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By Arthur W. Cooper

This paper contains a review of the development of blast furnace? slag handling and processing technology in the Ironmaking industry over the past 30 years, with an emphasis on economic and environmental factors. The requirements and practice of air-cooling slag for use as aggregate and of pelletizing and granulating slag for use in cement manufacture are described. The operation of slag pits, slag pots or ladles, the slag pelletizer and early granulation systems are compared with the new continuous .granulation, dewatering and handling systems developed in the past decade.

Jan 1, 1992

By Anja Pfennig, Axel Kranzmann, Sabrina Schulze

The CCS technique involves the compression of emission gasses in deep geological layers. To guarantee the safety of the site, C02-corrosion of the injection pipe steels has to be given special attention when engineering CCS-sites. To get to know the corrosion behaviour samples of the heat treated steel 1.7225 42CrMo4, used for casing, and the stainless injectionpipe steel 1.4034 X46Cr13 were kept at T=60 °C and ambient pressure as well as p=lOO bar for 700 h - 8000 h in a C02-saturated synthetic aquifer environment similar to possible geological on-shore CCS-sites in the northern German Basin. The isothermal corrosion behaviour obtained by mass gain of the steels in the gas phase, the liquid phase and the intermediate phase gives surface corrosion rates around 0.1 to 0.8 mm/year at ambient pressure and much lower about 0.02 to 0.2 mm/year at 100 bar where the C02 is in its supercritical state. Severe pit corrosion with pit heights around 4.5 mm are only located on the 42CrMo4 steel. Main phase of the continuous complicated multi-layered carbonate/oxide structure is siderite F eC03 in both types of steel.

Jan 1, 2013

By Yury Kapelyushin

Formation of cementite in the reduction of hematite by CO–CO2 gas was studied in situ using high temperature XRD (HT XRD) analysis. Reduction of hematite was examined in the temperature range 873–1173 K by CO–CO2 gas mixture with high carbon activity. When carbon activity in the system was 1.5, cementite was formed only at 1023 K; it was not observed in experiments at 973, 1073 and 1123 K. Formation of cementite was observed at 923–1073 K when carbon activity increased to 3–5; and at 873 K when carbon activity was 10. Formation of cementite at 973–1073 K proceeded through metallic iron; however, in the reduction of hematite at 873 and 923 K, iron was not observed; cementite apparently was formed directly from wüstite. XRD spectra were used to estimate concentration of carbon in austenite in the process of cementite fromation.

By Frederico Muylaert Margem, Jarbas Bravo Neto, Sergio Neves Monteiro

"The mechanical behavior and the fracture characteristics of composites with DGEBA/TETA epoxy matrix reinforced with up to 40% in volume of continuous and thinner ramie fibers were evaluated by tensile tests. Specimens with selected thin fibers aligned along the tensile axis were room temperature tested to rupture. The fracture surface was analyzed by scanning electron microscopy. The results showed significant increase in both the ultimate tensile strength and the elastic modulus. The fracture analysis indicated the possible mechanism for the fiber/matrix interaction, which could be responsible for the composite performance.IntroductionThe fiber reinforced polymer composite emerged in the middle of last century as a versatile engineering material for applications requiring mechanical resistance in association with lightness. Its most commonly used example is ""fiberglass'', i.e., a thermoset polymer matrix composite reinforced with glass fiber. Indeed, ""fiberglass"" has a specific strength of the order of 500 MPa.cm3/g, which is the double of the strongest steels like the maraging. This motivated, at earlier times, ""fiberglass"" to replace many conventional materials including wood and natural fiber composites. Today, ""fiberglass"" has a wide range of uses from aerospace systems and appliances to sport and leisure components. However, its fabrication as well as those of any synthetic fiber such as carbon and aramid composites, requires a relatively large amount of energy. Presently, a growing concern exists regarding the consequences to the environmental by gases like C02 associated with both the energy consumption and the processing of synthetic fibers and their composites. These gases are well known responsible for global warming [1]."

