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By M. G. Driessen, H. E. Criner

THE cyclone thickener has two important applications in wet washing plants: (1) water clarification, and (2) fine coal recovery. The thickener consists of a conical chamber into which the fluid is injected through a tangential nozzle at the periphery of the large end. The solids of the slurry are concentrated and removed from the apex of the cone while the "thinner" portion is discharged from a central tube in a flat head at the large end, fig. 1. The advantages of the cyclone thickener are that large volumes of slurry may be treated with small space requirements and that the underflow concentration may be controlled easily and readily to meet varying feed conditions. Control of Washery Water Solids Concentration: The first requirement, in the process of controlling solids concentration, is that the solids be removed from the body of circulating water at the rate at which they are introduced. If this condition is satisfied the concentration will remain at a fixed value and will not increase to uncontrollable levels. The second requirement is that the solids concentration

Jan 1, 1951

By W. J. Verner, J. R. Lucas

Billions of tons of bulk solid materials are processed through our industrial plants each year, and the tonnage is steadily rising. It has been estimated that for every dollar spent in industry as a whole, approxinlately 30 cents is consumed in the handling of bulk solid materials. It is in this category that tremendous savings are possible through the use of improved techniques. Since World War 11, the mining, steel, chemical, and grain industries, among others have made use of increased materials-handling automation in order to gain some of these savings. However, in a chain of automatic operations, every link must be completely reliable, for if there is a single failure, the whole system immediately becomes ineffective. Only too often the weak link in the chain proves to be the flow of bulk solids from bins. To contribute to the fundamental knowledge in this area, a research study has been continuing at The Ohio State University. The principal objective of the investigation has been to study the internal stresses existing in confined bulk solids. LITERATURE SURVEY Literature studies have revealed that many outstanding people have made contributions to the field of bulk solids. For instance, C. F. Jenkin,1 suggested: a. The pressure on a bin wall is not directly proportional to the depth beneath the surface of material in the bin. b. The vertical pressure distribution on the base of a bin is not actually uniform but is a variable. c. Arches form in bins as a result of very small deformations of the material in the bin. This deformation causes a series of gaps to appear, and consequently causes the disappearance of diagonal forces that cannot act across these gaps. The removal of the diagonal forces causes horizontal forces to be introduced which seem to be the chief cause of arching. 11. A. Janssen,4 in 1895 in connection with his experiments on bins, derived a differential equation to describe both the lateral and vertical pressure in bins with vertical sides. This represents a significant contribution to bulk solid theory, and thus its solution is reproduced as follows: L = KV = RW/U' [l-e -U'KY/R] I where L is the lateral pressure of the bulk solid in psf., V is the vertical pressure of the bulk solid in psf., K is the ratio of the lateral pressure to the vertical pressure at any point, R is the hydraulic radius of the bin in feet, W is the density of the bulk solid in lbs. per cubic feet, U' is the coefficient of friction between the stored material and the bin wall, and Y is the head of material above the point in question in feet. In 1903, Jamieson,6 in an elaborate series of experiments on full sized bins measured vertical and lateral pressures by hydraulic diaphragms. He determined many values for mediums of corn, wheat, peas, and flaxseed. In 1951, Caughey, Tooles, and scheer3 measured both lateral and vertical pressure in deep bins by using strain guages on steel bands. Values were calculated for cement, gravel, sand, soy beans, shelled corn

