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By D. M. Milne, R. F. Stoner, W. Bakiewicz

The Lower Indus Basin deposits form a substantial unconfined alluvial aquifer of excellent quality. This aquifer contains basically highly saline groundwater, overlain in places by considerable amounts of fresh water whose origin can be traced to the present and historical courses of the River Indus. In the past, the main source of groundwater recharge has been direct river seepage and water tables were generally deep. Since the establishment of a perennial irrigation regime however, deep percolation from the increased irrigation supplies has predominated and the water table has risen to within a few feet of the surface. The river system itself is being progressively devel-oped for irrigation and very shortly a situation will arise where the entire low winter flow will be utilized. Fresh groundwater will then be exploited to supplement the surface supplies, and at the same time a drainage system, mainly based on wells will be used to stabilize the water table at safe depths. This paper discusses some of the methods used to ensure optimum economic development of the fresh groundwater and describes the general design philosophy evolved by the authors' firms for both irrigation and drainage wells, with respect to both well configuration and operation. Water quality standards are discussed insofar as they affect subsequent use of the groundwater. A few particular aspects are considered, including the values of the relevant aquifer constants, the construction of wells, and the determination of screen losses. A major problem solved during the Lower Indus Project investigations has been the design of wells to produce fresh water from layers overlying saline water. This solution is also discussed. The recent interest in the groundwater of the Lower Indus Plains of West Pakistan has two main aspects. Firstly, soil waterlogging and the associated salinity hazards caused by rising water tables are a serious problem in agriculture, and the ease with which drainage requirements can be met by aquifer pumping makes this an obvious solution. The second interest stems from the rapid intensification of irrigation agriculture and the growing shortage of water supplies. In the areas where the groundwater is of suitable quality it can be used immediately for irrigation at relatively small cost and with large financial returns. In addition, the aquifer forms a potential storage reservoir which could be recharged from high river flows and depleted by pumping at times of scarcity. SOURCE OF GROUNDWATER The Lower Indus plain is a relatively long and narrow alluvial basin on a north-south axis, some 23,000 sq miles in area, bounded by higher land to the east and west. One hypothesis to explain the distribution and quality of groundwater in the region1 presupposes a river system considerably larger than, but very similar to the present river. This is characterized by a single mainstream, with subsidiary overspill channels in times of flood, running along the crest of a self-deposited ridge and with an extensive advancing delta. Sea water is contained in the alluvial pores of the advancing delta, forming the native groundwater. This has been partially displaced from two sources, namely direct seepage of fresh water from the river channel in meander flood plain areas and percolation from flood spillage in cover flood plain areas. Percolation has been subject to much re-evaporation and is thus slightly saline even as it reaches the groundwater. The whole complex has been further affected by two main influences: evapotranspiration from the land surface that tends to salinize the groundwater and down-valley flow that tends to bring fresher water

Jan 1, 1970

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By D. R. McCord

Data of a known statistical quality has been successfully used in a system of conventional fluid mechanics equations essentially free of empirical "conformance factors to prediet early detailed field 03 in a reservoir where gravity drainage is important and oil and rock properties vary con. siderably. The system is useful where comparative recovery predictions for one or more cases of natural depletion and gas cap pressure maintenance are needed and the reservoir is not too heterogeneous. INTRODUCTION Many authors, have examined various facet* of the gravity drainage-gas cap pressure maintenance problem over the last several years. Two of them. Burtchaell and Elkins, have published practical studies. In the case described in the present paper the best development and operating plan for one of the important reservoirs of the Bolivar Coastal Field in Western Venezuela was urgently needed. It was requested that sound comparative economics be presented along with an engineering evaluation of no additional drilling, maximum drilling. several cases of gas pressure maintenance, of water flooding and combination cases. A rapid analysis of the effect on recovery of the range of crude and rock properties indicated that none of the published methods using average properties would yield adequate comparative predictions. This paper covers the predictive system developed to deal with natural depletion and gas cap pressure maintenance. The large amount of data available for this field permitted statistically reliable correlations to be made of most rock and oil properties, and the evident smooth areal variations of these properties encouraged the construction of a lineal mathematical model of material balance and fluid flow equations, which could be manipulated by a modified iterative procedure. The manipulation is much more adaptable to computing machines than manually operated calculators and subsequent studies have been prepared for the IBM Card Program Calculator. A matrix as opposed to linear model has been tentatively worked out by other members of our group to deal with more heterogeneous reservoirs. It is more adaptable to computers such as IBM-701 or the Remington-Rand Univac. In 1950, when the system reported below was developed, no rapid computing machines were available to the author. Their existence and promise encouraged an initial approach by hand. Some details of oil and rock Property correlation are included because there are a surprisingly large number of medium-sized reservoirs in the world that show systematic property variations which are significant for a rigorous analycon. All large reservoirs (over half a billion barrels recovery) with which the author is familiar contain at minimum a significant temperature variation. Using the rock and oil property correlations, past pressure and production, the gas-oil ratio history of the reservoir was computed and found to be in close agreement with field measurements. The future performance under cases of natural depletion, gas injection of 100 MMcf/day, and of 130 MMcf/day, was then computed; a 70 MMcf/day case was also carried far enough to provide data for comparative economics. The 130 MMcf/day case proved to be the most attractive. A 50,000 horsepower gas turbine driven centrifugal compressor plant to take this quantity of adjacent field gas from 30 to 1,950 psia and inject it into the reservoir is under construction. The total cost of the project will exceed 20 million dollars.

