Showing papers in "Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science in 1995"

Coupled turbulent flow, heat, and solute transport in continuous casting processes

Abstract: A fully coupled fluid flow, heat, and solute transport model was developed to analyze turbulent flow, solidification, and evolution of macrosegregation in a continuous billet caster. Transport equations of total mass, momentum, energy, and species for a binary iron-carbon alloy system were solved using a continuum model, wherein the equations are valid for the solid, liquid, and mushy zones in the casting. A modified version of the low-Reynolds numberk-e model was adopted to incorporate turbulence effects on transport processes in the system. A control-volume-based finite-difference procedure was employed to solve the conservation equations associated with appropriate boundary conditions. Because of high nonlinearity in the system of equations, a number of techniques were used to accelerate the convergence process. The effects of the parameters such as casting speed, steel grade, nozzle configuration on flow pattern, solidification profile, and carbon segregation were investigated. From the computed flow pattern, the trajectory of inclusion particles, as well as the density distribution of the particles, was calculated. Some of the computed results were compared with available experimental measurements, and reasonable agreements were obtained.

Heat transfer and microstructure during the early stages of metal solidification

Abstract: Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m2 to peak values of 0.95 to 2.0 MW/m2. A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m2 °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (µm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.

Permeability for cross flow through columnar-dendritic alloys

Abstract: Experiments for measuring permeability in columnar-dendritic microstructures have provided data only up to a volume fraction of liquid of 0.66. Hence, the permeability for flow perpendicular to the primary dendrite arms in columnar-dendritic microstructures was calculated, extending our data base for permeability to volume fractions of liquid as high as 0.98. Analyses of the dendritic microstructures were undertaken first by detecting the solid-liquid interfaces with a special computer program and then by generating a mesh for a finite-element fluid flow simulation. Using a Navier-Stokes solver, the velocity and pressure at the nodes were calculated at the microstructural level. In turn, the average pressure gradient was used to calculate the Darcy permeability. Permeabilities calculated by this versatile technique provided data at high volume fractions of liquid that merged with the empirical data at the lower volume fractions.

Numerical Study of Steady Turbulent Flow through Bifurcated Nozzles in Continuous Casting.

Abstract: Bifurcated nozzles are used in continuous casting of molten steel, where they influence the quality of the cast steel slabs. The present study performs two-dimensional (2-D) and three-dimensional (3-D) simulations of steady turbulent(K- e) flow in bifurcated nozzles, using a finite-element (FIDAP) model, which has been verified previously with water model experiments. The effects of nozzle design and casting process operating variables on the jet characteristics exiting the nozzle are investigated. The nozzle design parameters studied include the shape, angle, height, width, and thickness of the ports and the bottom geometry. The process operating practices include inlet velocity profile and angle as well as port curvature caused by erosion or inclusion buildup. Results show that the jet angle is controlled mainly by the port angle but is steeper with larger port area and thinner walls. The degree of swirl is increased by larger or rounder ports. The effective port area, where there is no recirculation, is increased by smaller or curved ports. Flow asymmetry is more severe with skewed or angled inlet conditions or unequal port sizes. Turbulence levels in the jet are higher with higher casting speed and smaller ports.

Effect of the bubble size and chemical reactions on slag foaming

Abstract: Slag foams have been investigated with smaller bubbles than those used in the previous studies.[5,6,7] The bubbles were generated by argon gas injection with the nozzle of multiple small orifices and by the slag/metal interfacial reaction of FeO in the slag with carbon in the liquid iron. The foam stability in terms of the foam index for a bath-smelting type of slag (CaO-SiO2-Al2O3-FeO) was determined for different bubble sizes. The average diameter of bubbles in the foam was measured by an X-ray video technique. When the foam was generated by the slag/metal interfacial reaction at 1450 °C, it was found that the average bubble diameter varied from less than 1 to more than 5 mm as a function of the sulfur activity in the carbon-saturated liquid iron. The foam index was found to be inversely proportional to the average bubble diameter. A general correlation is obtained by dimensional analysis in order to predict the foam index from the physical properties of the liquid slag and the average size of the gas bubbles in the foam.