Jan 1, 1961

By W. T. Malone, J. R. Williams, R. L. Tiner, J. M. Tinsley

Hydraulic fracturing methods for production stimulation have become a common procedure in the oil and gas industry. Fracturing treatments are performed on wells of various potentials to help increase the production rate. In addition to the desire for increased production is the need to predict what increase might be expected. This knowledge is useful in economical treatment planning to accomplish the desired production goals for the well. Theoretical production increases due to horizontal radial fractures may be calculated using equations developed from mathematical analyses and electrical models.1,2,6 It also is possible to predict theoretical production increases due to vertical fractures using curves developed from electrical3 and mathematical models.8 However, these studies assumed that the vertical fracture height and the formation height were equal, which may not be true." In addition, the final fracture height through which fluid is produced may not be equal to the created height. The development of vertical fracture proppant transport relationships has made unrealistic the assumption that propped fracture height is equal to created fracture height. Through the use of published proppant transport equations,4'12 it is possible to calculate the height of a bed of propping agent deposited in a fracture of a given height. Assuming that the fluid flowing in the fracture moves through only the propped portion of that fracture (i.e., that the un-propped part of the fracture heals) it becomes essential to know how production increase varies with the ratio of propped fracture height to formation height. It should be recognized that future investigation may determine that the fracture does not heal completely and that a highly permeable channel exists over the deposited bed of proppant. The effect of this channel was not considered for the present study. The following analysis of experimental data allowed development of curves to determine theoretical production increases considering fracture height as a variable. Discussion In designing a fracturing stimulation treatment a number of variables must be considered. The size of the treatment, type of proppant used, proppant concentration, treatment fluid properties and well conditions are all factors affecting the dimensions and permeability of the fracture. Production increase due to a vertical fracture is affected by propped length, height, width and permeability of the fracture for a given set of formation conditions. Production increase may be defined as the ratio of production rate after fracturing to the production rate before fracturing at the same pressure differential, pe — pw. The producing rate in an

Jan 1, 1970

By J. H. Bain, D. C. Haigh, L. C. Parsons

Jan 1, 1964

By W. C. Winegard, A. Galibois, C. J. Beingessner

The effects of solutes on the distribution of two-dimensional configurations of grains in zone-refined tin have been studied. When solutes with partition coefficients (ko) greater than unity are added, three-sided pains become more prevalent and the growth law changes. It is shown by electron-Probe micro-analysis that a solute buildup occurs ahead of a moving grain boundary when ko > 1. It has been found recently1, 2 that solutes with partition coefficients greater than unity have a larger retarding effect on grain growth than solutes with k, less than unity. ko is defined as the ratio of the concentration of solute in the solid to the concentration of solute in the liquid with which the solid is in equilibrium. Niessen and winegard2 have suggested that this effect is probably due to the complex shape changes which occur during the process of grain growth and that no theory based on single boundary motion3-5 can explain the results. They suggested that the dissociation of the unstable fourfold junction was delayed in alloys where ko was greater than 1 because the boundaries at the junction had to move into a region of high solute concentration. If indeed this mechanism were correct, it was felt that not only would the dissociation of fourfold junctions be affected by the solute buildup ahead of the boundaries, but the collapse of three-sided grains would be impaired. These combined effects would naturally lead to a modification in the distribution of the number of sides per grain seen on a two-dimensional section. The present investigation was undertaken to test these hypotheses by examining the grain-growth process in detail. EXPERIMENTS The Distribution of Grain Configurations in Zone-Refined Tin as Seen on a Two-Dimensional Section. Following the method of Bolling and Winegard,6 zone-refined tin was cast into button-shaped specimens and, subsequently, plastically deformed under a drop hammer at room temperature. The resulting flat coin-shaped samples were annealed at 200°C, some for 50 sec and others for 100 sec. The specimens were then examined to determine the distribution of the number of sides per grain, i.e., the num- ber of crystals adjacent to any particular grain in the section. For simplicity, the grains were classified as three-sided, four-sided, and so forth; this concept is schematically illustrated in Fig. 1. As indicated by smith,' it was necessary to examine every grain within an enclosed area to obtain a proper distribution of the relative frequency of each type. The distributions for the two annealing times are illustrated in Fig. 2. The total number of grains examined is also indicated on the figure. It is evi-

