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By W. T. Stuart

THE increased demand for iron ore has necessitated a re-examination of ore-bearing lands on which the presence of water previously has indicated hazardous and expensive operating conditions. In view of the importance of iron ore production to the national economy and defense, the Ground Water Branch of the U. S. Geological Survey, in cooperation with the state of Michigan, began a study of mine drainage in the Iron River district in 1945, and later extended the work to the Marquette district. The purpose of these studies was to define the principles involved in the movement of surface and ground water toward the mined areas, with the hope that the information obtained in the research would lead to the development of methods of water control and to a reduction in the total mining costs. Not only are the direct costs of drainage increasing, but also the indirect operational costs of working a wet mine are becoming a larger proportion of the total mining costs. For some wet mines the direct costs of pumping and drainage may range from 35 to 40Ø per ton of ore produced, but the indirect costs due to handling wet ore and controlling the water may be five to ten times this amount. The methods of study were formulated as the work progressed, and inasmuch as they were the first large-scale studies of their kind, they should serve as a guide for the solution of similar problems in other mining areas. The Iron River district was chosen for a pilot study because in this district the longest records of mine pumpage and water-level observations were available, including, as they do, the records for the Homer mine of the M. A. Hanna Co., where pumping from surface wells began in 1930. The results of the first investigation by the Michigan Department of Conservation have already appeared." The first section of the report on a similar study of the Marquette district, which was started in 1948, will be published this year. Methods of Study In an effort to reduce the flow of water into the mine workings in the Iron River district, about 4500 gpm was pumped from the bedrock being mined and about 9000 gpm from the glacial overburden. In the Marquette district in the vicinity of Ishpeming and Negaunee, about 5000 gprn was pumped from the bedrock and about 4000 gpm was pumped from the glacial overburden. Where the water was pumped only from the bedrock, the rate of pumping ranged from a few hundred gallons per minute in the dry mines to many hundred gallons per minute in the wet mines. In each district, pumping from the overburden was localized on a few properties where costly pumping installations had been made and the expenditures for power had been large. In each district a comprehensive ground-water investigation was made of the whole area, involving the collection and interpretation of all the available data bearing on the source and quantity of water to be controlled. Although it is not the purpose of this paper to discuss the methods of making a ground-water investigation, it should be pointed out that a drainage study follows a pattern of engineering analysis that determines the occurrence, source, movement, disposal, and quantities of water involved. The investigation in the iron-mining districts of Michigan began with the construction of a map of the buried bedrock topography. Because the ground-water reservoirs occupy the low points in the bedrock basins, this map gives information concerning their areal extent, depth, shape, and degree of interconnection. The depth to water in the drillholes and wells indicates the altitude to which the ground-water reservoirs are filled, and the logs of the material penetrated in the drillholes and wells indicate the general character of the materials filling the reservoir. The slope of the ground-water surface indicates the direction of flow through the reservoir, the water movement being from the points of higher altitude to points of lower altitude. By analysis of the rise and fall of the ground-water levels in response to additions of water through recharge and to changes in the rate of discharge through pumped wells, estimates of the total quantity of water in storage and of the rate of flow through the reservoir

Jan 1, 1952

By E. R. Borcherdt

METHODS and equipment are subject to study in the Butte district at all times in order that advantage may be taken of any new developments that might serve to increase efficiency and lower costs. Detailed time studies of each operation involved in the entire mining process have been of invaluable assistance in analyzing the individual operation for possible improvement. In other words, the fact that a practice has been in vogue for many years does not exempt it from change provided an easier and cheaper method can be found. EXPLORATION Ore occurs in the Butte district in such manner that structures must be drifted on, no matter how small or unimportant they appear when intersected by a crosscut. Parallel structures also add to the crosscut requirements. This prospecting work, which formerly was done entirely by drifting and crosscutting, is now being supplemented by diamond drilling, to aid in greatly decreasing the amount of waste. In long-shot prospecting, or in second or third class prospecting, where the chances of developing commercial ore are not very great, diamond drilling is of particular value. In prospecting where chances of encountering commercial ore are certain or where crosscuts can be used later for haulage or ventilation, drilling obviously is not applicable. Improvement in drilling machines and bits has contributed greatly to the present success of diamond drilling. STOPING For many years square-set filled sloping was the principal mining method used in the Butte district. Later timbered and untimbered rill stopes were used, also some horizontal cut-and-fill sloping where both ore and walls were particularly strong. Because of the amount of timber required for square-set stoping, and the relatively low production per scope unit, experiments with horizontal cut-and-fill scopes were begun in ore bodies of which many had fairly weak walls. It was felt that increase in the speed of the stoping operation, followed closely by filling, to avoid weight being produced by permitting ore and walls to remain insufficiently supported over comparatively long periods, would maintain the walls and backs in safe condition without the use of timber and without ore dilution from wall slough. Cycles of drilling, scraping ore, and filling were devised, which have materially increased stope production and decreased timber consumption, so that both stope labor and supply costs were lowered appreciably without materially affecting grade control. In the larger mines of the district, where wide veins favor this stoping method, half of the total production is now being mined by horizontal cut-and-fill stopes (Fig. I). The increase of the filling rate demanded by the increased stoping rate was the greatest obstacle encountered in the accelerated stoping operations. Finally this problem was solved by replacing the time-honored method of transferring filling waste by small cars, which were hoisted or lowered in the auxiliary shaft, by a transfer