Multiparticle interfacial drag in equiaxed solidification

Abstract: A physical model is proposed for the solid/liquid interfacial drag in both globular and dendritic equiaxed solidification. By accounting for the presence of multiple particles and the nonsphericity and porosity of the individual equiaxed crystals, a drag correlation is developed, which is valid over the full range of solid volume fractions. It is shown that neither the solid liquid interfacial area concentration nor the grain size alone is adequate to characterize the interfacial drag for equiaxed dendritic crystals in both the free particle and packed bed regimes; thus, the present model is based on a multiple length scale approach. The model predictions are compared to previous analytical and numerical results as well as to experimental data available in the literature, and favorable agreement is achieved.

The synthesis of nickel aluminides by multilayer self-propagating combustion

Abstract: The synthesis of Ni-Al intermetallic thin films by self-propagating combustion reactions was investigated for the 1:1 and 3:1 Ni/Al stoichiometries. The dependence of the combustion wave velocity on the individual layer thickness was determined. The marked decrease in velocity with layer thickness was consistent with results of modeling studies on multilayer systems. Activation energies for the synthesis of NiAl were determined to be in the range 127.9 to 149.8 kJ · mol−1, and those for the synthesis of Ni3Al were found to be in the range 133.8 to 146.3 kJ · mol−1. In the case of NiAl, the experimental value is attributed to a diffusion process of Al in NiAl. Differential thermal analysis (DTA) showed the sequence of steps in the formation of NiAl and Ni3Al. The dependence of the thermal peaks on the heating rate for both cases was found to be consistent with theory. The activation energies obtained from the DTA analysis were compared to previous results obtained with relatively thin layers.

Heat and metal transfer in gas metal arc welding using argon and helium

Abstract: This article describes a theoretical investigation on the arc parameters and metal transfer in gas metal arc welding (GMAW) of mild steel using argon and helium shielding gases. Major differences in the predicted arc parameters were determined to be due to large differences in thermophysical properties. Various findings from the study include that an arc cannot be struck in a pure helium atmosphere without the assistance of metal vapor, that a strong electromagnetic cathode force affects the fluid flow and heat transfer in the helium arc, providing a possible explanation for the experimentally observed globular transfer mode and that the tapering of the electrode in an argon arc is caused by electron condensation on the side of the electrode.

Measurement of bubble characteristics in a molten iron bath at 1600 °C using an electroresistivity probe

Abstract: A two-needle, electroresistivity probe was developed to measure bubble characteristics such as gas holdup, bubble frequency, and bubble rising velocity in a molten iron bath at 1600 °C. The probe’s electrode was made of a 0.5-mm platinum wire coated with ZrO2 cement and an outer coat of alumina as insulator. The life of this probe at 1600 °C was 15 to 20 minutes, making it possible to systematically measure bubble characteristics. The measured values of the bubble characteristics were compared with their respective empirical correlations derived from cold model experiments. Good agreement between the measured values and the empirical correlations was seen for each bubble characteristic. This electroresistivity probe allows us to measure bubble characteristics in actual metallurgical reactors with gas injection at high bath temperatures.

Optimal riser design for metal castings

Abstract: The optimal design of a casting rigging system is considered. The casting geometry is systematically modified to minimize the gate and riser volume, while simultaneously ensuring that no porosity appears in the product. In this approach, we combine finite-element analysis of the solidification heat-transfer process with design sensitivity analysis and numerical optimization to systematically improve the casting design. Methods are presented for performing the sensitivity analysis, including the sensitivity of important solidification parameters such as freezing time, temperature gradient, and cooling rate. We also present methods for performing Newton-Raphson iteration for solidification models that use the boundary-curvature method to represent the sand mold. Finally, the methods are applied to design risers for an L-shaped steel plate to control microporosity and for a steel hammer to control macroporosity. It is demonstrated that the size of a conventionally designed riser can be reduced by a significant amount while retaining the quality of the cast product.

