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By Frederick Laist

(Butte Meeting, August, 1913.) WHILE remodeling No. 1 section of the concentrator at the Washoe Reduction Works of the Anaconda Copper Mining Co. during the summer of 1912, for the purpose of ascertaining what additional metal recoveries could be made by improvements in concentration practice which had been developed by the staff of the Boston & Montana Reduction Department, at Great Falls, it was deemed advisable to carry on some experiments on the treatment of the regular mill tailings by roasting and leaching, to see whether the losses of metal values might not be still further decreased. In the course of these experiments about 5,000 tons of tailings were roasted, and of the resulting calcine about 200 tons were leached. The results were so satisfactory that it was decided to continue the work on a larger scale, particularly as regards the leaching end of the process, and construction work on an 80-ton roasting and leaching plant was accordingly commenced during the latter part of February, 1913, and is being pushed as rapidly as possible. 80-Ton Leaching Plant. This plant will consist of one 20-ft. roasting furnace of the MacDougall type, specially adapted to the work of roasting for leaching; two leaching tanks, .32 ft. in diameter by 12 ft, deep, together with the necessary solution tanks, air lifts, precipitating launders, etc. It has been decided to precipitate the copper from solution on scrap iron, so as not to hamper the roasting and leaching departments by any weakness that might develop in the precipitating department. It is, however, the intention to experiment with a number of different methods of precipitation ; for example, by electrolysis and by hydrogen sulphide.

Jan 7, 1913

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 G. D. Just

INTRODUCTION Large scale underground mining involves the bulk handling of fragmented material. The cost and efficiency of the mining systems is there- fore significantly influenced by material flow characteristics. Flow problems may occur in the form of ore pass blockages which interrupt the free flow at extraction openings. The costs of such delays can be readily assessed and compared to the costs incurred in reducing blockages by improved fragmentation or larger ore passes. In practice the problem is more complex than this statement suggests because it is generally un- economic to design for zero ore blockages. Another major flow problem occurs in the form of relative movement of ore and waste as the fragmented material is extracted. This produces waste dilution in the recovered ore and influences total ore recovery. This flow problem is much more complex than the ore block- age phenomena. Many questions concerning the precise flow characteristics remain unanswered because of the variability of size distributions, particle shapes, material properties and the total extraction layout and design. Model studies can provide a visual and quantitative illustration of probable flow characteristics but full scale data collection is necessary to evaluate the precision of such information. The methods and types of data obtained must be carefully selected to recover the maximum volume of useful information for operational control and future design. It is essential that honest precision levels are assigned to the data and any subsequent analyses. Grade control data may give misleading short term information on flow characteristics because of the difficulty in knowing the true grade of the mass of material before extraction commences. However, in the long term control of extraction grades is vital to the profitable operation of the mining system. The most efficient extraction design and operational schedule can only be determined after all of the facts and variables are known. This is usually only possible after the orebody has been completely extracted. However, if design and operational personnel have a full appreciation of the nature and variability of material flow under different conditions the best possible results should be achieved. The most significant features of material flow are out- lined in this paper in order to provide mine planning and mine management personnel with some of the necessary information relating to material flow. Available facts and reliable figures from selected publications are noted in association with unbiased and hopefully accurate opinions of the relevance of the data to mine design and mine system control. Possible future developments and profitable areas for research into material flow problems are also detailed. MATERIAL FLOW AND MINING METHODS The effects of material flow on the design and operation of an integrated underground ore handling system is one factor which is common to most mining methods. Analysis of the system as detailed by Just, 1980, permits the identification of unit process objectives. For example, a typical underground ore handling system as illustrated in Figure 1, involves the following unit operations:- (i) Gravity flow of ore in stope (ii) Ore extraction at base of stope (iii) Ore haulage on the production level (iv) Dumping of ore into ore pass system (v) Gravity flow of ore in the ore pass (vi) Underground crushing of ore (vii) Haulage of crushed ore to shaft (viii) Hoisting of ore to the surface. Average flow rates in each of these unit operations can be misleading due to variability in incremental capacity caused by flow blockages and machine delays. Thus to effectively analyse the probable performance of the system, it is necessary to have a measure of the flow loading and haulage rate variability. Mechanical equipment performance specifications can be used to provide such information for loading, haulage and crushing; however, in the case of the gravity flow of material field measurements are required to relate the probability of "hang-ups" to the degree of fragmentation. Factors affecting the frequency of flow stoppages are, size, distribution and cohesiveness of broken material and the geometry and size of the flow channel. Ore pass channel design is relatively simple since regular cross-sectional shapes are used