Jan 1, 2011

By E. T. White, Dean Ilievski

"The population balance is one of the basic relations for analysing particulate mineral processing operations. It is an exact relation. The principles of the population balance are reviewed and applications in the minerals industry discussed.IntroductionMathematical modelling has proved to be a very successful approach for improving the design and performance of mineral processes, particularly since the availability of computers to handle the complexity usually necessary to give a useful model.Mineral processes almost invariably involve particles, as either solid fragments, liquid drops or bubbles. Process performance usually is highly dependent on the behaviour of these particles. In modelling particle behaviour, the basic relation to be used is the population balance. This paper discusses the role of the population balance and the range of its applications in minerals processing.The Population BalanceThe population balance was developed for demographic studies, ego predicting the change in the population (numbers) of, say, school children between one census and the next. The first sustained application to the processing industries appears in the 1960s for crystallization. However it was recognised almost immediately that it had application to all particulate processing."

Jan 1, 1996

By K. C. Liddell

"Cu/Ni multilayers exhibiting giant magnetoresistance were deposited from a single electrolyte under stepped potentiostatic control. To enable transport measurements to be made without remounting the multilayer film, we developed a novel method that involved plating on a thin metallic basal layer atop a rigid non-conducting Si substrate. Rotating ring-disk electrode techniques were used to monitor the composition and thickness of individual plated layers. Transmission electron microscopy confirmed that the interfaces between adjacent layers were sharp and that the structure of the layers was uniform throughout the film. Atomic force microscopy images indicated that the film's surface was smooth and free of defects.ELECTRODEPOSITION OF THIN MULTILAYER MAGNETIC MATERIALSI. IntroductionElectrodeposition of compositionally modulated films will in all likelihood continue to be used to produce the read heads for stored magnetic data. However, the next generation of head materials will require both improved sensitivity and reduced film thickness. Certain multi layers consisting of thin alternating ferromagnetic and nonmagnetic layers exhibit giant magneto resistance and consequently are promising candidates for read head applications. We have successfully made multilayer films with giant magnetoresistance that have total thicknesses as low as 25 nm, approximately 120 times thinner than the thinnest similar films reported in the literature. This paper describes early results from our work on electrodeposition and characterization of Cu/Ni multilayers, a model system with enhanced magnetic and mechanical properties, including the GMR effect. The structure and composition of the multilayers were determined using TEM, AFM, and electrochemical methods, and their magnetoresistance was measured by the standard four-probe technique. A novel method developed in this work enabled the transport properties of the ultrathin films to be measured reliably without the need to dissolve the cathode or handle the films. To provide a context for these results, short accounts of other work on giant magnetoresistance and multilayer electrodeposition are also included."

Jan 1, 1997

By Yuhsuke Mizukami

Crude high Cr containing steel such as tool steel, heat-resistant steel or stainless steel is produced by dissolution of high carbon ferro-chromium into molten crude steel. In the refining process, decarburization is performed at the first stage, and deoxidation is followed in the next stage. Therefore, the equilibrium relation between dissolved Cr and 0 in molten Fe-Cr alloy after decarburization is very important when yield of deoxidizer is considered for the ovemll control and optimization of the process. It is well known that the yield of deoxidizer does strongly depend on the kinds of refractories of furnace in the secondary refining process. In the present work, the equilibrium relation between dissolved Cr and O in molten Fe-Cr alloy has been measured in a Cr2O3, MgO or Al2O3 crucible at steelmaking temperature. O contents at given Fe-Cr components have been lower in order of Cr2O3, Al2O3 and MgO crucible. The present results have been discussed based on the activities of the constituents in pure solid Cr2O3, and FeO-Cr2O3, MgO Cr2O3 and (AI,Cr)2O3 solid solutions.

Jan 1, 2003

By S. Neogy, M. Gupta, D. Srivastava, V. Kain, S. Roychowdhury, R. C. Prasad, G. K. Dey