Jan 1, 1953

By Ihor A. Kunasz

Introduction Lithium minerals occur predominantly in pegmatites which contain mineral assemblages derived from the crystallization of postmagmatic fluids or from the metasomatic action by residual pegmatitic fluids. They have been the traditional sources of raw materials for ceramic and chemical industries. With the discovery of Searles Lake, brines became new sources of lithium. Indeed, the 1960s may well be referred to as the "brine decade" because several brine bodies of significant economic importance were discovered. In the United States, the brines of Clayton Valley, Nevada, are presently exploited by Foote Mineral Co. The brines of the Great Salt Lake of Utah, the Smackover formation, and the Imperial Valley geothermal field, have been defined as important resources of lithium. In South America, new occurrences have been identified in Bolivia and Argentina. At the Salar de Atacama, Chile, new production capacity is scheduled for 1984. Following the termination of the AEC purchase program in 1959, several companies such as Maywood Chemical Co., American Lithium Chemicals, and Quebec Lithium Corp. were forced to close their operations. Nevertheless, with the development of new applications in glass ceramics, air conditioning systems, synthetic rubber, and metallurgy (aluminum potlines), the lithium industry grew steadily, and with the potential application of lithium metal in batteries and nuclear reactors, a healthy growth can be foreseen. New products and new applications are likely to stimulate exploration for expanded, reserves as well as the search for new sources from which lithium could be extracted economically. Geochemistry of Lithium Lithium is the third element in the periodic table. It is the lightest of all the metals, having an atomic weight of 6.938, an ionic radius of 0.68Å and a charge of +1. The geochemistry of lithium has been extensively studied and has been summarized by Rankama and Sahama (1950), Goldschmidt (1937), and Hortsman (1957). The distribution of lithium in igneous rocks is controlled by its size and its charge, and by the (MgO+FeO) / Li2O ratio. In the early stages of crystallization of a magma, that ratio is very large. Consequently, both magnesium and iron are removed by ferromagnesian minerals in preference to lithium which is then concentrated in the residual magma. This results in an enrichment of lithium in silicic rocks and pegmatites (Strock, 1936). Pegmatites are coarse-grained igneous rocks formed by the crystallization of postmagmatic fluids. Minerals within pegmatites may also form by metasomatism (Jahns, 1955). Genetically, the pegmatites are associated with neighboring intrusives. Mineralogically, granitic pegmatites contain feldspar, quartz, and mica as the main constituents and a variety of exotic elements such as lithium, beryllium, tantalum, tin, and cesium, which may or may not occur in economically significant concentrations. Detailed studies by numerous investigators (Cameron et al., 1949, 1954; Hanley et al., 1950; Jahns, 1953, 1955; Page et al., 1953) indicate that pegmatites often exhibit an internal zonal arrangement, with each zone containing a specific suite of minerals. The lithium minerals are usually found in the intermediate zones, and although as many as 13 zones have been recognized by Cameron, et al. (1949), a complete zonal arrangement is rarely found. Zoning of pegmatite bodies has also been observed on a regional basis. The regionally zoned pegmatite sequences exhibit mineral assemblages and complexity according to their re-

Jan 1, 1983

By C. K. Ferguson, J. A. Klotz

This paper describes experimental investigations conducted at the California Research Corporation's model oil well. The first part describes filter loss from several drilling muds through bore hole walls during mud circulation and drill string rotation. The effect of mud properties and drill string rotation with mud circulation is described. Filtration from a bore hole full of drilling mud, not circulating, but under pressure for extended time periods, is also discussed. The second part describes filter loss to permeable formations from beneath a drilling bit where filter cuke has no opportunity to develop appreciable thickness. If potential flow theory is applied to predict filtrate invasion from this hole bottom, targe invasions arc calculated. But model well experimentation shows that filtrate invasion from the hole bottom is controlled by mud particles that penetrate the formation ahead of the bit. This experimentation provides data to estimate the effect of mud particle penetration on fluid loss to formation. The third part presents an estimate of mud filtration during drilling of a well. INTRODUCTION As oil wells are drilled by the rotary method, drilling mud circulates up the annulus between drill pine and well wall. Drillers adjust mud density so that the pressure at the bottom of the mud column is several hundred psi greater than the pressure of reservoir fluid. As a result of this pressure difference, the liquid part of the mud filters into the rock around the bore and mud solids deposit as a filter cake on the well wall. For many reasons the petrogleum industry, within the past 20 years, has spent much money and energy to determine the volume of mud filtrate that enters rock around the well bore and dedicated much research effort to reduce this volume. Among the reasons for attempts to determine the volume of mud filtrate and to reduce this volume are the following: 1. If filtrate damages the permeability of oil sand, the resultant damage to oil well productivity will depend on the distance that the filtrate invades the oil sand; reduction of filtrate volume may, therefore, increase well productivity. 2. Filtrate that penetrates shale sections may cause the shale to swell and to slough into the well bore. Uncontrolled sloughing may stick drill pipe. Reduction in filtrate volume may reduce drilling trouble. 3. Electric log resistivity curves are changed by invasion of a mud filtrate; the change depends on the depth to which filtrate invades. Knowledge of this depth is necessary before resistivity logs can be interpreted accurately. For these reasons, specifications the place an upper limit to drilling mud filter loss are now written into almost all drilling programs. These specifications are based on APT Recommended practice 29, Standard Field Procedure for Testing Drilling Fluids,' which describes a static filtration test operated at 100 psi filtration pressure and at ambient temperature. Although this test is adequate for mud control, it cannot be used to compare filtration properties of different muds. Schremp and Johnson' showed, for example, that mud with a low API filter loss does not necessarily have low filter loss at bottom hole temperature and pressure. Also, no information has been available about the effect of bottom hole mechanics (mild circulation, drill string rotation, and bit action) on mud filtration. This paper discusses filtration data measured in the California Research Corporation's model oil well, which models closely oil well bottom hole geometry and hydrodynamic conditions. The filtration processes that

