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By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Samuel B. Christy

As is well known, the ore at New Almaden is cinnabar. Native quicksilver occurs also; but, as a rule, in small quantities only. Pyrite occasionally accompanies the ore. Bitumen is quite common,

Jan 1, 1885

By T. Leser, A. W. Jenike

The problems of caving and underground subsidence can be considered as the failure of a highly compacted rock and its subsequent flow in the form of broken rock. The problem is complex because the propagation of failure and flow have to be considered simultaneously; the yield strength of the virgin rock and the broken rock are different; and, while under certain conditions it is sufficient to consider the virgin rock as homogeneous, the density and the yield function of broken rock are both pressure and time dependent. A study of the failure and flow of solids with a pressure dependent yield function has been published recently by Jenike.' In this paper the density of the broken rock is assumed to be only time dependent and the consequences are examined in the case of one-dimensional vertical subsidence into an initial cavity. The following describes an attempt to develop a tool which, in combination with other tools, may lead to mathematical solutions of real problems of caving and subsidence. STATEMENT OF THE PROBLEM An underground cavity of horizontal cross section 4 = 1 and height 6 is assumed to exist at some depth below the surface. At the time t = 0 rock above the cavity fails and completely fills out the cavity with expanded broken material. With passing time the broken rock consolidates and subsidence proceeds continuously upuard in a vertical shaft. The phenomenon is one-dimensional (see Fig. 1). The problem consists of finding the displacement and the velocity with which the frlmt of the subsidence (wave front) moves upward as a function of the time and of the rock properties. DIFFERENTIAL EQUATIONS CONTROLLING THE PHENOMENON With the assumptions that the broken rock is a continuum and that the subsidence occurs continuously, we can apply the one-dimensional differential equation of contitiuity (conservation of mass) and the equation of preservation of momentum The latter equation is replaced by an assumed relation based on experience, which takes care of the

Jan 1, 1962

T. L. Joseph (University of Minnesota, Minneapolis, Minn.)—Mr. Killian is to be commended for his inquiry as to why a decrease of 15.3 pct in coke consumption was accompanied by a decrease of only 1.9 pct in the CO/CO, ratio of the top gas. Although I encouraged him in his efforts to find a more significant and meaningful carbon-gas ratio, the method, calculations, and conclusions originated entirely with the author. Whether we agree entirely with the assumptions underlying his corrected ratio, I think we can all agree that a better ratio is needed, and that he deserves credit for recognizing the need and for doing something about it. To be most useful, the CO/CO, ratio for the top gas should reflect the way in which the carbon is gasified in the furnace, particularly the degree of oxidation and the extent of heat release. The effect of CO, from the decomposition of the limestone and the effect of the reaction of CO and water vapor in the upper part of the furnace on the quality of top gas should be isolated from the effect of more basic reactions such as ore reduction and solution loss. The reduction of sufficient iron oxide to produce a ton of pig iron and the accompanying changes in the proportions of the carbon gases can be expressed on a mol basis as follows: 16.5FeA + 16.5CO - 33FeO + 16.5CO, [1] 33FeO + 33.0CO = 33Fe + 33CO. [2] The CO, from eq 1 normally escapes from the furnace because it does not react with coke at the temperature of its release. However, as much as 50 pct of the CO, from eq 2 may react with coke because it is released at temperatures above 1000°C: 16.5CO. + 16.5CO2 = 33CO [3] Thus we see that the gasification of 16.5 mols or about 200 lb of C in solution loss will regenerate as much CO as is required for the last stage of reduction. The pronounced effect of reaction 3 on the final proportions of CO and CO, in the gas stream is obvious. It also follows that reaction 3 materially alters the heat release but it cannot be entirely eliminated in Lake ore practice. A previous study indicates that 100 lb of solution loss may be necessary to maintain the reducing power of the gas. A reduction of 100 lb from the normal level of 200 lb would mean that over 1,-000,000 additional Btu are released in the process. The 100 lb of additional carbon which will be burned at the tuyeres will release 437,000 Btu and the absorption of 583,000 Btu by eq 3 would be prevented. One of the chief objectives of sized ore burdens and more uniform distribution of the gas stream is to minimize solution loss by completing reduction higher in the furnace and in turn to release the maximum amount of heat from the carbon charged. It was odd, indeed, to find that the use of sized ore and sinter in the careful tests reported by Dobscha had changed the CO/CO2 ratio very little. The author has stressed the close correlation between his corrected CO/CO, ratio and production. A correlation of fuel consumption and the CO/CO, might be more logical. Fuel consumption on the prepared ore burden decreased 15.3 pct whereas the corrected CO/CO2 ratio decreased 19.0 pct. Although this agreement between the reduction in fuel and the reduction in corrected CO/CO2 ratio is not as close as the correlation with tonnage, it indicates the corrected ratio is superior to the normal ratio which decreased less than 4 pct. Some adjustment should be made for the reaction: CO + H2O = CO2 + H2 —700Btu [41 because there is evidence to indicate that about one half of the hydrogen is formed in the upper 21 ft of