"Austenitic stainless steels are an important material of construction for Boiling Water Reactors (BWR). These stainless steels are amenable to strengthening by strain hardening. Various deformation modes at different test temperatures and strain become active. In the present investigation type 304LN stainless steel was used in the annealed and strain hardened condition. Thin foils were prepared from gauge section for transmission electron microscope (TEM) investigation after tensile testing at room temperature and at 288°C. TEM investigation reveals that twinning is the major mode of deformation for the tests done at room temperature while dislocation cross-slip is the major mode of deformation at higher temperature. Stacking faults were also observed to a limited extent. The extent of twinning was much higher for the tests done using the rolled material. The formation of martensite in the stainless steel due to straining was investigated by the analysis of selected area diffraction patterns.IntroductionAustenitic stainless steels (type 300 series) are an important material of construction in Boiling Water Reactors (BWR). These stainless steels cannot be heat treated but can be strengthened by cold working [1]. Nitrogen alloying of these stainless steels result in high strain hardening rates and higher strength without any loss in toughness [1]. Stress Corrosion Cracking (SCC) in BWR of these types of stainless steels have been attributed to surface strain hardening and strain hardening ofregions adjacent to constrained weldment [2].The test temperature [3, 4], prestrain [5] and nitrogen level [5] has been reported to affect the deformation mechanism during tensile testing. Byun et al. [3] have reported the formation of martensite, dislocations, stacking faults and twinning during tensile deformation, the extent of each depending on the test temperature. Strain localisation has been reported to occur during tensile deformation in irradiated stainless steels [ 6]. The behaviour of rolled material during tensile testing is similar to that of irradiated material to a large extent [3]. Austenitic stainless steels are low stacking fault energy (SFE) materials in which various types of microstructures have been reported to form during tensile deformation and the strain is also highly heterogeneous in nature in these stainless steels which aides SCC in BWR environment to a large extent [7]. During cold working of austenitic stainless steels second order twinning has also been reported [8]. Knowledge about the deformation mechanisms operative in the strain hardened austenitic stainless steels during tensile testing at different temperatures is essential to understand the material deformation behavior and the present study aims at enhancing the existing understanding."

Jan 1, 2011

By A. A. Hejja

The effect of composition on electrical conductivity, viscosity and liquidus temperature of the slags was investigated in the temperature range of 1300" to 1450°C. The synthetic slags containing CaO, MgO, SiO,, A1,0, and FeO were similar to those employed in the electric furnace smelting of sulphide Cu-Ni concentrates containing PGM (Platinum Group Metals) from the Merensky Reef of South Africa. FeO and SiO, were found to affect the viscosity and conductivity the most while liquidus temperature depended on MgO content in addition to these. The activation energy for electrical conduction was found to vary from 67 to 159 kJ/mol and that for viscosity from 125 to 209 kJ/mol. Optimization of the slag composition was attempted on the basis of opposite trend of the viscosity-electrical conductivity relationship with slag composition.

Jan 1, 1994

By K. Yamada, T. Takaoka, A. Ozeki, M. Yamaga, Y. Kawai, S. Nishioka, Y. Kikuchi

"Recently, smelting reduction of chromium ore in BOF has been actively investigated as a key unit process for an innovative future stainless steelmaking. The prominent feature of this new process route is energy and process saving, and production cost saving. The development is already in the midst of application to the commercial production, however there still remain the following key technologies to be established for the full use of the process. One is a speed up of the reduction of chromium ore to match with sequential continuous casting, and the other is efficient combustion of carbonaceous materials in BOF to reduce their consumption, and hence to assure the steel quality. High degree of post combustion technology and new charging technology, i.e., ore-coal-flux-oxygen mixed injection, could be effective for those two subjects. In 2000 or beyond, the new process would have become quite popular owing to the establishment of those key technologies.Introduction Since stainless steel was invented, its production has continued to expand because of its attractive combinations of functions of excellent corrosion resistance, good formability, a pleasing appearance, and a wide range of strength levels. New types of stainless steels as well as new applications are continually being developed.Compared to the production of ordinary steels (1), stainless steel production (2,3) shows steady growth worldwide, while the former production remains on the same level, as Figure 1 shows. It can be estimated that future production would show further growth since materials consumer demands are more fashionable, or more functional, which could be satisfied by stainless steels.Thus market needs would be met, if it could be produced with reasonable production cost. The emergence of an innovative production technology is then potentially requested as VOD and AOD processes have emerged, which has saved substantial production cost. This paper describes a possibility of a future stainless steelmaking process, which uses the in-bath smelting reduction of chromium ore in BOF, and which would save production as well as energy cost."