Heat transfer in the hot rolling of metals

Abstract: The heat-transfer coefficient (HTC) in the roll gap during the hot rolling of AA5XXX-series (aluminum-magnesium) alloys has been measured in a laboratory mill with the aid of thermocouples attached to the surface and embedded in the interior of test samples. The heat-transfer coefficient was calculated from the sample temperature response using an implicit finite-difference model over a range of temperatures, strain rates, and pressures. Values of 200 to 450 kW/m2 °C were obtained by backcalculation. A comparison of the results from this study with those measured in a previous investigation on two steel alloys has led to the development of an equation which characterizes the HTC as a function of the ratio of the rolling pressure to the flow stress at the surface of the workpiece. This relationship has been employed to explain the apparent differences in the heat-transfer behavior of different metals at similar rolling pressures.

Simultaneous optimization of thermochemical data for liquid iron alloys containing C, N, Ti, Si, Mn, S, and P

Abstract: A data base of thermochemical parameters for liquid iron-base alloys containing C, N, Ti, Si, Mn, S, and P is presented. A matrix of linear inequalities describing the experimental data among these elements was constructed. A set of internally consistent thermochemical data permitted by the uncertainties of the experiments was evaluated by means of a linear programming algorithm. Expressions for the interaction parameters of the solutes and the Gibbs energies of formation of the carbides, nitrides, carbonitrides, and sulfides of titanium were simultaneously optimized. It is shown that the resulting thermochemical data base reproduces the experimental data satisfactorily.

The Impact of Bubble Dynamics on the Flow in Plumes of Ladle Water Models

Abstract: Bubbly plumes are widely encountered in metallurgical processes when gas is injected into liquid metals for refining purposes. Based on the experimental findings from a water model ladle, this phenomenon was simulated with a mathematical model, paying special attention to the dynamics of the bubbles in the plume. In the model, the liquid flow field is first calculated in an Eulerian frame with an estimated distribution of the void fraction. The trajectories of bubbles are then computed in a Lagrangian manner using the estimated flow field, experimentally measured information on bubble drag coefficients, lateral migration due to lateral lift forces, and variation in bubble size due to breakup. Turbulence in the two-phase zone is modeled with a modifiedk-e model with extra source terms to account for the second phase. The computed void fraction and turbulent liquid flow field distributions are in good agreement with experimental measurements.

The effect of an electric field on self-sustaining combustion synthesis: Part II. field-assisted synthesis of μ-SiC

Abstract: Self-sustaining combustion synthesis of β-SiC is shown to be possible in the presence of an electric field. Above a threshold field of ∼6.8 V · cm−1, a combustion wave resulting from the reaction between silicon and graphite powders can be self-sustaining. A linear relationship between the applied field and the measured wave velocity is observed, in qualitative agreement with the model (as discussed in the previous article). At relatively high fields, >21 V · cm−1, simultaneous combustion occurs. Microstructural examinations of quenched combustion fronts provided evidence of melting of the Si reactants. This experimental work provides evidence of the validity of a model in which chemical and electrical heat generation are contributing inside the combustion front.

Studies on addition of inclusions to molten aluminum using a novel technique

Abstract: Considerable initiatives have often been taken to introduce specific solid particles directly into molten metals in a desirable quantity, but little success has been achieved, particularly in the case of reactive particles. Therefore, alternative routes such as production of solid particles through chemical reactions within the melt are often used. While these methods are capable of producing solid particles within the melt, the chemistry of the melt changes and control of particle size and chemistry is difficult. In the present study, a direct addition technique has been used to introduce many types of inclusions into liquid aluminum and Al-Si alloys, irrespective of their wettability and chemical reactivity, while preserving the surface characteristics and melt chemistry. A uniform particle distribution can be obtained even at low volume fraction of addition and with particle sizes of the order of 2 to 5 µm. This technique allows valuable information regarding the behavior of many inclusions, such as TiB2, TiC, SrO, and Sr(OH)2, in liquid aluminum to be studied. Several such examples are presented.

