorus Partition and Phosphate Capacity of Basic Oxygen Steelmaking Slags

Blast furnace hearth refractories are a key component in achieving long furnace lives. These refractories can be degraded by among other things reactions with coke ash products. Recent studies have shown that these coke ash products could be calcium aluminate based. To understand and characterize the effects of these calcium aluminates on hearth refractories a study has been carried out that investigates the reaction kinetics of CaO.Al2O3, CaO.2Al2O3 and CaO.6Al2O3 in contact with an aluminosilicate blast furnace hearth refractory. The experimental program covered the temperature range 1 450° to 1 550°C. The temperatures were chosen to represent the hot face temperatures of the hearth refractories. From this study it was found that the rate of reaction with the aluminosilicate refractory and CaO.6Al2O3 was much slower than that of CaO.Al2O3 and CaO.2Al2O3. The prevailing kinetics of the aluminosilicate refractory with CaO.Al2O3 and CaO.2Al2O3 was found to be consistent with the linear rate law. The slow rate of reaction of the refractory with CaO.6Al2O3 prohibited identification of the prevailing kinetic regime. In characterizing the reaction interface between the aluminosilicate and the calcium aluminates it was found that there was significant reaction between the refractory and CaO.Al2O3 and CaO.2Al2O3 but little reaction with the CaO.6Al2O3. The reaction layers formed at the interface between the couples were found to consist of CaO.2Al2O3, CaO.6Al2O3, corundum (Al2O3), plagioclase (CaO.Al2O3.2SiO2) and melilite (2CaO.Al2O3.SiO2). The formation of a layer with these phases could result in spalling/wear of the hearth refractory.

Reactivity of Coke Ash on Aluminosilicate Blast Furnace Hearth Refractories

Phosphorus Partition and Phosphate Capacity of TiO2 Bearing Basic Oxygen Steelmaking Slags

Phosphorus is generally undesirable in steel. Decreasing availability of low phosphorus iron ores and the desire to recycle waste materials like basic oxygen steelmaking (BOS) slags is driving renewed interest in phosphorus removal. A number of phosphorus partition (LP) equations have been proposed in the literature for specific slag compositions and temperature ranges at equilibrium. These LP equations have been evaluated against the historic data on the phosphorus removal from an industrial top blown bottom stirred basic oxygen convertor. Further, the performance of these partition equations has been used to inform the development of a new LP model more suitable to the prevailing conditions in the Australian steelmaking industry. The new model has been used to isolate the key factors controlling dephosphorisation, namely lower temperature, higher basicity and higher oxygen potential. This LP model has allowed secondary factors influencing dephosphorisation to be assessed, including TiOx load, heat duration and stirring rate.

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Phillip Brian Drain

Papers

A review of phosphorus partition relations for use in basic oxygen steelmaking

Phosphorus Partition and Phosphate Capacity of Basic Oxygen Steelmaking Slags

Reactivity of Coke Ash on Aluminosilicate Blast Furnace Hearth Refractories

Phosphorus Partition and Phosphate Capacity of TiO2 Bearing Basic Oxygen Steelmaking Slags

Development of a new phosphorus partition relation for Australian steelmakers