Jan 1, 1953

By M. N. Brodie, John Chapman

INTRODUCTION - DEFINITION & HISTORICAL PERSPECTIVE While this symposium is concerned with comminution which, by definition, relates to all stages of size reduction of an ore body to a form suitable for mineral separation, the electrical drive aspect of the grinding section will receive most attention in contrast to the crushing, screening and materials handling elements of the process. The reason for this is that today's large mills, thirty feet diameter and upwards, present mechanical and electrical problems which require a degree of sophistication in their solution not previously required. The ability to satisfy these demands, so far as electrical technology is concerned, largely results from the development of semi-conductor devices. These can now handle typical electrical distribution power levels within remarkably s m all volumes and with high efficiency when compared with the motor-generator sets, mercury arc rectifiers, rotating amplifiers, magnetic amplifiers and vacuum tubes which were commonly used to provide speed and torque controls as recently as the early nineteen-sixties. The hardware available to the electrical engineer has changed dramatically whereby even the simplest control system formerly using hard-wired relays is now superseded by the program m able logic controller with its computer-like memory containing the sequence of operation, in other words, the software. Reverting now to the mineral process itself, it is assumed that the ore body has been mined using explosives and is delivered to the concentrating plant in its 'run of mine' form. The problem becomes one of reducing the material to a size which will permit an acceptable recovery of the mineral with the most economical use of energy. The size of 'run of mine' material will range from about minus five feet for high tonnage open pit operations to minus two feet for the smaller underground mine. The final reduction in size may range from minus ten mesh to minus two hundred mesh (exceptionally as fine as minus six hundred mesh) depending upon the concentration method and dissemination of the mineral values within the ore. There is no single circuit that satisfies all applications, but the pattern of metallurgical equipment use shown in Table 1 appears discernable from current practice, in general terms.

Jan 1, 1982

By W. F. Baldwin

The timing circuit generally employed in Carter Reservoir Behavior Analyzers consists of a synchronous motor driven cam which actuates a microswitch. A mechanically actuated timer of this type has several inherent disadvantages, among which are the following: 1. The first time interval may not be of uniform length, depending on the exact position of the cam at the conclusion of a previous run. 2. The positioning adjustments on the microswitch lever arms are critical and require periodic readjustment. 3. The mechanical system is subject to wear which will ultimately impair its accuracy. It was therefore considered desirable to devise an alternate method which would eliminate these difficulties without introducing others that would be equally troublesome. This note describes the design of an electronic timing device which has been incorporated in the analyzer constructed by the Field Research Laboratories of Magnolia Petroleum Co. The electronic timer circuit is built around a simple neon glow tube relaxation oscillator, the complete circuit diagram of which is shown in Fig. l. The operation of the circuit is as follows: Condenser C, is charged to the critical firing voltage of the neon glow tube VR-75 by battery B1 through resistors R1 and R2. When the neon glow tube fires, the condenser C, is discharged, The charging cycle then repeats itself,