Kinetics of pyrite oxidation in sodium carbonate solutions

Abstract: The kinetics of pyrite oxidation in sodium carbonate solutions were investigated in a stirred vessel, under temperatures ranging from 50 °C to 85 °C, oxygen partial pressures from 0 to 1 atm, particle size fractions from −150 + 106 to −38 + 10 µm (−100 + 150 Mesh to −400 Mesh + 10 µm) and pH values of up to 12.5. The rate of the oxidation reaction is described by the following expression:−dN/dt = SbkpO 2 0.5 [OH−]0.1 whereN represents moles of pyrite,S is the surface area of the solid particles,b is a stoichiometric factor,k is an apparent rate constant, pO```2`` is the oxygen partial pressure, and [OH−] is the hydroxyl ion concentration. The experimental data were fitted by a stochastic model for chemically controlled reactions, represented by the following fractional conversion(X) vs time (t) equation: (1−X)−2/3−1 =k STt The assumption behind this model,i.e., surface heterogeneity leading to preferential dissolution, is supported by the micrographs of reacted pyrite particles, showing pits created by localized dissolution beneath an oxide layer. In addition to the surface texture, the magnitude of the activation energy (60.9 kJ/mol or 14.6 ± 2.7 kcal/mol), the independence of rate on the stirring speed, the inverse relationship between the rate constant and the initial particle diameter, and the fractional reaction orders are also in agreement with a mechanism controlled by chemical reaction.

Interfacial tensions of liquid Fe-Ni alloys and stainless steels in contact with CaO-SiO2″AI2O3-based slags at 1550 °C

Abstract: In the present work, the interfacial tensions of Fe-Ni alloys in contact with slags of the CaO-Al2O3-SiO2 system were measured at 1550 °C. Nickel additions to the alloy were found to decrease interfacial tension. The effects of alumina and titania additions to the slag on the interfacial tension of the Fe-20 wt pct Ni alloy were determined: alumina was found to increase the interfacial tension by a small amount, while titania was found to decrease it drastically. Using the present interfacial tension data for the CaO-Al2O3-SiO2 system and the ones measured by Jimbo and Cramb, Girifalco and Good’s interaction coefficient (ϕ) was determined as a function of the slag composition using regression analysis and was found to be a useful means of correlating interfacial tension data. The interfacial tension of an Fe-20 wt pct Ni-2.39 wt pct Al alloy in contact with a CaO-Al2O3-SiO2 slag was found to decrease drastically in the first 60 to 75 minutes of the experiment due to the dynamic effects of mass transfer. Slight lowering of interfacial tensions of industrial stainless steels due to sulfur transfer from liquid metal to slag was also observed. The equilibrium interfacial tensions of type 304 stainless steels were found to be more dependent on the slag chemistry than on the nickel and chromium content of the alloy.

Effect of carbonaceous particles on slag foaming

Abstract: Use of carbonaceous particles such as coke or coal char in controlling slag foaming is of great practical significance for bath-smelting and other steelmaking processes. The foamability of the liquid slag in terms of the foam index has been determined with the presence of different amounts of coke and coal char particles. Different sized and shaped particles were used in the experiments. It was found that the foam index decreased significantly as the ratio of the total cross-sectional area of the particles to the liquid slag surface area increased. When the foam was generated by argon gas injection through an alumina nozzle (i.d. = 1.5 mm), a liquid slag, CaO-SiO2-CaF2-(Al2O3), depending on the alumina content, could have an initial foam index of about 2 to 4 seconds at 1500 °C without any carbonaceous particles. When the slag surface was covered only 15 ~20 pct with either coke or coal char particles, the foam was totally suppressed regardless of the initial foam index. In order to understand the mechanism of the antifoam effect of the carbonaceous particles, interactions of a coke sphere, an iron ore pellet, an alumina tube, and a coal char particle with the liquid slag foam were examined by X-ray observation. It was concluded that the antifoam effect of coke or coal char particles is primarily contributed by the nonwetting nature of the carbonaceous materials with the liquid slag. Possible mechanisms of carbonaceous particles rupturing a slag film could be (1) the rapid thinning of the liquid slag film driven by a difference between the instantaneous contact angle and the equilibrium contact angle or (2) the “dewetting” of the liquid slag from the interface when the film is “bridged” by the particle.