Jan 1, 1955

By A. M. Sarem, J. M. Campbell

Molecular refraction is introduced as a new and improved third parameter for prediction of the PVT behavior of hydrocarbon systems. This parameter, characterizing the complex as well as the pure hydrocarbon systems (1) is a direct measure of London dispersion forces which affect the PVT behavior; (2) can be measured directly, accurately and easily for complex as well as pure hydrocarbon systems; (3) varies significantly between the reference substances thus allowing accurate interpolation of PVT properties; and (4) has a fundamentally sound basis. Molal average molecular refraction was used with the pseudocritical mixing rule proposed by Leland and Mueller to predict the molal volume of liquid and vapor for 84 published data points on nC4-nCI0, Cl-nC5, Cl-nC4-nC10 systems in the region of coexisting vapor-liquid and at the critical point. The same technique was applied to predict the densities of liquid hydrocarbon mixtures in the two-phase and single-phase regions near the critical point for seven different systems each having different properties of the heptanes-plus fraction, but all simulating the fluids of either gas-condensate or volatile oil reservoirs. A modification of the Leland-Mueller mixing rule for the determination of pseudocritical properties is also presented which yields more accurate liquid density predictions than the original form when used with the proposed third parameter. INTRODUCTION The PVT behavior of multicomponent systems has received widespread attention in the literature in recent years. A large portion of the reported work has stemmed from attempts to overcome the inherent difficulties encountered when using the standard compressibility-factor chart which shows 2 as a function of reduced temperature T, and and reduced pressure p,. This chart assumes that z, is constant for all systems. The error in this assumption is not pronounced for pipeline-type gases high in methane and low in heavy ends, particularly when contained at moderate pressures. For such gases the error in the calculated z is usually less than 2 to 3 per cent. However, the reliability of this approach becomes somewhat nebulous for gas condensate and volatile oil systems at high pressure. One logical approach has been to recognize the variation of 2,. This idea was first suggested by Meissner and Seferianl and used by Lyderson, Greenkorn and Hougen2 to prepare extensive tables of thermodynamic properties. Other third parameters have been proposed by Stockmeyer, Kihara, Riedel, Lightfoot, Bloomer and Pitzer. These were tested by Satter and Campbel13 for many gas mixtures and it was shown that they were inter-related. All of these third parameters have a common fault — they cannot be directly evaluated for the heptanes-plus fraction. Consequently, one necessary requisite of an improved method for predicting the density of multicomponent hydrocarbon systems, was development of a third parameter that could be evaluated for that fraction. PREVIOUS MULTICOMPONENT DENSITY PREDICTION METHODS Sage and Lacey4 suggested a method of using partial molal volumes for computing the density of hydrocarbon gas mixture for pressures to 3,000 psi. In this technique, they approximate the complex multicomponent gaseous mixtures by a quarternary system of methane, ethane, propane and butane. Sage, Hicks and Lacey5 suggest a method of using partial molal volumes for computing the density of hydrocarbon liquids. The results agree within 3 per cent of the experimental values. However, the composition range is limited to about 10 per cent by weight of methane. Consequently, this correlation does not cover the low-molecular-weight liquid similar to natural gasoline and high-pressure gas condensates.

Jan 1, 1966

G. F. LOUGhlin,* Washington, D. C.—With reference to Mr. Bain's paper: The scarcity of adequate geologic data on building stone reflects, among other things, a lack of interest on the part of geologists. It has been one of my duties to attend to matters relating to building stone and other structural materials that have come to the U. S. Geological Survey, but for several years my principal administrative and other duties in the Section of Metalliferous Deposits have prevented me from giving structural materials the attention that they deserve. I have felt that investigations relating to structural materials should be assigned to someone else, but thus far nobody with a sufficient interest in the subject has come forward; further, the specific calls for these investigations have been so few and far between that it has not seemed practical to draft any one for the job. The general situation is such that steady and substantial progress in the application of geology to the utilization of structural materials is not likely to be made unless someone with keen interest in the subject takes the initiative. If the start is once made, I know from experience that cooperation from the more progressive members of the quarry and building industries will be readily forthcoming. Mr. Sales' suggestions are all constructive and most welcome. A thorough, detailed discussion of them might be as long as his manuscript, but could largely be summarized with the one word "amen" qualified by the alibi that a chronic shortage of funds and therefore of personnel has prevented us from carrying out some of his suggestions already. A few of them might call for an Act of Congress before we could undertake them, and one or two, such as the preservation of mine maps, with which I heartily agree, would call for much additional space as well as clerical and supervising help. Several items in Mr. Sales' paper—for example, the question of balance between the scientific and more directly practical studies and the surveys or resurveys of the larger and smaller mining districts—have been covered in my contribution to the symposium. The suggestion of frequent reviews of progress in the study of ore deposits is excellent and can be followed without serious diversion from projects already on the Survey's program. Brief reviews by Survey men have been published in periodicals, and the contributions by several of them to the Lindgren Volume1 may also be cited as serving this purpose to some degree. The practice of publishing short papers by Survey men in outside journals rather than in Government reports is largely the result of experience and expedience. Our printing funds are limited, and considerable time must elapse between the transmittal of a paper and its publication. Time is saved therefore by sending papers to outside journals, and the editors of those journals are usually glad to receive them. Members of the Survey would doubtless prefer to have the products and byproducts of their official work appear in official Survey publications if conditions were more favorable. If we were left entirely to ourselves the balance between the more scientific and the more directly practical studies would be somewhat better than it is, but the

Jan 1, 1935

G. F. LOUGhlin,* Washington, D. C.—With reference to Mr. Bain's paper: The scarcity of adequate geologic data on building stone reflects, among other things, a lack of interest on the part of geologists. It has been one of my duties to attend to matters relating to building stone and other structural materials that have come to the U. S. Geological Survey, but for several years my principal administrative and other duties in the Section of Metalliferous Deposits have prevented me from giving structural materials the attention that they deserve. I have felt that investigations relating to structural materials should be assigned to someone else, but thus far nobody with a sufficient interest in the subject has come forward; further, the specific calls for these investigations have been so few and far between that it has not seemed practical to draft any one for the job. The general situation is such that steady and substantial progress in the application of geology to the utilization of structural materials is not likely to be made unless someone with keen interest in the subject takes the initiative. If the start is once made, I know from experience that cooperation from the more progressive members of the quarry and building industries will be readily forthcoming. Mr. Sales' suggestions are all constructive and most welcome. A thorough, detailed discussion of them might be as long as his manuscript, but could largely be summarized with the one word "amen" qualified by the alibi that a chronic shortage of funds and therefore of personnel has prevented us from carrying out some of his suggestions already. A few of them might call for an Act of Congress before we could undertake them, and one or two, such as the preservation of mine maps, with which I heartily agree, would call for much additional space as well as clerical and supervising help. Several items in Mr. Sales' paper—for example, the question of balance between the scientific and more directly practical studies and the surveys or resurveys of the larger and smaller mining districts—have been covered in my contribution to the symposium. The suggestion of frequent reviews of progress in the study of ore deposits is excellent and can be followed without serious diversion from projects already on the Survey's program. Brief reviews by Survey men have been published in periodicals, and the contributions by several of them to the Lindgren Volume1 may also be cited as serving this purpose to some degree. The practice of publishing short papers by Survey men in outside journals rather than in Government reports is largely the result of experience and expedience. Our printing funds are limited, and considerable time must elapse between the transmittal of a paper and its publication. Time is saved therefore by sending papers to outside journals, and the editors of those journals are usually glad to receive them. Members of the Survey would doubtless prefer to have the products and byproducts of their official work appear in official Survey publications if conditions were more favorable. If we were left entirely to ourselves the balance between the more scientific and the more directly practical studies would be somewhat better than it is, but the