Jan 1, 1988

By Denise Corrêa de Oliveira

Common dry batteries use zinc as the negative electrode. Producers commonly use additives such as mercury to prevent corrosion and to increase the mechanical resistance of the zinc anode. Alkaline batteries also contain it, as an anti-corrosive agent. When mixed with the common municipal solid waste, heavy metals as zinc and mercury pollute soil and ground water supplies, moving to the food-chain and affecting human health. Due to these possible damages, this kind of waste must be properly disposed, or recycled. Thus, even in low amounts (ppm) in batteries, mercury has to be eliminated or, at least, its content should be reduced. This work presents the use of pyromettalurgical processes, to reduce mercury content and recover zinc. The tests involved batteries treatment at temperatures from 300° to 1000°C. Mercury is eliminated up to 650°C, and zinc is evaporated at higher temperature treatment. C

Jan 1, 2001

By Vinicius Alves Gomes, Jean Igor Margem, Frederico Muylaert Margem, Sergio Neves Monteiro, Marina Rangel Margem

The interface between the matrix and the reinforcing fiber plays an important role in the efficiency by which an applied load is transmitted through the composite structure. The shear stress at the fiber/matrix interface can be associated with this load transference and, consequently, affects the composite strength. In the present work, pullout tests were used to evaluate the interfacial shear stress of malva fiber in epoxy matrix composites. A small critical length was found for the malva fiber embedded in epoxy, which corresponds to a relatively weak fiber/matrix bond and lower interfacial strength.

Jan 1, 2015

By Z. Yang, R. W. Smith, Jr. Wharton

"Microorganisms have the ability to remarkably adsorb and/or absorb heavy metal ions. Hence they are being studied widely as a means of removing metal ions from aqueous solutions both in order to clean up toxic streams and to recover valuable metals from these and other streams. It is often difficult to harvest organisms such as bacteria and unicellular algae since they are usually too small to be readily screened out. Froth flotation may prove to be a feasible method to harvest such organisms subsequent to the ad/absortion of the metal Ions. The present paper discusses the surface/electrokinetic properties of microorganisms and the modifier-collect conditions under which they should float. The zeta potential of the green alga Chlorella vulgaris was measured in the presence of AI(III) and Pb(II) ions and in the presence of dodecylammonium chloride and sodium dodecylsulfate. Present and past data suggest that the organisms should behave similarly to other finely divided, charged (polar) solids with their behavior sometimes modified by the non-polar surface regions present.IntroductionThe overall field of bioengineering is growing at a remarkably accelerating rate. Hydrometallurgy and mineral processing are included among those disciplines where there has been actual or proposed commercial use of bioorganisms. Further, the actual or proposed use includes bacterial enhancement of leaching of a number of different types of ores (1-5), modification of the flotation or oil agglomeration separation of minerals by bacteria (6,7) and microorganism (algae, bacteria or fungi) concentration of metal ions present in effluent or other mineral processing or hydrometallurgy aqueous streams (8-23)."