Jan 1, 1941

By J. E. Owen

A model of a porous body is presented in which the pore space consists of a system of voids and interconnecting tubes. Relationships between porosity and resistivity formation factor are determined partly by calculation, partly by experiment. Con triction effects characteristic of the model are shown to be sufficient to account for high formation factors. It is shown that constriction may be combined with moderate amounts of tortuosity to give model pore systems exhibiting to a first approximation porosity and resistivity properties similiar to those of natural porous bodies. INTRODUCTION The relationship between the electric resistivity of a fluid-filled porous body and the geometry of its pore space is so complex that the calculation of the resistivity of a natural porous rock is a practical impossibility. Both the resistivity of a body and its porosity are measurable quantities, however, and previous successes at relating them have been reached by an empirical approach. Efforts at obtaining theoretically derived formulae relating them have generally been unsatisfactory. One of the reasons for this may lie in the pore geometry that has been assumed. THE TORTUOSITY CONCEPT A Parameter called the formation factor is useful in dis-cussing the resistivity of a fluid-filled porous body. This parameter is the ratio of the resistivity of a fluid saturated porous body to the resistivity of the saturating fluid. Formation factors are often available from measurements on cores or from electric logs, and many attempts have been made to correlate formation factors and porosities of geological formations. Whenever a successful correlation is found, the engineer working with electrical logs has a useful tool for the determination of porsities of pay section?. One of the more successful formulae applicable to these correlations is the familiar equation empirically obtained by Archie.' which F is the formation factor. $ is the porosity, and rn is an exponent called the cementation factor. When the for- mula applies, the cementation factor usually is found to be between 1.3 and 2.2. The values for formation factors experimentally obtained are often higher than simple pore geometry would lead one to expect. In an effort to account for such high values certain formulae have been derived based on a so-called "tortuosity concept." In deriving these formulae a synthetic porous body is usually assumed in which the solid material is an electrical non-conductor. and in which the pore system consists of three sets of fluid-filled tubes of uniform diameter connecting opposite faces of the body which, for convenience, is considered to be cubical in shape. The three sets of tubes account for the whole of the effective porosity of the body, and usually, it is specified that they do not interconnect. By considering that the pore tubes are not straight but tortuous, their resistance to the flow of electric currents can be made as high as needed to explain high formation factors. Such an explanation has some basis in fact, but it appears that the tortuosity concept is often incorrectly applied when other factors are largely responsible for observed high resistivities. Recently, Wyllie and Spangler have recognized that tortuosity as calculated by conventional formulae has little if any physical significance.' RESISTIVITY AND THE CONSTRICTION CONCEPT Any explanation of high formation factors which depends solely on tortuosity of uniform pore paths necessarily ignores the effect that variations in the cross-sectional area of the conducting paths have on the resistivity of a body. Although, as previously pointed out, the calculation of such paths for an actual body is impossible, it will he shown that a synthetic pore network can be devised which will yield to analysis, and lead to results in agreement with the experimental data represented by Equation (1). The porous body to be considered is assumed to be homogeneous and isotropic or, for present purposes, identical in its characteristics in the three directions parallel to its coordinate axes. It will he assumed to be built of identical unit cubes, each of which contains a single pore network connecting all faces of the unit cube. A unit of such a pore network is shown

Jan 1, 1952

By Orville R. Lyons

THE relative performance of coal washing equipment, or the effectiveness with which any type or make of equipment removes impurities from coal, has been most difficult to evaluate in the past. The most widely used yardstick is the Frazer and Yancey efficiency formula developed in 1922,1 but Yancey in a later article states that "washers treating coals of different density composition or operating at different densities of separation cannot be compared directly on the basis of this criterion."' Prior to and since 1922, a variety of other methods has been used for comparison purposes, including the distribution curve, the error area, and the "ecart probable" or probable error. Yancey and Geer in discussing these methods conclude, "Performance can be evaluated in a number of different ways, with the choice of the proper method to use being dictated by the objectives of the investigation and the data available."' It is true that performance can be evaluated in a variety of ways, but if the equipment is to be evaluated on an effectiveness basis, there should be only one universal comparison method. Varying methods have been used because one universal comparison method has not been found or developed. In the article previously quoted, Yancey and Geer state in clear terms the primary concept for a universal comparison method: "One of the simplest, and certainly one of the most obvious evaluations of washery performance is the quantity of sink material in the washed coal and the float material in the refuse. If the washery products are tested at the density at which the washing unit is operated, the sink in the washed coal and the float in the refuse represent material that has been misplaced." The quantity of misplaced material was used as a criterion of washery performance by Lincoln in 1913,8 by the United States Bureau of Mines in 1938,4 by Hancock in 1947,3 and by the national French research agency Cerchar in recent years.2 In 1950 Anderson' proposed the use of this criterion as an efficiency value to replace the Frazer and Yancey formula. However, none of the above-mentioned investigators used the misplaced material concept in a manner that would provide universal coal-cleaning equipment comparisons. The Correlation Theory The ideal coal cleaning process would treat all sizes and would make a perfect separation at any given specific gravity. All material lower in density than the desired value would report in the coal product and all material higher in density would report in the refuse product. Unfortunately, no known cleaning process achieves this goal and there seems little likelihood that any process yet to be invented will do more than approach it. When coal is treated in volume under operating conditions, it is impossible to avoid mechanical entrapment, fluctuations in throughput and effective gravity of separation, and the creation of turbulent currents, even when a true heavy-liquid bath is used and the feed is closely sized and contains little intermediate gravity material. This being so, it is possible to appreciate the difficulties inherent in trying to obtain a perfect separation when treating a wide range of sizes and a feed containing high percentages of intermediate material, using turbulent currents to help create the effective separation gravity, under operating conditions which normally tend to be on the overload side. When coal is separated from refuse in any coal cleaning equipment, some refuse always reports to the coal and some coal to the refuse; the writer therefore assumed that there should be a relationship between the total amount of misplaced material produced by any given piece of equipment and the difficulty of separation as represented by the percentage of near gravity material in the feed. With small amounts of near gravity or ±0.1 material in the feed there should be less misplacement of material than would occur with large amounts of near

Jan 1, 1952

IN A broad sense, the subject of slag control includes not only the adjustment of the composition of the slag but also of its relative weight in terms of percentage of the metal-bath weight. The slag is made up essentially of (1) oxides formed by oxidation of silicon, manganese, phosphorus, and iron in the charge, (2) SiO2, MnO, and other oxides charged as such, and (3) lime charged or fed to the heat to neutralize the “acidic”: oxides present (Si02 and P2O5). Obviously, if practically perfect control were possible over the composition of the charge as well as over the oxidation process during the melting period, both slag weight and composition would be very nearly predetermined, and the control problem would be solved. Unfortunately, we have only a somewhat. imperfect control over these factors, so that beginning at about the lime-boil period in the heat, and later in the early refining period, it becomes necessary for the first helper, as the heat progresses, to make quick estimates of the composition and physical state of development of the slag (as well as of the amounts of phosphorus, sulphur, and carbon in the metal) from which he can judge how much extra lime, roll scale, fluorspar, and other additions will be needed not only to give the desired final slag composition, but also to hasten the complete fusion or shaping to a desired viscosity in the liquid state. The discussion in this chapter is limited essentially to those more or less practical rapid methods of slag estimation that have been used, or at least tried, for these purposes under actual open-hearth shop conditions. Another aspect of importance here is the extent to which the freedom of choice to the operator is limited by available charge materials, product specifications, and the oxidation and other chemical- reaction effects which inevitably occur under the conditions of this furnace process. For a better understanding of these control limitations and of the chemical and physical background of the subject, the reader is urged to read at least part of the discussion in Chapters XVII and XIX. Charge materials are discussed in Chapter IV, and many of the details of charging, melting, and refining practice closely related to slag control are given in Chapters VI and VII.