Jan 1, 1935

By J. S. Crump, H. L. Stone

Laboratory studies have indicated that displacement of oil from a reservoir by means of a condensing gas drive results in extremely high oil recovery, approaching 100 per cent under the most favorable circumstances. A condensing gas drive is defined as a gas drive in which the gas utilized is appreciably soluble in the oil it is displacing. The laboratory studies consisted of a number of gas drive displacement experiments, all using a horizontal, sand-packed, steel tube as the laboratory reservoir. The experimental results indicate that the more soluble a gas is in the oil to he displaced, the more efficient that gar is as a displacing fluid. Experiments were conducted utilizing both a light, volatile crude and a heavy, asphalt crude as the in-place oil. In both cases, oil recovery was appreciably enhanced by solubility of the displacing gas. It is believed that the use of condensing gas drives would result in increased oil recovery from many reservoirs during either primary or secondary phases of production. INTRODUCTION Since the early days of the oil industry there has been an increasing awareness of the problems of oil recovery. During the last few decades particularly a growing recognition of the problems has led to widespread attempts on the part of the industry to increase oil recovery by improved technology. One method which has been used to increase recovery is the maintenance of reservoir pressure by injection of gas. Part of the beneficial effect resulting from this gas injection was to prevent evolution of the gas dissolved in the reservoir oil, since such evolution would cause the oil to shrink and become more viscous, thereby adversely affecting oil recovery. In most instances, the gas injected was predomillantly methane, and so the possibility of oil recovery by retrograde vaporization existed. Laboratory investigations of displacement of reservoir oils by methane, carried out at high pressure, have indicated that considerable additional recovery of light oils could be effected by vaporization, but only at the cost of a severe volumetric shrinkage of the residual oil which would cause a decrease in relative permeability to oil in the reservoir. Consequently, recovery of oil by physical displacement would be impaired. The study suggested, therefore, that recovery of oil might be enhanced by injecting into the reservoir a gas known to be appreciably soluble in the oil at reservoir conditions. Swelling of the oil due to solution of gas should result and yield a consequent increase in the relative permeability to oil. The work described in the following sections was, therefore, undertaken to investigate the possibility of increased recovery by this mechanism. Research similar to that reported in this paper has been conducted by The Atlantic Refining Co.1,2,3 In these studies, Whorton, et al, and Slobod, et al, used methane-rich gas to displace oil from model reservoirs. Solubility of the gas was achieved by keeping the reservoir pressure greater than the saturation pressure of the original oil, and the degree of this solubility was varied by operating at different reservoir pressures. Thus the Atlantic project was primarily a study of the effect of reservoir pressure upon oil recovery by gas drive. The objective of the work reported in this paper was to study the effect of gas composition upon oil recovery while holding the reservoir pressure constant. DESCRIPTION OF EXPERIMENTS The discussion of the preceding section suggests that

Jan 1, 1957

By M. R. Annis

Drilling mud rheological and gel property changes due to elevated temperatures frequently cause problems in drilling deep wells. A laboratory investigation of the effects of time, temperatures up to 3001; and mud composition on these properties was made with concentric-cylinder, rotational viscometers of the Farm type. The viscometers were sealed from the atmosphere to prevent dehydration of the sample. Gel strengths were found to be more sensitive than viscosities to changes in temperature and mud cornposition. The high-temperature gel strengths of bentonitic clay drilling fluids were not predictable from low-temper.atl4t-e measurements. At high temperatures, [lie clay flocculates. The floccu-lation temperature depends on the concentration and type of solids in the mud and the degree of chemical defloccula-tion. As the bentonite content of a mud increases, floccrrla-tion temperature decreases. Lignosulfonnte treatment raises the flocculation temperature. To minimize adverse high-temperatrrre effects on mud properties, the mud should be maintainted at minimum solids content, properly treated with. a defloccullant which is stable at the maximum ten?perature encountered and maintained at a pH high enough to insure activation of the deflocculant for the duration required. The Methylene Blue Test for cation exchange cnpacity of a clay was found to be a useful guide in deter.niinirig when a mud contains a dangerously high clay conWnt. INTRODUCTION In drilling a well it is desirable, for several reasons, to know the effects of time and temperature on the rheological and gel properties of the drilling fluid in the hole. Problems associated with drilling fluids normally occur down-hole: so it is reasonable to be interested in the properties of drilling fluids at the conditions which exist down-hole. It has long been observed that high pump pressures are often needed to start circulation after a trip and that the "bottom-up" mud that is circulated back to the surface is usually more viscous than it was before "cooking" at the bottom of the hole for several hours. Burk-hardt' showed that a knowledge of rheological proper-ties of muds under down-hole conditions is necessary to predict pressure surges. He showed that the viscosity of a mud greatly influences the magnitude of pressure surges and the likelihood of lost returns. McLean et aL~ showed that the rheological properties of a mud under down-hole conditions are very important to cementing operations. This paper presents data showing the effects of time and temperature on rheological and gel properties of water-base drilling fluids. Measurements of gel strengths and rheological properties were made with two different concentric-cylinder rotational viscometers of the Fann type. One was the conventional six-speed viscometer modified to operate at temperatures up to 350F and at the vapor pressure of the liquid at test temperature. The other viscometer was newly designed to operate at temperatures up to 500F and pressures up to 1,000 psi. Tests with both instruments were made under essentially the same operating conditions. The new viscometer is shown in Fig. I. In this investigation, great emphasis has been placed on the rheological properties of clay suspensions, since clays are largely responsible for a mud's thixotropic and gel-

