Mathematical modeling of sulfide flash smelting process: Part III. Volatilization of minor elements

The mathematical model described in Part I^[14] was extended to include the minor element behavior inside a flash-furnace shaft during flash smelting of copper concentrate. The volatilization of As, Sb, Bi, and Pb was computed, and experiments were carried out for Sb and Pb in a laboratory flash furnace. Satisfactory agreement between the predicted and measured results was obtained for antimony and lead. From the computational results, the behavior of each minor element was predicted for various target matte grades. The model predictions show that the elimination of As and Bi to the gas phase increases sharply at about 0.3 m from the burner; however, that of the Sb increases gradually along the flash-furnace shaft, and that of lead occurs suddenly at about 0.6 m from the burner. The predicted results also show that the elimination increases for Bi and Pb as the target matte grade increases; however, it is relatively independent of the target matte grade between 50 and 60 pet Cu for As and Sb. At higher target matte grades above 60 pet Cu, the elimination of As and Sb decreases as matte grade increases. formerly Graduate Student, Department of Chemical Engineering, University of Utah,     

Mathematical modeling of sulfide flash smelting process: Part I. Model development and verification with laboratory and pilot plant measurements for chalcopyrite concentrate smelting

A mathematical model has been developed to describe the various processes occurring in a flash furnace shaft. The model incorporates turbulent fluid dynamics, chemical reaction kinetics, and heat and mass transfer. The key features include the use of thek-ε turbulence model, incorporating the effect of particles on the turbulence, and the four-flux model for radiative heat transfer. The model predictions were compared with measurements obtained in a laboratory flash furnace and a pilot plant flash furnace. Good agreement was obtained between the predicted and measured data in terms of the SO₂ and O₂ concentrations, the amount of sulfur remaining in the particles, and the gas temperature. Model predictions show that the reactions of sulfide particles are mostly completed within about 1 m of the burner, and the double-entry burner system with radial feeding of the concentrate particles gives better performance than the singleentry burner system. The model thus verified was used to further predict various aspects of industrial flash furnace operation. The results indicate that from the viewpoint of sulfide oxidation, smelting rate can be substantially increased in most existing industrial flash furnaces. Formerly Graduate Student, Department of Metallurgical Engineering, University of Utah.     

Transport phenomena in electric smelting of nickel matte: Part II. Mathematical modeling

A three-dimensional mathematical model was developed to simulate the distributions of electrical potential, heat release, temperature, and velocity in the slag and matte in a six-in-line 36 MVA capacity furnace for smelting nickel calcine. From Part I of this series, it was found that there was a substantial electrical potential drop at the electrode surface, likely due to arcing through evolved carbon monoxide. The incorporation of this phenomenon into the model permitted accurate calculation of the current, power, and temperature distributions in the slag and matte. The slag was found to be thermally homogenized due to the evolved gas, and to a lesser extent by natural convection. In contrast, the matte was thermally stratified; this finding was attributed to poor momentum transfer across the slag/matte interface. Ninety percent of the electrical energy was used in smelting reactions in the calcine; to simulate the heat transfer from the slag to the calcine, a heat transfer coefficient was deduced from plant data. The implications of these findings for stable furnace operation are discussed.     

镍闪速熔炼过程的模糊建模

针对冶金工业中镍闪速熔炼复杂工艺过程,提出了利用模糊理论建立镍闪模型的方法。一种方法是利用专家知识和操作经验（即ＩＦ－ＴＨＥＮ规则）建立闪速炉的先验模型;另一种方法是利用自适应模糊神经网络方法建立闪速炉的学习模型。综合考虑两种模型的建模结果,建立整个的模型。经过两个月的现场离线指导表明,这种建模方法能够较为准确地反映镍闪速炉的运行过程。     

脆硫铅锑矿闪速熔炼过程热力学分析

基于最小吉布斯自由能原理,采用元素势法,研究建立了脆硫铅锑矿闪速熔炼过程多相平衡热力学模型,考察了吨矿氧量（OVPTC）、富氧浓度（OG）和熔炼温度（T）对铅与锑在各平衡产物中分配比的影响。结果表明,对一定成分的脆硫铅锑矿,铅在合金中的分配比随OVPTC的增大不断下降,随T的升高略有上升;锑在合金中的分配比随OVPTC的增大有所下降,随T的升高大幅上升;熔炼烟气量随OG的增大而大幅减少。综合考虑铅和锑的直收率,脆硫铅锑矿闪速熔炼应控制一定的OVPTC,适当提高OG和T。      

Mathematical modeling of minor-element behavior in flash smelting of copper concentrates and flash converting of copper mattes

A mathematical model has been developed to describe the behavior of minor elements during flash smelting and flash converting. The model incorporates equations describing volatilization of minor elements from the molten particles and distribution of these elements between the molten phases in the settler. The basic premise of the volatilization model is that at the surface of the molten particle, the partial pressures of the minor-element species are those at equilibrium. Transport of the minor-element species to the gas then is described by external mass transfer. Good agreement has been obtained between observed and predicted behaviors. The effects of oxygen enrichment, matte grade, and wall temperature, as well as the bath temperature, on minor-element behavior have been elucidated. Formerly Assistant Professor, Department of Metallurgy and Metallurgical EngineeringUniversity of Utah, Salt Lake City, UT Formerly Metallurgical Engineer Kennecott, Salt Lake City, UT     

