Kinetics of the zinc slag-Fuming process: Part i. industrial measurements

A study involving industrial measurements and mathematical modeling has been conducted to eluci-date kinetic phenomena in the zinc slag fuming process. In the first part of this three-part paper, the results of industrial measurements and observations are presented. In Part II a mathematical model of the process is developed, and finally in Part III the implications of a kinetic conception of the process for process improvement are explored. The industrial work consisted primarily of slag sampling through the fuming cycles of five different fuming operations. In addition, tuyere back-pressure mea-surements, tuyere photography using a tuyerescope, and sampling of the fume product were under-taken at one operation. Analysis of the slag samples has shown that, in general, the zinc elimination curve is linear with time and that a portion of the injected coal entrains in the slag. Analysis of tuyere back-pressure fluctuations and movie photographs of the tuyere tip indicate that the coal-air mixture enters the slag in the form of discrete bubbles. From these results it can be deduced that the fuming furnace consists of two reaction zones which are created by the division of coal between the slag and the tuyere gas stream. The coal entrained in the slag reduces ZnO and Fe₃O₄ in a “reduction zone” which is responsible for fuming. The coal remaining in the tuyere gas stream combusts in an “oxidation zone” although a fraction passes through the bath unconsumed and reports to the solid products. The oxidation zone supplies heat to the endothermic reduction reactions and heat losses. Formerly Graduate Student     

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     

A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part II. Results from a physical model and testing of the mathematical model

A physical model of an electromagnetic caster was constructed. The model was intended to provide measured data for comparison with the predictions of the three-dimensional (3-D) mathematical model described in part I. The physical model consisted of a molten Wood's metal pool (176×176 mm seen from above) on the top of an aluminum-bronze block. Probes were used to measure electric and magnetic fields, the deformation of the liquid surface, and the electromagnetically driven flow, at many positions within the melt, as a function of model geometry. Agreement between the measurements and the predictions of the mathematical model was generally good. The melt flow was 3-D and strongly influenced by the position of the electromagnetic screen interposed between the inductor and the metal pool.     

A mathematical model of the nickel converter: Part II. Application and analysis of converter operation

In Part I[1] of this article, a mathematical model of the nickel converter was developed based on the assumption that the three phases in the converter vessel are in chemical and thermal equilibrium. In this article, a sensitivity analysis of the model is conducted to assess the uncertainties in model predictions and to delineate the critical process variables. Following from the equilibrium assumption, the rate-controlling process in the operation is the rate at which oxygen can be supplied to the matte. Routes to process improvement then lie in increased blast volumes or oxygen enrichment and improved operating procedures to reduce idle time. Temperature was not seen to exert a significant chemical effect on the process. More important to matte composition were variables such as ladle volume and cold charge composition. These variables directly affect either the matte volume or the overall bath composition and so are more important than those variables which have only an indirect effect through changing the conditions of equilibrium. An analysis of heat distribution in the furnace indicates the overwhelming fraction of heat removed by the off-gas.     

A mathematical model for the dynamic behavior of melts subjected to electromagnetic forces: Part II. Measurement of surface waves and comparison with predictions of the mathematical model

The waves on the surface of a cylindrical mercury pool subjected to a 3 kHz electromagnetic field have been observed. Oscillations were found to correspond to the known eigenfrequencies of a cylindrical liquid pool with a free surface. Which of the eigenfrequencies was dominant depended on the field strength and the relative position of the pool in the surrounding inductor. The amplitude of the oscillations was found to increase with increasing inductor current. The measurements showed fair to good agreement with the predictions of the mathematical model described in Part I. A tentative mechanism for the excitation of the eigenfrequencies by the electromagnetic field is advanced and implications for electromagnetic casting are discussed.     

Learning to reach: A mathematical model.

Presents a mathematical model of the development of reaching that assumes that the major problem facing infants is their lack of lower level motor control and that infants learn to adjust their reaching strategies as a consequence of their previous experience and to match their current level of control. The model hypothesizes that infant reaches are a series of submovements, with the goal being to get the hand to the target in the face of errors in executed submovements. To relate actual infant reaches to this model, reaching data were decomposed into submovements, using a polynomial fitting algorithm that assumed minimum-jerk submovements. The model makes quantitative predictions about the course of development that are supported by existing results. The validity of the model's underlying assumptions was assessed by comparing the directional variability of the submovements with the variability assumed in the model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

利用数学模型分析复吹转炉吹炼工艺

在冶金热力学和动力学及反应工程学原理的基础上，建立了模拟复吹转炉冶炼过程的数学模型．在用梅钢150t复吹转炉工业试验的结果对模型加以验证之后，利用模型对具有中高磷铁水特点的梅钢转炉吹炼工艺进行了分析讨论．     