Jan 1, 1950

By R. P. McLaughlin

IN most branches of the mining industry it is a well-recognized fact that care must be taken to protect the mineral deposit from undue physical injury. It is comparatively easy to grasp this idea when the mineral is a solid and the lives of workmen depend directly upon the care with which it is removed from its natural position, but when the product is a liquid. drawn up from pools several thousand feet beneath the surface of the ground through openings only a few inches in diameter, it requires some imagination to picture underground conditions and the changes which must often occur. The development of the petroleum deposits of California has been attended by numerous accidents, the results of which are readily noticed at the top of the wells and in the profit and loss accounts of the operators. Determination of the cause of these accidents has been the subject of considerable study, which naturally has fallen upon men familiar with technical methods. The greatest damage to the oil deposits of California has resulted from water finding its way into the oil-bearing sands, and it is the purpose of this paper to set forth briefly this phase of the oil industry. Much of the material here presented has previously appeared inn publications issued by the California State Mining Bureau, which, under the direction of State. Mineralogist Fletcher McN. Hamilton, has investigated the subject and taken steps toward improvement of conditions. The writer, having been in charge of this branch of the Bureau work, has gained considerable knowledge of existing conditions.

Jan 12, 1915

By Walter Weeks

THE process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. CASE I If compressed air is allowed to expand to the atmospheric pressure through an orifice in an air line that is supplied by a running compressor, no cooling results except the negligible one due to the Joule-Thompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected.

Jan 1, 1937

By Robert J. Hite, Samuel S. Adams

Potash, the generic term for a variety of potassium-bearing minerals, ores, and refined products (Table 1), owes its importance as an industrial mineral to the potassium requirement of growing plants. The term potash originally referred to potassium carbonate produced by the leaching of wood ashes. This process, for which the first US patent was issued in 1790, was the basis for the largest United States chemical industry in the early nineteenth century. The agricultural use of potash soon eclipsed the chemical applications following the German discovery in 1840 that potassium is essential to plant growth. The initial discoveries of large deposits of soluble potassium minerals, essential for agriculture applications, were made in 1857 in Germany and in 1914 in the United States. More than 90% of the 27.5 Mt K20 produced in the world in 1980 (Searls, 1981) was derived from marine evaporite deposits and approximately 90% was used in fertilizers. The potassium content of an ore, mineral, or product is customarily expressed as % K20, a unit of measure which is neither a natural nor synthetic compound of potassium (1.0% K is equivalent to 1.2046% K2O). Geology Potassium, the seventh most abundant element in the earth's crust, is present in silicate minerals in igneous, sedimentary and metamorphic rocks. Potassium is also a major constituent of many surface and subsurface brines (Table 2). Economic potash deposits are essentially restricted, however, to widespread, thick accumulations of marine chloride evaporite deposits. These deposits yield high grade, large tonnage ore bodies, many of which are amenable to low cost mining and beneficiation. The products from these deposits are, moreover, ideal for use in fertilizer because of the high relative solubility of the potassium chloride and sulfate evaporite minerals. World potash production and reserves for such deposits so vastly overshadow other sources of potassium that the following discussion will be limited largely to potash deposits in marine evaporites with brief reference to certain potash-rich brines. Approximately 85% of current domestic production is from bedded salt deposits and much of the balance is from brines. Marine evaporite deposits are accumulations of salt minerals deposited in structural sedimentary basins through the evaporation of seawater or mixtures of seawater and other brines. The salt minerals are precipitated in assemblages and sequences of assemblages as determined by the compositions of the brines and the solubility relations in the salt systems (D'Ans, 1933). The evaporation of seawater normally yields carbonate minerals as the first precipitates (Table 3). Further evaporation and concentration of the brine leads to the precipitation, in succession, of sulfate, chloride, and supersaline mineral assemblages including the salts of potassium and magnesium. The common minerals, ores, and products of potassium deposits are listed in Table 1. Many potash deposits contain accessory evaporite minerals together with a variety of detrital and authigenic silicates (Braitsch, 1971). The structural basins within which marine evaporites occur are of two main types: (a) cratonic basins formed by broad epirogenic movements (for example, the Michigan Basin of the midwestern United States and the Permian Zechstein Basin of eastern Europe), and (b) grabens, commonly related to continental

