Kinetics of the zinc slag-Fuming process: Part III. model predictions and analysis of process kinetics

In the final part of this paper the mathematical model of the slag fuming process, developed in Part II based on the analysis of industrial measurements from Part I, has been subjected to a sensitivity analysis, then employed to elucidate the rate limiting steps and to predict the influence of process variables on fuming. The kinetics analysis has been based on model predictions of fuming efficiency (Zn/coal) of the coal particles injected into the slag. The model predicts that fuming efficiency passes through a maximum with increasing residence time of coal particles in the slag. At shorter times, the zinc reduction kinetics are governed by the Boudouard Reaction, but at longer times, beyond the time at which the peak fuming efficiency is reached, the diffusion of ferric iron to the interface between the secondary bubbles containing the coal and the slag is rate determining. The level of ferric iron in the slag, which depends on ferrous iron oxidation rate, melting/freezing of slag at the water-cooled jacket, and ferric iron reduction by coal entrained in the slag, is therefore an important variable affecting the fuming kinetics. With respect to the influence of manipulable process variables, the model predicts that zinc fuming can be enhanced by increasing the fraction of coal entrained by the bath up to an optimum value at a fixed coal rate. An increase in entrainment could be achieved by injecting the desired portion of the coal at high pressure and solids loading through a small number of tuyeres. This strategy is preferable, from the standpoint of fuming efficiency, to simply increasing the rate of coal injection at normal pressures. Similarly, there is an optimum charge weight and bath height for a given furnace size. The best coal for zinc fuming, according to the model, has the following properties: low moisture and ash content, high fixed carbon (or volatiles), and high reactivity. Model predictions also suggest that there are advantages to fuming in a continuous operation rather than in a batch mode. Formerly Graduate Student     

Kinetics of the zinc slag-Fuming Process: part II. mathematical model

A mathematical model of zinc slag fuming has been formulated based on the kinetic conception of the process developed in Part I of this paper. Each of the major reaction zones in the furnace — the slag bath where reduction of zinc oxide and ferric oxide takes place and the tuyere gas column where oxidation of coal and ferrous oxide occurs — have been characterized mathematically. The two zones and the water-jacketed furnace wall have been linked by overall heat and mass balances. Insufficient information is available, however, to characterize quantitatively two of the important kinetic processes occurring in the furnace: the division of coal between entrainment in the slag, combustion in the tuyere gas column and bypass; and oxygen utilization. To overcome this problem the model has been fitted to the data from eleven industrial fuming cycles. Consistent values have been obtained for these kinetic parameters over five different fuming operations indicating that the kinetic conception of the process is sound. The results indicate that about 33 pct of the injected coal is entrained in the slag, 55 pet combusts in the tuyere gas column, and 12 pct bypasses the bath completely. Oxygen utilization has been found to be high and can be correlated to bath depth. Formerly Graduate Student     

Mathematical modeling of the argon-oxygen decarburization refining process of stainless steel: Part II. Application of the model to industrial practice

The mathematical model proposed and presented in Part I of the present work has been used to deal with and analyze the austenitic stainless steel making (including ultralow-carbon steel) and has been tested on data of 32 heats obtained in producing 18Cr9Ni-grade steel in an 18-t argon-oxygen decarburization (AOD) vessel. The results indicated that the carbon concentrations and bath temperatures at the endpoints of blowing periods, calculated by the model, are in excellent agreement with the determined data, and the Cr content after the predeoxidization, obtained from the model predictions, also agrees very well with the observed value. The Gibbs free energies of the oxidation reactions of elements can be used to characterize fully the competitive oxidation among the elements during the refining process and to determine reasonably the corresponding distribution ratios of oxygen. The critical carbon concentration of decarburization (after which the decarburization changes to become controlled by the mass transfer of carbon in molten steel) for the AOD refining process of austenitic stainless steel in an 18-t AOD vessel is in the range of 0.25 to 0.40 mass pct. The model can provide some very useful information and a reliable basis for optimization of the technology of the AOD refining process of stainless steel and control of the process in real time and online.     

