Search Documents

By Hans M. Ewoldsen

The generation and evaluation of solutions to body force problems is of extreme interest to the geotechnical profession, as all natural stress states must necessarily include some contribution from the weight of the material. In this chapter the elastic solution for the stress field around a circular, horizontal tunnel at an arbitrary depth beneath the surface of a half-space is reexamined. The influences of body force, initial stress, and free surface proximity are examined and related to in-situ cases. The solution as presented deals only with an isotropically elastic medium; this medium is further considered only in a half-space configuration. It is readily apparent that these restrictions impose severe limitations if analogies are attempted with in-situ cases where geologic discontinuities, inhomogeneities, and irregular boundaries exist. The question might be raised as to the propriety of geotechnically oriented researchers even considering such idealized conditions. There is, however, much to be gained from study of such solutions. The lack of geologic discontinuities and inhomogeneities allows the investigator to separate and leisurely examine such parameters as are included in the solution, without worry of interrelationships of a host of other parameters. Further, elastic solutions have had extensive usage prior to the development of such techniques as the finite-element solution. It is interesting to compare body force solutions with the external field solutions which in the past have been used for design purposes. Finally, the exact solution may be used to verify the accuracy of the finite-element type of solution. The mathematical solution on which this chapter is based was originally developed by R. D. Mindlin.l Because of the complexity and length of the solution, no attempt was made to determine the resultant stress fields until the advent of the present-day high-speed digital computer. How-

Jan 1, 1972

By John W. Brauns, David H. Orr

9.1-1. Description and Basic Function. A conventional railroad haulage system for a surface mine performs the function of transporting the ore and/or waste out of the pit to a crushing plant or dump. Trains consisting of a locomotive and gondola or side-dump care suitable for loading by power shovels are used. Gondola cars are restricted to hauling ore as a rotary dumper is required to unload them. Side-dump cars are more versa- tile, being satisfactory for carrying both ore and waste; but because of their additional dumping mechanism they are likely to be more expensive to maintain (12). Also they weigh up to two times as much as a flat-bottom car of the same capacity, and, therefore, fewer cars can be hauled per train. Standard-gauge track is most commonly used. Track systems incorporate temporary track of low quality in areas where moves are frequent and permanent track of high quality on main lines. Rail haulage enabled open pit mining to establish its reputation, for efficiency. Prior to World War II it was the principal type of transportation used in large pits. Other successful surface mine haulage methods have been developed since that time. These have served to supplement railroad transportation, permitting selection of a method that is best adapted to the peculiar requirements of each mining project. 9.1-2. General Applicability and Controlling Physical Conditions. For handling rough rock, the shovel-train system is unexcelled (6). The ideal application is in a physically large, but not excessively deep, open pit mine from which the coarsely blasted ore and waste must be transported distances in excess of three miles. If, in addition, a high production rate is to be maintained, railroad haulage will probably afford a lower cost per ton transported than will any other haulage method. Relatively gentle

Jan 1, 1968

By F. H. Labee

Questionnaires and special letters soliciting information were sent to a great many geologists, petroleum engineers, independent operators, and representatives of large companies in Arkansas, Louisiana, Texas and New Mexico. Replies to more than 50 per cent. of these letters were received. A survey of the facts and opinions presented in this correspondence will be made a little later, but first some of the general aspects of the problem will be reviewed. By "unit operation,"1 we mean the development and operation of a single entire pool, or reservoir, of petroleum by one management, on a systematic and scientific plan which is best calculated ultimately to extract from the pay sand and bring to the surface of the ground the largest possible amount of oil with the greatest possible total profit. No one, as far as the author has been able to ascertain, denies the advantages, both scientific and practical, of unit operation. All are agreed that it is sound in theory. It permits the proper distribution of wells, which should always be spaced on the ground according to a regular geometric plan with the intention of maintaining the same spacing all the way down and into the pay sand, or pay sands. This spacing will be different for different fields, depending on such variable factors as the lithologic character of the pay formation, the nature of the controlling structure, the depth of drilling, the viscosity of the oil, and so on. From the viewpoint of engineering practice, as applied to economical extraction of oil, there is no more important consideration than well spacing—well spacing in the pay formation, and not merely on the surface of the ground —for the method of well spacing has a direct bearing upon all such engineering practices as pressure control, repressuring by gas, the water drive, and SO on. H. C. Miller2 summarized the advantages of an ideal cooperative development plan as follows: "Among the more important advantages of