By G. H. Kennedy, H. E. Criner

CYCLONE thickeners are "hydraulic centrifuges" designed either to produce a maximum practical separation between the water and solids of a feed slurry or to classify the slurry solids according to particle settling rate. The possibilities of utilizing the thickener to "close" plant water circuits have been investigated. Since the thickener becomes an integral part of the plant water circuit when installed, the basic means by which the solids content of all circulating water systems must be controlled is reviewed. All coal not separated from the circulating water by means of dewatering screens or settling devices must be bled from the plant at the same rate as they are being fed or created by degradation. If this were not true, the circulated volume would finally be completely filled with solids. If the rate of bleed is low, the solids concentration in the bleed and circulating water generally will be high. To keep a reasonable circulating water concentration, large amounts of fresh water must be supplied and the bleed rate must be high. These conditions are usually undesirable because of the difficulty in securing fresh water, the loss of large quantities of coal, and the pollution of nearby streams. Thickeners are the primary stage in the separation of the water contained in the bleed from the coal. Since a thickener, when operating with reasonable efficiency, usually cannot be expected to deliver an underflow containing less than 50 pct water, secondary dewatering devices such as a slurry screen or vacuum filter must be used to separate additional water from the bleed. The surface area required by the filter or screen will be nearly proportional to the total water which must be handled, and therefore the thickener becomes necessary to hold down the original cost. The water separated from the coal is then returned to the plant circuit to maintain the water balance and thus becomes the source of fresh water. It is not necessary to return clear water to the plant to maintain control of the circulating water concentration. It is only necessary that the bleed dewatering devices remove coal in all sizes at a rate equal to that at which these sizes are entering the circulating water. However, practically speaking, in order to maintain low solids concentration, it is usually necessary that the thickener have good recovery characteristics on bituminous coals in those sizes down to 400-mesh. The thickener can remove the smaller sizes from the closed-circuit system at the "solids in" rate and prevent their "build up" in the circulating water as shown in Fig. 1. With the portion of the feed water going directly to the underflow, comes the very fine solids not concentrated by the cyclone. All the larger solids are removed from the feed and delivered in a concentrated condition at the underflow. To apply thickeners with some reasonable assurance that operating requirements will be met, it is necessary to know the rate at which solids of all sizes must be removed from the circulating water and to know the thickener characteristics. The required removal rate of fine solids not recovered by other dewatering devices may be estimated from the size distribution and tonnage of the plant feed with a reasonable allowance for degradation in the circulating water system. A more reliable estimate may be secured by sampling the plant bleed water during a constant load period.

Jan 1, 1952

By L. W. Sink, B. H. Kear, S. M. Copley, M. F. Hornbecker

IT is well known that under appropriate conditions of chill casting, many metals and alloys develop a columnar grain structure having a high degree of preferred orientation.' In cubic materials, this principle has been employed to produce shaped castings with a unidirectional cube oriented columnar grain structure as well as shaped single crystals with a cube axis parallel to the growth ais.' "he purpose of this note is to describe how this same principle can be enlployed to produce wires, rods, or more complex crystal Shapes with a variety of conlpositions in cube or random orientations by a single casting operation. The procedure for directional solidification of in Fig. 2. Examination under crossed polarizers indicated that the striations were a second phase (presumably the B19 phase) which frequently forms initially at primary grain boundaries and then grows toward the interior as thin ribbons. X-ray studies on filings of this alloy reannealed at 1300°C for 15 min indicated a strong pattern of the fcc phase together with a substantial pattern of the B19 phase. The un-annealed filings, however, showed only the pattern of a cold-worked, fcc structure. In these two-phase alloys it appears, therefore, that the B19 phase is transformed into a disordered fcc structure by cold-working. The mechanical properties of these alloys would be of some interest since a fcc structure might be expected to possess greater ductility than the or-thorhombic B19 structure from which it forms. The author wishes to thank Mr. Harvey Yakowitz and Mr. Richard Manuszewski for obtaining the photomicrograph in Fig. 2. This research was partially supported by Research Grant DE-02455 from the National Institute of Dental Research. columnar grained ingots involves pouring a melt into a preheated mold having a water-cooled copper chill at its base? and controlling the temperature gradient in the mold so as to maintain columnar grain growth from end to end of the ingot.4 This is illustrated schematically in Fig. l(a). It should be noted that the longitudinal temperature gradient promoting unidirectional columnar grain growth is maintained by heat loss primarily through the solidifying ingot to the chill, so that both the temperature gradient and the growth rate diminish with increasing distance from the chill. As the distance from the chill increases? the columnar structure coarsens, and the perfection in preferred orientation tends to increase progressively. Using this same procedure of gradient solidification, Fig. l(b) shows a simple scheme for producing a batch of crystals having the same cube orientation rather than an assemblage of columnar grains. Wires and rods are produced by cementing ceramic tubes to the wall of the mold. The steep temperature gradient produced in the central chamber is controlled by the mold heater to produce favorable conditions for crystal growth. Clearly the success of the operation lies in the selection of individual growing columnar grains by some kind of orifice at the base of each channel in the mold. Using simple constrictions, experience with nickel-base alloys has shown that 4 -in.-diam holes at a distance of -1 in. from the chill yield crystals within 7 deg of (100); closer control of orientation is possible by placing the crystal selector farther away from the chill.

Jan 1, 1970

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

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

Jan 1, 1962

By G. Thodos, R. B. Grieves

A method has been developed For predicting the critical temperatures and critical pressures of binary mixtures of carbon dioxide, hydrogen sulfide, nitrogen, hydrogen, carbon monoxide and oxygen with the normal paraffin hydrocarbons. For carbon-dioxide and hydrogen-sulfide systems, relations are presented that take into account the peculiar behavior of mixtures with closely boiling components, such as carbon dioxide-ethane and hydrogen sulfide-propane mixtures which exhibit minimum critical temperature points. For hydrogen, nitrogen and carbon-monoxide systems, the extreme critical behavior caused by wide differences in pure component properties is established In addition, those fixed gas-paraffin systems which resemble paraffin-paraffin systems are also accounted for. For a mixture of known composition, the pure component critical temperatures, critical pressures and normal boiling points are all that are required to determine its critical point. Graphical relations are presented relating Tc and PC , of the mixture to the pure component properties. From the treatment of 12 carbon-dioxide and hydrogen-sulfide systems reported in the literature (74 mixtures), the expected error lor the critical temperature is approximately 1.5 per cent, and for the critical pressure, approximately 2 per cent. From the treatment of six hydrogen, nitrogen and carbon-monoxide systems reported in the literature (30 mixtures), the expected error for both the critical temperature and critical pressure is approximately 2.5 per cent. The relationships, which have been developed with only normal paraffins as the hydrocarbon components, may be extended to those isoparaffins and olefins which fall within the allowable volatility ranges. INTRODUCTION Many of the fixed gases — carbon dioxide, hydrogen sulfide, nitrogen, hydrogen, carbon monoxide and oxygen — occur in natural mixtures with hydrocarbons. Carbon dioxide and hydrogen sulfide are frequent components of the fluids produced from underground petroleum reservoirs. Nitrogen, carbon dioxide and hydrogen sulfide are present in varying quantities in most natural gases and gas-condensate well effluents. Hydrogen mixtures are of considerable interest in many phases of refining processes of petroleum. The determination of the critical temperatures and critical pressures of such mixtures is of value in vapor-liquid equilibrium studies, for the prediction of the characteristics of underground reservoirs, and for reduced-state correlations of PVT, transport and thermodynamic properties. The accurate estimation of the critical point for binary mixtures is an important initial step toward a complete analysis for the establishment of the critical temperatures and pressures of multi-component mixtures. Methods for predicting the critical temperatures and critical pressures of binary hydrocarbon systems have already been presented in the literature.8 It is possible to apply these existing methods to fixed gas-paraffin mixtures, but due to their unusual critical behavior, values calculated deviate considerably from experimental values. For systems containing trace quantities of the fixed gases, these methods are acceptable; however, for systems containing more than 5 mol per cent of the fixed gases, these utterly fail to produce reasonable critical values. Consequently, in this study a method has been developed for handling such binary mixtures over the entire composition range. CARBON-DIOXIDE AND HYDROGEN-SULFIDE SYSTEMS The critical behavior and the vapor pressure behavior of mixtures of carbon dioxide and hydrogen sulfide with paraffinic hydrocarbons may be quite similar or quite dissimilar to that of paraffin-paraffin mixtures, depending on the volatilities of the components involved. The critical temperature and normal boiling point of carbon dioxide are very close to the corresponding values for ethane, while its critical pressure is considerably higher than that of ethane. The normal boiling point of