Settling and clustering of silicon carbide particles in aluminum metal matrix composites

Abstract: The settling of 14-μm silicon carbide particles in an aluminum-silicon alloy was monitored with an electrical resistance probe to measure thein situ particle voluem fraction. The rate of settling was much greater than expected from hindered settling of single 14-μm particles. From the observed settling rate, an equivalent hydrodynamic diameter and density of clusters of particles were deduced, 38 μm and 2740 kg/m3, respectively. Other work was analyzed with the same procedure; it was concluded that if the stirring prior to settling were intense, then the clusters would be smaller than with weaker stirring. The implications for foundry practice and mechanical properties are discussed.

In situ combustion synthesis of dense ceramic and ceramic-metal interpenetrating phase composites

Abstract: A model exothermic reaction is used to demonstrate the application of simultaneous combustion synthesis, conducted under a consolidating pressure, as a one-stepin situ synthesis technique for the production of dense ceramic and ceramic-metal interpenetrating phase composites (IPC). The addition of an excess amount of metal,e.g., Al, and/or a diluent,e.g., Al2O3, lowers the combustion temperature and aids in the refinement of the microstructure, facilitating an increase in compressive strength and elastic modulus. The effects of the important process parameters,e.g., reaction stoichiometry and diluents, green density, pressure, and temperature, on microstructure and properties of these high-performance composites are discussed.

Kinetics of the solid-state carbothermic reduction of wessel manganese ores

Abstract: Reduction of manganese ores from the Wessel mine of South Africa has been investigated in the temperature range 1100 °C to 1350 °C with pure graphite as the reductant under argon atmosphere. The rate and degree of reduction were found to increase with increasing temperature and decreasing particle sizes of both the ore and the graphite. The reduction was found to occur in two stages: (1) The first stage includes the rapid reduction of higher oxides of manganese and iron to MnO and FeO. The rate control appears to be mixed, both inward diffusion of CO and outward diffusion of CO2 across the porous product layer, and the reaction of carbon monoxide on the pore walls of the oxide phase play important roles. The values of effective CO-CO2 diffusivities generated by the mathematical model are in the range from 2.15 x 10−5 to 6.17 X 10−5 cm2.s−1 for different ores at 1300 °C. Apparent activation energies range from 81. 3 to 94.6 kJ/kg/mol. (2) The second stage is slower during which MnO and FeO are reduced to mixed carbide of iron and manganese. The chemical reaction between the manganous oxide and carbon dissolved in the metal phase or metal carbide seems to be the rate-controlling process The rate constant of chemical reaction between MnO and carbide on the surface of the impervious core was found to lie in the range from 1.53 x 10−8 to 1.32 x 10−7 mol . s−1 . cm−2. Apparent activation energies calculated are in the range from 102.1 to 141.7 kJ/kg/mol.

Experimental investigation of thermomechanical effects during direct chill and electromagnetic casting of aluminum alloys

Abstract: The deformation and the temperature field within direct chill (DC) and electromagnetic (EM) cast aluminum ingots have been measured in-situ using a simple experimental set-up. The deformation of the cross section of the cold ingots has also been characterized as a function of the casting speed, alloy composition and inoculation condition. The pull-in of the lateral rolling faces has been found to occur in two sequences for DC cast ingots whereas that associated with EMC was continuous. The pull-in was maximum at the center of these faces (about 7-9%) and strongly depended upon the casting speed. Near the short sides of the ingots, the deformation was only about 2% and was nearly independent of the casting parameters and alloy composition. Based upon these measurements, it was concluded that the pull-in of the rolling faces was mainly due to the bending of the ingots induced by the thermal stresses. This conclusion was further supported by a simple two-dimensional thermoelastic model.