Jan 1, 1930

By D. T. MacRoberts

Tins paper embodies the results of theoretical studies concerning gas reservoirs, especially the effect of drilling programs of various intensities upon pressure depletion and ultimate recoveries. The primary objective has been to determine the net quantity of recoverable gas that could be obtained as a result of each additional well, in comparison with the gas that might be secured from a single well ideally placed with respect to both acreage and geological structure. No method is yet known whereby the relative merits of intensive and sparse drilling can be compared experimentally; a reservoir must either be drilled closely or developed with wide spacing, but both programs cannot be conducted simultane-ously. Hence, the analytical method seems to be the only approach to the problem. While the present state of our theoretical knowledge does not offer a precise solution to the problem of gas flow in sand bodies, it takes such appropriate cognizance of the limitations of the methods used as to restrict any answer obtained to the realm of engineering accuracy. In solving the problem for the average gas field, it was found that practically the same answers resulted as to pressure distribution, regardless of the size of the drainage radius, even though the latter was assumed to vary from a few feet as a minimum to that of the entire reservoir as a maximum. Such limits represent extreme possibilities; therefore, the practical conditions that are associated with normal development programs, in which wells are placed in the center of tracts varying in size from 40 to 640 acres, will of necessity result in less extreme variations than those indicated in the tables accompanying this paper. Stated more concisely, the amount of gas unrecovered at abandonment (of the particular field used for illustrative purposes) will lie somewhere between 4.6 and 6 per cent of the total original content, no matter how intensively the field is drilled.

Jan 1, 1938

By Laurance S. Reid, Joe A. Porter

Gas dehydration plays an important part in the production of natural gas. Effective dehydration prevents formation of gas hydrates and the accumulation of water in transmission Systems,2,6,7 insuring uninterrupted gas deliveries at maximum efficiency under the most adverse weather conditions. At the present time, most gas companies require a maximum water vapor content of seven lb per million standard cu ft of gas. so that virtually all gas tendered for sale must he dehydrated to meet this specification. For a number of years it has been common practice to produce gas and gather it at a common point for dehydration prior to discharge into the transmission system.1,3,11,16,17 However, higher transmission line pressures, long gathering lines and relatively low ground temperatures have made it necessary to dehydrate gas at. or near. individual. wells in order to gather gas from a number of newly developed fields without unusual difficulty. Where gas has been dehydrated at pressures ranging from 300 to 800 psi in the past. future trends indicate that these processes may be operated at pressures as high as 2,000 psi. Economics of gas dehydration are of great importance, partitularly where facilities must he provided to process relatively small quantities of gas, such as the production from an individual well. Although the adsorption of water vapor from gas on a granular sorbent material such as activated bauxite, activated alumina, or one of the alumina-silica gels is highly effective and produces virtually "bone dry" gas, the cost of a small unit of this type is substantially greater than that of an absorption process which, through proper selection of the absorbing liquid, will dehydrate the gas sufficiently to meet pipe line specifications. For this reason, a great deal of emphacis has been placed on the development of small, inexpensive dehydration units8,24 and the search for more effective absorb. ent liquids has been intensified. A wide variety of methods for dehydrating gas are known' and many of these have been used in industry. Earlier applications of the absorption process employed concentrated solutions of calcium and lithium chlorides as the absorbent. The severe corrosion problems inherent in handling these solutions and the relatively small dew point depressions obtained caused early abandonment in favor of, or conversion to. diethylene glycol when it was found that aqueous solutions of this organic liquid were more hygroscopic than the brines and were non-corrosive. Processes employing diethylene glycol-water solutions are widely used for gas dehydration at pressures ranging as high as 1,200 psi.13,14,15 At nominal pressures a dew point depression of 45° to 50°F may be be and the data of Russell et al." indicate that a minimum dew point is obtained from the effluent gas at a pressure of approximately 1,200 psi when the gas is in equilibrium contact with a 95 per cent by weight diethylene glycol solution. In a number of instances the dew point depression obtained with diethylene glycol-water solutions is not sufficient to produce a specification product without cooling the inlet gas. In a recent search for a better absorhent, triethylene glycol was used in a small commercial dehydration unit and subjected to rather exhaustive field tests.' The data obtained were encouraging and indicated that, at pressures ranging from 300 to 500 psi, triethylene glycol porduced a substantially greater dew point depression than diethylene glycol. These results led to an investigation of the system natural gas-water-triethylene glycol in an effort to obtain vapor-liquid equilibrium data, to determine pressure limitations, and to develop other data pertinent to the design of gas dehydration processes. A review of the literature has failed to reveal any data which permit reasonably accurate calculation of the vapor-liquid equilibrium conditions for a solution of water and triethylene glycol in contact with natural gas at high pressure. Since these constituents form a non-ideal system, the Poynting equation18,21 or the usual combination of Raoult's and Dalton's laws19,20,22 would not be valid. Correction of Raoult's and Dalton's laws by the use of activity coefficients2' is not feasible for available data are insufficient for the prediction of the actual increase in the ratio of the activity of one component in the vapor phase to its activity in the liquid. Therefore. experi-