By L. A. Panek

During the past three years, USBM has developed an apparatus and technique for direct measurement of existing pressure and change of pressure in mine rock. This relatively simple and inexpensive monitor is reliable for months after being installed. It is used to determine shift of ground pressure created by different sequences of mining, to ascertain the cause of rock failures, and to evaluate the need for artificial support. The technique has been employed to measure pressures in limestone, greywacke, concrete, diabase, and soft iron ore. When rock is subjected to a load it is deformed. Ordinarily this is observed in a mine as the displacement of one point with respect to another—the deflection of the roof, which may be observed as a convergence between roof and floor; or the extrusion of material from the rib, which may be observed as a decrease of the distance between the rib and the post of a timber set. The effect of excessive pressure may be a rockburst if the rock is strong, or it may be squeezing ground if the rock is soft. Some desirable effects of high stress (high in relation to strength) are the caving of roof in a longwall mining operation, the caving of ore in block caving, and the decrease in mechanical energy required to break down the mineral seam in a retreating pillar-robbing operation. In any case, whether the observable effect of rock load is desirable or undesirable, it is a displacement, and depends on the following four factors: 1) The structure—the size and shape of openings, pillars, and linings, the geologic bedding and jointing. 2) The mechanical properties of the rock—prin-cipally the strength, modulus of elasticity, and flow characteristics. 3) The load or applied stress—primary sources are the weight of superincumbent rock, which increases with depth, and unrelieved tectonic stresses; secondary sources are redistributed pressures caused by other nearby openings, especially large mined out zones (rock pressure depends partly on the rock structure created by mining). 4) Duration of load, related to the length of time the opening is exposed. CONTROL OF ROCK DISPLACEMENT Rock displacement can be controlled by control of these four factors. Consider now the means of exercising such control over these factors. Control of the structural features is obviously possible to a great extent, as such control is exercised largely by choosing the method of mining and the methods of natural and artificial support. Rock properties vary, even within a particular mine, but they are controllable only in the limited sense that control may be exercised by choosing the beds or zones to be mined so that rocks with undesirable properties will not occupy critical positions within the rock structure created by mining. Rock pressure is the most complex of the four factors through which ground control can be achieved because it is invisible, difficult to measure, and poorly understood. Rock pressure is controllable only to the extent that control is exercised on the rock structure created by mining. Considering openings within a particular mine, time of exposure varies, and is readily controllable because it is easily measured and easily understood — the longer an opening stands, the greater the likelihood of failure or excessive convergence. Control is exercised by choice of an appropriate sequence of driving openings of different classes, such as haul-ageways and rooms, which are required to remain well supported for different lengths of time under different conditions. Again, control is exercised through the method of mining. All controllable factors can be controlled by proper design of the mining method. The orientation and relative positions of the mine workings and the sequence of their excavation are likely to be much more important to ground control than is the design of artificial support. This implies that the major decisions in regard to ground control are made, knowingly or not, at the time the mining method is chosen. WHY MEASURE ROCK PRESSURE In addition to restrictions on the several factors, control implies the measurement of these factors in some sense, whether only qualitatively by visual observation, or by actual quantitative determination with a measuring instrument. Rock pressure is the most difficult of these factors to measure, largely because of the interaction between the measuring device and the rock. Nevertheless, the quantitative