Jan 1, 1988

By Run Huang, Xuewei Lv, Lei Lei, Guibao Qiu, Chenguang Bai

"The TiO2-rich slag and pig iron can be produced from ilmenite concentrate by the electric furnace process. In this study, ilmenite concentrate was reduced in a vertical furnace equipped with a weighting data acquisition system. The effects of reducing agent (carbon) amount on the iron reduction were studied. The phase transformation, morphology and chemical compositions of reduced samples were investigated by X-ray diffractometry (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS), respectively. It was found that the reductive degree of ilmenite concentrate increased with the increase of reducing time. The phases of reduced samples were mostly iron, rutile, Ti3O5 and Fe2TiO5. The mass loss percentage increased with increasing the carbon amount from 8% to 12%. When the carbon amount exceeded 12%, the mass loss percentage decreased with the increasing of carbon amount.IntroductionIlmenite and rutile are the main raw materials for producing titania pigment and titanium metal. With the development of the titanium industry, huge amounts of titanium resources are needed. As sources of high-grade titania mineral decrease worldwide, more attention should be paid to the processes involving low grade mineral such as ilmenite ore. In ilmenite, MgO and CaO are the gangue parts. Therefore, the ilmenite refining becomes more and more popular. In the previous studies, the methods of ilmenite refining are electric furnace smelting, direct acid leaching, selective chlorination and thermal reduction [1]. Electric furnace smelting method is widely used in the titanium industry, however, which consumes a great deal of energies and has a high CO2 emission. Its essence is to remove iron oxides and obtain a high titania slag. So the thermal reduction of ilmenite concentrate is an important step in titanium industry, which can decrease carbon reagent consumption and save energy.Over the past several decades, many studies have been carried out on the mechanism and kinetics of the reduction of different ilmenite ores, which are as follows: The carbothermal reduction of Panzhihua ilmenite initiated at about 860 oC. In the temperatures ranging from 900 oC to 1400 oC, the reaction rate was changed like a shape of “M”. That was to say that the reaction rate increased with the growth of temperature at first, then decreased, afterward increased again and at last the reaction was arrested [2]. The Mohammad A.R group [3, 4] showed that the carbothermal reduction of primary ilmenite concentrate was faster in hydrogen and initiated at a lower reduced temperature than in argon and helium. The reduction in argon and helium had about the same rate and extent. Titanium oxycarbide started at 1000°C in hydrogen. The conversion of primary ilmenite concentrate to metallic iron and titanium oxycarbide at 1200 °C was completed in 300 minutes. Monoxide as the reductant to reduce ilmenite had been studied intensively by a few research groups [5, 6]. The rate and the degree of reduction depended on the formation of a metallic shell of iron which inhibited the transfer of CO to the reaction zones; titanium had a strong effect on the mechanism and rate of reduction of iron oxides. Wang and Yuan [7] studied the reductive kinetics of the reaction between a natural ilmenite and carbon. At temperature below 1100°C, chemical reaction was the rate controlling step, at 1100 to 1250°C mixed controlling was rate controlling step, above 1250°C diffusion through the product layer controlled the reaction. Zhang [8] investigated the reduction of natural, sintered and preoxidized ilmenite concentrates in hydrogen methane mixtures. Preoxidation and sintering of ilmenite concentrates changed their phase composition and caused a sharp decrease in specific surface area of raw materials and an increase in carburization temperature. Sintering also increased the metallization temperature of iron."

Jan 1, 2011

By C. J. Beyke

The U.S. Bureau of Mines has developed a process for the selective recovery of Pb metal from a mixed Pb-Zn concentrate. The concentrate was leached in recycled H2SiF6 at atmospheric pressure and 95° C with a redox potential of 570 mV (Eh). Eighty-five pct of the Pb was selectively leached from the concentrate while 87 pct of the Zn remained in the residue. Pressure leaching of the concentrate was slightly less successful, with 78 pct of the Pb leaching from the concentrate and 80 pct of the Zn remaining in the residue. Pure Pb metal was successfully electrowon from a purified PbSiF6-H2SiF6 solution with 96 pct current efficiency and 0.69-kW.h/kg energy consumption.

Jan 1, 1991

By Jose Bengoa

Low metal prices and environmental restrictions are always a challenge for copper smelters operation and its productivity. Thus, in order to reduce production costs and control gas emissions, improvements of the Teniente Converter (CT) operation were made at 110 Smelter Plant of Southern Peru Copper Co" 110, Peru, and the main objective was to increase its capacity for smelting copper concentrates without affecting normal operation, The present work eorresponds to a recent study conducted during the normal industrial operation of the Teniente Converter in this plant and, it shows the effect of increasing air oxygen enrichment from 28 to 34% on its productivity. The results show an increasing of concentrate smelting rate from 800 to 1370 tpd and hence a notorious improving in copper production, and practically no effect on the refractory consumption. The increment of the concentrate throughput, increases also the SO2 concentration and the sulfuric acid production, showing the effort done by this operation in order to accomplish the environmental Peruvian regulation,

Jan 1, 2003

By Herbert Pöllmann

Waste disposals are needed for safe deposition of different kinds of materials which can not be used as secondary raw materials. Often high contents of heavy metals must be bonded tightly to cristalline compounds to protect the environment from contamination. Therefore it is important. to find minerals which are capable to incorporate different heavy metals and protect the ground water. The power of resistance against leaching out effects of highly water-soluble salts can be increased. Mineral groups of metal hydroxy salts, ettringites, apatites, sodalites and calciumchlorosilicates and their hydrates are recommended for their formation in mineral reservoirs. Different wastes as red mud, gasification ash, garbage combustion ash and fluidized bed ashes were included in this study. The formation of different new compounds and their properties were determined.