Fluid dynamics in bubble stirred ladles: Part II. Mathematical modeling

A mathematical model which describes the fluid flow in a bubble stirred ladle is presented. The model predicts mean flow, turbulent characteristics, bubble dispersion, and gas-liquid interaction from fundamental principles. Numerical predictions for a water model of a ladle show very satisfactory quantitative agreement with experimental results for all regions of the ladle. The model is applied to the study of refractory wear and yields results that are in qualitative agreement with practical experience.     

Fluid dynamics in bubble stirred ladles: Part II. Mathematical modeling

A mathematical model which describes the fluid flow in a bubble stirred ladle is presented. The model predicts mean flow, turbulent characteristics, bubble dispersion, and gas-liquid interaction from fundamental principles. Numerical predictions for a water model of a ladle show very satisfactory quantitative agreement with experimental results for all regions of the ladle. The model is applied to the study of refractory wear and yields results that are in qualitative agreement with practical experience. Formerly with the Department of Chemical Engineering and Fuel Technology, Sheffield, United Kingdom     

Mathematical modeling of the argon-oxygen decarburization refining process of stainless steel: Part I. Mathematical model of the process

Some available mathematical models for the argon-oxygen decarburization (AOD) stainless steelmaking process have been reviewed. The actual situations of the AOD process, including the competitive oxidation of the elements dissolved in the molten steel and the changes in the bath composition, as well as the nonisothermal nature of the process, have been analyzed. A new mathematical model for the AOD refining process of stainless steel has been proposed and developed. The model is based on the assumption that the blown oxygen oxidizes C, Cr, Si, and Mn in the steel and Fe as a matrix, but the FeO formed is also an oxidant of C, Cr, Si, and Mn in the steel. All the possible oxidation-reduction reactions take place simultaneously and reach a combined equilibrium in competition at the liquid/bubble interfaces. It is also assumed that at high carbon levels, the oxidation rates of elements are primarily related to the supplied oxygen rate, and at low carbon levels, the rate of decarburization is mainly determined by the mass transfer of carbon from the molten steel bulk to the reaction interfaces. It is further assumed that the nonreacting oxygen blown into the bath does not accumulate in the liquid steel and will escape from the bath into the exhaust gas. The model performs the rate calculations of the refining process and the mass and heat balances of the system. Also, the effects of the operating factors, including adding the slag materials, crop ends, and scrap, and alloy agents; the nonisothermal conditions; the changes in the amounts of metal and slag during the refining; and other factors have all been taken into account. []—metal phase; ()—slag phase; {}—gaseous phase; and 〈〉—solid phase     

Mathematical and physical modelling of fluid flow and heat transfer in electric smelting

Heat and momentum transfer in a submerged electric smelting furnace were investigated in a physical model, using oil and an aqueous calcium chloride solution to simulate the slag and matte phases, respectively. Gas evolution at the electrode was simulated by the injection of gas through the electrode in the model. A mathematical model for fluid flow and heat transfer in the model was also developed. The measured temperature distributions near the oil⧹solution interface could only be reproduced in the mathematical model by the imposition of a no-slip boundary condition at the interface. This condition impedes the transfer of heat and momentum into the lower phase; the implications for smelting are discussed.     

Mathematical modeling and computer simulation of the rotating impeller particle flotation process: Part II. Particle agglomeration and flotation

Effective removal of unwanted particles from a molten metal alloy by flotation relies on purging a gas into the melt through a rotating impeller. This device is commonly known as a rotary degasser. Unwanted particles in the melt attach to the rising gas bubbles and rise to the slag layer where they are removed from the metal bulk. In addition, the turbulence created by the rotating impeller causes the randomly distributed solid particles to agglomerate into relatively large clusters. These clusters float up or settle down due to the difference between their density and that of the melt. A mathematical model has been developed to describe the particle dynamics and particle agglomeration that occur during the rotary degassing of aluminum melts. While previous investigations addressed particle collisions in low intensity turbulent fields where the size of the colliding particles is smaller than the Kolmogorov length scale, this model is more encompassing as it considers both low intensity and high intensity turbulence. Consequently, this model is more representative of a typical industrial rotary degassing operation.     