Jan 1, 1950

By C. Ernest Birchenall, Robert F. Mehl

Application of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion cocfficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner¹ derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smith5 on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 Activities in Brass9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by

Jan 1, 1947

By C. Ernest Birchenall, Robert F. Mehl

Application of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion cocfficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner¹ derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smith5 on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 Activities in Brass9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by

Jan 1, 1947

Robert Carl Sticht, member of the Institute since 1886, an American metallurgist of world-wide reputation, died in St. Margaret's Hospital, Launceston, Tasmania, on April 30, 1922, after an illness of eleven months, against which he fought with the highest courage and characteristic fortitude. The news of his passing came as a great shock to a host of his friends and former associates here, but on account of his long absence from the United States, exact biographical details have been heretofore lacking. Throughout Tasmania, the expressions of public sorrow were many and impressive, and the flags were flown at half-mast in Queenstown, Zeehan, and the entire Mt. Lyell district, in honor of the man who had won his place in the community as a great captain of industry and a man universally admired and loved. Sticht had been connected with the Mt. Lyell Mining & Railway Co. in Tasmania throughout its entire productive period. He had originally been induced to go to Tasmania through the good offices of the late Dr. E. D. Peters, then professor of metallurgy at Harvard University, who after personally examining the undeveloped Mt. Lyell properties, recommended Sticht as the best possible man to work out the complex metallurgical problem which that great orebody presented. Sticht had already made himself the leading authority on pyritic smelting, having taken up the idea as suggested and partly worked out by Lawrence Austin and carried it through to a certain degree of perfection in the case of limited tonnages of special ores. After studying the situation at Mt. Lyell, Sticht found the conditions there to be almost ideal for pyritic smelting, and he had the courage to adopt as the basis for a permanent, and eventually successful, solution of the metallurgical problem, a process that was then little more than a theoretically interesting possibility. The thorough studies and remarkable results attained at Mt. Lyell were published as chapters in Doctor Peters' various publications on the metallurgy of copper, Doctor Peters giving full credit to Sticht for their authorship. These chapters by Sticht practically constitute the: best literature of the art of pyritic smelting. The accuracy of observation,

Jan 1, 1923

By Richard D. Divine

In the Parkes process of extracting precious metals from lead, zinc is added to the molten lead containing gold, silver, copper, and some antimony. These metals, with the exception of antimony, form an alloy with the zinc by reason of their greater affinity for it than for the lead, and this alloy, being lighter than lead, rises to the top, carrying the precious metals with it, whence it can be removed by skimming. These skimmings are further treated for the separation of the zinc therefrom, and the recovery of the precious metals, the zinc being driven off by heat and again used for another operation. In addition to the zinc that combines with the silver, etc., a certain amount is necessary to saturate the lead, and it is therefore necessary to treat the desilverized lead to free it from this residual zinc. TO do this it is heated again in a reverberatory furnace and air or steam is blown through it. This oxidizes the zinc together with a small amount of lead and antimony, leaving the lead free from zinc and antimony, and forming oxides of these metals, which rise to the top and are skimmed off. This process relates to the separation of the metals in these oxides or skimmings. The skimmings are cooled, crushed, and mixed with carbonate of soda and pulverized oil coke. The mixture is heated in a reverberatory furnace on a bath of lead, to about 1,000" C. The metals are reduced by the coke, the lead and antimony go into the lead bath, while the zinc is volatilized and burned to oxide. This impure oxide is at the present time treated at Omaha by the Hall process of electrical precipitation, making a very pure metallic zinc. It can also be very easily refined by the old Schnabel process of using ammonia and carbon dioxide as a solvent. It seems to be in an ideal form for this purpose, and very few changes from the original method are required to obtain the zinc oxide practically C. P., leaving the lead and antimony as residues. There has been considerable difference of opinion regarding the effect