Jan 1, 1965

By E. C. Olsen

This paper describes the unusual hazardous conditions encountered in mining thick, inclined coal beds under heavy cover in Carbon County, Utah. This description includes heavy roof conditions, sloughing ribs, steep pitches, and severe bouncing experience. Emphasis is placed on the top bench system of mining and development in the top half of a 16-ft seam, under the roof rock, which is bolted, and the recovery of the bottom coal on retreat; success of bolted roof and ribs; and shuttle car haulage on pitches up to 25%. The use of protective cages for operators of face equipment, the guarding of belt conveyor systems to prevent injury associated with deliberate entry, and the positive lockout of electrical equipment is described and illustrated. Most coal mining areas of the Western United States are characterized either by thick beds, steep pitches or heavy cover. Individually, each of these may present inherent safety hazards that in- fluence mining. When all are met at one location, the combined effect is to make the safe operation of the mining property a challenge to management. These combined conditions are met in the coal mines of the Columbia-Geneva Steel Div. of the United States Steel Corp., in southeastern Utah. This coal bed measures up to 16 ft in thickness, the pitch is as much as 25% and mining is under a cover approaching 3000 ft. The Sunnyside coal bed is found in the Book Cliff Mountains, a great escarpment extending from west of Castle Gate, Utah, some 180 miles to Grand Junction, Colo. West of Green River, Utah, the Book Cliffs swing sharply to the north because of the domelike uplift of the San Rafael Swell to the southwest. It is in this northerly extension of the Book Cliffs that the Sunnyside coal in the Blackhawk Formation of the Mesa Verde Group, Upper Cretaceous Age is found. The strata are transected by numerous faults with from a few inches to as much as a hundred feet of displacement. All of these faults have had some effect on the mining operation, either in roof control or, in the case of major faulting, the pattern of mine development. MINING PRACTICES Mining has generally been confined to the Lower Sunnyside Seam which measures from 7 to 16 ft in

Jan 1, 1963

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By E. H. Jr. Dix

THE use of magnesium as an alloying element in aluminum alloys has been limited, in general, to comparatively small quantities. In duralumin-type, strong-aluminum alloys, magnesium is present to the extent of ½ to ¾ per cent. and various grades of Magnalite and the "Y" alloy of the National Physical Laboratory of England contain up to 1 1/2 per cent. In this country small quantities of aluminum alloy sheet containing 4 per cent. magnesium are produced commercially. All commercial aluminum contains sufficient silicon to convert a portion of the magnesium added to the compound Mg2Si. It is well known that the solubility of both magnesium and magnesium-silicide decrease with decrease in temperature. It is, therefore, impossible to separate the age-hardening effect of the magnesium-silicide from that of magnesium, except by the use of aluminum of such high purity that the silicon content is negligible. The present paper is the fifth1, 2,3,4 of a series from the laboratories of the Aluminum Co. of America reporting the results of investigations of the equilibrium relations in aluminum-rich alloys made from the high purity aluminum manufactured by this company .5

Jan 1, 1929

By G. E. Perry, R. D. Seba

The steam soak process is the most widely applied and most successful thermal supplemental recovery process in use today. This process, which consists of injection of steam in various quantities into a well that is subsequently used as a producer, can be repeatedly applied to the same well. The treatment, if successful, will increase the production rate of the well for a given period. For this reason, the steam soak process should be considered primarily as an acceleration method rather than as a method for producing oil that could not be recovered by primary means. However, application of this process to reservoirs containing viscous crude may produce oil that otherwise would have zero present value or would be produced at such low rates by primary methods that it would not be profitable. A major necessity for the successful application of the steam soak process is a source of natural energy. This source of energy may exist in one or more of the following forms: expansion of fluids, compaction, gravity drainage. This study was undertaken to determine the effect of gravity drainage on steam soak production and recovery and to develop a method for predicting production rates, ultimate recovery, and heat requirements when applying this process to a reservoir in which the primary driving mechanism is gravity drainage. (For additional discussion of some of the factors that affect recovery of viscous oils by the steam soak process, see Ref. 5.) Model The model developed for analyzing the performance of the steam soak process in gravity drainage reservoirs is a modified form of that developed by Matthews and Lefkovits.1,2 The model used in this study consists of two concentric cylindrical volumes of productive formation with cap and base rock of impermeable material. The inner cylinder, extending from the radius of the wellbore to some predetermined radius, is referred to as the hot zone; and the outer cylinder extending from the exterior boundary of the hot zone to the outer drainage boundary will be referred to as the partially heated zone. Fig. 1 is a schematic cross-section of the model, indicating its thermal properties. Horizontally the reservoir is divided into two regions, the upper region having a high gas saturation and residual liquid saturation, and the lower region containing a high liquid saturation. The boundary between these two regions is referred to as the free surface, which drops and changes shape as fluid is produced from the reservoir. The model was used to analyze the steam soak process by applying the following assumptions: 1. The horizontal formation is composed of one or more homogeneous noninterconnected layers containing incompressible fluids. Each layer is treated separately. 2. The hot zone is heated by the initial soak and is maintained at the steam temperature corresponding to atmospheric pressure by resoaking. 3. The height of the free surface at the producing well is at all times zero (producing well is pumped off). 4. The position of the free surface at the start of