An experimental study of process behavior in planar flow melt spinning

Abstract: A parametric study concerning the process behavior in planar flow melt spinning (PEMS) of Pb−Sn alloy ribbons is presented in this article. Experiments were conducted to develop correlations between the produced ribbon thickness and process variables, including wheel speed, crucible pressure, nozzle-wheel gap, and melt superheat. The ribbon thickness was found to vary with the wheel speed to the power of −2/3 and the crucible pressure to the power of 1/3. Puddle lengths were found to increase linearly with crucible pressure. The ribbon thickness behaved in a two-term exponential manner in relation to the melt superheat. A processing window for the production of high-quality ribbons was determined using dimensionless parameters. Five distinct ribbon patterns were identified, and their respective surface roughnesses were measured and reported.

Standard enthalpies of formation of neodymium alloys, Nd+Me (Me≡Ni, Ru, Rh, Pd, Ir, Pt), by high-temperature direct synthesis calorimetry

Abstract: The standard enthalpies of formation of 13 dysprosium alloys with late transition metals have been determined by direct synthesis calorimetry at 1474 ± 2 K. The following values of Δ f o (kJ (mole atom)−1) are reported: DyNi, -(35.2 ± 1.5); DyNi5, -(27.4 ± 0.7); DyRu2, -(27.3 ± 0.9); DyRh,-(76.5 ± 2.0); DyRh2, -(62.3 ± 0.8); Dy7Rhm3, -(56.8 ± 2.2); DyPd, -(83.3 ± 2.0); Dy3Pd4,-(86.6 ± 2.1); DyPd3,-(76.2 ± 1.5); Dylr2, -(69.9 ± 2.1); DyPt, -(109.4 ± 1.8); DyPt2, -(98.1 ± 2.8); and DyPt3, -(82.8 ± 2.2). The results are compared with predicted values from the Miedema model and with available literature data for DyNi, DyNi5, DyPd, and DyPt.

The effect of an electric field on self-sustaining combustion synthesis: Part I. modeling studies

Abstract: An analysis of the effect of an electric field on self-propagating high-temperature synthesis (SHS) reactions is presented. Using the synthesis of SiC as a model, the analysis showed that the imposition of a field results in a highly localized distribution of the current density. It was shown that the current is primarily restricted to the region just ahead of the combustion zone. Thus, in addition to the chemical heat release, this zone also includes heat release from an electric source, a value equivalent to σE2 where σ is the conductivity andE is the field. From the dependence of the degree of conversion to the product on the applied voltage, it is shown that the velocity of the combustion wave is linearly proportional to the field.

A general model for partitioning of gases between a metal and its plasma environment

Abstract: When a metal or an alloy is exposed to a pure diatomic gas such as nitrogen, the concentration of the species in the material can be predicted from Sieverts law. However, such calculations cannot be used to understand processes in which the gas phase near the metal contains excited molecules, atoms, ions, and electrons, in addition to the diatomic gases. The presence of plasma leads to species concentrations in the metal that are much higher than the values predicted by the Sieverts law. At present, there is no unified theoretical model to understand the partition of nitrogen, oxygen, and hydrogen between a metal and its plasma environment. In this work, a theoretical model has been developed to understand the enhanced solubility of gases in metals exposed to plasma environment. The model has been applied to explain several different sets of independent experimental results available in the literature. The analysis of the data shows that the enhanced solubilities can be explained on the basis of superequilibrium concentration of atomic species near the metal surface. Both the enhanced solubilities and the maximum species concentrations predicted by the model are in good agreement with the independent experimental data for various systems.