Jan 1, 1991

By M. J. Adam

As part of its research program, the U.S. Bureau of Mines is investigating the partitioning of complex minerals to simpler phases using sulfidation reactions for selective extraction of mineral constituents of value from extraneous elements early in processing schemes. This report describes research in which thermal processing of the complex Ti -bearing mineral ilmenite (FeTiO, ) resulted in partitioning of the valuable Ti metal to the simpler compound rutile (Ti0 ). Samples of ilmenite were blended with elemental S for thermal treatment a2 various temperatures under controlled atmospheres in an effort to dissociate the Fe from the ilmenite complex. Product characterization revealed that the Fe was partitioned from the ilmenite, forming a rim of pyrrhotite/pyri te (FeS/FeS,) on a rutile core. The products were agate milled and then subjected to cursory magnetic and flotation techniques in an attempt to physically separate the partitioned phases. Partitioning results and phase concentration data are reported relative to thermal treatment variables and physical separation techniques.

Jan 1, 1993

By Jinxing Ji

Several fundamental aspects related to the nickel electrowinning from chloride electrolytes have been addressed in this paper. The thermodynamic study includes the activity coefficient of the hydrogen ion and the speciation diagram of NiCI2 solutions. The activity coefficient of the hydrogen ion (YH+) was calculated and estimated experimentally using a combination glass pH electrode. It was found that YH+ was greater than one in concentrated NiCl2 solutions and increased significantly with increasing NiCl2 concentration. The speciation diagram for NiCl2 solutions was plotted with YH+ and the effect of the ionic strength on the equilibrium constants being taken into account. It was discovered that the predominant nickel species in the acidic region were Ni2+ and NiCI+ in 0.937 M NiCl2 solution at 25°C. Electrodeposition tests demonstrated that higher Nit' concentration in the electrolyte improved the current efficiency of nickel electrodeposition (CENi). The additions of H3BO3, and NH4Cl increased very little the current efficiency of nickel electrodeposition at pH 1.5 and temperature 60°C. However, the addition of sulfate decreased the current efficiency of nickel electrodeposition. Nickel electrodeposition was also found to be a steady-state process since the amount of acid added to the electrolyte at a constant pH increased linearly with time during galvanostatic electrodeposition. The cathode surface pH during nickel electrodeposition was measured using a flat-bottom combination glass pH electrode and a 500-mesh gold gauze as cathode. The cathode surface pH was found always to be higher than the pH in the bulk electrolyte, and if the current density was sufficiently large, it would eventually reach a level causing precipitation of insoluble Ni(OH)2(s) on the cathode surface. Rotating disc electrode studies revealed that the rate of nickel electrodeposition was first order with respect to the activity of nickel ion and zero order with respect to the activities of chloride and hydrogen ions. The rate of hydrogen evolution was found to be first order with respect to the activity of hydrogen ion and to be zero order with respect to the activities of nickel and chloride ions. These findings indicate that nickel deposition and hydrogen evolution proceed independently.

Jan 1, 1995

By Dieter Neuschiitz, Pengfu Tan

"In order to understand the sintering phenomena during iron ore sintering process, a CFD model of iron ore sintering has been developed, combining with the kinetics of 15 relevant chemical reactions with the aim of describing the temperature fields and the gas flow patterns in the sintering bed. This CFD model can be used to simulate the concentrations of the gaseous and solid species, temperatures of the gas and solid, melting and molten fractions of the mixture, gas velocities, temperature zones and residence times of the gas in each temperature zone. IntroductionThe off-gas analyses clearly revealed that the off-gas of a sinter strand does not have a composition corresponding to thermodynamic equilibrium, for example, the CO, CO2 and O2 concentrations are not the mutually consistent equilibrium values. Apparently the chemical reactions in the sinter bed are controlled kinetically. Therefore kinetic modeling of sintering reactions combined with CFD modeling is necessary to understand the sintering phenomena during iron ore sintering process.Several models of iron ore sintering have been developed since 1970 [l-l 4l, each being more refined than its predecessor. The models were formulated as a series of differential equations to describe chemical and physical changes occurring at a point in the bed. These equations were solved numerically in a vertical plane along the strand. The present CFD model, based on the Nath's model [14], has been published in the reference [15]. In this work, some new chemical kinetic models of gas-solid reactions are incorporated in the present CFD model. The concentrations of gaseous and solid species, temperatures of gas and solid, melting and molten fractions of solid, velocity of gas, and residence time of gas in each combustion zone can be calculated by this model."

Jan 1, 2004