A mathematical model of slag and metal flow in the ESR Process

Through the statement of the turbulent Navier-Stokes equations and Maxwell’s equations a mathematical representation is developed for the electromagnetic force field and the velocity field in the slag phase and the metal pool of cylindrical ESR units. Computed results are presented for both industrial scale (0.5 m electrode diameter) and laboratory scale (0.05 m electrode diameter) units operating with direct currents. It was found that for industrial scale units, the computed slag velocities ranged from 5 to 10 cm/s, while the velocities in the metal pool were substantially lower, except at the slag-metal interface. At a given spatial position, the velocity was found to increase in an almost linear fashion with the current density. The flow was found to be predominately laminar in the laboratory scale units and for comparable current densities the melt velocities were very much smaller. Some 600 to 900 s were required on a CDC 6400 digital computer for the solution of each case involving turbulent flow. Presently on leave from Institute of Chemical Engineering and Technology, Punjab University, Lahore-1, Pakistan.     

利用数学模型分析复吹转炉吹炼工艺

在冶金热力学和动力学及反应工程学原理的基础上,建立了模拟复吹转炉冶炼过程的数学模型.在用梅钢150 t复吹转炉工业试验的结果对模型加以验证之后,利用模型对具有中高磷铁水特点的梅钢转炉吹炼工艺进行了分析讨论.     

A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part I. The mathematical model

This first of two related articles describes a mathematical model for electromagnetic casting in three dimensions,i.e., where the dependent variables are functions of all three spatial coordinates. It is shown how the method of inductances can be extended to three dimensions in order to solve Maxwell's equations for the electromagnetic field in and around the caster. The principal task here is the calculation of the inductances between loops of irregular shape, and the method by which this is done is described. The computations are self-consistent ones in that the free surface of the molten metal is adjusted in response to the supporting electromagnetic forces which are themselves dependent on the shape of that surface. The computed electromagnetic forces are input into a second phase of the calculation where melt flow is computed in three dimensions using the finite element package FIDAP.     

Reaction Kinetics of Immobilized-Cell Denitrification. II: Experimental Study

Laboratory experiments were conducted to characterize the performance of an immobilized-cell denitrification process treating nitrate-contaminated groundwater and to provide supporting data for the validation of a quasi-steady state model based on half-order reaction kinetics. The treatment process consists of laboratory-scale, plug-flow reactors packed with biocatalyst particles. Pseudomonas denitrificans (American Type Culture Collection 13867), a heterotrophic denitrifier, was cultured and immobilized in calcium alginate particles. Ethanol was used as the source of organic carbon. Thirty concentration profiles were obtained at four levels of nitrate concentration and at three ranges of flow rate. An analysis of the nitrate and nitrite concentration profiles suggested that a half-order reaction rate model could be used to describe the reduction of both nitrate and nitrite. The half-order reaction rate constants for nitrate and nitrite reduction were dependent on the age of the biocatalyst particles and the nitrate loading history. The validity of the half-order denitrification model was satisfactorily tested with experimental data. As illustrated by preliminary calculations, the immobilized-cell denitrification process is feasible for practical applications, particularly for small drinking water systems.     

A mathematical model for the solution mining of primary copper ore: Part II. leaching by solution containing oxygen bubbles

The one-dimensional model developed previously to simulate thein situ leaching of copper from deeply-buried low-grade copper ore deposits is used to simulate thein situ operation in which the oxygen-saturated solution containing oxygen bubbles is introduced at the bottom of the chimney. The physical and chemical processes incorporated in the present model include the axial convective transport of mass and heat, axial dispersion of mass, mass transfer between the liquid and gas phases, fluid-solid mass transfer, diffusion of oxygen in the pores of ore fragments, and the dissolution of sulfide minerals. The coupled model equations are solved numerically by an implicit finite-difference method. Calculations have been made for various values of the volume fraction of oxygen bubbles (up to 0.1) in the fluid just downstream of the oxygen sparging nozzle. Calculated results indicate that, for a specific chimney considered, the total amount of copper extracted increases with increasing volume fraction of undissolved oxygen bubbles in the inlet fluid and increasing superficial velocity of the solution (up to 20 m per day). However, a further increase in the superficial velocity of liquid or undissolved oxygen bubbles does not enhance copper extraction. Calculated results also indicate that the total fractional recovery of copper increases with decreasing pyrite to chalcopyrite molar ratio, ore grade, particle size, and shape factor.     