Jan 1, 1915

C. W. GOODALE, * Butte, Mont.-In regard to the employment manager, the North Butte Mining Co. has undertaken that line of work and the rest of the companies are watching the experiment. If it is proved to be the proper thing, the system will be introduced into other mines. We have to combat the opposition to the use of the "rustling card. It is nothing more nor less than asking the nationality, where the plan formerly worked, and whether he is married or single. ROBERT RHEA GOODRICH, Anaconda, Mont. (written discussion?).¬Since the efficiency of the different phases of personnel work employed by industrial concerns, which are bringing about greater efficiency and lessening the labor turnover, the latter being intimately connected with "contentment of mind," depends on the individual workman, it is highly desirable, as far as industry is concerned, to keep the workman's mind and body in trim in order to lessen accidents and produce a higher grade of work. Prevention being better than cure, health supervision of the workmen during employment should be maintained by the employers in order that mental alertness and physical well-being may be obtained. I have long believed, from observation in many plants, that when any problem is dependent on the individual workman, what he believes and what he does is vitally dependent on his health. I will follow with much interest what is to be clone in the future in relation to the subject of health supervision during employment (as well as medical examinations at the time of employment), and I hope this idea will be generally instituted in personnel work. A workman with good health and a contented mind should be an ideal component of a progressive industrial concern. The contentment of the workman is fostered by a number of admirable phases of welfare work which are being still further developed. The mental and physical well-being of labor should be the issue in Labor vs. Capital in the new period of the industrial promotion of the United States into which we are now entering.

Jan 4, 1919

Robert Carl Sticht, member of the Institute since 1886, an American metallurgist of world-wide reputation, died in St. Margaret's Hospital, Launceston, Tasmania, on April 30, 1922, after an illness of eleven months, against which he fought with the highest courage and characteristic fortitude. The news of his passing came as a great shock to a host of his friends and former associates here, but on account of his long absence from the United States, exact biographical details have been heretofore lacking. Throughout Tasmania, the expressions of public sorrow were many and impressive, and the flags were flown at half-mast in Queenstown, Zeehan, and the entire Mt. Lyell district, in honor of the man who had won his place in the community as a great captain of industry and a man universally admired and loved. Sticht had been connected with the Mt. Lyell Mining & Railway Co. in Tasmania throughout its entire productive period. He had originally been induced to go to Tasmania through the good offices of the late Dr. E. D. Peters, then professor of metallurgy at Harvard University, who after personally examining the undeveloped Mt. Lyell properties, recommended Sticht as the best possible man to work out the complex metallurgical problem which that great orebody presented. Sticht had already made himself the leading authority on pyritic smelting, having taken up the idea as suggested and partly worked out by Lawrence Austin and carried it through to a certain degree of perfection in the case of limited tonnages of special ores. After studying the situation at Mt. Lyell, Sticht found the conditions there to be almost ideal for pyritic smelting, and he had the courage to adopt as the basis for a permanent, and eventually successful, solution of the metallurgical problem, a process that was then little more than a theoretically interesting possibility. The thorough studies and remarkable results attained at Mt. Lyell were published as chapters in Doctor Peters' various publications on the metallurgy of copper, Doctor Peters giving full credit to Sticht for their authorship. These chapters by Sticht practically constitute the: best literature of the art of pyritic smelting. The accuracy of observation,