Jan 1, 1983

By Hans E. Gustafsson

INTRODUCTION The Kiirunavaara iron ore mine is situated in northern Sweden about 150 km north of the Arctic Circle. The ore body has a sheetlike shape, stretches about 4000 m N-S dipping 60°E and has an average width of 85 m. The ore body is known to a depth of more than 1500 m. Mining at present has reached a depth of about 500 m. The mineral is a magnetite containing 66-68% Fe. The ore body was originally mined as an open pit from 1900-1957. From then on the mining method has been sublevel caving. Production for the last few years has been 20-25 million tons /year. Sublevel caving is a mining method with many merits. One of the most valuable is the ability of using a high degree of mechanization. Today, 25 years after sublevel caving was introduced at Kiirunavaara, the advantages of the method have been more or less exhausted, and the disadvantages are more obvious as the rock pressure increases with depth. One of the disadvantages is the high degree of waste rock in the hoisted ore. Today the waste rock content is about 25% by weight of which 20% comes from the caved rock. Second, we are calculating a relatively high loss of ore (20%). Third, selectivity is unsatisfactory when mining different grades of ore. Field testing sublevel shrinkage caving (MSTM) is primarily aimed at lowering the content of waste rock compared to sublevel caving. ECONOMIC TARGET A simple calculation shows that if the waste rock content can be lowered from 25 to 15% the operational costs of mining will be lowered by about 40 million SEK/year (US $9 million) at a production level of 20 million tons/ year. A 15% waste content is the target of the field test. In the long range a decrease in waste rock dilution will mean lower investment costs for deeper levels. DESCRIPTION OF THE MSTM MINING METHOD One reason for decision to carry out the field test was that with MSTM the development drifts from sublevel caving could be utilized and thus the project could start without delay. The only additional development work needed was the loading level. Fig. 2 shows a profile through the MSTM area 66-68% Fe. and Fig. 3 shows the loading level.

Jan 1, 1981

H. H. Bleakney (Dept. of Mines and Technical Surveys, Ottawa, Canada)— The work of Dr. Machlin and his colleagues at Columbia University is so scholarly that one hesitates to take issue with them. Nevertheless the writer feels compelled to enter a demurrer to the mechanism of intercrystalline cracking proposed in this paper. The principal obstacle to its acceptance is found in its preoccupation with purely mechanical influences and its disregard for the chemical effect of impurities. The writer believes that the destruction of metallic cohesion by concentration of impurities at the grain boundaries is a necessary and sufficient condition for the development of intercrystalline cracking; and he believes that discussion of the numerous mechanical explanations proposed should wait until some valid objection to the chemical hypothesis has been advanced. It is nearly twenty years since Gillett" drew attention to the possibility that the chemical influence of precipitation might be the cause of intercrystalline cracking. As early as 1935, Greenwood'" remarked that grain-boundary precipitation of impurities in lead appeared to promote intercrystalline cracking. Again in 1939, Scott commented as follows on a paper by Thielemann and Parker:'" "There are at least two familiar phenomena that can influence grain-boundary cohesion: 1) intergranular oxidation; and 2) grain boundary precipitation. An important consideration in this work, therefore, is to determine which, if either, of these factors is responsible for the low values of cohesive strength observed." In 1952. the writer presented evidence," some original and some abstracted, which indicated that in copper, silver, aluminum, lead and iron, intergranular cohesion was a function of the purity of the metal. In 1954 Glen, discussing a paper by Ridley and Tapsell14 indicated his belief in a precipitation mechanism for the intercrystalline embrit-tlement of molybdenum steel and suggested that with an absolutely pure metal it would be almost impossible to obtain an intercrystalline crack. This suggestion has