Jan 1, 1970

By F. A. Forward, A. H. Ross, J. Halpern

Application of the carbonate leaching process to carno-tite ores has often been limited by the difficulty of obtaining simultaneous high recoveries of uranium and vanadium. The chemical aspects of this problem are discussed and the effect of prior roasting procedures on this discovery is described. IN treating carnotite ores by carbonate leaching it is often necessary to subject the ore to a prior roast. Among the advantages that may result from roasting are: 1) improvement in settling and filtering characteristics of the ore; 2) destruction of carbonaceous impurities that would otherwise contaminate the leach solution and consume carbonate reagent; and 3) substantial increase in extraction of vanadium, which is usually low when the un-roasted ore is leached. Recovery of vanadium may be an important factor in processing carnotite ores, and the fact that vanadium is usually recovered in good yield by acid leaching has often been an economic advantage over results obtained with carbonate leaching. It has been found that response of an ore to carbonate leaching, following roasting, depends primarily on its composition and on the conditions of the prior roast treatment, particularly with regard to the roasting temperature, the atmosphere maintained above the charge during roasting and cooling, and the presence of certain reagents. These factors, especially the last, virtually determine the extractions of uranium and vanadium attainable by carbonate leaching, as well as the reagent consumption on leaching, whereas adjustment of the leaching conditions has only a limited influence. These variables were examined systematically to elucidate roasting and carbonate leaching of carnotite ores and to establish a treatment yielding high recoveries of both uranium and vanadium. Tests were conducted on samples of four different Colorado Plateau ores, described in Table I. Roasting Procedure: The roasting tests were conducted in an electrically heated furnace in which the temperature was controlled to ±15°C. The ore (usually a 500-g charge) was ground to —100 mesh, mixed with the desired reagent, and spread in a silica tray to a bed depth of about 1/2 in. During the roast the charge was rabbled at intervals of 15 min. To provide free access of air the furnace was usually ventilated; however, in a few experiments a controlled atmosphere such as carbon dioxide or hydrogen was maintained above the charge. Leaching Procedure: The pulp, generally comprising 500 g of ore and a 2000-cc solution containing 80 g per liter of Na2CO8 and 20 g per liter of NaHCO3, was agitated in an autoclave at 120°C, under 30 psi 02. Samples were withdrawn periodically, and the solution and ore residue were analyzed. Under the conditions employed, maximum attainable extractions were generally achieved in 4

Jan 1, 1959

By M. Prats

Most of the information available on the heat efficiency of hot fluid injection processes, both water and steam, has been obtained from calculated temperature distributions in the pay zone and adjacent formations. The usual approach has been to write the heat balance equations in terms of the temperatures, and then to introduce whatever simplifications are necessary to help obtain an analytical or a numerical solution. In either case, the assumption has often been made that the vertical thermal conductivity in the flooded interval is infinite, so that the temperatures within the flooded interval are then independent of vertical position. Because it was first made by Lauwerier,l and has been used extensively since, this assumption will be referred to as the Lauwerier assumption. Excellent reviews of the literature on the heat efficiency of hot fluid injection processes have been given by Spillette,2 Flock et al.,3 and Ramney.4 Of course, the most significant contributions take into account the effect of a finite vertical thermal conductivity on the vertical temperature profile. The most general analytic expression for the heat efficiency of a hot fluid injection process is that of Antimirov5 who considers injection of a heated incompressible fluid into a reservoir through an arbitrary number of wells. The rate of heat injection into the reservoir, as well as the injection temperature, is an arbitrary function of time. The geometry of the horizontal flow is arbitrary, although the reservoir is considered to be of uniform thickness and properties and to be of infinite areal extent. Heat transfer within the reservoir is by horizontal convection and conduc- tion, and by vertical conduction. In the formations adjacent to the flooded interval, heat transfer is by conduction in any direction. Thus, the available expression for the heat efficiency due to hot water injection has been developed for rather general conditions. This degree of applicability has not been obtained for other thermal recovery processes. By making the Lauwerier assumption we have been able to obtain expressions for the heat efficiency that are essentially independent of the thermal recovery process, be it steam, hot-water, or underground combustion. Clearly, then, the approach followed here is more restrictive than that of Antimirov5 in that it uses the Lauwerier assumption. At the same time less restrictive assumptions are made about the horizontal heat transfer mechanisms, either in the flooded interval or in the formations adjacent to it. The main difference between our approach and that of other investigators is that the heat balance in the pay zone is expressed for the pay zone as a whole rather than for a volume element within it. The Lauwerier assumption is introduced after the problem is developed along these lines as far as possible. The details of the development of the heat efficiency are given in the Appendix, while the main features of the model are discussed in the next section. Results and their implications are discussed later in a separate section. The Model Certain assumptions have been made to determine