Jan 1, 1923

By H. H. Evinger, M. Muskat

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By M. Muskat, H. H. Evinger

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By Henry J. Welge

The approximate methods which are now in use for calculating oil displacement from reservoirs by gas-cycling or gravity-drainage at constant gas pressure, or by water flooding, make use of fundamental relationships derived by Leverett' and Buckley and Leverett.2 The mathematical equations needed are derived by applying Darcy's law to the flowing phases, and by material balance considerations. ln general, any treatment of this type gives. for any particular exploitation time considered, a plot of oil saturation against distance in the reser-voir. The oil recovery must then be obtained by integrating in some manner the area under the plot. A useful analytical method has been derived for computing the average saturation, and hence the oil recovery. Use of this method simplifies the calculations because it makes unnecessary any numerical integrations. and even the saturation distribution plots are not needed. A further advantage of the method is that knowledge of the relative permeabilities is required only for a limited and intermediate saturation range. In both the Buckley and Leverett method and the method discussed here, a linear sand section is assumed, and in the case of gas drive the gas pressure is assumed sufficiently constant both with respect to reservoir position and time so that changes in gas density. solubility, or reservoir volume factor are negligiklle. Thus, the exploitation contemplates oil displacement as by an immiscible phase. Examples are given to illustrate how the new method can be used. INTRODUCTION AND THEORETICAL BACKGROUND This paper treats a simplified method for computing oil recovery when the oil is displaced, from the reservoir sand by a fluid which, within the limits of accuracy desired, can be assumed to be incompressible and immiscible with the oil. The method makes use of two basic relations originally developed for the case of water displacing oil. However, the case of gas displacing oil saturated with gas at a constant (or nearly constant) pressure may also be considered a displacement by an immiscible fluid. This is possible for the reason that the concentration of the gas in the oil never changes if tile pressure is fixed. consequently, any additional free gas must remain undissolved in the oil, and so must act essentially as an immiscible phase. For convenience, the cape of gas drive will be considered first. Both of the two basic relations needed refer to a linear reservoir, or one which may be somewhat idealized so that a constant cross-section is exposed to fluid flow. Further, the displacing phase is injected at one end, or face; of the reservoir, while the produced fluids are understood to emerge at one point only. which is the opposite face of the reservoir. As indicated in Fig. 1, the reservoir may he inclined by some angle 8. The first of the required equations may be derived by applying Darcy's law to both displacing and displaced phases, and subtracting the two equations. The result for water drive has been given previously, as Equation (13) of the reference by

Jan 1, 1952

By F. G. Miller

Earlier studies of the mechanism of flotation showed that coal flotation products are contaminated by composite coal and mineral particles. The mineral matter of these particles has the dual effect of increasing the specific gravity and decreasing the coal surface of the particle available for bubble attachment. The present study showed that these particles are more loosely held in the froth column than the high grade coal particles, especially in the coarser sizes. Consequently, it is possible in the laboratory to produce a secondary concentration of the product by sprinkling the froth product with water to wash these loosely held particles from the froth during formation and recovery. To improve coal flotation, Bethlehem Steel Corp.'s research department has been working on a number of related problems based on both physical and chemical factors. The ideal is of course full understanding of the interrelated effects of both sets of factors. However, detailed studies1 of each physical factor have produced immediately usable results in commercial coal flotation and are providing the basis for our current work on the effect of chemical factors. Since these detailed studies provided the basis for the present investigation of froth sprinkling, their key results are highlighted here. For example, for a highly floatable bituminous coal, particle floatability was shown to be directly related to the percentage of coal surface available for bubble attachment and inversely related to particle mass. The data also underscored that in a given size range the addition of mineral matter to a particle makes flotation more difficult both by adding to the mass of the particle and by decreasing the amount of coal surface available for bubble attachment. Size also affects particle floatability in that as the size of particles of a given specific gravity increases, mass increases and the ratio between coal surface area and mass of the particle decreases. Flotation tests showed that any recovery of the coarsest particles in a coal feed is accompanied by progressively higher recovery of finer and finer particles. Consequently, fine high-specific-gravity particles are recovered with the coarse good coal. As a result, when the entire 14 mesh x 0 size range is processed by froth flotation, the good coarse coal is contaminated with high-specific-gravity fines. It is the small quantities of these fines that must be rejected from the froth product if flotation efficiency is to be increased above its present level. These principles and findings, together with work by Professor V. I. Klassen,' led to the froth sprinkling investigation reported in this paper. Working with Russian coals, Klassen had shown that froth sprinkling washes loosely held refuse particles from the froth and compensates for the water lost in the upper froth layers and increases its stability. As a result, the coal particles are retained in the froth and the loss of coarse coal from the froth is prevented. Decreases in ash of 0.1% to 1.5% were reported by Klassen. Working with a 28 mesh x 0 American coal, the author of the present paper found that single-stage flotation coupled with froth sprinkling produced a product comparable to that obtained by the more expensive method of roughing and cleaning.3 The investigation reported in the present paper expanded study of the effect of froth sprinkling to include each of the standard size fractions of a bituminous coal. The main findings are as follows: (1) For those size fractions between 48 mesh and 150 mesh, froth sprinkling produces a marked reduction in both sulfur and ash. In the case of those sizes coarser than 48 mesh, while this reduction is not as significant, the additional benefit of shorter retention time is still a plus for froth sprinkling. Furthermore, when froth sprinkling is coupled with normal fast flotation, the product purity approaches that obtained by starvation reagent feeding, i.e., gradual feeding of flotation reagent to float the recoverable coal from the pulp slowly in several increments. The specific results for these two size groups are: (a) 14 x 48 Mesh. By using froth sprinkling with fast flotation, product sulfur can be reduced to a level