Jan 1, 1961

By F. L. Toy, C. E. Sims

PNEUMATIC processes for converting molten pig iron to steel were the major producers of steel during the latter half of the 19th Century and until shortly after the turn of the century, when these processes began losing ground to their rival—the basic open hearth process. The first pneumatic process for converting molten pig iron to steel was introduced almost simultaneously by Sir Henry Bessemer in England and by William Kelley in the United States during the decade 1850-1860, but it was Bessemer who pushed it to a successful commercial operation. The process itself is so basically simple that it has not lent itself to many extensive or revolutionary improvements since its inception. During the first 30 yr, numerous' designs of vessel and many modifications of practice were tried before the industry standardized on something resembling current practice. The evolution in construction has resulted in proportions and arrangements based more on mechanical expedience than on metallurgical requirements. Many of the early converters were stationary and had to be tapped similarly to the cupola or open hearth furnace. Such types were used for many years in Sweden and Germany, but the rotating or tilting types were favored in England and the United States. There was evident trouble with bottom tuyeres, becAuse about half of the early designs were constructed for side blowing with tuyeres submerged below the metal-bath surface. Even portable tuyeres, introduced from above, were tried. The principal advance, which made bottom blowing practical, was the invention, in 1863, by Henry Bessemer, and subsequent improvement by A. L. Holley, of a detachable bottom so that the tuyere section could be renewed. In the meantime, it was the demonstration, by Robert Mushet, of the value of manganese in overcoming hot-shortness in converter steel, that made the process metallurgically feasible. At first, only the acid practice was used, and Swedish pig iron, because of its low sulphur and phosphorus, was in great demand. The development of a suitable basic lining, by Sidney G. Thomas and Percy G. Gilchrist in 1876-1879, made the process applicable to the high-phosphorus ores of Europe. From the beginning of the use of the Thomas-Gilchrist process, trouble was experienced in obtaining sufficiently high temperatures in the blown metal, particularly in small heats. It is necessary, of course, to have the low-carbon blown metal at a considerably higher temperature for handling from vessel to ladle to molds than is needed for the molten pig iron. All of the increase in temperature in a pneumatic process must be obtained from the heat of combustion of the elements contained in the pig iron plus that from silicon when ferrosilicon is added. In bottom blowing practice, carbon is almost completely burned, but inasmuch as it cannot be oxidized to a higher state of oxidation than to CO when in contact with liquid iron, only a minor portion of the heat-producing capacity is utilized. Under such conditions, it is not considered to be an efficient source of heat. In the acid practice, therefore, silicon and manganese are the large heat producers, are quickly oxidized, and are efficient fuels. Too much manganese, however, thins the slag greatly and tends to promote excessive slopping or throwing of slag and metal from the converter during the blow. Most operators, therefore, like to keep the manganese content of the iron below 0.60 pct, and thus the main source of heat is the silicon, which must be at least 1 pct and sometimes 2 to 3 pct for small blows such as for castings. Ferrosilicon is sometimes added during the blow to obtain an adequate temperature level. In the basic (Thomas) practice, even more heat is required, because cold lime is added to flux the phosphorus after it is oxidized, and the basic slag must be maintained at a proper temperature. Silicon

Jan 1, 1951

By P. Datta, L. L. Handy

For a wetting phase displacing a nonwetting phase from a porous medium the distribution of the residual fluid may depend on displacement conditions. Although this subject has been debated in the literature, only a few experiments have been cited to support the various conclusions. Experimental results presented in this paper show that fluid distributions are dependent on imbibition pmcedures. Results agree qualitatively with predictions from the pore doublet model. If the rate of water imbibition is restricted, the nonwetting phase is trapped preferentially in .the larger pores as expected. But if the rate of water imbibition is unrestricted, trapping occurs somewhat more in the smaller pores. These conclusions were deduced primarily from relative permeability measurements. INTRODUCTION Relative permeabilities are known to depend on the saturation history of the porous medium. For either continuously increasing or continuously decreasing wetting phase saturations, however, they have normally been assumed to be single-valued functions of saturation. Severat investigators have compared relative permeabilities measured by different methods and have reported acceptable agreement.1-5 Studies of simple models of the displacement process suggest that the distribution of residual fluids can be influenced by the displacement method. If this is so, relative permeabilities also should depend on the method of displacement. These predictions have not been supported by experimental data. The object of this paper is to investigate experimentally some of the predictions of these model studies. The particular question of importance is whether steady-state and unsteady-state methods should be expected to give the same values of relative permeability. Much of the reported data showing agreement between steady-state and unsteady-state methods have been obtained on un consolidated sand. Johnson, Bossler and Naumann, however, compared steady-state and unsteady-state results for Weiler sandstone and found no significant differences.5 Levine made a detailed study of pressure and saturation distributions for a laboratory waterflood in a consolidated system but made no attempt to calculate performance from steady-state relative permeability data Bail and Marsden in a somewhat similar set of experiments did attempt a comparison of observations with predictions but the results were inconclusive.7 Excluding gravity, two forces affect the distribution of wetting and nonwetting phases during an unsteady-state, immiscible displacement: viscous and capillary forces. If relative permeabilities are indeed the same when measured by steady- or unsteady-state methods, the fluid distributions at the same fluid saturations must be similar for both methods. Furthermore, the implication is that the relation between capillary and viscous forces is the same for both methods insofar as the effect on microscopic fluid distributions is concerned. Unsteady-state displacements are normally run at high rates to maximize the ratio of the viscous to capillary forces. The objective is to reduce the effect of capillary forces on macroscopic fluid distributions. For floods in which the phase which wets the porous medium displaces the nonwetting phase, capillary forces compete with viscous forces in determining fluid distributions.8 The residual nonwetting phase is discontinuous. Competitive aspects of viscous and capillary forces and the resulting effect on water-oil distribution in porous media have been illustrated in an elementary way using a pore doublet model. This model and predictions from it have been discussed at considerable length by Rose and Witherspoon, Rose and Cleary and by Moore and Slobod.9-13 Rose and Witherspoon show that so long as water invades the model at a rate equal to or greater than the free imbibition rate, the water will move through the larger capillary of a doublet first and trap oil in the smaller capillary. On the other hand, if a negative pressure is applied to the water

Jan 1, 1967

By Leons Kovisars

Introduction Competitive analysis is the collection and evaluation of data on a product, a product line or on an entire industry. Much of the focus of competitive analysis centers on production volume and the price targets of the competitors. In actual practice capacity may be used in place of production volume. Similarly, unit production costs and individual producing units - mines, mills, smelters, refineries - may be the targets of the analysis. The purpose of competitive analysis is to provide information for strategic planning. The analysis will locate the position of the company in the industry and define the competitive margin -- or lack of a margin - between the company and other producers. The analysis can show the current situation and may be expanded to examine the outlook for the future. The forecast option is particularly valuable because it will show the opportunities for new project development or the expansion of current production. Similarly, the forecast will show the potential threat from new entrants, and may provide early warning to reconsider operations that may become uncompetitive in the future. Production cost analysis is a clearly understood means to evaluate producers and estimate the outlook for their profitability. The cumulative cost for the industry outlines the supply structure and defines the marginal cost of production used in developing price forecast as explained in the sub- sequent section of this paper. Competitive analysis is particularly important to the mining industry, notably to metal producers. The final product is typically a purified metal conforming to standards, and interchangable with the output of other producers, i.e. a fungible commodity. Brand loyalty is questionable in the mineral industry. Consumers will show a preference for specific brands, but this preference will be limited to a premium of several percent over the general market price. Price and assurance of supply are the keys to marketing success. Assurance of supply depends on geopolitical considerations and production capabilities. Price will be closely related to cost of production and a thorough competitive analysis should describe the cost structure of the industry. This snapshot will locate one's own position and provide an immediate and readily understandable evaluation of the hazards and opportunities inherent in this position. In the following section we shall discuss elements, methods and sources for competitive evaluation. ELEMENTS OF COMPETITIVE ANALYSIS The practice of systematic collection and analysis of data on competition is hardly a new concept; see, for example, Wall (1) or Porter (2). However, most discussions have been in the context of conventional industrial or manufacturing industries, with a focus on product lines and brand marketing. These considerations are not irrelevant to mining but they do have only a limited application. The key to success in the mining industry is minimizing the cost of production. However, this simple concept becomes complex when we consider relevant costs and the planning horizon. Production costs include the factors consumed in production, namely labor, fuel, energy, materials and supplies. The cost also includes purchased and contracted services such as freight, smelting and refining, sampling and sales required to convert ore to the finished metal. Royalties and ad valorem taxes paid on gross production are direct expenses, as is the cost of administration required by the production units. The sum of these outflows is the total cash cost, the expense that has to be paid in cash in order to continue production. Indirect costs incurred by a producer will commonly include allocated headquarters expenses, as well as the capital charges associated with equity investment and debt. Profit is not generally considered an indirect cost even though it represents the cost of using the owner's capital; similarly, income taxes represent the government's participation in the profits of the enterprise. Interest payments are considered as a direct expense in some cost studies, but many competitive evaluations would consider