Jan 1, 1981

By Warren L. Howes

This paper deals primarily with an investigation of ball-mill liners that was conducted by the writer over a period of six years at the Mammoth mill in Arizona. The investigation covered a wide variety of designs of liners in both primary and secondary mills. The comparative results are presented herein as evidence of the extent to which design influenced liner life and mill performance. Flowsheet The feed to the Mammoth mill was a complex, oxidized, gold-silver-lead-molybde-num-vanadium ore with rhyolite, andesite and granite as gangue. Although the ore varied between stopes, the long-term average in character remained substantially the same. Capacity was 560 tons per day.† Fig. I shows an abbreviated flowsheet of the grinding section of the mill. Primary Ball Mill A 3-ft. Symons shorthead crusher in open circuit crushed to 1/4-in. maximum one-way dimension the feed to the 5 by Io-ft. Marcy open-end ball mill. The mill rotated at 80 per cent of critical speed and was charged with 4-in. forged steel balls. Cast balls were used for a few months at a slight reduction in ball cost, but breakage of the large balls reduced the ball size and grinding capacity to a point where the over-all costs suffered out of proportion to the saving in cost of balls. For metallurgical reasons, the finished product of the mill was maintained at minus 8-mesh. This coarse product, plus the very abrasive ore and the absence of fines in the feed, caused abnormally rapid wear of the mill liners. The resultant high operating cost led to the most extensive phase of the investigation. In order to clarify the difference in design of the various types of liners used, Fig. a shows the profiles with the arrangement in which grinding balls of maximum size would lie on the face of the liners. The results with each type of shell liner in the primary mill are shown in Table I. Since most of the testing was done with

Jan 1, 1943

By Warren L. Howes

This paper deals primarily with an investigation of ball-mill liners that was conducted by the writer over a period of six years at the Mammoth mill in Arizona. The investigation covered a wide variety of designs of liners in both primary and secondary mills. The comparative results are presented herein as evidence of the extent to which design influenced liner life and mill performance. Flowsheet The feed to the Mammoth mill was a complex, oxidized, gold-silver-lead-molybde-num-vanadium ore with rhyolite, andesite and granite as gangue. Although the ore varied between stopes, the long-term average in character remained substantially the same. Capacity was 560 tons per day.† Fig. I shows an abbreviated flowsheet of the grinding section of the mill. Primary Ball Mill A 3-ft. Symons shorthead crusher in open circuit crushed to 1/4-in. maximum one-way dimension the feed to the 5 by Io-ft. Marcy open-end ball mill. The mill rotated at 80 per cent of critical speed and was charged with 4-in. forged steel balls. Cast balls were used for a few months at a slight reduction in ball cost, but breakage of the large balls reduced the ball size and grinding capacity to a point where the over-all costs suffered out of proportion to the saving in cost of balls. For metallurgical reasons, the finished product of the mill was maintained at minus 8-mesh. This coarse product, plus the very abrasive ore and the absence of fines in the feed, caused abnormally rapid wear of the mill liners. The resultant high operating cost led to the most extensive phase of the investigation. In order to clarify the difference in design of the various types of liners used, Fig. a shows the profiles with the arrangement in which grinding balls of maximum size would lie on the face of the liners. The results with each type of shell liner in the primary mill are shown in Table I. Since most of the testing was done with

Jan 1, 1943

By R. E. Head

SOME mixtures of sulphide and oxide ores from the Tintic district in Utah are of a sufficiently good grade to be shipped to the smelter without beneficiation. In mining this type of ore, however, a material tonnage of ore of a similar composition but of lower grade is obtained. It is a question of economics whether such ore should be shipped with a certainty of a small return or concentrated if that would yield a sufficiently increased return to amortize plant construction and upkeep and yield a higher rate of profit than at present. It may be assumed that the tonnage of this borderline ore is constantly increasing and that eventually it will attain such proportions as to justify plans for milling on a relatively large scale. Under existing conditions, the producer of mixed sulphide and oxide ores is not greatly concerned about the physical characteristics of his ore or of its mineralogical complexities, since his contract with the smelter calls for payment on the basis of chemical analysis. When concentration is contemplated an entirely different picture is presented. Percentages of valuable metal content must then be considered in terms of minerals, for it is in the form of minerals that recoveries are made and losses sustained. In describing the performance of a given flotation mill and reagent combination, it may be stated as a generality that a specific percentage recovery of valuable elements is made. Technically, however, the concentrator is really constructed and the reagents are selected to recover the valuable minerals. These considerations must be given prominence in discussing border- line ores from the Tintic district because of their physical characteristics and mineralogical composition. Because of these peculiarities they may be justly termed complex, since their lead, silver, and copper contents are each represented by two or more minerals of different chemical composition and presenting widely divergent physical properties. This paper sets forth the results of a microscopic study of a type of borderline ore from the Tintic district that is now being treated by direct smelting. A