Jan 1, 1970

By G. A. Vissac

The only fine coal washer with proved automatic controls, the feldspar jig is capable of good efficiencies even at low separating gravities, handles a variety of products, and treats 150 tph and over. IN continental Europe the feldspar jig is used almost exclusively for cleaning the fine sizes of coal; it operates with an artificial bed, made up generally of pieces of feldspar or of any other hard and heavy rock with good cleavages. A primitive form of this machine requiring close supervision was used in this country years ago, but output was small. The modern machines are generally air-pulsated Baum-type jigs, with capacities up to 150 tph, and treat sizes from % in. to 0, usually previously dedusted or deslimed. These jigs are equipped with very accurate and sensitive automatic controls insuring satisfactory operation even at low separating gravity and with feeds irregular in quality and quantity. This paper will deal more particularly with coal cleaning separation, but the technical studies apply equally to all minerals. Theory of the Feldspar Jig To understand fully the operation of the feldspar jig and to appreciate its potential value, it is necessary to measure and analyze the motion of small particles of various specific gravities, falling in various media, under various conditions. As no practical formulas were available for that purpose, the writer has developed new theories and established new sets of formulas, which cannot be demonstrated here. They are applicable to all minerals and to many problems of coal or mineral concentration. These formulas do not pretend to absolute accuracy, but results, tested by comparison with experimentally recorded data, are sufficient for practical purposes, as they give definite indications of trends, relative values, and order of magnitude of the many factors involved. For pulsating motions no earlier formulas are available. In the case of continuous currents or motions, such formulas as Rittinger's, Allen's, or Stokes', over a hundred years old, apply only to special shapes and sizes of particles, involve factors and coefficients difficult to measure or appreciate, and deal only with free motions. They are of little use in solving practical problems. Units used with the formulas presented here are in the CGS system. Lateral friction and suction have been taken into account according- to methods currently used in aerodynamics, and only hindered motion is dealt with. As the feldspar jig is primarily intended to create a fluid bed condition, the mixture of fluids and solids obtained is homogeneous, and the apparent specific gravity of the separating medium is calculated accordingly. For instance, if 20 pct of the volume is coal and shale, with an average of 1.60 sp gr, in a liquid of 1.10 sp gr, the actual specific gravity of the separating fluid is 0.80 x 1.1 + 0.20 X 1.6 = 1.20. The fundamental equations are as follows: The general motion of a particle falling in a medium of specific gravity equal to u, hindered motion. is dv/dt = g/Ls [ L (s-u) - u/g v2 [1] g = 981 cm per sec, acceleration of gravity, and L = thickness of the particle of specific gravity (s) and velocity (v). The initial acceleration dv/dt = g (1-u/s ) [2] is a function of the specific gravity of the particle, only for a given medium, and independent of its dimensions—an ideal separating condition. The terminal velocity Vt = gxL- (s-u)/u, [3] for a given value of u, is a function of s and L. Two particles, L, s, and L2 s2, are said to be equivalent if they have the same terminal velocity, and accordingly L1/L2=s2-u/s1-u. [4] Two such particles cannot be separated by continuous currents, in any concentrating device. Because the initial accelerated motion, which provides for efficient separation, is followed by a constant velocity, which has a limiting effect, it is essen-