Jan 1, 1944

By E. Martinez, M. L. Hollander

Sulfurization of copper oxides was investigated using differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). When mixtures of cuprous oxide and sulfur were heated, the surface of the cuprous oxide was converted to cupric sulfide at the melting point of sulfur (119°C); additional sulfuriza-tion took place when the sulfur vaporized above 200°C. Cupric oxide also reacted with sulfur to form cupric sulfide but the starting temperature was approximtely 225°C. When the cupric oxide and sulfur were physically separated, sulfurization still occurred indicating a reaction with the vapor phase of sulfur. Sulfurization was obtained in runs with cuprite, chrysocolla and basic copper carbonate. Further decomposition of cupric to cuprous sulfide was noted at somewhat higher temperatures. The DTA-TGA data made it possible to set up postulated reactions in each system. These techniques were found to be well suited for studies of this type. Because of the difficulty encountered in flotation of many metallic oxide minerals, efforts have been made to find suitable reagent combinations to sulfi-dize these minerals in the flotation circuit. Recently Bautista and Sollenberger,1 using a different approach, showed that the surfaces of many oxide minerals can be converted to sulfides by heating them with sulfur to temperatures between 150° and 225°C. This technique was effective even with chrysocolla, a mineral which is very difficult to sulfidize. The primary objective of the present study was to obtain information on the reactions between the oxide minerals and suIfur. A better understanding of the mechanisms involved might prove useful in pointing the way to improvements in the process. A secondary objective was to demonstrate the value of thermo-analysis in investigations of this type. Bollin and Kerr2 have reported the use of a modification of differential thermal analysis to study the thermal reactions which occur on heating elemental constituents in a closed system to synthesize copper sulfides and iron sulfides. Differential thermal analysis (DTA) was used to detect enthalpic changes as mixtures of minerals and sulfur were heated. The DTA indicated the temperatures at which reactions started and whether they were exothermic or endothermic. Weight change data were obtained by thermal gravimetric analysis (TGA). These data could often be used to support postulated reactions and to eliminate consideration of other possible reactions. EQUlPMENT Differential thermal analysis (DTA) involves measuring the temperature difference between the sample being tested and a thermally inert reference, generally aluminum oxide, as both are heated at a uniform rate. Series connected thermocouples in the sample and reference are used to detect the temperature differences that occur as the sample undergoes enthalpic changes.3 Crystalline transitions, fusions, vaporizations, dehydrations, decompositions and many solid state reactions can be detected. A DTA unit manufactured by the Robert L. Stone Co., Austin, Tex., was used in this investigation with a temperature rate increase of 10°C per min. The samples and reference were placed in Inconel cups with wells in the bottom into which the differential thermocouples fit, and run in a nitrogen atmosphere. Thermal gravimetric analysis (TGA) measures the changes in weight that a sample undergoes as it is heated. A Chevenard thermobalance converted electronically for graphic recording was used with a heating rate of 5°C per minute. An X-Y recorder plotted temperature on the X axis and weight changes on the Y axis. A flow of 250 ml per min of nitrogen was streamed through the furnace. Samples were placed in a porcelain crucible open at the top, unless otherwise noted. EXPERIMENTAL RESULTS Sulfur: Two sulfur samples from different sources were tested. The DTA of a high purity sulfur and a reagent grade sublimed sulfur are shown in Fig. 1. Nearly all the tests were run with the sublimed sulfur due to the difficulty in grinding and high electrostatic charge encountered with the high purity sample. Sulfur undergoes three endothermal reactions below 200°C. The first is a solid-solid crystalline transi-

Jan 1, 1964

By L. J. Erck, T. E. Ban

A discussion of laboratory procedures used to determine pellet quality and to simulate handling and firing conditions. Strength-temperature relationships in pelletizing; effect of chemical additives on agglomeration; and crushing, abrasion, and impact resistance of the pelletized products are discussed with respect to five different iron ore concentrates. IN most routine experimental work on products and processes, method:; of operation and product evaluation are established from accurately controlled laboratory tests. With particular emphasis on the pelletization of fine iron ore concentrates, standardized procedures of laboratory production and product testing have been established at Cleveland-Cliffs Iron Co. Research Laboratory at Ishpeming, Mich. A program of this nature was used for investigating the agglomeration characteristics of various iron ore concentrates. The factors which control the process were studied and subsequently controlled for these investigations. Pelletizing as applied to iron ore agglomeration involves the preparation of spheroidal masses from a fine moist concentrate, followed by high-tempera-ture firing to produce a final product. The preparation of moist spherorids is generally designated as balling. This produces the so-called green pellets or balls. After, these have been fired they are called pellets. Balling is accomplished by rolling moist concentrates in a revolving drum until small spheroids form by a snow-balling action. These balls are then heated in a shaft furnace, or a modification of this device, to a temperature high enough to cause agglomeration within the individual balls while they descend countercurrent to hot oxidizing gases. By this process the lour strength balls are converted through various chemical and physical-chemical processes into hard pellets. With correct balling and firing, the pellets are strong, resist abrasive action and handling treatments, and provide a suitable blast furnace and open hearth feed. In 1950 Tigerschiold and Ilmoni developed a working hypothesis to explain the formation and stability of green pellets.' Their work was presented on the basis of geologists' discoveries concerning the soil-water system and C. V. Firth's early postulates of green pellet formation.' Fundamental reactions oc-curing within fired pellets have been described by Cooke and Ban, who showed the microstructure changes caused by different firing temperatures." All these investigators have provided scientific clarifications of agglomeration by the pelletizing process and have opened avenues for greater development. Mineral grain growth and ceramic bond formation are the two basic phenomena imparting coherency to particles within a fired pellet of iron ore. Each of these is established by the transfer of thermal energy to the mineral particles. Grain growth mechanisms are chiefly physical reactions wherein smaller particles consolidate into larger ones, with resulting decrease in surface energy conforming with the second law of thermodynamics. Ceramic bond formation is a chemical reaction usually between basic and acid metallic oxides of the gangue and ore minerals. CaO, MgO, A1203, and FeO of Fe3O4, react in varying proportions with SiO, or Fe2O3, to form a great series of compounds or amorphous solid solutions. These product bond iron mineral particles together by a bridging action or by direct reaction with the surfaces of the particles. The result of the grain growth-ceramic bond formations is a consolidated, coherent compact of gangue and iron minerals formerly held together by much weaker bonds of interstitial water and forces common to dry, unconsolidated particles.4 With respect to iron ore agglomeration, these high temperature bonding reactions have been described by Schwartz, who referred to the bonds in sinters," and by Cooke and Ban, who referred to the bonds in fired pellets." The extent of the bonding phenomena and the consequent strength of fired pellets is governed by