Jan 1, 1959

By W. W. Mullins, F. A. Nichols

Solutions are developed, assuming surface diffusion and both internal and external volume diffusion, for the relaxation of bodies slightly perturbed from spherical and cylindrical geometries. Combined with those previously published for the nearly planar case, these results provide a means of gaging the relative contributions of the two diffusional proc-cesses in any given case. It is shown that in all sintering experiments to date, and probably in any attainable in practice, surface diffusion has played the dominant role, although most previous authors have assumed otherwise. It is also shown that surface diffusion predominates in normal field-emission tip blunting and also for the coalescence of gas bubbles introduced into metals by a bombardment. The surface-diffusion solutions for a perturbed sphere are combined with previous results for volume diffusion to show that the inclusion of interface diffusion permits considerably larger spheres to develop in diffusion-controlled precipitate growth before the onset of instability. A mechanism is also proposed for the spheroidization of precipitate platelets as well as rods. In a previous paper1 the relaxation of a nearly plane surface to flatness by the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion has been analyzed under the assumption that all surface properties are independent of orientation. In this treatment, criteria were developed for deciding which process predominates, and solutions valid in the latter stages of the sintering of small wires and particles to a plane were obtained. A numerical solution, valid throughout the entire particle-sintering process for the case of surface diffusion, was subsequently obtained by the present authors.' It was found that the analytic solution (which assumed small slopes everywhere) is accurate to within -10 pct when the maximum slope of the profile is less than 0.3; the wire-sintering problem has also been solved nu- merically for the case of surface diffusion and here again the results converge to the analytic small-slope solution at late stages of the process, the two solutions agreeing in this case to within 10 pct when the maximum slope of the profile is less than -0.6. The purpose of this paper is to extend the perturbation solutions to nearly spherical and nearly cylindrical geometries. We treat only the two principal diffusional processes, i.e., surface and volume, but for these geometries we discuss volume diffusion both inside and outside of the solid. Our results, when coupled with Mullins' solutions1 for nearly planar surfaces, provide criteria for gaging the relative contributions of surface and volume diffusion to the over-all transport process in three basic geometries. A very interesting feature in the cylindrical case is the occurrence of instability for longitudinal perturbations with wavelengths greater than the cylindrical circumference, a classical result. This instability of the cylindrical surface is applied to give a quantitative explanation for the often-observed "erratic" pore closure in the late stages of the sintering of wire compacts; also, the theory previously presented for the spheroidization of rod-shaped precipitates by surface (interface) diffusion' is expanded now to include volume diffusion inside and outside of the particle. The results for circumferential perturbations on a long cylinder allow quantitative estimates for gaging the relative importance of surface or volume diffusion in the early stages of the sintering of spheres or wires. The results here demonstrate clearly that surface diffusion has played a very important, if not dominant, role in all sintering experiments discussed in the literature, although the surface-diffusion contribution to the kinetics has usually been ignored. The results for the sphere (surface-diffusion case) are added to the results obtained previously by Mullins and sekerka3 concerning instabilities of a growing spherical precipitate particle (with interface diffusion disallowed) to obtain a general solution to this problem including interface diffusion. The inclusion of interface diffusion is found to increase significantly the range of stability of a growing spherical precipitate for typical metallurgical cases. The following assumptions are made: (i) the initial surface lies everywhere near and has a slope differing only slightly from that of the reference

Jan 1, 1965

By S. E. Craig

UPON entering the Uranium Field it was a pleasant surprise to find almost absent two factors that have always been a problem to the lead-zinc miner: 1) milling cost per ton, and 2) transportation cost to the milling site. Another interesting condition was the fixed price for the product. Under such conditions it seems rather simple to calculate the economics of a mining venture when grade and tonnage of a uranium ore deposit is known. That is assuming, of course, there is a market for the ore. It has been quite generally assumed by operators that a guaranteed price carried with it a guaranteed market, a subject about which there has been a great deal of discussion in the past several months. The fixed price for uranium in crude ore, calculated to U3O8, varies only slightly in value per pound from rather low grade ore to rather high grade ore. It is by taking advantage of this slight variation in price per pound in certain ranges that miners and shippers may increase substantially the monthly returns from ore shipments.

