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By Ward S. D

When using grinding time for a batch grinding operation as a measure of the energy usefully employed for comminution; the assumptions made are often not valid. A kinetic approach, based on a study of the rate constant, or k, value for the material is more acceptable. The Rosin-Rammler distribution equation has been theoretically derived from the general equation for first-order batch grinding. This relationship, incorporating a term for k, was used in a study of the rod milling of a binary mixture of quartz and limestone.The presence and degree of interaction between the components was considered by comparing the size distribution of the mill product with that predicted by assuming the overall distribution equal to the sum ofthe distributions given by the Rosin-Rammler equations for each component weighted according to its volume fraction in the mixture. The interaction was found to be complex and particularly sensitive to particle size.A simple graphical procedure was devised to predict the size distribution of the mill. Product components and this gave a fairly good approximation to experimental data.

Jan 1, 1976

By Wendell H. Wiser

A comparison is presented of coal pyrolysis at temp¬eratures ranging from 4090 to 497°C and thermal dissolution of coal in tetralin at temperatures ranging from 350° to 450,°C, both utilizing a Utah high-volatile bituminous coal. The initial coal pyrolysis reactions are second order with an enthalpy of activation of 35.6 kcal per mole. The fraction of total product yield produced under second order conditions ranges from 67% at 409°C to 96% at 497°C. The process then gradually deteriorates to a first order reaction in the later stages with enthalpy of activation of 4.1 kcal, per mole. The initial reactions of solution of coal in tetralin are second order with an enthalpy of activation of 28.8 kcal per mole. The fraction of total product produced under second order conditions ranges from 63% at 350°C' to 94% at 450°C. The dissolution process then gradually changes to first order in the later stages with enthalpy of activation of 15.6 kcal per mole. A model is presented which relates the two processes and explains, the significance of the above similarities.

Jan 1, 1967

By Ibrahim Yusufoglu, Ahmet Orkun Kalpakli, Cem Kahruman, Sedat Ilhan

"The effects of oxalic acid concentration, temperature, stirring rate and particle size on the dissolution rate of synthetically prepared calcium molybdate were investigated. Dissolution of calcium molybdate in oxalic acid solutions takes place as a series - parallel type reaction. In the first reaction step, which proceeds according to the ""Langmuir - Hinshelwood Mechanism"", calcium aqua oxalato molybdate is formed as a complex chelate intermediate product. In the second reaction step, molybdic acid is formed during the slow hydrolysis of calcium aqua oxalato molybdate, and it reacts rapidly with oxalic acid to form the polymeric hydrogen oxalate dimolybdate chelate as an end product. Activation energies were calculated as 41.4 and 49.9 kJ mol-1 for the first and zero order reactions. The fractional conversion versus time relationship can be given by the following equation.IntroductionMolybdenum is used widely in electric-electronic, metal working, aerospace and aeronautic, nuclear, glass and petrochemical industries because of its high melting temperature and resistance against chemical effects. However, the largest molybdenum consumers are the iron-steel and super alloy industries where molybdenum is used as an alloying element. Industrially important molybdenum minerals are limited to molybdenite (M0S2), powellite (CaMo04) and wulfenite (PbMo04), which are considered as primary molybdenum resources. Secondary molybdenum resources are spent catalysts and scrap [1-4].Molybdenum has been produced by pyrometallurgical processes in the past. Since it is possible to process low grade molybdenum ores and industrial wastes by hydrometallurgical processes, which are more environmentally friendly than pyrometallurgical processes, the importance of the use of hydrometallurgical processes has increased in the molybdenum production industry."

Jan 1, 2012

A kinetic model for leaching of various metals with different lixiviants in a batch system has been developed. Material balances for reactants and products at the solid/liquid interface were formulated and solutions to these balances were obtained in view of practical conditions. Special emphasis has been given to examine mixed controlled reaction systems where both heterogenous reaction and mass transfer play important role on the overall rate expression. The resulting kinetic expressions for either powder or rotating disc are discussed in light of experimental findings for various metals. Examples of the metal dissolution systems considered in this study include cobalt, nickel, copper and gold in acid, cyanide or ammoniacal solutions.

Jan 1, 1992

By J. J. Jonas, G. R. Stewart, A. M. Elwazri

Two important parameters for dynamic recrystallization can be derived from the changes in the strain hardening rate: the critical strain for initiation of dynamic recrystallization and the point of maximum softening. In this work, these values are determined from the flow stress-strain data obtained in continuous compression testing in the range 900-1100°C. The resulting strains are used to calculate a kinetic model of dynamic recrystallization for two materials: 304 austenitic stainless steel and a hypereutectoid plain carbon steel. The mechanical parameters used to define the proposed model are confirmed with quantitative metallographic analysis of the recrystallized microstructure.