Jan 1, 1938

By A. M. Guadin

Direct quantitative comparison of the results of concentrating operations on different ores is frequently desired but almost impossible to obtain if comparison has to be made by means of two quantities for each ore, as must be done at present. This paper represents the outgrowth of attempts to arrive at a single-number quantitative measure of the segregation between minerals or metals as the result of concentrating operations. The usual practice in estimating the effectiveness of concentrating operations, particularly those of ore dressing, has been to determine the recovery of the metal or mineral of interest and the grade of the concentrate. The difficulty in quantifying the effectiveness of concentration by the usual criteria may be illustrated by a few examples. Consider, for instance, two lead ores which yield by flotation the same recovery of lead, say 92 per cent., and the same grade of concentrate, say 60 per cent. Pb. If a substantial difference in the grade of the feed had existed, say if one ore contained 5 per cent. Pb and the other 10 per cent., it is clear that the concentrating operation was more effective in the case of the lower grade ore. It is difficult, however, in the light of these data to state how much more effective was the concentration of the lower grade ore. Consider again two lead ores containing 5 and 10 per cent. Pb and yielding concentrates containing 60 and 72 per cent. Pb respectively, with recoveries of 93 and 92 per cent. respectively; it is well-nigh impossiblc to tell from these figures which results represent the best separation of the minerals. It may be noted that in the usual method of estimating the effectiveness of the segregation of mineral values, no consideration is given to the rejection of the unwanted substances from the concentrate, except in the very indirect manner in which it enters into the grade of the concentrate. Consideration of the rejection of gangue from the concentrate, adequately weighted with recovery of the desired mineral in the concentrate, should supply an adequate criterion of concentration effectiveness.

Jan 1, 1930

ATHOUGH the open-hearth charge contributes CO, CO2, and water vapor to the combustion gases and absorbs oxygen from them, in the main the thermal effects in the melting charge and molten bath can be considered independently of those in fuel combustion, the latter being regarded simply as the source of any extra heat required to finish a heat of steel. First of all, it should be remembered that a large percentage of the heat supplied to the bath is furnished by oxidation of the various elements in the charge itself. If this charge consisted of 80 to 100 per cent of hot metal and the oxidation were obtained by blowing in air or oxygen, as is the case in the Bessemer converter, then the net heat absorption would be negative, that is, the bath would contribute part of the heat required to keep the melting chamber hot, in addition to that contained in the finished steel and slag. In actual open-hearth practices, probably the nearest approach to this is in the duplex furnace, charged with Bessemer-blown metal and some hot metal, where very little heat is required to complete the refining and nearly all the heat energy from fuel combustion is used to keep the roof and walls of the melting chamber up to around 2900 to 3000°F. (1600 to 1650°C.) so that the bath will not cool off during the refining. The other extreme is with all-cold charges containing around 80 per cent steel scrap and 20 per cent cast iron or cold pig iron, in which case a very large proportion of the heat in the bath at tap is supplied from the fuel combustion. THERMAL EFFECTS IN MELTTNG In the previous chapter it was pointed out that in a typical heat, the fuel furnishes about four million B.t.u. per ton of steel produced. The heat required for the metallurgical processes is not easily defined in useful manner (as is shown later), but it ranges downward from about one million B.t.u., depending not only on the charge but on the manner of calculation. In any event this requirement appears quite small in comparison with the heat furnished by the fuel and invites