Jan 7, 1958

By G. H. Gilman

The campaign now being waged to improve the quality of the rock-drill bit is the natural outcome of the scientific development of the drilling machine during the past twenty years. In this development there has been a great increase of power output per unit of weight of machine. But the development of the rock drilling engine has been seriously hampered by the need of a drill bit that would withstand, without undue wear or breakage, the heavy rapid blows of the improved pneumatic hammer. This problem was difficult to solve because an increase in the weight or section of the drill-steel bar resulted in decreased cutting speed and higher operating costs of both the bit and its actuating engine. The solution, therefore, is to make the bit of steel that, for a given weight or section, will be more shock and wear resisting. In the attempt to meet these requirements, many of the drill-steel manufacturers alloyed the steel with vanadium, chromium, nickel, etc. on the assumption that such elements would improve the rock-drill bit but due to the sensitiveness of such steel to forging and heat treatment, higher cost, and lack of continuity of effort on the part of the steel manufacturer to perfect this product, but little progress has been made in the adoption of these steels and the so-called straight carbon steel is today recognized as the standard material for all rock-drill bits. The first step in improving drill-bit efficiency is the determination of the cause of breakage and wear. For this reason, in 1917, certain rock-drill manufacturers, in conjunction with some of the larger mining interests, conducted exhaustive tests in both the field and the laboratory. It was then found that, in the main, the cause of drill-steel troubles is not attributable to the duty imposed upon it by the normal operation of the drilling engine, but to improper forging and heat treating of the bit and to the subjecting of the bit to improper use. The fact that it is possible to minimize the troubles attributable to improper heat treatment of the drill steel has been demonstrated and it is recommended that such knowledge be made available by teaching those interested in the production, use, and up-keep of drill bits the principles on which success in this direction may be achieved. Unfortunately, but little attention has been given to the education of the drill smith. But a few years ago, the instructions given the man

Jan 1, 1922

By J. R. Cahoon, W. V. Youdelis

In a recent publication by Flemings and Nereo, equations for the calculation of the solute distribution in castings were developed, and the solute distributions for unidirectionally solidified A1-4.5 pct Cu ingots cast under various thermal conditions were calculated. The equations derived by Flemings and Nereo for the dendrite "expansion" and "steady-state" zones are essentially equivalent to those previously published by Kirkaldy and Youdelis, 16 for, although the flow velocity cooling rate, and temperature gradients appear in the fundamental differential equations, calculation of the solute distribution requires that the above be explicitly related to the assumed or measured solid-liquid mass distributions during solidification. In the treatment of Kirkaldy and Y-oudelis the mass distributions are simply assumed or measured without any prior and explicit association of the mass distributions to a velocity parameter. The treatment of Flemings and Nereo permits solidification conditions more complicated than the simple unidirectional case to be considered (although in principle the treatment of Kirkaldy and Youdelis could also be extended to include the more general solidification case); however, we note some limitations in the treatment of Flemings and Nereo, and the purpose of this discussion is to point these out and also to indicate those points of similarity in the mass distribution models used which make the two treatments equivalent. Both the Kirkaldy-Youdelis and Flemings-Nereo treatments consider a zone of dendrite "expansion" followed by a "steady-state" zone. However, Flemings and Nereo have failed to consider a zone of "collapse" which begins at the base of the first dendrites to reach the top of the ingot. The omission of this zone of "collapse" results in too high a value for the solute concentration in the latter portion of the ingot to solidify and the conservation of total solute is not possible. In the zone of "collapse" the solute concentration rapidly decreases, which may be accounted for as follows: consider a mushy zone of length X,, shown schematically in Fig. 11 (a), which develops at the chill face and then moves as a steady-state configuration along the length of a solidifying ingot. The solute distribution in this zone, when it first attains the steady state, is shown qualitatively in Fig. 11(b). The segregation is positive (above Co) in the region ab because this region contains primary dendritic solid, ranging from kco to kcE in composition (where k is the partition coefficient and CE is the composition of the eutectic liquid), and liquid metal near eutectic composition. The segregation is negative (below Co) in the region bc because it contains primary dendritic solid only slightly above kco in average composition and liquid metal only slightly above Co in composition. As the zone X, moves as a steady state