Jan 1, 1954

By J. P. Morris

PREVIOUS investigations1,2 have shown that alloying elements in liquid iron influence the thermodynamic activity of sulphur and thereby affect the partition of sulphur between metal and slag in the desulphurization process. For example, the greater efficiency of desulphurization in the blast furnace as compared to the open hearth can be attributed in part to a higher level of sulphur activity in blast-furnace metal due to the higher concentration of carbon and silicon. In the present investigation, a short study was made of the influence of manganese on the activity of sulphur in liquid iron and iron-carbon alloys. In contrast to carbon and silicon, manganese was found to decrease the activity coefficient of sulphur; and in iron-carbon alloys it counteracts to some extent the influence of carbon. However, at manganese concentrations normally present in the blast furnace or open hearth, the effect of manganese is small. Since manganese sulphide has a limited solubility in iron, manganese can act, under certain conditions as a desulphurizing agent. Considerable data on the manganese-sulphur product in carbon-saturated melts were obtained in the investigation and have been included in this report. The experimental procedure was the same as that used in the earlier investigations on the effect of silicon' and carbon' on sulphur activity. Briefly, the method was as follows: The molten alloy, contained in a graphite or sintered alumina crucible, was brought to equilibrium at a constant temperature with a mixture of hydrogen and hydrogen sulphide of constant composition by bubbling the gas through the metal. Samples of' the melt were taken for analysis at regular intervals by suction through a 2 to 3 mm bore silica tube dipped into the metal. The experiments were run in a graphite spiral resistance furnace with melts weighing 50 to 60 g. The gas bubbling tubes were made of sintered alumina and were 5/16 in. OD, 1/16 in. ID, and 24 in. long. Equilibrium was assumed to have been attained when the sulphur content of the liquid metal reached a constant value. During an experiment there was a rapid loss of manganese from the melt by volatilization. To offset this loss, small additions of manganese were made periodically. The rate of manganese addition needed to maintain a constant manganese concentration was determined in preliminary tests. In all of the experiments, deposits of manganese sulphide formed above the melts in a cooler region of the furnace. Apparently, these deposits resulted from a reaction between manganese vapor and hydrogen sulphide in the gas. To prove that manganese sulphide did not volatilize from the melts to a measurable extent, an experiment was run in which helium was bubbled through liquid iron containing both manganese and sulphur. Although manganese volatilized rapidly in this test, there was no appreciable loss of sulphur. Volatilization of manganese sulphide from a melt would have led to an apparent equilibrium condition in which the sulphur content of the metal was lower than the true equilibrium value. The experimental results are shown in the first seven columns of Table I. The data in the last two columns were obtained from the previous work on the effect of carbon' and show what the results would have been in the absence of manganese but with temperature, gas composition, and carbon content of the metal remaining the same. Comparison of the last four columns show that, in the presence of manganese, the sulphur content of the metal increased at equilibrium and the activity coefficient of sulphur decreased. However, the results show that, for manganese concentrations below 3 pct, the effect of manganese is small. The values for activity coefficient of sulphur given in Table I were calculated from the following relations: S (in liquid metal) + H2 (gas) = H2S (gas) [l] K ph2s/?s X %S X phg = 0.00251 [2] where K is the equilibrium constant for the reaction, PH2S and ph2 are the partial pressures of hydrogen sulphide and hydrogen, respectively, and ?s is the activity coefficient of sulphur. The standard state for sulphur was taken to be a 1 pct solution of sulphur in pure iron. The numerical value for K at 1600°C was determined in the earlier work. For the purpose of showing graphically the results of the tests run at 1600°C, the activity coefficients of sulphur were recalculated so as to correspond to a manganese concentration in the metal of 2 pct in each case. In the calculation it was assumed that the increase in sulphur content of the metal at equilibrium caused by the presence of manganese

Jan 1, 1953

By J. G. Kura, P. D. Frost, L. W. Eastwood

THE preparation and general properties of mag-nesium-lithium base alloys have been described in earlier papers.l,2 Lithium forms solid solutions with pure magnesium, lowers its density, and improves its formability. The improved isotropy and better formability of these alloys are attributed to the ability of lithium to convert the magnesium lattice from hexagonal (alpha phase) to body-centered-cubic (beta phase) structure. This change in structure is, however, accompanied by some limitations which make it difficult, if not impossible, to combine all the desirable properties in one composition. The most important of these limitations is the tendency of the high-strength alloys to overage and lose strength at temperatures of the order of 150" to 200°F. A study was made of the effects of composition and heat treatment on the age-hardening character- istics of the alloys. Stability of properties was determined by hardness and tensile testing of the alloys at room temperature after various periods of exposure to elevated temperatures. Precipitation-hardening curves are shown for a number of magnesium-lithium-zinc alloys in fig. 1. All the alloys were solution treated at 700°F and aged at 200°F. The reason for using the drastic quench, toluene at —105°F, was to reduce the rapid precipitation of the hardening phase which takes place at room temperature. Previous experience has shown that a hardness of about 90 to 95 Rockwell E is indicative of yield strengths in the range of 35,000 to 40,000 psi. This is a desirable strength level for magnesium-lithium base alloys with specific gravities of the order of 1.65 or less. Although the hardness level is raised by large zinc contents, a corresponding decrease in the cold formability of these alloys occurs with increasing zinc content. Thus, alloys containing up to about 10 pct Zn and having hardnesses of the order of 70 to 75 Rockwell E may be bent over a very small radius; however, the 16 pct Zn alloy requires a bend radius of more than 8T. The hardness relationships illustrated in fig. 1 can be explained by the partial phase diagram shown in fig. 2. The zinc-free magnesium-lithium alloys are entirely body-centered cubic (100 pct beta phase) when the lithium content of the binary is 10.3 pct or higher. When zinc is added, the boundary between the beta and alpha-plus-beta fields at 700°F is shifted to lower lithium contents. In addition, the solubility of zinc at 700°F decreases with decreasing lithium content. It is shown by a study of micro-structures that the limit of solid solubility of zinc in the 6Mg/Li* matrix at 700°F is about 19 pct. It is believed from a study of the aging curves that this limit is about 2 to 3 pct at 200°F. Zinc additions up to about 2 pct increase the hardness and strength of the magnesium-lithium base solid solution. Larger additions of zinc effect further hardness increases, but precipitate during prolonged aging at 200°F. Alloys having 14 to 20 pct Zn precipitation harden extremely rapidly during quenching, even when quenched in toluene at —105° F. The high-zinc alloys overage at 200°F but are capable of maintaining reasonably high hardnesses for periods up to 1000 hr.