Effect of temperature on slag foaming

Abstract: Slag foaming has become important not only for the modem electric arc furnace but also for basic oxygen steelmaking and new ironmaking processes, such as bath smelting. In the electric arc furnace, foaming practices are widely used to shield the refractories from the arc and to protect metal from the atmosphere. Slag foaming is also used to stabilize the arc in the modem electric arc furnace. The control of the foaming height is required for steady-state operation in the bath-smelting process. Several investigations on slag foaming have been previously carried out. Cooper and Kitchened q measured the foam lives of CaO-SiO2 slags as a function of CaO/SiO2 ratio, concentration of P205, and temperature. The |bam life increased with decreasing temperature and decreasing CaO/SiO2 ratio. Cooper and Kitchener's results indicate that the apparent activation energy for foaming is much higher than that for viscous flow. Swisher and McCabe 121 have also measured the foam life of CaO-SiO 2 slags. Their experimental results indicate that the foam lives increase with decreasing basicity and temperature. Hara and Oginol~l studied the effect of slag composition, surface active additives, and gas composition on the foaming behavior of FeO-SiO2-CaO slags. The foam height increases sharply when the ratio O/Si is decreased below 3.5. Hara and Ogino considered that melt viscosity does not have a role in the foaming behavior of the slags. However, they found that surface tension plays an important role on foam lives. In previous workJ 4.sl the foaming index, ~, and foam life, 7-, were introduced to describe the experimental results. These parameters are defined as

Mathematical modeling of the zinc pressure leach process

Abstract: A comprehensive mathematical model is described for the zinc pressure leaching process. Generic kinetic expressions were derived from experimental data found in the literature for the following reaction events: (1) dissolution of marmatite, (Zn,Fe)S, (2) oxidation of ferrous to ferric, and (3) precipitation of lead jarosite. Aqueous solution properties, oxygen solubility, density, enthalpy, and vapor pressure, were correlated with solution composition and temperature. Subsequently, a kineticsbased model for simultaneous sulfide dissolution and iron precipitation in a multistage, three-phase reactor was developed. The population balance method was used for sulfide mineral material balances, and apparent equilibrium was assumed for iron precipitation. A gas-phase material balance was included, which allows for prediction of oxygen utilization. The model was solve for a particular operation of the Cominco Ltd. (Trail, BC) autoclave, and prediction results were shown to be in very good comparison with actual plant performance.

Kinetics of pyrite oxidation in sodium hydroxide solutions

Abstract: The kinetics of pyrite oxidation in sodium hydroxide solution were investigated in a stirred reactor, under temperatures ranging from 50 °C to 85 °C, oxygen partial pressures of up to 1 atm, particle size fractions from -150 + 106 to -38 + 10µm (-100 + 150 mesh to -400 mesh + 10 µ), and pH values of up to 12.5. The surface reaction is represented by the rate equation:-dN/dt = Sbk″pO0.5 2[oH- 0.25/(1 +k‴ pO2 0.5) where N represents moles of pyrite, S is the surface area of the solid particles,k″ andk″ are constants,b is a stoichiometric factor, pO2 is the oxygen partial pressure, and [OH-] is the hydroxyl ion concentration. The corresponding fractional conversion (X) vs time behavior follows the shrinking particle model for chemical reaction control: 1 - (1 -X)1/3 =k ct The rate increases with the reciprocal of particle size and has an activation energy of 55.6 kJ/mol (13.6 kcal/mol). The relationship between reaction rate and oxygen partial pressure resembles a Langmuir-type equation and thus suggests that the reaction involves adsorption or desorption of oxygen at the interface. The square-root rate law may be due to the adsorption of a dissociated oxygen molecule. The observed apparent reaction order with respect to the hydroxyl ion concentration is a result of a complex combination of processes involving the oxidation and nydrolysis of iron, oxidation and hydrolysis of sulfur, and the oxygen reduction.