Jan 1, 1944

By Olof Löfgren

PART 1 INTRODUCTION All modern pelletizing plants are equipped with either the drum or the disc circuits. Choice of one or the other circuit is not simple and it is desirable to establish a firm basis for such a task. For a meaningful and a fair comparison it is necessary to have the two systems working in parallel in the same plant with the same concentrate under the same supervision. Furthermore, the comparison has to be based on a defined green ball quality and size distribution. BALLING CIRCUITS The LKAB straight grate plant at Malmberget, Sweden, was started up in Septenber 1973. It was designed for a 2.5 Mton annual capacity and was equipped with five balling drum circuits. During the first year of operation it was found that the induration plant had the potential for a higher capacity which required increased balling capacity. For this purpose it was decided to install a balling disc circuit complete with a roll screen. The reasons for selecting a disc were space limitations and LKAB's desire to gather experience on balling disc circuits. The disc circuit was started up in 1975 and was run in parallel with the balling drums in the same plant and with the same raw material and under the same operating personnel. The necessary conditions for a comparison were thereby fulfilled. The data for the size distribution and quality of the green balls were obtained on random sampling during one year of operation, so that all the variations which appear in a commercial plant are covered.

Jan 1, 1977

By Glenn C. Waterman

Richard Strong (Oliver Iron Mining Div., U. S. Steel Corp.)—Mr. Waterman states (p. 59, Trans., January 1954): "Core-sludge combining factors have been calculaied for any combination of core-sludge recovery on the basis of several logical assumptions: 1—The sludge sample loses reliability geometrically as sludge recovery drops. 2—The sludge sample should not be used if the percentage of sludge return is less than the percentage of core recovered. 3—A core sample should receive a weighting at least equal to the percentage of core recovery." Assumptions 1 and 2 seem justified at Chuquicamata and most geologists would agree to the validity of assumption 3. However, contrary to the statement quoted above, the core sample does not in general receive a weighting at least equal to the percentage of core recovery when the Chuquicamata methgd is used. Furthermore, the basic Chuquicamata method is identical to the Longyear or relative volume core-sludge assay combining method. Finally, the Chuquicamata method does not, in its present form, reflect true geometric loss in sludge sample reliability according to the relationship L = AR (N-1) The basic equations representing the two steps of the Chuquicamata method can be combined algebraically as follows (using the symbology of the original article except as noted): Vol A + B Assay 2 = ASA = Assay 1 Vol A VolB Core Assay [I] Vol A CA.F + ASA (100 —F) Combined grade =[21 100 Pct where F and (100 — F) are the core and adjusted sludge assay factors from Fig. 3. Substituting Eqs. 1 and 2 and collecting terms Combined grade = Vol B Vol A + B CAF (100—-F) + Assay 1 (100-F) Vol A Vol A 100 pct Eq. 3 is a unified and general statement of the Chuquicamata method. The true core factor includes not only the factor F from Fig. 3 but also the quantity VolB ------------- (100 — F), which is implicit in the value of Vol A the adjusted sludge assay. This quantity is real and positive for all values of F and core recovery less than 100. Therefore the true core factor is always less than F except when F is equal to 100. If sludge recovery is 100 pct, Eq. 3 can be further simplified as follows: Let F = percentage of core recovered. Let Vol A = Vdh (100 Pct — Pct CR) where Vdh is the total volume of the sampled interval and let Vol B = (Vdh — Vc.) Pct CR where V, is the core volume in the sampled interval at 100 pct core recovery. Then combined grade = Vo V. CA Pct CR- + Assay 1, 100 Pct — Pct CR Vdh Vdh [4] 100 Pct Eq. 4 shows that when sludge recovery is 100 pct the laboratory sludge assay receives significant weight in the Chuquicamata method, even at 100 pct core recovery. The maximum weight assigned to the laboratory sludge assay depends on drillhole size, as follows: Eq. 4, with suitable changes in symbology, is identical to Royce's formula 8,' which is a statement of the Longyear or relative volume method of combining core and sludge assays. If Mr. Waterman's assumption 3 is of paramount concern to the geologist, the Royce method (for core recoveries of 60 pct and above) or a method employing the percentage of core recovered as a core weighting factor are the only recognized methods known to the writer which achieve the desired result. A modification of the latter method embodying Mr. Waterman's assumptions 1 and 2 would result from applying the factors from Fig. 3 directly to the laboratory core and sludge assays.