Jan 1, 2004

By E. A. Brinkmann

A kinetic model framework for single particle kinetics in combined diffusion and adsorption processes is presented. The framework applies to the general case in which both diffusion and the adsorption reaction play important roles in determining the overall rate in processes where the migrating species can both adsorb and accumulate. The technique, which should be applicable to a wide range of reaction mechanisms, consists of an iterative integration procedure for the coupled diffusion and reaction equations. The case of a reversible linear adsorption reaction rate is developed. In order to verify the technique as a legitimate method of model development, an analytical solution for the identical case is derived and compared to the numerical solution. Excellent agreement exists between the two solutions.

Jan 1, 1987

By Paul E. Mather, Matthew J. M. Krane

Anode or fire refining is the final pyrometallurgical step in the production of copper anode. Part of this process purifies liquid copper by reducing its dissolved oxygen with a natural gas-steam mixture. Until now there have been no transient models of this process coupling the injected gas jet mass transport with its chemical reactions. A transient, 1D flow, chemical reaction model was made to estimate the time-dependent behavior of anode copper composition, soot formation, and the transient gas jet composition along its height. Model estimates were made for reduction rate, soot emission rate, and exergy loss and destruction distributions for two melt temperatures and a range of steam addition rates. It was found that increases to melt temperature and steam addition rate increased reduction rate and decreased soot emission, while having little effect on exergetic performance. Estimates for reduction histories were compared to industrial data. INTRODUCTION Anode/fire refining is the final pyrometallurgical step in the production of copper anodes; it is essential for removing dissolved gases which cause porosity in cast anodes. Despite its significance, the open literature appears devoid of any transient models of the entire process; furthermore, there are very little published process data with which to validate any models made. This dual dearth of modelling work and process data inhibits studies of the tradeoffs between process and performance changes, desirable for decreasing reduction time and soot formation as well as quantifying changes in the exergy losses and destructions of the process. This work introduces a reduced-order, transient model of reduction during fire refining, examines performance trends with operating conditions, and compares model estimates with industrial data. Overview of anode refining The purpose of anode refining is to produce liquid copper which can be cast with minimal gas porosity, which disrupts the downstream electrorefining process. Dissolved sulfur is removed first, then oxygen, by reactions with different injected gases. The removal of oxygen (the reduction step) is the subject of this proceeding and is effected by the bubbling of natural gas, typically mixed with steam, through the melt from tuyeres. A typical refining run reduces dissolved oxygen from 3000 ppm to 300 ppm in 2–3 hours (Schlesinger, King, Sole, & Davenport, 2011). The refined copper is then cast as anodes. Figure 1 shows a schematic of the furnace vessel.

Jan 1, 2019

By Neng-Wen Yu, Shau-Jun Zhu, Ji-He Wei

The desulfurization process by powder injection and blowing in the RH refining of molten steel and its mechanism have been considered and analyzed. Based on the two-resistance mass transfer theory and the mass balance of sulfur in the system, a kinetic model for the process has been developed. The related parameters of the model, including the mass transfer coefficients and the effective amount of powder in the molten steel being treated for desulfurization, have been more reasonably determined. Modeling and predictions of the process of injecting and blowing the lime-based powder flux under assumed operating modes with the different initial contents of sulfur and amounts of powder injected and blown in a RH degasser of 300 t capacity have been carried out using the model. The relevant circulation rate of the liquid steel and the powder injection and blowing rate were taken to be 100 t/min and 150 kg/min, respectively. The initial contents of sulfur in the liquid steel to be treated and the amounts of powder injection and blowing were respectively assumed to be 0.007, 0.006, 0.005, 0.004, 0.003, 0.002 mass-% and 10, 8, 6, 5, 4, 3 kg/t-steel. The total treatment time for desulfurization under each mode was set up at 24 min, equivalent to eight circulation cycles of the liquid steel to be treated. The results indicated that the predictions made with this model are in good agreement with some data of the industrial experiments and practice. Injecting and blowing the lime-based powder flux with the composition of 85 mass-% lime (CaO) + 15 mass-% fluorspar (CaF2) of 3-5 kg/t-steel, it is possible to decrease the sulfur content in the molten steel to ultralow level below (5-10)x10·4 mass-% from (60-80)x 10·4 mass-%. The total treatment time needed will appropriately be 12-20 min. Intensifying the powder injection and blowing operation and increasing the circulation rate of the liquid steel may effectively' raise the rate of the process in RH refining. The model may be expected to offer some useful information and a reliable basis for determining the reasonable process parameters and help in optimizing the technology of desulfurization by powder injection and blowing in the RH refining of molten steel.