Jan 1, 1951

By D. W. Mitchell

While pure magnesium does not corrode rapidly the presence of even very small quantities of certain other metals accelerates corrosion remarkably. Because magnesium is such an electropositive metal (E° = +2.34 volts)' the presence of substances that permit galvanic activity is extremely undesirable. It is stated that as little as 0.017 pct of iron in magnesium causes a marked increase in the corrosion rate.2 Magnesium and its alloys are commonly melted in iron or steel pots; consequently the commercial metal has the opportunity to pick up iron if it has that tendency. Quantitative data on the solubility of iron in magnesium are of practical as well as of academic interest. Some magnesium alloy castings tend to have large grain size unless suitable treatment is given to the liquid metal just prior to casting. One method of grain refinement consists of "superheating" the metal just prior to casting. "Superhcating" is heating to a temperature 100 to 200°C above the casting temperature and holding for a short period of time. Superheated metal has a much finer grain than unsuperheated metal. A satisfactory explanation of this phenomenon has not been forthcoming. One hypothesis attributes the grain refinement in the superheated metal to precipitation of some phase that is mis-cible at the temperature of superheat but not miscible just below the casting temperature and which is thought to provide nucleating centers for crystallization. This phase, if the foregoing hypothesis is correct, would probably be a metal or an intermetal-lic compound. Of the metals likely to be found in magnesium alloys, iron is one of the most likely candidates for the role of grain refiner for iron occurs in small quantities in all commercial magnesium and magnesium alloys. A. Beck³ states that magnesium, in either the liquid or the solid state, cannot dissolve iron and that iron exists as a finely divided suspension which does not settle out because of its extreme fineness. Beck also presents a micrograph showing a large iron dendrite in magnesium but does not comment on the crystallization of iron from a solution supposed to contain none. It is doubtful that dendrite formation from suspended iron -would be possible. This suspension theory is the basis of patents4 covering the removal of iron from magnesium by allowing the iron particles to act as nuclei for the formation of primary magnesium crystals which can be separated by segregation. Also covered by patents is the removal of iron by the addition of another metal to form an intermetallic compound with the iron which, because of its increased particle size, is able to settle out of the molten metal. Here, too, quantitative information on the extent of iron solubility in liquid magnesium is of more than theoretical interest. M. Hansen,5 in his critical collection of the data on binary alloys, states that iron is not soluble in liquid magnesium. W. R. D. Jones% ho studied the physical properties of low iron magnesium alloys observed a 57°

Jan 1, 1949

By E. S. Grumell

The correct sampling of coal and coke is becoming important to an ever increasing number of producers and consumers. This, therefore, may be an opportune moment to examine where we stand with regard to existing and proposed methods. In this paper an attempt will be made to review, as briefly as possible, some of the considerable amount of painstaking research which has been done in the last 10 years, and which has unquestionably led to a much better understanding of the subject. In so doing we shall try, on the one hand, to make clear where substantial progress has been made, and on the other hand, to draw attention to points that require further investigation. The paper is divided into sections in order to emphasize the major divisions of the subject; further, in order to retain this emphasis, detailed consideration of some of the points has been relegated to appendixes. No attempt has been made to give a complete survey of the literature, as this has already been done by L. A. Bushell.2 The following abbreviations will be used: A.E., average error; P.E., probable error; S.W.R., size-weight ratio; B.S.I., British Standards Institution. Section 1.—Cost It has often been stated that the cost of sampling should bear some relationship to the value of the product, and since coal is a relatively cheap raw material it would be a major error to specify, for ordinary commercial purposes, elaborate and costly methods of sampling which nobody would adopt. Specifications must be of such a nature that they will be used. We believe that one of the achievements of the last 10 years has been to reduce the cost of sampling. There is, however, another point to be considered; via., that the cost of sampling should bear some relationship to the value of the investigation. Correct sampling is a cog (possibly a small one) in the wheel

Jan 1, 1940

By T. Rosenqvist

From the chemical, metallurgical, and mineralogical points of view, the importance of thermodynamic data for metal-sulphides and sulphur dissolved in molten metal has long been realized. Such data will give a basis for thermo-dynamic calculations of processes such as roasting and the distribution of sulphur between molten metal and slags. Furthermore, it will help us understand the chemical forces which tie sulphur to the metal and to the melt. Thermodynamic studies of solid sulphides and the equilibria between solid sulphides and metals have been carried out in a rather large number of cases by several investigators. An excellent review of this work is given by Kelley.1 On the other hand, very little is known about the thermodynamic properties of molten sulphides and of sulphur dissolved in molten metal. The only system which previously has been investigated in this respect is the iron/sulphur system. The purpose of the present investigation was primarily to obtain further data for metalisulphur melts and the system silver/sulphur was chosen, not because this system was expected to be of special interest in itself, but because the silver/sulphur system is a typical example of a metal/sulphur system. Because of the low melting temperatures, the work could be carried out without appreciable furnace and refractory difficulties. The sulphur in this system possesses a rather high escaping tendency compared to most other metal/sulphur systems. By the method employed (reaction with hydrogen to form hydrogen sulphide) this gives ratios Ph2s/Ph2 up to 0.30, which may be determined accurately. 'rhermodynamic investigations of the heterogeneous reaction Ag2S +H2 —+ 2Ag + H2S have previously been carried out by Pelabon,2 Keyes and Felsing,3 Jellineb and Zakowski,4 Wat-anabe,6 and Britzke and Kapustinsky.6 Their results are in rather poor agreement. Experimental Part PRINCIPLE In the present invehgation the escaping tendency of sulphur from the condensed phase was determined by the reaction: S + H2 = H2S The ratio Ph2s/Ph2 is at constant temperature, directly proportional to the escaping tendency of sulphur and to its chemical activity in the condensed phase. (This ratio will subsequently be denoted by H2S/H2.) From this ratio and its variation with temperature and with change in the com- position of the condensed phase, thermodyrlamic quantities such as free energy and heat of reaction can be derived. The apparatus used is shown in Fig 1. The silver/sulphur alloy was placed in a crucible inside a refractory tube and mounted inside the furnace to the left. The tube was a part of a closed, gas-tight system in which the gas mixture could circulate until equilibrium was established. Circulation was maintained by the glass propeller to the right, driven by an external magnet, and promoted by the chimney action of the furnace. The gas passed up through the furnace, down into the crucible where it came in contact with the alloy, passed rapidly up through a narrow tube and out of the hot zone. After equilibrium was established between the gas and the condensed phase, the composition of the gas mixture was determined from its density. In its circulation, the gas mixture passed through a chamber (lower right on Fig 1) containing a buoyancy-balance, where the density of the gas was determined by magnetic balancing. From the measured density,