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     

A mathematical model of aluminum depth filtration with ceramic foam filters: Part II. Application to long-term filtration

The mathematical model to compute the efficiency of depth filtration of molten aluminum, previously presented in Part I, was further developed and applied to study long-term filtration. In this case, the incoming suspension entering the unit cell was not assumed homogeneous, and the times and positions of particle at the inlet were obtained stochastically from a random number generator. The particles that were transported by the fluid flow to the wall and collided against this surface remained attached to the wall and accumulated within the domain. The accumulation of particles decreased the effective area for fluid to flow through the pore, causing distortion of the overall velocity field in the domain. The flow field was obtained from the numerical solution of the continuity and Navier-Stokes equations for transient flow, the particle trajectories were calculated using the Langrangian motion equation including the buoyancy, and the viscous drag force corrected for the wall effect. The model predicted a preferred particle accumulation around the windows to form a cake of particles and the effect that inclusion accumulation has on the flow field, pressure drop, and filtration coefficient. This work studied the influence of particle concentration and fluid velocity on the evolution of the filtration coefficient and pressure drop. It was found that these quantities were practically constant for TiB₂ particles suspended in aluminum at a concentration of 1 ppm and filtered during 60 minutes through the unit cell of a 30 ppi foam filter. However, at a particle concentration of 10 ppm, the model predicted that the filtration coefficient and pressure drop changed appreciably for the same period of filtration. The results, obtained from first principles, provide a rationale to explain fluctuations of the filtration coefficient and pressure drop, reported in the literature, without introducing any empirical or probability factor in the respective equations.     

A mathematical model of the elastoplastic mechanism of deformation of porous sintered materials. II. A generalized rheological model of deformation of porous materials

Translated from Poroshkovaya Metallurgiya, No. 12 (360), pp. 1–10, December, 1992.     

Primary mediastinal tumors: part II. Tumors of the middle and posterior mediastinum

Lymphoma, mediastinal cysts, and neurogenic neoplasms are the most common primary middle and posterior mediastinal tumors. Lymphoma may involve the anterior, middle and/or posterior mediastinum, frequently as lymphadenopathy or as a discrete mass. Foregut cysts are common congenital mediastinal cysts and frequently arise in the middle mediastinum. Pericardial cysts are rare. Schwannoma and neurofibroma are benign peripheral nerve neoplasms, represent the most common mediastinal neurogenic tumors, and rarely degenerate into malignant tumors of nerve sheath origin. Sympathetic ganglia tumors include benign ganglioneuroma and malignant ganglioneuroblastoma and neuroblastoma. Lateral thoracic meningocele is a rare cause of a posterior mediastinal mass.     

The information-loss model: A mathematical theory of age-related cognitive slowing.

A model of cognitive slowing is proposed with the following assumptions: Information is lost during processing, processing occurs in discrete steps with step duration inversely related to the amount of information currently available, and the effect of aging is to increase the proportion of information lost per step. This model correctly predicts a positively accelerated relation between latencies of older and younger adults and provides a unified account of the effects of task complexity, practice, speed–accuracy tradeoffs, and fluctuations in individual performance. Strong support for the thesis that cognitive slowing is global, and not localized in specific age-sensitive components, is provided by the fact that the model accurately predicts the latencies of older adults on the basis of those of younger adults, without regard to the nature of the task, across a latency range of nearly 2 orders of magnitude. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Fashioning of aortic isthmoplasty patch. A mathematical model

The present study was designed to reveal whether astrocytic activation following axotomy causes a numerical increase of nuclear bodies (NBs) in chicken astrocytes. Astrocytes in the spinal cord were activated by a unilateral spinal nerve transection. The frequency of NBs was calculated at the lateral motor columns of the normal group and at the ipsi- and contralateral sides of operated group. In the growing chickens, NBs of each astrocyte were a few and decreased steadily in number with age. In the operated chickens, the frequency of NBs elevated temporarily both in the ipsi- and contralateral sides, and reached its maximum value by 30 post-operative days. The frequency of NBs increased more prominently in the operated side than in the unoperated side. Thus, the present study provides the first evidence for a significant increase in the number of NBs in the hyperactive astrocytes caused by axotomy.     

A mathematical model of the nickel converter: Part I. Model development and verification

A mathematical model of the nickel converter has been developed. The primary assumption of the model is that the three phases in the converter are in thermal and chemical equilibrium. All matte, slag, and gas in the converter is brought to equilibrium at the end of each of a series of short time steps throughout an entire charge. An empirical model of both the matte and slag is used to characterize the activity coefficients in each phase. Two nickel sulfide species were used to allow for the modeling of sulfur-deficient mattes. A heat balance is carried out over each time step, considering the major heat flows in the converter. The model was validated by a detailed comparison with measured data from six industrial charges. The overall predicted mass balance was shown to be close to that seen in actual practice, and the heat balance gave a good fit of converter temperature up to the last two or three blows of a charge. At this point, reactions in the converter begin to deviate strongly from “equilibrium,” probably due to the converter reactions coming under liquid-phase mass-transfer control. While the equilibrium assumption does work, it is not strictly valid, and the majority of the charge is probably under gas-phase mass-transfer control.