Jan 1, 2000

By E. V. Cilento, K. A. DiGregorlo, R. C. Lantz

A kinetic model was developed to describe the production of superoxide (02) by single pulmonary alveolar macrophages (PAM). Model predictions were compared to experimental results obtained from single rat PAM. The O2 - was quantified by measuring the reduction of nitroblue tetrazolium (NBT) to a diformazan precipitate (NBTH2) from video-recorded images of individual cells. The kinetic model considered three reactions: (1) the production of extracellular 0 - from the reduction of oxygen by NADPH oxidase using intracellular NADPH as the substrate, (2) the subsequent dismutation of o2- to from O2 , and (3) the reaction of o2- and NBT. NBT specificity for o2- was analyzed by comparing results in the presence and absence of superoxide dismutase (SOD) which catalyzes the dismutation of o2- to H2o2. Measured PAM heterogeneity was accounted for by varying the concentration of intracellular NADPH, its rate of depletion, and the concentration of intracellular NADPH oxidase in the kinetic model. Model predictions compared favorably with experimental results except when SOD was present. This discrepancy may be due to diffusional limitations since NBT is a relatively small molecule (818 MW) compared to SOD (34000 MW). In addition, the cell surface is both ruffled and negatively charged, which may introduce steric hindrances and/or electrostatic effects since SOD is also negatively charged.

Jan 1, 1988

By E. V. Cilento, K. A. DiGregorio, R. C. Lantz

"DIGREGORIO, K. A., E. V. CILENTO, AND R. C. LANTZ. A kinetic model of superoxide production from single pulmonary alueolar macrophages. Am. J. Physiol. 256 (Cell Physiol. 25): C405-C412, 1989.-A kinetic model was developed to describe the production of superoxide (02) by single pulmonary alveolar macrophages (PAM). Model predictions were compared with experimental results obtained from single rat PAM. The 02 was quantified by measuring the reduction of nitro blue tetrazolium (NBT) to a diformazan precipitate (NBTH,) from video-recorded images of individual cells. The kinetic model considered three reactions: 1 ) the production of extracellular 02 from the reduction of oxygen by NADPH oxidase using intracellular NADPH as the substrate, 2) the subsequent dismutation of 02 to form H,O,, and 3) the reaction of 02 and NBT to form diformazan. NBT specificity for 02 was analyzed by comparing results in the presence and absence of superoxide dismutase (SOD) that catalyzes the dismutation of 02 to H,O,. Measured PAM heterogeneity was accounted for by varying the concentration of intracellular NADPH, its rate of depletion, and the concentration of intracellular NADPH oxidase in the kinetic model. Model predictions compared favorably with experimental results except when SOD was present. This discrepancy may be due to diffusional limitations because NBT is a relatively small molecule (818 mo! wt) compared with SOD (34,000 mol wt). In addition, the cell surface is both ruffled and negatively charged, which may introduce steric hindrances and/ or electrostatic effects, since SOD is also negatively charged, whereas NBT is positively charged.PULMONARY ALVEOLAR MACROPHAGES (PAM) protect the lungs by phagocytizing foreign debris and bacteria. This process is accompanied by the production of superoxide anion (02) at the surface of the plasma membrane (3, 31). Superoxide readily dismutates to form H20 2 and subsequently, other oxygen metabolites which have been shown to be both antibacterial and cytotoxic (21, 25, 35).Superoxide is produced from the reduction of extracellular O, at the surface of the cell membrane by NADPH oxidase by the following reaction (3, 4)"

Jan 1, 1989

By F. A. Olson, S. L. Pohlman

A unique method of measuring weight loss as a function 3 of time, with a sensitivity of 10-5 grams, while leaching copper minerals with a flowing acid leach solution has been developed. Kinetic results obtained coupled with visual and microprobe analyses show topochemical reaction for the leaching of chrysocolla with sulfuric acid. The kinetics follow a shrinking core model and show ion diffusion through a product layer, chemical reaction at the unreacted core interface and mass transfer through the boundary layer as being important.