Jan 1, 1970

By B. S. Gottfried

This paper is concerned with possible transport mechanisms which occur during segregated burning (i.e., burning in an oil reservoir in which the oil-bearing formation is overlain by a "clean" porous zone containing only gas). ,Two analytical models are presented. In the first, burning is assumed to occur at the gas-oil interface, and the dominant mechanism is taken to be the rate at which oxygen diffuses to the interface. The second model assumes that combustion occurs within the clean zone, with the dominant mechanism being the mechanism of fuel deposition from the oil-bearing formation to the clean zone. ,Comparison of the results of the analyses with limited experimental data indicates that the latter mechanism is much more plausible. Both models are idealized representations of the actual process and are somewhat conjectural, however, owing to the lack of more definitive laboratory or field data. INTRODUCTION In recent years there has been considerable theoretical and experimental research directed toward understanding the recovery of crude oil by underground combustion. Although two different recovery schemes have been proposed, known as forward and reverse combustion, it is only forward combustion that shows promise of becoming a practical recovery technique.17 Most of the analyses of the forward combustion process have considered it to be pistonlike; i.e., oil is displaced by a vertical combustion zone which, with its ensuing gases, pushes die oil forward as the flame front is propagated through the reservoir.l-8,ll,l2,14-16 However, information gained in field pilot studies indicates that, at least to a certain extent, forward combustion proceeds in a segregated manner in oil reservoirs.10 An ideal segregated system is one in which the oil-bearing formation is overlain by a "clean" porous zone containing only gas. The location of the combustion zone in such a system is not immediately evident, although combustion is believed to occur either at the gas-oil interface or within the clean zone. In either case, the combustion zone may be horizontal and it moves in parallel rather than in series with the produced oil. The purpose of this paper is to explore the likely mechanisms by which segregated burning can occur, and to determine the sensitivity of the resulting models to changes in various physical parameters. Two governing mechanisms are considered: the case of a horizontal combustion zone at the gas-oil interface with the rate of combustion governed by the rate at which oxygen diffuses to the interface, and the case of combustion within the clean zone with the combustion process controlled by the transport of fuel from the oil-bearing formation to the clean zone. Both models are somewhat hypothetical and involve considerable simplification of the actual process. However, the results allow some preliminary understanding of segregated burning which is useful in the absence of more definitive laboratory or field pilot data.

Jan 1, 1967

By Edna A. Dancy, Gerhard J. Derge

Jan 1, 1963

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959

By S. M. M. Safvi, A. Jowett

Small-scale continuous flotation tests are described in which the influence of 1) pulp density and 2) feed rate on the rate of flotation are investigated. The results provide further evidence of first-order kinetics for flotation and indicate that tests at different feed rates provide a particularly simple method of determining rate constants. Flotation kinetics are discussed in general terms. Over a period of many years numerous research workers have studied the rate of recovery of valuable materials from flotation pulps with a view to deter-mining the mechanism of the froth flotation process. Froth flo ation is fundamentally a collision process involviug at some stage collision and then mutual attachment between air bubbles and mineral particles. It is possible to draw analogies therefore between the flotation process involving mainly macroscopic particles and the ordinary processes of chemical reaction kinetics involving collisions between atoms, molecules and ions. By adopting this analogy we may postulate a general equation representing the kinetics of the flotation process: -dC/dt =K.CC ,Aa (1) The rate constant, K, will be a complex function involving reagent concentrations, particle and bubble sizes, induction times and no doubt flotation cell design. However, these are factors which can be kept constant in any series of experiments, permitting investigation of the exponents a and c, which determine the order of the reaction occurring in flotation. The various research investigations carried out so far have all aimed at evaluating a and c and in the majority of cases only since the concentration of air has usually been kept constant in a series of tests, so that a relationship of the following type has been investigated: -dC/dt = K1 Cc (2) The techniques of both batch testing and continuous testing have been used to investigate this relationship. The technique of continuous testing, in which steady-state conditions are established, permits direct investigation of the above equation. In the case of batch testing, C is decreasing continuously