Decarburization of stainless steel: Part II. A mathematical model and a process optimization for industrial scale systems

A mathematical model is presented for describing the bath temperature and composition trajectories for the decarburization of stainless steel for processes operating on an indus-trial scale. The model is based on a set of component balances, written with the aid of driving force expressions, the appropriate equilibrium relationships and the heat balance. The resultant set of ordinary differential equations were solved numerically. The predic-tions based on the model were compared with experimentally measured bath composition and temperature paths obtained for the operation of a 40 ton electric furnace. The predic-tions and measurements showed very good agreement. The mathematical model was then combined with a trajectory optimization technique to compute the optimal blowing programi .e., oxygen-argon content of the gas supplied) such that the total cost of the operation is minimized. This calculation was repeated for a series of cost factors. On leave from Department of Iron and Steel Engineering, Nagoya University, Nagoya, Japan     

Oxidation of cobaltite: Part I. process mineralogy

The control of arsenic is important in oxidation roasting and leaching of cobaltite. Oxidation roasting below 823 K did not show any crystal structural change in cobaltite, but heating to 923 K yielded Co-As-oxide, whose composition is varied. Direct oxidation of cobaltite to cobalt oxides with traces of arsenic was observed by roasting at 1023 K or above. The distribution of arsenic within the particles gradually decreased from the outer region to the center of the particles. The arsenic concentration within the particles decreased with the increase of temperature, suggesting temperature dependence on arsenic removal from the lattice of cobaltite. In this article, the process mineralogy of the oxidation of cobaltite is presented at various temperatures. The results from X-ray diffraction (XRD) analysis, reflected light microscopic analysis, and scanning electron microscopic analysis of the roasted cobaltite concentrates together with a rationalized thermodynamic analysis are presented.     

Thermomechanical fatigue,oxidation, and creep: Part i. Damage mechanisms

Isothermal fatigue tests and both out-of-phase and in-phase thermomechanical fatigue tests were performed in air and in helium atmospheres. A wide range of temperatures from 20 ‡C to 700 ‡C was considered in these tests on 1070 steel specimens. A procedure for inert atmosphere testing using encapsulated specimens is described. Results indicate that the fatigue lives are 2 to 12 times greater in helium than in air. Interrupted tests were performed to characterize the pro-gression of damage in the material. Results indicate that oxidation-induced crack nucleation and crack growth are detrimental at high temperatures for isothermal and out-of-phase thermome-chanical fatigue tests. In these tests, transgranular cracking is observed. However, creep-induced intergranular cracking is the dominant damage mechanism during in-phase thermomechanical fatigue tests.     

Thermosolutal convection during dendritic solidification of alloys: Part i. Linear stability analysis

This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state .e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10^-3 cm s^-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips,G _L ,vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1g,0.5 g, 0.1g, and 0.01g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10^-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G _L ≤ 100 K-cm^-1).     

Spouted bed electrowinning of zinc: Part I. Laboratory-scale electrowinning experiments

Two types of laboratory cells have been constructed to electrowin zinc from sulfate electrolytes: one cell was cylindrical while the other had a rectangular (flat) geometry. Cells were operated on industrial or synthetic electrolytes to electrodeposit zinc onto a spouted bed of zinc particles in the range of 0.75 to 1.45 mm. Current efficiencies and cell voltages have been measured during the course of batch experiments, enabling the calculation of the energy consumption per kilogram of zinc deposited. Electrolyte samples have been analyzed. Current densities (current per unit of cell cross-sectional area) were in the range of 1380 to 6200 A/m². Most catholytes were initially neutral and contained on the order of 150 g/L of zinc. Final acid contents were in the range of 39 to 114 g/L of sulfuric acid. The performance of the cells (particularly with respect to current efficiency) was superior to prior work on fluidized bed electrowinning from similar electrolytes. The flat cell was superior to the cylindrical cell and showed energy consumptions of less than 3 kWh/kg zinc at current densities up to 3500 A/m² when used to take the zinc content from 150 to 100 g/L zinc. Current efficiencies in this application ranged from 91 to 92 pct.     

硫酸锌沉淀法处理高铜氰化废水的动力学研究

采用硫酸锌沉淀工艺处理含有高浓度铜离子的氰化提金废水,利用二级反应动力学模型对铜离子和游离氰化物的沉淀过程进行了试验研究。研究结果表明,在试验条件下,铜离子和游离氰化物的沉淀过程均符合二级反应动力学模型,其反应速率常数分别为3.492 dm3/(mol·min)、1.837 dm3/(mol·min)。该研究结果对高浓度铜离子氰化提金废水的沉淀处理技术应用,具有一定的指导意义。     

Optimization and continuous casting: Part II. Application to industrial casters

The optimization of the operation and design of continuous casters is formulated and solved using a nonlinear programing (NLP) strategy. Using objective and constraint functions that relate to casting performance and steel quality, the optimization is performed using a successive quadratic programming (SQP) algorithm applied to a heat flow model. Theoretical development for this approach was presented in Part I of this study.^[2] In this article, we present the results of this approach for 12 casting cases. Here, billet and slab caster models were considered for rate maximization, rate minimization, and maximization of enthalpy at the.cutoff point. Both of these are two-dimensional heat flow models based on industrial continuous casters. The results show that optimization is a viable and effective tool for developing operating strategies for casters. Moreover, many of the optimal solutions are not likely to be discovered through normal operating practice or case study. For example, spray heat-transfer coefficients need not be in decreasing order, and the maximum casting rate may be slightly different from the case for maximum enthalpy in the strand. Formerly with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University.     