Jan 1, 1956

By D. I. Bardos

The occurrence of Laves phases (AB,) in various binary alloy systems has been reviewed in recent papers.13 Iron forms Laves phases with Sc-, Ti-, V- and Cr-group elements. However, two of the corresponding Laves phases with cobalt, namely MoCo, and WCo,, are missing. Nickel forms binary Laves phases with Sc and Y, but not with any Ti-, V-, or Cr-group element. These conditions are schematically illustrated in Table I. That electron concentration is a significant factor in determining which type of Laves phase is formed in a given case was recognized long ago by Laves and Witte,4 This concept has been more recently applied to Laves phases formed by transition ele-ments. It now appears that the average electron concentration (average number of electrons per atom outside of the closed shells of the component atoms) may be an important factor also in determining whether or not a Laves phase can occur at all in a given system. As shown in Table I, in the transition element systems considered Laves phases are absent at electron concentrations of 8, or larger (to the right and below the double line in Table I). These absences clearly cannot be accounted for on atomic size considerations, as evidenced by the many inconsistencies apparent in Table 11. While the ideal radius ratio for Laves phases is 1.222, in the systems which do have Laves phases the ratios of CN 12 radii range from 1.10 to 1.46. The consistent absence of Laves phases at RA/RB< 1.10 might be attributed to the low values of these radius ratios. However, Table II shows that absences also occur irregularly throughout the radius ratio range covered. In a previous paper7 it was concluded that, in transition element systems forming u-phases, silicon may act as an acceptor of electrons, thus stabilizing the u-phase at electron concentrations higher than

Jan 1, 1962

By R. G. Ward, John Henderson. R. G. Hudson, G. Derge

Densities of melts of the iron oxide-silica system in contact with solid iron have been measured by the maximum hubble pressure method in the composition range O to 37 wt pct SiOz and the temperature range 1255 to 1410C. The constitution of the melts is discussed and it is postulated that the structure changes from a dislribution of iron ions in an oxygen ion network at pure "FeO" to a distribution. of iron ions in a network of silicate tetrahedra at the orthosilicate composition. JOHN HENDERSON, Junior Member AIME, was formerly with the Metals Research Loborotory, Carnegie Institute of Technology, Pittsburgh, Pa., on leave from Broken Hill Proprietary Co., Ltd., Research Division, Shortland, Australia. R. G. HUDSON, formerly with Metals Research Laboratory, is now with the John Jay Hopkins Loborotory for Pure and Applied Science, General Atomic Division, General Dynamics Corp., LaJolla, Calif. R. G. WARD, was formerly with the Department of Metal lurgical Engineering, Carnegie lnstitute of Technology, while on leave from the Department of Metallurgy, University of Sheffield, England. G. DERGE, Member AIME, is Jones and Laughlin Professor of Metallurgical Engineering, Carnegie lnstitute of Technology. Manuscript submitted January 19, 1961. ISD The system iron oxide-silica is an important one metallurgically because it forms the basis of several complex slag systems in use for industrial smelting and refining processes. In recent years considerable work has been done on liquids of this system but there are still many points of difference among workers using different experimental techniques and theoretical approaches. Phase equilibria/"3 activity,4-6 electrical conductivity,&apos; current efficiency,&apos; transference number,8 viscosity,9 surface tension,&apos;&apos; and density" measurements have all contributed to an understanding of the problem. Measurement of density is one procedure which is directly indicative of liquid structure since any deviation from ideality must be a result of structural interactions. Liquids of the iron oxide-silica system are of special interest because this is one of the few metal oxide-silica systems on which measurements can be carried out conveniently over the entire composition range from pure oxide to silica saturation. This includes the range of high basicity which has received relatively little attention in other systems. Although one investigation of density in this system has previously been undertaken," the results seem of sufficient importance to warrant the independent redeter-mination reported here.