Jan 1, 1950

By C. B. Alcock, R. A. Oriani

Some simple models of solutions are described; these include the regular solution, the subregular solution, and the quasichemical model. The assunzption underlying these models, the physical signzficance thereof, and the experimental manifestations are discussed. Examples are presented from the fields of liquid and solid metallic solutions, liquid slags, mattes, liquid and solid ionic solutions, and mixed carbides to show under what conditions and for which systems these solution models are fair descriptions. The deviations of real solutions from the models are of theoretical interest. Some such deviations, both for dilute and for concentrated solutions, arc pointed out and their Physical sigtzzficance discussed. DURING the past half century there has been a gradual accumulation of thermodynamic data for systems of interest to the metallurgist. There remain many gaps in the data, however, and the metallurgist must often face the problem of estimation of thermodynamic quantities where measured values do not exist. One might hope that the experimental progress would be matched by theoretical advances which would make such estimations possible with a high degree of confidence. However, theoretical progress has been disappointingly slow even for the simplest kinds of solutions, and since the multicomponent systems in which the metallurgist is interested are very complex, one cannot expect theory to be of much help to the metallurgist. In this situation, therefore, it seems worthwhile to examine some simple models of solutions from two points of view: firstly, to see if such crude models represent the thermodynamic facts in as many types of solutions as possible sufficiently well for the needs of the metallurgist, and secondly to see what the deviations from such models show to be important for consideration by theorists. BOND ENERGY MODELS OF SOLUTIONS The simple models that we will examine from these points of view may be termed statistical models, in that they are concerned with the thermodynamic consequences of some simple assumptions about the energy of an assembly of atoms, molecules, or ions, and do not inquire into the physical basis of the interaction. The underlying assumption of these models is that the energy of an assembly of molecules (by which we include also atoms or ions) is given by the sum over all interaction energies of molecules taken two at a time; we will discuss only those models in which the pairwise interactions are restricted to those between nearest neighbors. Thus, in a pure substance of bond energy EAA, the internal energy (with respect to some specific reference state) will be expressed as NAA EAA where NAA is the number of nearest-neighbor pairs. A solution of molecules A and B will be characterized by NAA EAA + NBB EBB + NAB EAB where the Eij represent the bond energies of the nearest-neighbor i-j pairs. If one assumes that the EAA and EBB are the same in the pure components as in the solution, and that the coordination numbers in the two pure substances and in the solution are the same, then the energy of the solution with respect to the pure components (i.e., the energy of solution) is a function of the following linear combination of the bond energies: EAB - 1/2(EAA +EBB) = w. The thermodynamically ideal solution is defined as one in which the activity of each component is equal to the mole fraction of that component at all concentrations and all temperatures. It follows that

Jan 1, 1962

By C. L. Pillar

INTRODUCTION The location, size, character of the ore de- posit and its adjacent formations will deter- mine the mining system best used for its ex- traction. The mining system chosen will have to be engineered to suit the ore deposit and the people that will extract it. What can be done in the Philippines cannot always be accomplished in the upper Northwest Territory of Canada. Mining operations developed under a free enterprise system are planned to achieve a satisfactory return on the capital required to place them into production. Hence, the choices made in planning and developing the mining system must be dictated by sound economics. The mining system planned must favor: 1. Maximum ore extraction of the deposit with minimal grade dilution. 2. The amount of capital expenditure used to develop and equip the mine must be in harmony with the financial policy of the group yet be sufficient to provide a reliable mining system. Excessive frills and extras that are not required for efficient, safe production should not be provided. 3. Mine production costs are determined by the amount of men, material, equipment and energy used in the production process. These must be kept to minimal limits in order to insure dependable, low cost production. Extras that later are needed in the production operation can be added as required by the operator. Basically block caving is a mining system that is normally used to extract deep seated, massive, low grade deposits of copper, molybdenum and iron where stripping ratios for open cast mining are economically prohibited. The caving system is limited in its selectivity. It is a mass production type of underground ore extraction that under favorable conditions is one of the most efficient, low cost mining systems in the world today. Usually block cave mining systems are large. They are capable of producing ore at a rate of 10,000 to 100,000 tons/day from large deposits at costs that are comparable with many open cast mining systems burdened by high waste to ore ratios. Block cave mining systems differ basically in the plan of the area layout, the method of undercutting and the method of draw. The balance of the mining system is the mechanical transportation of the drawn ore to the surface, the mine supply, drainage and ventilation systems. This paper deals mainly with the methods of draw. The method of draw to be used in a block caving system dictates the development plan of the mining area, is highly influential in the method of undercutting to be employed and the supply and ventilation system to be used. There are three basic methods of draw commonly used in today's operations. They are: Gravity draw Slusher draw LHD draw The type of draw planned will have a major affect on: Capital expenditure and time required to bring a deposit into production. Productivity, efficiency and cost of the production operation. Percent recovery of the ore deposit in both tonnage and grade. Degree of production reliability Fundamentally the type-of draw used must be compatible with the physical characteristics of the deposit to be extracted and the financial position of the mining operation. The type of draw chosen must work to advantage with the size, configuration, depth, strength and fracture pattern of the deposit and its adjacent formations. It must favor the financial protection of the planned mining operation. A Gravity Method of Draw requires a finely fragmented, easy flowing product from the caving action of the deposit. To obtain the desired economic advantage the ore deposit must also have sufficient area and height of column to permit minimal development cost on a per ton basis. The gravity system re- quires the maximum amount of development openings and uses the minimum amount of mechanized equipment of all the caving systems. It is unskilled, labor-intensive and is highly sensitive to size of ore fragmen-