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials,mold temperature measurements,and mathematical modeling

An extensive study has been conducted to elucidate mold behavior and its influence on quality during the continuous casting of slabs. The study combined industrial measurements, mathe matical modeling, and metallographic examination of cast slab samples. The industrial mea surements involved instrumenting an operating slab mold with 114 thermocouples in order to determine the axial mold wall temperature profiles for a wide range of casting conditions. A three-dimensional (3-D) heat-flow model of the mold wall was developed to characterize the heat fluxes in the mold quantitatively from the measured mold temperature data. Furthermore, heat-flow models were developed to examine steel solidification phenomena and mold flux behavior at the meniscus. Slab samples collected during the industrial trials were examined metallographically to evaluate the cast structure and defects. Owing to the length of the study, it is presented in two parts, the first of which describes the experimental techniques employed in the instrumentation of the mold together with the details of the industrial trials and mold temperature measurements. Also, the mathematical modeling technique applied to determine the axial heat-flux profiles from the measured mold temperature data is presented. It is shown that a fully 3-D model of the mold wall is needed to convert the measured temperatures to heat-flux profiles properly. Formerly Graduate Student, Centre for Metallurgical Process Engineering, The University of British Columbia Formerly with Research and Development, Stelco Inc.     

Effect of te on morphological transitions in Fe-C-Si alloys: Part i. Directional solidification

Directional solidification experiments have been carried out on Fe-3.4 wt pct C-2 wt pct Si alloys with and without the addition of 0.06 wt pct Te. The effect of the Te addition upon the gray-to-white transition velocity and the white-to-gray transition velocity has been determined. Quenched solid/liquid interface studies on mixed structures, white + type D gray and type D gray + type A gray, have determined the temperature differences at the growth front for these structures.     

Thermal analysis of the arc welding process: Part I. General solutions

An analytical solution for the temperature-rise distribution in arc welding of short workpieces is developed based on the classical Jaeger’s moving heat-source theory to predict the transient thermal response. It, thus, complements the pioneering work of Rosenthal and his colleagues (and others who extended that work), which addresses quasi-stationary moving heat-source problems. The arc beam is considered as a moving plane (disc) heat source with a pseudo-Gaussian distribution of heat intensity, based on the work of Goldak et al. It is a general solution (both transient and quasi-steady state) in that it can determine the temperature-rise distribution in and around the arc beam heat source, as well as the width and depth of the melt pool (MP) and the heat-affected zone (HAZ) in welding short lengths, where quasi-stationary conditions may not have been established. A comparative study is made of the analytical approach of the transient analysis presented here with the finite-element modeling of arc welding by Tekriwal and Mazumder. The analytical model developed can determine the time required for reaching quasi-steady state and solve the equation for the temperature distribution, be it transient or quasi-steady state. It can also calculate the temperature on the surface as well as with respect to the depth at all points, including those very close to the heat source. While some agreement was found between the results of the analytical work and those of the finite-element method (FEM) model, there were differences identified due to differences in the methods of approach, the selection of the boundary conditions, the need to consider image heat sources, and the effect of variable thermal properties with temperature. The analysis presented here is exact, and the solution can be obtained quickly and in an inexpensive way compared to the FEM. The analysis also facilitates optimization of process parameters for good welding practice.     

Unidirectional transformation of Fe-0.8C-Co alloys: Part II. Kinetics of the eutectoid reaction

Unidirectional transformation techniques have been applied to a study of the kinetics of eutectoid growth in Fe-0.8C-Co alloys. The technique readily yielded kinetic data which it is shown could be used to indicate the rate controlling process for pearlitic growth. Accurate measurements of interlamellar spacing (λ) could be made at controlled growth rates (V) and analyzed in terms of the expressionVλⁿ, where the exponentn can indicate the rate controlling process. The results obtained by unidirectional transformation were compared with those achieved by conventional isothermal transformation, both to aid in the initial interpretation of the more unfamiliarV:λ data and also to show that the two different experimental routes lead to equivalent kinetic data. Analysis of the results obtained for Fe-0.8C-Co alloys suggested control by interfacial diffusion of carbon at high growth rates (n=3) changing towards volume diffusion of carbon at lower growth rates (n=2), but also revealed an unexpected region at very slow growth rates (n=4). This anomalous region could be explained in terms of the partitioning of cobalt as the growth rate decreased. It was also shown that cobalt additions decreased the pearlite interlamellar spacing at constant undercooling or growth rate. B. G. MELLOR, formerly Research Student, Department of Metallurgy and Materials Science, University of Cambridge, U. K., is now     