Jan 1, 1974

By F. -Z. Ji, A. G. Irons, M. Barati, K. Coley

In order to optimize carbon injection into oxidizing slags, in terms of carbon and iron yield, we must have a detailed understanding of the kinetics of the reactions involved. The current study measures the rate of carbon oxidation during injection at steelmaking temperature by means of injections of coal into EAF slags. The compositions of analysed outgoing gas were used to calculate gas flow rate and hence the gasification rate of carbon. A fundamental equation to predict residual carbon in slags was developed. The predictions using this model at moderate injection rates are in good agreement with experimental data. The reaction rate of EAF slag with carbon is under mixed control by the slag gas and the gas carbon reactions. The relative importance of each step depends mainly on the v-ratio of slags. A relative reactivity parameter ? has been defined and it is found to be important to carbon-slag reaction kinetics and slag foaming. Key words: carbon-slag reaction, kinetics, slag foaming.

Jan 1, 2004

By V. Annamalai, J. B. Hiskey

Abstract-The kinetics of copper cementation on a rotating disc of pure aluminum were studied as a function of chloride ion concentration, rotational speed of the aluminum disc, hydrogen ion concentration, copper ion concentration, and temperature. The optimum experimental conditions for all the parameters were determined. Chloride ion was found to destroy the naturally existing aluminum oxide film, and enabled the cementation reaction to proceed. A two-step rate, observed in most of the experiments, was attributed to the attainment of a roughened surface. An Evans diagram for the copper-pure aluminum system was constructed and utilized in predicting the controlling mechanism of the system. At low temperatures (<33°C), the rate with an experimental activation energy of 20.36 kcal mol-1 was controlled by the presence of an oxide layer. While at higher temperatures presence of an oxide layer. While at higher temperatures (>33° mol-1 was controlled by ionic diffusion. The deposits obtained were pure copper and not a copper-aluminum alloy. The amount of aluminum dissolved was determined for each experiment, and the maximum excess consumption was found to be only 40%. The structural characteristics of the copper deposits were studied using a scanning electron microscope. These observations indicated that the deposits were either bulbous, massive crystalline, or dendrites of different degrees of fineness depending on the experimental variables. The reaction rates seemed to depend on the deposit structures in a predictable way when a particular experimental parameter was varied.

Jan 6, 1978

By V. Annamalai, J. B. Hiskey

The kinetics of copper cementation on a rotating disc of pure aluminum were studied as a function of chloride ion concentration, rotational speed of the aluminum disc, hydrogen ion concentration, copper ion concentration, and temperature. The optimum experimental conditions for all the parameters were determined. Chloride ion was found to destroy the naturally existing aluminum oxide film, and enabled the cementation reaction to proceed. A two-step rate, observed in most of the experiments, was attributed to the attainment of a roughened surface. An Evans diagram for the copper-pure aluminum system was constructed and utilized in predicting the controlling mechanism of the system. At low temperatures (<33°C), the rate with an experimental activation energy of 20.36 kcal mol- 1 was controlled by the presence of an oxide layer. While at higher temperatures presence of an oxide layer. While at higher temperatures (>33° mol- 1 was controlled by ionic diffusion. The deposits obtained were pure copper and not a copper-aluminum alloy. The amount of aluminum dissolved was determined for each experiment, and the maximum excess consumption was found to be only 40%. The structural characteristics of the copper deposits were studied using a scanning electron microscope. These observations indicated that the deposits were either bulbous, massive crystalline, or dendrites of different degrees of fineness depending on the experimental variables. The reaction rates seemed to depend on the deposit structures in a predictable way when a particular experimental parameter was varied.

Jan 1, 1979

By F. M. Doyle, Jiang Tao, Xu Shi, Chen Jin, E. Peters

Tafel curve technique and leaching tests have been applied to study the kinetics of gold leaching with thiosulfate. Results show that cupric ions and ammonia play the part of catalysts in the leaching of gold with thiosulfate. The activation energy of gold dissolution is calculated as 27.99 KJ/mol in the absence of both cupric ions and ammonia. However, the energy is reduced to 15.54 KJ/mol in a solution of 0.01 mol/L Cu (NH3)2 4* and 0. 5moVL total ammonia. The reaction order of Cu (NH,) g is one in the range of 0.001~0.1mol/L. These results support the electrochemical-catalytic mechanism pro- posed by the authors and explains the behavior of cupric ion and ammonia (Jiang Tao, et al., 1993)