Jan 1, 1981

By F. T. Selleck, H. H. Reamer, B. H. Sage

An experimental investigation was made of the effect of temperature upon the three-phase pressure associated with the propane-water and propene-water systems when hydrates were present. In addition, the characteristics of the propane-propene-water system were established over a limited range of ternperatureo under conditions such that hydrate was formed. The hydrate phase for this system may he a solid solution and the distribution of propane and propene in it is similar to that found in the coexisting hvdrocarhon liquid phase. INTRODUCTION A knowledge of the characteristics of hydrates of the hydrocarborrs encountered in industrial practice is of importance in connection with the design of process equipment. Villardl.1,2 carried out early studies of hydrates, and de Forcrand1 con-sidered the more probable compositions of the hydrates of hydrocarbons. Hammerschnid1 presented information about the propane-water and the isobutane-water systems. Scheffer5 studied the hydrate of hydrogen sulfide in detail, and de For-crand reported on the hydrates of krypton, argon, and xenon.1 Roberts and co-workers1,2 determined the nature of the hydrates formed in the methane-water and ethane-water systems. Carson and Katz10 studied the methane-propane-water, methane-pentane-water, and the methane-hexane-water systems in the four-phase region. The results of this rather extensive investigation indicated that the paraffinic hydrates formed solid solutions. The experimental evidence now available does not Support the existence of hydrates of the pentanes-antl-heavier hydrocarhons but it cannot be stated with certainty that such hydrates are not formed. Stackelherg. 11,12,13 made extensive studies of the crystal structure of paraffinic hydrate; by means of x-ray techniques and found that hydrates poses; a definite structure and composition. The existence of such a Structure does not preclude the firmation of Solid solutions of hydrates in aqueous systems containing two or more hydro-carbon~. Wilcox, Carson and Katz" reviewrd the information on the hydrates of importance in the processing of natural gas and presented data concerning their formation from natural gas. Kobayashi and Katz1' made studies at high pressure of the Hydrate of methane. and Unruh and Katz"' investigated hy-drates in mixtures of carbon rlioxide and methane. Frost and Deaton contributed to the knowledge of the composition of the paraffinic hydrates The irregularities in the experimental results were several times the expected uncertainties. This experience confirms the behavior encountered by other investigators indicating that hydrates tend to occlude water during their formation, thus rendering difficult the direct measoremeut of their composition. Miller and Strong2 investigated a number. of paraffinic hydrates from the standpoint of their possible application to (, the industrial storage of gas. Powel1 studied the effect of solutes upon the decomposition temperature of paraffin hydrates. Marked lowering of the decomposition temperature at a given pressure may he obtained by the use of such additive agents as ethylene glycol, urea. and sodium chloride. APPARATUS AND METHODS Two method* were here employed to study the behavior of hydrates. The first involved a glass capillary within which the hydrocarbons and water were confined over mercury. The second made use of a double-ended weighing bomb technique." The glass capillary equipment has been described elsewhere.'" A schematic drawing of it is presented in Fig. 1, where the arrangement of the agitator and mercury reservoir is shown in some detail. The lower part of the glass capillary, D, was enlarged to afford space within which the fluids used in the investigation could he stored at low pressures after their introduction through the valve. G. The temperature of the capillary was controlled by the circulation of a hydrocarbon oil of low viscosity from the agitated bath, B, through the vacuum jacketed column. C. The pump, A, was employed for the circulation of this oil. A relatively clear view of the capillary tube, D, was obtained through the vacuum jacket. Mercury was introduced into the lower part of the vessel, E, from

Jan 1, 1952

By Charles T. Baroch, Charles J. Baroch

Nuclear energy probably has greater potentialities for changing the world's way of life than any other recent discovery. The atomic-bomb bursts over Hiroshima and Nagasaki suddenly changed the concepts of war. Peaceful uses of nuclear energy are advancing so rapidly that no study of economic trends is complete without giving them consideration. The minerals specialist, especially, must be aware of this new force in our lives, as minerals and metals are essential in harnessing the new force, and atomic energy itself is rapidly improving its competitive position in the energy field. Future historians may chronicle December 2, 1942, as the beginning of the Atomic Age. On that day Enrico Fermi and his co-workers at the University of Chicago produced and controlled the first self-sustaining nuclear chain reaction. Lie many inventions, the first application of nuclear energy was as a weapon of war. However, its potential usefulness in man's work and welfare far outweighs in economic importance its destructive use in war, unless its military effect would be considered so great and all-embracing that no major power will hereafter chance a world conflict. Recognition of this potential has generated a vast international effort to exploit the atom for peaceful beneficent purposes. Like its physical manifestation, the advent of nuclear energy has unleashed chain reactions that have pervaded the political, social, and economic environments of the world. The impact of nuclear developments in one of many fields is exemplified by the uranium mining industry. Uranium was discovered in 1789 and in the next century and a half it found only an insignificant use as a ceramic coloring agent; in fact, in the latter part of that period, it was a largely unsalable by-product of the radium and vanadium industries. Up to 1940 the total quantity of uranium metal produced was not more than a few grams, of doubtful purity. Thus the production of 12,400 pounds of pure

Jan 1, 1964

By H. R. Crawford, P. B. Crawford, A. F. Tragesser

A method has been developed to calculate wellbore temperatures during mud circulation and the actual cementing operation to aid in the design of cement slurries. The method agrees within 10F with previously measured values. The calculation technique provides temperatures, as functions of time, at varying depths in both the casing and annulus. The technique also provides this information if a relatively cool cement slurry is pumped into the well immediately following circulation of hot mud. Circulating bottom hole temperatures of brine and a bentonite mud were measured. INTRODUCTION As wells are drilled deeper, greater demands are being made on all phases of the industry, and new technology has been developed to provide satisfactory well completions. However, little or no work has been conducted on accurately determining bottom-hole, static and circulating temperatures.. In designing a cement slurry, such factors as density, fluid loss control, viscosity, deterioration from ternperature, compressive strength and pumping time must be considered. Individual well conditions often make it necessary to include still other factors. Pumping time is a primary consideration and, as wells are drilled deeper, encountering higher bottom-hole temperatures, this property becomes even more important. Cement slurries must be designed with sufficient pumping time to provide safe placement in the well; however, the slurry cannot be overly retarded as this will prevent the development of satisfactory compressive strength. The pumping time of a specific cement is currently obtained by subjecting the cement to simulated conditions of temperature and pressure. A reasonably accurate bottom-hole pressure may be obtained by considering hydrostatic heads of fluids, friction pressure and wellhead pressures. However, accurately determining bottom-hole temperatures is much more difficult. Bottom-hole static temperatures are estimated by considering several sources of information, including logging temperatures, published temperature gradient maps and field experience. This information is usually questionable due to disagreement of data from the various sources. Temperature gradient maps were constructed based on temperatures recorded many years ago while running bottom-hole pressure tests. These thermal gradients then represent an average of well conditions and cannot always apply to a specific well. Also, logging temperatures may be affected by the time since fluid was last circulated, rate of penetration, circulating rate and many other factors. Therefore, even though logging temperatures are available, the question still exists as to the correction factor that should be applied to obtain an accurate static temperature. After obtaining static bottom-hole temperature, it is then necessary to relate this to circulating temperatures actually encountered by the cement slurry. This is accomplished by selecting a test schedule from the API RP-10B corresponding to the estimated well conditions.' The API-recommended practice for testing oilwell cement provides testing schedules for various well depths and conditions. These schedules are intended to simulate down-hole conditions during cementing. They provide a rate at which both temperature and pressure are increased until the estimated circulating conditions are reached. These testing schedules represent circulating temperatures for an average well and, although there is flexibility in choosing the test schedule that most accurately simulates the temperature of an individual well, it still is not possible to consider all the well conditions that will affect the bottom-hole temperature. Many factors affect cement temperatures; for example, the length of time a well has remained static prior to running casing and cementing, the circulation time, the temperature of fluids used in cementing, fluid density and flow properties of fluids. The pumping time for a typical retarded cement could vary from 2 to 4 hours with a 10F change in testing temperature. Variations in pumping time are the most critical in highly retarded cements used in deep, hot wells; yet, predicting bottom-hole circulating temperatures is more difficult in these wells. This work was conducted to develop a means of calculating circulating temperatures as a function of well depth, casing and hole size, pumping rate and time, fluid and reservoir physical properties and thermal status of the well. PREVIOUS WORK In 1941 Farris reported on a study to develop information leading to a more practical laboratory evaluation of oilfield cementing mixtures and performance.' It was then recognized that the pressure factor was being neglected,