Jan 1, 1961

By O. E. Palasvirta

Several drum-type, low-intensity dry magnetic separators have recently been described 1,2,3,4 all of which share at least two generic similarities. The magnet consists of a multiplicity of poles of alternating polarity and, the speed of the drum shell, relatiw to the magnet, is such that the magnetics are agitated through rotation of the magnetic particles around their individual axes. The speed of the drum relative to the magnet (differential speed) determines the frequency of the field reversals. For effective agitation this frequency generally has to be above a specific value, which varies according to the mean particle size of the magnetics. With separators of small diameter, say less than 11/2 ft., a sufficient differential speed for treatment of fine magnetite can be attained only by rotating both the magnet and the drum separately; separators of large diameter may attain sufficiently high differential speeds with stationary magnets. Separators of large diameter thus have the advantage of simplicity of design. The capacity of a separator of this type is directly proportional to the speed of the shell. As the centrifugal force opposing the magnetic force increases at a slower rate than the peripheral speed of the shell when drum diameter is increased, large drums can be operated with higher peripheral speeds. Thus they have a higher capacity than smaller drums. Separation is also a statistical phenomenon, i.e. the grade of concentrate improves as the number of agitations or rotations of the magnetic particles per separation increases. As separators of large diameter have space for a large number of magnets they are best suited for production of optimum grade concentrate. The statements above are general clues For separator design. In the following an expression IS derived showing a more exact relationship between the pertinent separator variables. As both magnetic attraction and centrifugal forces are directly proportional to the volume of the affected bodies, complications in mathematical analysis, arising from variable particle size, are avoided by considering the force per unit volume of affected material. For the magnetic force per unit volume Runolinna (3) gives the following equation: V " 1 + N(ur, - 1) uo dr (1) where ur and uo stand for the relative permeability and the permeability of vacuum, respectively, N is the demagnetization factor, B the intensity of the magnetic field, and r the distance from the face of the magnetic pole. The permeability of a specific magnetite ore can generally be considered as a constant. For ground, liberated material N can also be treated as a constant, and the first simplification can be made by writing ur-1 1=k1. 1 + N(ur - 1) uD k1. Fig. 1 shows the field intensity curves for two U-magnets of different size, but of roughly similar geometry of cross-section as plotted against the distance from the plane of the pole faces. The curves

Jan 1, 1961

By Charles H. Jacoby

The solution mining of evaporites has a history of approximately 5,000 years. The insitu leaching of metalliferous ore will have many of the same characteristic problems which have confronted industry for years in the production of evaporite minerals. Basically we will be converting the less soluble forms of valuable metals into their more soluble salts and producing these in much the same manner as, for example, sodium chloride. There are a number of problems which we are faced with that are more complex and complicated and, therefore, will require a higher degree of sophistication than previously employed. One of our most important undertakings will be the clearcut definition of the problems involved. While a great deal of expertise can be drawn from the solution mining of evaporites and the oil industry, problems peculiar to the hydrometallurgical field will need to be solved. One of these is the introduction of permeability into an impermeable rock so as to expose the sought after values of metals which by volume are infinitesimal when compared with sodium chloride, potash or other type water soluble mineralization. After establishing this permeability which will be miniscule when compared to a solution cavity, there will be the maintenance of this permeability. In general, salt deposits are of a somewhat uniform chemical composition and thus their chemistry was relatively simple. Each metalliferous ore body is somewhat unique in its chemistry and will need to be treated accordingly.