Jan 1, 1993

By Hu Long

Pyrite, as the host mineral in refractory gold ores and concentrates, has been treated by pressure oxidation in sulfuric acid solutions at temperatures above 180°C to liberate gold prior to cyanidation since the 1980&apos;s. However, no data is available on the kinetics of pyrite during acid pressure oxidation over the temperature range of 180 to 230°C which is the range employed by most commercial plants. The dissolution of pyrite (FeS,) in sulfuric acid solution under oxygen pressure was investigated at temperatures ranging from 170 to 230°C. The effects of temperature, particle size, agitation speed, oxygen partial pressure, and pulp density were evaluated. The effects of foreign ion addition and the concentration of sulfuric acid were also examined. The apparent activation energy was estimated to be 42.6 kJ/mol in the temperature range 170 to 230°C. The reaction orders with respect to particle size and oxygen partial pressure were found to be -1.5 and 0.5 at 210°C, respectively. Experimental evidence suggests that the kinetics are limited by the surface chemical reaction initially, and then also to some extent by the diffusion of ferrous ions away from the particle surface.

Jan 1, 1999

By M. E. Wadsworth, P. H. Yu, C. K. Hansen

A study of the rate of dissc5lution of chalcopyrite (CuFeS2) in acidic solutions under oxygen overpressures was carried out by measuring the rate of formation of cupric ions in solution. Effects of temperature, oxygen partial pressure, surface area, and concentration of sulfuric acid were evaluated. A sized batch of chalcopyrite was leached in the temperature range of 125° to 175°C and in the pressure range of 75 to 400 psi of oxygen. In 0.5 N H2SO4 all products of reaction went into solution except for trace amounts of elemental sulfur. The dissolution of chalcopyrite followed linear kinetics and was essentially independent of hydrogen ion concentration for H2S04 concentrations between 0.2 and 0.5 N. The oxygen dependence indicated adsorption approaching limiting values with increasing oxygen pressure. The linear mechanism was explained in terms of steady-state adsorption of oxygen at the chalcopyrite surface followed by a surface reaction. The enthalpy of activation for adsorption of oxygen was found to be approximately 33 kcal per mole. An activation enthalpy of approximately 9 kcal per mole was observed for the surface reaction. Charge transfer reactions are not rate controlling in the process.

Jan 1, 1973

By G. Gabra

The kinetics of acidified thiourea leaching of pyrite concentrate was investigated at temperature ranging form 20 °C to a 60 °C. The effect of various parameters on the dissolution rates are discussed. The gold extraction was found to be zero and first orders with respect to Fe (111) and thiourea concentration, respectively. The order of the reaction with respect to sulfuric acid was found to be zero. The activation energy was determined from the Arrhenius plot as 2,039 kcal mole -1 (for a freshly prepared acidic solution containing Fe (111) as the oxidant and at 800 rpm stirring speed. This relatively low activation energy value suggests that the gold extraction is controlled by a-physical phenomenon. Under optimum conditions, more than 90% of gold has been dissolved in about 30 min. and 95% in 60 min. Attempt to recover gold from thiourea solution using active carbon is also discussed.

Jan 1, 1984

By Milton E. Wadsworth, W. Martin Fassell, William H. Dresher

A study of the rate of dissolution of molybdenite (MoS2) in alkaline solution was carried out under carefully controlled conditions. Effects of temperature, oxygen over-pressure, and KOH concentration were evaluated. Studies were made in the temperature range 100°C to 175°C and in the pressure range 0 to 700 psia of oxygen. Under these conditions molybdenite was found to leach according to a linear mechanism. Both oxygen over-pressure and KOH concentration were found to control the rate of leaching. The mechanism has been explained in terms of adsorption of oxygen at the molybdenite surface followed by configurational rearrangement of the adsorbed molecules. The hydroxyl ion dependency is believed to be diffusion-controlled. Laboratory batch studies have shown that molybdenite can be readily dissolved in alkaline solutions under moderate conditions of temperature and pressure. Commercial application of this process to the production of ferro-molybdenum and molybdenum chemicals is promising in view of the ease of dissolution of molybdenite and the relatively noncorrosive conditions involved in the process.

Jul 1, 1956

By Raul A. Deju

This paper shows how one can relate the chemical reactions between water and a silicate bed to the equations of flow. First the reaction mechanism is studied both theoretically and experimentally. Once the reaction mechanism is established, the equations of flow are solved and a solution (under physically reasonable side conditions) is obtained. Experiments to substantiate the solution are also presented.

Jan 1, 1969