By M. T. Simnad, R. F. Mehl, L. Yang

Techniques for studying marker movement in K-Rb interdiffusion have been worked out. The results indicate that Rb diffuses faster than K and that the ring mechanism of diffusion cannot be the dominant one operating in this case or probably in cases involving other alkali metals, despite their low ion core repulsive energies. SEVERAL theoretical attempts have been made in the past decade to elucidate the mechanism of diffusion in body-centered-cubic metals. No general agreement, however, has been reached by different authors. Zener,1 and later LeClaire,2 on the basis of a correlation between the entropy of activation for self-diffusion and the temperature dependence of the elastic constants, predicted that a ring mechanism should operate in the diffusion of body-cen-tered-cubic metals. Paneth3 calculated the activation energies of various ring, vacancy, and interstitial mechanisms for the self-diffusion in alkali metals and concluded that the most likely one was based on the linear motion of "crowdions," which is in fact a different form of interstitial diffusion. Fumi,1 however, showed that the experimental values of the activation energies for self-diffusion in the alkali metals could be better accounted for if the diffusion process in these metals was assumed to follow a vacancy mechanism. The same conclusion was reached by Kojima5 for the self-diffusion in lithium. Experimental evidences published during the past few years seem to exclude the ring mechanism as the predominating one in the diffusion of body-centered-cubic metals. For instance, maker movement has been observed in ß-brass, first in this laboratory" and later by Resnick and Baluffi.5 Shewmon and Bechtoldh also found marker movement in the body-centered-cubic system Ti-Mo and showed that the argument which led Zener and LeClair to favor a ring mechanism was not incompatible with a vacancy mechanism. In spite of this, it seemed to the authors that further experimental tests should be made by studying the Kirkendall effect in body-centered-cubic systems that characteristically have small ion core repulsion, such as the alkali-metal systems. Since the ion core repulsion term constitutes the main part of the activation energy needed for the rotation of a ring, such a test should be the most critical of all. The system K-Rb was chosen for experimental study because these metals form a continuous series of solid solutions. Experimental Investigation Owing to the extremely active nature of these two metals, a brass dry box (18 x 11 x 10 in.) was built for making the diffusion couple. It had a big lucite window on top, two side ports through which neo-prene-rubber gloves were inserted, and another side port covered with an optically flat-glass window for microscopic examination of the sample. Inside the box there were a circulating fan driven with a rotating horse-shoe magnet located outside the box, a heater used to generate potassium vapor for getter-ing the box, and a cold trap for keeping the inside of the box cool. Chemically pure grade K and Rb were triple distilled before they were transferred in vacuum into cylindrical steel molds kept in pyrex-glass ampules, Fig. 1. The latter together with the tools needed for making the diffusion couple were put into the dry box. After the box was flushed with purified argon and gettered with potassium vapor, generated from a heated steel crucible inside the box, the glass ampules were broken and the mound on the top of the alkali-metal ingot was cut off with a razor blade to yield a flat surface. To make the diffusion couple, one K ingot and one Rb ingot were pushed out of the molds together with their steel supports by screwing a metal plunger into the bottom of each mold. They were then laid on a brass cradle inside the assembling carriage (shown separately in Fig. 2) with the flat faces opposite to each

Jan 1, 1959

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

By H. D. Keiser

Minor industrial minerals included in this chapter are: the alum minerals, bromine, calcium chloride, epsomite and other natural magnesium salts, iodine, meerschaum, quartz, industrial crystals other than quartz, and nonfuel gases (air, helium, carbon dioxide). Alum Minerals The natural alums comprise a group of hydrated double sulfates, the most important of which are potash alum, KAI(S04)2.12H20, the "alum" of popular usage; ammonium alum, (NH4)AI(SO4)2, known mineralogically as tschermigite; and soda alum, NaAI(SO4)2.12H20. Kalinite, KAI(SO4)2.11H20, and mendozite, NaAl(SO4)2, 11H20, are fibrous monoclinic alums, distinct from the isometric species potash alum and soda alum.4 Alunite, KAI3(S04)2(OH)6, also known as alumstone or alum rock, has been used as a raw material in the manufacture of alum since early times. All the natural alums are highly soluble and occur as surface evaporation products in arid regions or in sheltered places. Potash alum, together with the other natural alums, commonly occurs as an efflorescence or crevice filling in argillaceous rocks and brown coals that contain disseminated pyrite or marcasite. The mineral is derived by the action of sulfuric acid, formed during the weathering of the sulfide, upon alkali-rich aluminum silicates. Ammonia alum is found chiefly in lignite or broad-coal beds and bituminous shales. Alunite is most commonly associated with acid volcanic rocks, where the rock has been largely altered and alunite formed owing to the presence of sulfuric acid solutions or vapors. Aluminum sulfate, which for most uses is the essential ingredient of alum, may be found in saline residues resulting from the evaporation of natural water and may be formed by the action of acid waters upon aluminous rocks. A deposit of natural potash alum occurs in an irregular network of veins associated with sulfur in rhyolite in Esmeralda County, Nevada, about 35 miles west of Tonopah and 10 miles north of Silver Peak. Alum was recovered at a plant operated on the property between 1920 and 1923 by crushing the ore to ¾ in., grinding to minus 80-mesh, and counter-current leaching; the resulting alum solution was then filtered and crystallized. Alunite was of much interest during World War I as a source of potash and during World War II as a source of alumina. The wellknown deposits at Tolfa, Italy, are veins in trachyte and have been the basis of alum manufacture there since the middle of the fifteenth century. Pure alunite is insoluble in water and in common acids, but if it is heated to 500°C it loses its water of hydration, and the residue consists largely of anhydrous potash alum, part of which is readily soluble in water or acids. If the heat is increased beyond 500°C, most of the sulfur combined with the alumina is released as oxides and the residue consists of potassium sulfate and alumina. Thus, either potash alum (and aluminum sulfate) or potassium sulfate and alumina may be made. In the

Jan 1, 1960