Jan 1, 1974

By Y. Oka, H. Majima

When a rock particle is subjected to an external force, internal stresses and deformations are experienced by the particle. Assuming that the breakage of a rock is mainly due to tensile stresses generated by the action of a pair of concentrated loads, F, directed in compression towards the loading points at the shortest distance, as illustrated in Fig. 1, the stress and deformation experienced by a particle of irregular shape can be determined with the aid of the theory of elasticity. According to the photoelastic experiments made by one of the present authors,' the stress states in a rock particle of irregular shape are quite similar to that of an inscribed sphere of diameter x, as indicated in Fig. 1, but accompanied by the faint stresses, in the vicinity of the particle outside of the inscribed sphere. Therefore, the stress components in an irregularly shaped particle can be estimated by referring to stress components in a sphere. Applying polar spherical coordinates to an elastic spherical body, as shown in Fig. 1, the stress components are all expressed as multiples of F /x2 and more or less influenced by the loading angle and Poisson's number m. In general, the energy w, acting on a rock particle is defined as the product of loading compression F

Jan 1, 1970

By L. W. Bahney

MANY methods for the determination of gold or silver, or both, in cyanide solutions have been published, which with care in manipulation, and modification in some cases, will give results that are satisfactory. It is possible to classify or group these methods as follows: 1. Evaporating the solution in a porcelain or agate-ware dish containing litharge,1 or in a "boat" made of lead foil. 2. Forming a lead sponge containing the precious metals by means of zinc shavings,2 zinc dust,3 or a piece of aluminum.4 3. Decomposing the cyanide solution with an acid and precipitating the precious metals by the use of one or a combination of some of the following: Copper sulphate,5 sodium sulphite,6 hydrogen sulphide,7 cement copper.8 4. Precipitating the silver by zinc dust held in a Hooch crucible and determination with a standard solution of sulphocyanate.9 5. Electrolysis.10 6. Colorimetry.11

Jan 2, 1915

By L. A. Updegraff

Before discussing the application of capacitance for the measurement of moisture content in a moving stream of coal it might be well to first give a brief description of the process and then show how it can be applied to the coal industry. A capacitor may be described as a device having two conductors separated by an insulator, the conductors hereafter being designated as a test cell or test plates and the insulator as the dielectric. Capacitance, therefore, is a measure of the ability of a capacitor to store an electrical charge. Two basic factors that affect capacitance are the dimensions of the capacitor and the dielectric constant of the insulator. Capacitor dimensions which affect its capacity are the area A of the conductive surface, and the distance d between plates. Capacitance is inversely proportional to the distance between plates and directly proportional to area A, so if capacitance is indicated as C and the dielectric constant as K the equation for capacitance would be C = AK/d. The dielectric constant can be described as the ratio of the actual capacitance of any given material to that of a vacuum, which is unity. In industrial applications the area of the plates remains constant as also does the distance between them, leaving the dielectric constant as the only variable to affect the capacitance measurement. Figure 1 is a schematic diagram of an r-f excited capacitance bridge in which a test cell is part of the circuit. This bridge consists of four capacitors in two pairs connected across an a-c voltage source. In one side of the circuit the two capacitors are fixed but in the other side they are variable, one being the rebalance capacitor operated by the servo motor and the other the test plates between which the dielectric passes. Capacity of the plates is a function of the dielectric constant of the material between them and is measured at radio frequency. Within the recording instrument is an r-f oscillator and a 60 c ps modulator. The radio frequency signal is generated by the oscillator, modulated by a 60 cps wave, and sent to the bridge. Therefore the signal entering the capacitive bridge is a radio frequency carrier with a 60 cycle envelope, If the bridge is in balance as the signal enters there would be no voltage drop and so no output by the detector. As long as the dielectric constant remains the same the bridge will stay in balance. However, any change in the dielectric constant, which in this case would be a change in moisture content, would affect the bridge. Higher moisture increases the capacity of the test cell which causes less voltage to develop across it causing imbalance of the bridge. This in turn causes a radio frequency signal to appear at the detector. Output from the detector is a 60 cycle ripple which is in proportion to the imbalance of the circuit. A 60 cycle amplifier boosts the detector signal to enough power to drive the servo motor which positions the recording pen and also rotates the variable capacitor, to which it is mechanically connected, to bring the bridge back in balance. An increase in moisture causes the servo motor to rotate in one direction, but a decrease causes imbalance in the opposite direction, and thus rotates the motor in that direction. This brings the bridge back in balance and stops the motor. The bridge shown in Figure 1 has been modified so as to provide a wide range of adjustments. Coarse and fine span adjustments located in the recording instrument are set to govern the amount of pen movement for a given change in capacitance. A measuring head unit contains coarse and fine zero adjustments for

Jan 1, 1961