Jan 1, 1962

By Charles R. Cavanaugh, John F. Elliott

The activity of nickel in liquid Pb-iVi alloys which are rich in lead was measured in the temperature region of 700° to 1100°C by means of the galvanic cell: The electrolyte used was stabilized zirconia. Tlze data were correlated using the a function, and a plot of the temperature coefficient aE/aT All subsequent calculations of the thermodynamic properties are based on these two functions. The activity, activity coefficient, and molar properties of mixing of nickel are reported. Nicke1 shows extreme positive deviations frorn ideality while lead shows a very slight positive deviation in the composition range studied The study of the activity of nickel in liquid Pb-Ni alloys reported herein was undertaken to explore the use of stabilized zirconia, an oxygen-ion electrolyte, with liquid-metal electrodes, and to obtain further information on the thermodynamic properties of the liquid binary Pb-Ni system. The cell The reversible electromotive force of the cell results from the difference in the chemical potential of the oxygen at the two electrodes: po, (left) - p~ (right) = -4E5 [I] The chemical potential of oxygen on the right is fixed by the activity of nickel in the solution and pure solid nickel oxide. That on the left is set by pure solid nickel in equilibrium with pure solid NiO. By definition: Since the chemical potential of nickel is related to the chemical potential of oxygen through the equilibrium constant for the formation of NiO from nickel and oxygen gas, the electromotive force of the cell is also expressed In this case, n is 2, E is the reversible potential of the cell, and 5 is Faraday&apos;s constant. The work of Kuikkola and wagnerl and Schmalz-reid2 has shown that the stabilized zirconia electrolyte is essentially an ionic conductor at the oxygen levels encountered in the experimental arrangement of the work, i .e., PG > 10-l7 atm. THE EXPERIMENTS The advantage of this type of reversible cell over those using a liquid electrolyte is the simplicity arising because the electrolyte also functions as one of the containing crucibles. A further simplification was the choice of the Ni (sat.)-NiO electrode as the standard. This permitted a ready check on the behavior of the electrolyte, as the potential of the cell must become zero when the right electrode becomes saturated with nickel, either because of a change of temperature or because of the addition of nickel to the electrode. It also permitted the potentials being measured to lie in the most satisfactory experimental range of 0 to 100 mv. Although it was not theoretically necessary, lead was included in the standard electrode as it assured good contact between the electrode and electrolyte. Cell Design. The general arrangement of the experimental cell assembly is shown in Fig. l(a) and the details of the cell itself are contained in Fig. l(b). The anode lead wire on the interior of the cell was connected to a coil of perforated sheet nickel. Within this coil were nickel oxide pellets which were held beneath the surface of the liquid Pb-Ni alloy. A disc of nickel oxide was held at the bottom of the external crucible (alumina) by means of the thermocouple protection tube. The nickel oxide disc and pellets were compressed dry at 10,000 psi and sintered at approximately 1000°C for an hour in air. A major experimental difficulty of reversible electromotive force cells with liquid electrodes is the selection of suitable materials for connecting

Jan 1, 1964

By Howard R. Keil

Reactor at Carlton mill successfully calcines pyrite-telluride flotation concentrate for cyanidation. CARLTON mill in the Cripple Creek district, 45 miles southwest of Colorado Springs, Colo., has been in operation for approximately three years, treating the custom sulpho-telluride ores formerly handled by the Golden Cycle mill in Colorado Springs. At the new mill the pyrite-telluride flotation concentrates have been roasted, prior to cyani-dation, in a Dorrco FluoSolids reactor, which has proved capable of yielding calcine readily amenable to cyanidation. Incoming ores are crushed at Carlton to % in. and sampled in 30 to 75-ton lots before the individual lots are mixed in the fine ore bin. The composite ore then goes to the grinding circuit. Classifier overflow from the grinding circuit is treated by flotation to produce a concentrate containing approximately 85 pct of the values in 5 pct of the weight. The flotation concentrate goes to the FluoSolids reactor prior to cyanidation. Cyanide solution values are recovered by zinc dust precipitation. Flotation tailings are thickened and cyanided, the values from this part of the circuit being recovered from solution by activated carbon. Gold values in the flotation concentrates consist of a small amount of finely divided metallic gold; the tellurides, sylvanite and calaverite; and gold very intimately associated with the pyrite. The metallic gold and a part of the telluride values can be extracted from the concentrates by cyaniding without roasting. However, extraction on the tellurides by this method is not satisfactory, and the pyrite values are so intimately associated with the pyrite that very fine grinding and cyanidation for a prolonged period under ideal laboratory conditions does not yield good recovery. Upon roasting, the tellurides are oxidized to very finely divided metallic gold which is readily soluble in cyanide. The pyrite is oxidized mainly to a porous iron oxide which allows cyanide solution to penetrate to gold particles and take them into solution. Feeding the Reactor Flotation concentrates move by gravity to a thickener. Thickener underflow is discharged at approximately 60 pct solids, by means of a diaphragm pump, into a storage and blending agitator. From here the concentrates are pumped to a disc filter. The filter cake, at 84 to 88 pct solids, drops directly into a repulper where it is repulped into a slurry of 78 to 80 pct solids. The repulped filter cake flows into a 6x6-ft slurry agitator from which it is fed directly into the reactor by the Moyno pump. The Moyno pump has eliminated a large number of difficulties that were first encountered in feeding a wet concentrate to the reactor. On the original installation in Canada a screw feeder was used to introduce the filter cake directly into the reactor. Since the reactor is under a slight positive pressure it was necessary to have a suitable seal to prevent gas escaping from the reactor at this point. When the concentrates produced in flotation were coarse or granular they could be readily fed to the reactor but when fine-textured, clayey concentrates were produced a great deal of trouble was encountered.

Jan 1, 1955