Tree-ring formation during vacuum arc remelting of INCONEL 718: Part II. Mathematical modeling

Tree-ring grain formations, a common microstructural feature found in vacuum arc remelted (VAR) ingots of nickel-based superalloys, were characterized experimentally in Part I. The experimental observations led to the conclusion that tree rings are chains of fine-equiaxed grains interrupting a predominately columnar-dendritic structure. Several possible mechanisms for their formation were considered, and their implications correlated with experimental observations. The most likely mechanism was determined to be that process perturbations cause changes in the thermal (or solutal) fields ahead of the columnar-dendrite tips, temporarily altering the conditions to increase grain nucleation and, hence, forming fine-equiaxed grains. In this article, Part II, a multiscale mathematical model of the VAR process is presented that simulates the macroscopic heat and momentum transport and combines it with a mesoscopic model of the nucleation and growth of grains. Using this multiscale model, the transient development of the VAR grain structure was simulated with varying levels and durations of fluctuations in the principal process parameters: power supply, arc focus, melt rate, and the ingot-crucible heat-transfer coefficient. The simulations were shown to agree with optical and electron back-scattered diffraction (EBSD) measurements of grain morphology and crystallographic orientation. The model results predict that tree-ring structures (consistent with those observed experimentally) can be formed by process perturbations that alter the thermal field conditions at the solidification front. A sensitivity study of the effect of the different process fluctuations on the microstructure formation was performed, providing process maps predicting the range of conditions where tree rings will not form.     

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.     

Mathematical modeling and computer simulation of the rotating impeller particle flotation process: Part I. Fluid flow

Removal of unwanted particles from molten metal by flotation is one of the most useful melt cleansing techniques used by the foundry industry. An effective way of flotation of particles in a melt relies on purging a gas into the molten metal through holes in a rotating impeller. Impeller rotation creates turbulence inside the melt, which helps agglomerate the impurity particles and, thereby, enhances their removal from the melt. In addition, turbulence increases the probability of particles attaching to the rising gas bubbles and, therefore, enhances the chance of their removal from the molten metal. A mathematical model has been developed to simulate the turbulent multiphase flow field inside the flotation treatment furnace. Simulations based on the model were used to demonstrate the effect of the various process parameters on the performance of a batch-type rotating impeller particle flotation process.     

考虑辐射影响的接触传热模型与分析

应用GW统计接触模型,建立了粗糙表面之间的接触导热模型.与实验数据的对比分析表明:该模型能够正确地反映接触导热现象.在此基础上,对接触表面进行了合理的简化,建立了接触界面间的辐射传热模型.数值计算表明:当接触表面的温度高于400K时,辐射的影响已不可忽略;载荷对接触导热热导的影响明显大于对辐射热导的影响,导热热导随载荷的增大迅速增大,而辐射热导以及等效辐射系数均随载荷的增大有所减小,这主要是由接触界面的空隙面积减少造成的;在接触面几何参数中,粗糙峰等效斜率对等效辐射系数起着主导作用,在相同的量纲1的载荷情况下,粗糙峰等效斜率越小,等效辐射系数越大;通过对本文提出的等效辐射系数的误差检验,结果表明其最大相对误差为10^-3数量级,说明等效辐射系数仅仅为接触界面黑度、几何特性和接触载荷的函数,而与接触界面温度水平和温差无关,同时也间接证明了本文提出的等效辐射系数可以较为合理地描述接触界面间的辐射换热强度.     

Finite element modeling of transient heat transfer and microstructural evolution in welds: Part II. Modeling of grain growth in austenitic stainless steels

During welding, structures are subjected to localized heating and cooling cycles, as described in Part I.[1] A mathematical model is proposed to determine the metallurgical changes that occur in austenitic stainless steel due to the welding thermal cycle. The proposed kinetic model computes the austenite grain growth as a function of time and temperature. It is based on a Zener pinning grain growth model. The results obtained indicate that the model is in good agreement with the experimental data reported in the literature. Furthermore, it was observed that rewriting the kinetic constant in the grain growth equation as a function of the peak temperature led to improved results for the majority of the cases examined.     

高铁硫化锌精矿冶炼工艺研究进展

叙述了近年来针对高铁锌精矿冶炼工艺所开展的研究工作,详细介绍了高铁锌精矿中铁的自催化—高温加压浸出工艺。工业试验表明,该工艺锌浸出率达98.05%,铁浸出率为29.22%,可有效地实现锌的选择性浸出。     

单颗粒球体非稳态传热过程的数值计算

蓄热式换热器是一种利用烟气余热来预热助燃空气的关键设备。由于其内部复杂的传热特性，从单个球状蓄热体非稳态传热过程的特点入手，利用计算机编程对其进行了特定参数下的数值计算，并根据计算结果作图、理论分析，得出了不同参数对其各种指标的影响规律，为今后的应用提供了理论基础。     

Fluid flow in pachuca (Air-Agitated) tanks: Part II. Mathematical modeling of flow in pachuca tanks

A generalized mathematical model that combines Bernoulli’s equation and thek-ε model of turbulence, using only the gas flow rate and tank geometry as inputs, has been formulated to predict the fluid flow pattern in industrial-scale full-center-column Pachuca tanks. Predictions from this model reproduce reasonably well the trends that were observed in experiments when design and operating parameters, such as superficial air velocity and tank height/tank diameter ratio, were varied. Results from these calculations indicate that design parameters, such as tank height/tank diameter and draft tube/tank diameter ratios, have a significant effect on the flow pattern in full-center-column Pachuca tanks at large tank diameters or small tank height/tank diameter ratios.