A general mechanism of martensitic nucleation: Part III. Kinetics of martensitic nucleation

The growth of martensitic fault embryos in the fault plane, the development of their in-terfacial structure, and the thickening of the embryos normal to the fault plane are ex-amined as possible rate limiting steps in the total martensitic nucleation process. Growth of the embryos in the fault plane appears the most probable rate limiting step, capable of accounting for both the observed isothermal and athermal kinetic behavior depending on the parameters (such as activation volume) which control the motion of the transformational dislocations. The thermally activated nucleation of dislocation loops responsible for lattice invariant deformations is a possible rate limiting step for some isothermal transformations, though such deformations are not required for all marten-sitic transformations. Embryo thickening by the nucleation of discrete loops of trans-formation dislocations appears improbable in bulk material; instead, a plausible pole mechanism for embryo thickening is presented which incorporates existing “forest≓ dislocations intersected by embryos growing in the fault plane. Lattice softening phe-nomena may lower the critical chemical driving force for nucleation, but are not essen-tial for martensitic nucleation by the proposed faulting mechanism. This paper is Part III of a three-part series based on a thesis sub-mitted by G. B. Olson for the degree of Sc.D. in Metallurgy at the Massachusetts Institute of Technology in June 1974.     

A general mechanism of martensitic nucleation: Part III. Kinetics of martensitic nucleation

The growth of martensitic fault embryos in the fault plane, the development of their interfacial structure, and the thickening of the embryos normal to the fault plane are examined as possible rate limiting steps in the total martensitic nucleation process. Growth of the embryos in the fault plane appears the most probable rate limiting step, capable of accounting for both the observed isothermal and athermal kinetic behavior depending on the parameters (such as activation volume) which control the motion of the transformational dislocations. The thermally activated nucleation of dislocation loops responsible for lattice invariant deformations is a possible rate limiting step for some isothermal transformations, though such deformations are not required for all martensitic transformations. Embryo thickening by the nucleation of discrete loops of transformation dislocations appears improbable in bulk material; instead, a plausible pole mechanism for embryo thickening is presented which incorporates existing “forest” dislocations intersected by embryos growing in the fault plane. Lattice softening phenomena may lower the critical chemical driving force for nucleation, but are not essential for martensitic nucleation by the proposed faulting mechanism. This paper is Part III of a three-part series based on a thesis submitted by G. B. Olson for the degree of Sc.D. in Metallurgy at the Massachusetts Institute of Technology in June 1974.     

Gel electrode imaging of metal fatigue: Part i. cracks in 6061-T6 aluminum

A simple electrochemical technique is described which produces high-resolution, visible images of fatigue cracks in aluminum alloys, without conventional metallographic surface preparation. The only preparation required is the formation of a thin (14 nm) anodic oxide film on the surface. After fatigue cycling, a semisolid electrolyte is placed in contact with the specimen and a voltage applied. As the current flows to the fatigue cracks a clearly defined image is formed. The capabilities of the technique are demonstrated by measurements on6061-T6 aluminum, and the images are correlated with scanning electron micrographs of the specimens. The images are reproducible and record features of the cracks which are barely discernible with a scanning electron microscope. Fatigue cracks only ∼30 μm long have been detected. Measurement of the charge flow during imaging is a quantitative measure of the crack length. These measurements indicate that considerably smaller cracks should also be detectable.     

Thermodynamics of copper matte converting: Part I. Fundamentals of the noranda process

This paper presents a computer-oriented thermodynamic method to analyze copper matte smelting and converting, the system of which was ideally defined as consisting of five major components: Cu, Fe, S, O and SiO2. As an example of its application, the method was demonstrated in establishing a steady-state model for the Noranda Process producing either metallic copper or high grade matte. Process variables such as temperature, oxygen enrichment, charge (or concentrate) composition, matte grade and magnetite content of slag are integrated into one computer model. The model gives the chemical composition of metallic copper, matte and slag phases for any specified condition. Mathematical formulae accounting for physical entrainment in the melts are also presented to correlate the computed melt composition with that observed. The computer model can provide predictions as to the effects of operating and chemical parameters and can contribute to improved metallurgical control.