Jan 1, 1956

By F. L. Vogel

Densities and distributions of dislocations in plastically bent germanium crystals before and after annealing were studied. In the bent and annealed crystals, the theoretical relationship between radius of curvature and density of dislocations is confirmed. Before annealing, however, more dislocations are present than required, and these are distributed with a minimum at the neutral axis and maxima at the top and bottom surfaces. On annealing, three significant changes occur in the bent bars: 1) the average dislocation density is reduced, presumably by the annihilation of opposite signs; 2) dislocations migrate from the high density outside regions toward the low density neutral axis, thus producing the equilibrium distribution of dislocations; and 3) a polygonized structure is formed by movement of the dislocations into walls normal to the slip plane. ETCHING to reveal edge dislocations'-" offers a unique opportunity to study, in germanium single crystals, the functioning of dislocations in plastic deformation. Plastic bending is ideally suited to this purpose because it produces a static array of edge dislocations in an ideally plastic material which is predictable from the theory." " Nye" has given a rather complete treatment of the geometry of bent crystals in terms of dislocations. The density of excess dislocations is related to the radius of curvature of the slip plane of a bent crystal, as shown in Fig. 1, assuming the absence of macroscopic elastic stresses. The curvature of any plane in the zone of the bend axis is found by resolving the Burgers vector into that plane, so that for the usual case where the slip plane is inclined at some angle 0 to the neutral plane of the bar, the equation applies, with T equal to the radius of curvature of the neutral plane of the bent crystal. Two predictions which are relevant to this study may be made from Eq. 1. First, in crystals bent to various radii, the average excess dislocation density is inversely proportional to the radius and second, for a bar bent to a radius which is large compared with its thick-

Jan 1, 1957

THE CHAIRMAN (A. F. Lucas, Washington, D. C.).-Mr. Matteson has stated that the drilling of certain deep wells has proved a failure because they were abandoned too soon. He advises drilling more wells around salt domes, in the hope of finding additional oil sands. I have had some experience on the domes and believe that by drilling shallow wells, one loses time and money. I have advanced the opinion -that by drilling central wells in the -most likely location of a dome, showing is certain weakness, a better result could be obtained. I have in mind one locality where Mr. Knapp drilled a well through the salt¬the only location that I know of on the Gulf Coast where oil was found underneath the salt. Mr. Knapp found a great deal of gas in it. The salt itself was impregnated with oil and gas; and my opinion is that in such instances, instead of drilling so many wells around a dome, if you will attack at a weak point to as great a depth as a drill will go, the results will he much better. At present we have instances where drills have penetrated to 7300 or 7400 ft. in depth. Why couldn't the rich companies that are operating around the Gulf Coast arrange to get some special drilling apparatus and drill with the rotary first for, say, 3000 to 4000 ft., always in the likely location, and then proceed with the cable? I think we need just such work. In Mr. Matteson's paper lie quotes from an author whose writings in the Federal Bulletin and in the Louisiana Bulletins have been quite extensive. He states that oil and asphalt have originally been found on the surface of those domes. I have been over and examined nearly all of those domes (not all of them, because many have been developed in the last few years) and found no such occurrence at the time; and in the old well-known humps or big hills, as they generally called them; I have never found either salines or asphalt or petroleum. In only' one instance it looked as though asphalt night have exuded out of the ground, and that was in the Sour Lake, but right in that neighborhood years previous to that a company had operated commercially-they had a little refinery there-and had found it so unprofitable that they pulled up stakes and quit.

Jan 4, 1918

By Eric Hedburg

This paper was originally prepared as a picture of the situation presented by the mining industry referred to at the end of the year 1899; and some of the descriptions and drawings of special mines, etc., may not completely show their condition a year later. The statements made as to the cost of mining and concentration, however, still hold good. As to other general statements made in the paper, it is believed that the following additional facts cover all that is required to complete them for the additional year. The condition of the mining industry in the Joplin district was better at the close of 1900 than at any time during several preceding years. Values seemed to have adjusted themselves, in considerable degree, to the commercial and technical circumstances, the cost of mining-supplies of all kinds had returned to a normal basis, and the product of ore found a ready sale,