Jan 1, 1969

By R. J. Blackwell, A. L. Pozzi

Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments. If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascer tain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media. From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion. Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion. These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. INTRODUCTION One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated. Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies. Craig,et al,1 demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled. The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. Consequently, laboratory investigations were made of the dependence of recovery on dispersion and other variables,

By John L. Burns

The object of this chapter is to present data concerning the effect of the introduction of relatively slight amounts of carbon and nitrogen into supersaturated solution in iron. The study is confined to the alpha temperature range of both the Fe-C and Fe-N systems. The age-hardening characteristics of these two systems are considered. These data are compared to those of other age-hardening alloy systems and a "classification" is essayed. A.—Relation of Lattice Parameter and Electrical Conductivity to Changes in Physical Properties Due to Aging of Fe-C Alloys Since Whiteleyl in 1927 showed that some of the iron carbide that is normally present in slowly cooled low carbon-iron alloys disappears on rapid cooling from just below the A, point, interest has been manifested in the possibilities of age-hardening in these alloys. Masing and Koch,~ and at the same time and independently, W. Koster,~ proved these alloys to be age-hardenable. A. A. Bates4 a little later also published an interesting paper on changes in physical properties due to the aging of low-carbon steels. Many other papers have appeared showing changes in physical properties in specific instances due to this same phenomenon.

Jan 1, 1934

By John Burns

THE object of this chapter is to present data concerning the effect of the introduction of relatively slight amounts of carbon and nitrogen into supersaturated solution in iron. The study is confined to the alpha temperature range of both the Fe-C and Fe-N systems. The age-harden-ing characteristics of these two systems are considered. These data are compared to those of other age-hardening alloy systems and a "classifica-tion" is essayed. A.-RELATION OF LATTICE PARAMETER AND ELECTRICAL CONDUCTIVITY TO CHANGES IN PHYSICAL PROPERTIES DUE TO AGING OF FE-C ALLOYS Since Whiteley1 in 1927 showed that some of the iron carbide that is normally present in slowly cooled low carbon-iron alloys disappears on rapid cooling from just below the A1 point, interest has been manifested in the possibilities of age-hardening in these alloys. Masing and Koch,2 and at the same time and independently, W. Koster,3 proved these alloys to be age-hardenable. A. A. Bates4 a little later also published an interesting paper on changes in physical properties due to the aging of low-carbon steels. Many other papers have appeared showing changes in physical properties in specific instances due to this same phenomenon.

Jan 1, 1934

By Lawrence B. Wright, Lester G. Morrell

ON the steep slopes of the Kootenays, 15 to 20 miles south of Nelson, B. C., are a number of ore occurrences (Fig. 1). One that has many features of mining and geological interest is the Ymir Yankee Girl Gold Mines Limited. Discovery of this property was made in 1899 at an outcrop on the hillside, some 2500 ft. above the village of Ymir. This proved to be a branch vein 20 ft. long leading to two main veins, the Yankee Girl and the Spur (Fig. 5). The ore pattern as now delimited shows a remarkable increase in ore area with depth below the outcrop. This recent development is of interest particularly in view of the fact that the property was nearly condemned, professionally. Another interesting feature, which has a bearing upon its history, is the persistent excess of tonnage produced from period to period over visible reserves. This is not ascribed to lagging mine development, but to detailed vein characteristics, which we will endeavor to make clear by giving a description of the veins and their surroundings. HISTORY AND PRODUCTION Little interest was evidenced in this district until the building of the railway in 1893 provided easy access and the discovery of the Ymir mine [t] in 1896 attracted attention. As a result, the Ymir Yankee Girl group of claims was staked in October 1899. In 1907, an American syndicate took over the property and subsequently extended the 50-ft. drift and opened the present 400 and 540-ft. levels. In 1908, the Syndicate, without recording any shipments in the meantime, dropped its lease, which was taken up by H. L. Rogers, who bonded the Yankee Girl group. Rogers shipped 2622 tons of ore, mainly from the uppermost stope in the mine, which is reported to have yielded

Jan 1, 1938