Jan 1, 1902

By T. M Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static

By T. M. Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953

By A. M. Gaudin

Of the various reagents employed in the flotation of zinc-bearing ores none have attained the wide popularity that is enjoyed at present by xanthates, copper sulfate and cyanides. This situation suggests the existence of an unusual dependence in the reactions of these chemicals and of sphalerite. A study of the flotative characteristics of sphalerite when using xanthates as collectors, as related to the chemical properties of copper salts and cyanides, has therefore been conducted at the University of Utah by the writer and his associates1 during the period of 1926 to 1929. In perusing the technical literature concerning the flotation of zinc ores and of zinc-bearing lead and copper ores, a striking and general lack of agreement as to the floatability of sphalerite was observed. The underlying cause for the erratic behavior of sphalerite has not been definitely ascertained but the presence in various proportions of iron sulfide in solid solution in the sphalerite has frequently been implicitly regarded as a major factor in this respect. Although the effect of iron sulfide in solid solution in sphalerite has not been investigated in relation to the behavior of sphalerite in flotation, it is likely that it is not as important a factor as was thought at one time. The variable float-ability of sphalerite has led to the use of fairly large amounts of cyanide to prevent its flotation in the case of certain ores, whereas mere fractions of that amount of cyanide, or even none at all, have been sufficient to achieve the same result for other ores2 Similarly, the amount of copper sulfate used to promote the flotation of sphalerite has been found to vary widely. Effect of Copper Salts in Distilled Water on Sphalerite In the work at the University of Utah, over a year was spent in futile attempts at duplicating experiments until it was discovered that the

Jan 1, 1930

By Robert McClurkin

Over a long period of time considerable attention has been paid to the chemical properties of the materials entering the iron blast-furnace charge. Infinite care has been used in the selection of materials having the correct chemical composition. Little attention has been paid to the physical properties of either the ore, coke or limestone. Until comparatively recent times the coke as produced, as well as the ore, was charged into the furnace without any attempt to maintain uniformity in physical size. Recently some work has been done along the lines of sizing of coke and in some cases the sizing of ore has been applied. In each instance marked results in the efficiency of operation have been attained. The effect of changing the physical size of the materials entering the burden has been reflected directly in the coke consumption. From the experience of operators and the results of numerous investigations which have been conducted on blast-furnace materials, it may be stated definitely that the physical properties of the materials entering the charge have as much bearing on the efficiency of the process as the chemical properties of these materials. Structure of Sinter On the Continent and more recently in this country iron-ore sinter has been introduced in blast-furnace burdens. The effect of the use of sinter has resulted in a material reduction in the coke consumption and an increase in the capacity of the furnace. The effect of the use of sinter is due undoubtedly to its porosity and to its physical size and, incidentally, to the chemical condition of the iron in the sinter and to the absence of combined water. Compared with Mesabi ores, all sinters are generally larger in size than the ore particles, and the structure of the sinter differs considerably from the structure of the ore. In sinter the mass is porous and open and makes available a great deal of surface for gas contact during the process of reduction. Most ores are relatively dense and nonporous and when the particle size is large the time element required for reduction is materially increased. The result of a very thorough investigation on iron-ore sinter by Schwartzll has shown that sinter is completely cellular in structure and

Jan 1, 1932

By Dell H. Adams

COAL EXPLORATION Coal exploration may be defined as the acquisition of data necessary to define and acquire a block of coal which can be mined at a profit. Unlike ore minerals, coal resources are widespread and relatively abundant with supply exceeding demand in almost every case. Thus simple discovery of coal is generally not enough. The chemical and physical variability of individual coal seams, the capital intensive nature of coal mine development, and the changing patterns of utilization require that a multiphase, three-dimensional evaluation be made of each potential reserve. Factors which must be investigated include not only the quantity and quality of the coal but also the geologic, hydrologic, and engineering characteristics of the seam and its surrounding strata. Acquisition of property to provide a secure base for exploration and mine development is equal in importance to the geologic and engineering programs. The successful development of a coal reserve requires that control of coal and, in the case of a strip mine, the surface be in the form of contiguous blocks of sufficient size to support mining. PHASES OF EXPLORATION The high capital risks of coal exploration and land acquisition dictate that a multiphase program be utilized to minimize initial risk. In such a program, phased development of the data insures that each increase in capital expenditures will be justified by a corresponding increase in the level of confidence in the ultimate success of the project. Each phase is designed to provide sufficient data and property control to facilitate the decision whether to proceed to the next phase of development or to discontinue the program (Table 1). The first phase of a typical exploration program consists of a pre-

Jan 1, 1981

Dr. Rausch, from your vantage point as educator, engineer, and corporate executive, what would you say is the most fundamental need that must be satisfied for the continuing welfare of our society, our industry and our profession?

Jan 3, 1977