Jan 1, 1985

By Gordon H. Geiger, John M. Svoboda

One mechanism of metal penetration into mold aggregates by cast steels is vapor state mass transport. In order to further understand and quantify this mechanism, the steady-state diffusion of metallic vapors was studied at 1250" to 1600°C in controlled oxygen pressure atmospheres by measuring the weight loss from a metal bath whose vapors were allowed to diffuse through a porous aggregate compact held at constant temperature. Mass transport rates substantially greater than those predicted from the assumption that the vaporizing species was the elemental metal vapor were observed. Vaporization rates were found to increase with an increase in the oxygen partial pressure in the gas atmosphere with maximum vaporization occurring at oxygen partial pressures just below those in equilibrium with a liquid oxide layer at the given temperature. When the liquid oxide layer was present, no vaporization was observed. Metal carbonyls were ruled out as the vapor species involved because of their thermodynamic properties. The species with the enhanced volatility were deduced to be gaseous metal-oxygen molecules, probably the polynuclear oxides (FeO)2 and (Mn0)2. Diffusion followed the ordinary diffusion mode, and Knudsen diffusion is not important in normal foundry molds. The interdiffusivities of the metallic vapors and the mold atmosphere, through the porous aggregates, were measured. The effective interdif-fusivity of the vapor species and mold atmosphere through the aggregate may be expressed as follows: Deff,12 - — where E is the void fraction of the aggregate and 7 is the "tortuosity factor". Aggregate material had no effect on diffusion rates, and the only relevant parameter was the void fraction. Values for 7 ranged from 3 to 6 for normal foundry aggregates with 4 being considered a good representative value. An area of interest in high-temperature metallurgical processes which has received little attention in the past is the diffusion of metal vapor species in porous aggregates. Research into the metal penetration phenomenon' in foundry molds has shown that a major penetration mechanism is the vapor transport of metallic species into the porous foundry sand molds, followed by condensation of metallic films on the sand grains. Considerable study of the vaporization of metallic species has been reported in the literature, and the vapor transport properties of many metallic species have been determined.2'3 Many instances have been observed where the vaporization behavior could only be explained by the existence of a metallic species with a vapor pressure greater than the elemental metallic species. These species were identified or, in some cases, presumed to be carbonyls,4,5 hydroxides,6-9 or vaporous oxides.10-16 The diffusion of gases through porous aggregates has received considerable attention in the literature pertaining to catalysis, although primarily at low temperature, and more recently in the literature concerned with ore reduction.17-22 The following experiments were devised and carried out in order to determine the nature of the metallic species involved in the metal penetration phenomenon, and the effective diffusivities involved. EXPERIMENTAL APPROACH Steady-state diffusion was selected for experimental convenience. The experimental systems used, shown in Figs. 1 and 2, consisted of a porous aggregate specimen contained in an impermeable alumina tube held above, and just separate from a metal bath. The entire system was held at constant temperature and pressure in a furnace with a controlled oxygen partial pressure atmosphere. After a brief period of nonsteady state behavior, a steady flux of metal vapor through the porous aggregate will develop due to the concentration gradient of metallic vapor in the gas phase. The flux of metallic vapor from pressure may be neglected because there is no pressure gradient. There is no flux from convection because there is no net flow of gas within the metal-aggregate system, and thermal diffusion is negligible compared to the flux from ordinary diffusion. If the material being studied is allowed to vaporize until steady-state behavior is attained, the experimental results may be analyzed using Fick's First Law.

Jan 1, 1970

By O. D. Sherby

In 1938, Kanter' revealed that the steady-state creep rate of low-carbon iron alloys could be correlated by an activation energy expression, where the activation energy for creep, Qc, was found equal to about 90.0 kcal per mole for most of the alloys investigated. He suggested that creep at high temperatures might be controlled by some sort of solid self-diffusion process since the value of Qc was about equal to the known value for self-diffusion, Qd. Correlations were not further attempted along these lines until many years later, when new evidence2-8 was presented suggesting that Qc = Qd for many metals. This equality now appears to be established for ten metals (Al, Pb, Ni, Mg, Cd, In, a Fe, y Fe, Cu, and Au). This experimental fact prompted several investigators to postulate various mechanisms of dislocation motion which would yield an activation energy for creep equal to that for self-diffusion.7-9 Possibly the most accepted theory is that based on dislocation climb7 where a dislocation is envisioned to surmount a barrier by an atom-vacancy exchange process, thereby "climbing" from one slip plane to another. Such a model would suggest that the steady-state creep rate, i, should be directly proportional to the rate of self-diffusion, D, for a given creep stress. In order to more clearly reveal the relationship between creep and diffusion, and to eventually determine the correct model, it would be desirable to obtain data showing correlations between i and D, rather than with a comparison of the temperature coefficients, Q. It has been known for some time that the self-diffusivity of iron atoms is greatly decreased when body-centered-cubic (a) iron transforms to face-centered-cubic (y) iron. This has been ascribed to the more close-packed structure of y iron. The diffusivity ratio at the transition temperature is Da/Dy =350. Correlations of creep data for a and y iron5 reveal that the creep rates under a given stress at the transition temperature differ by about the same ratio (ea/ey 2 200). It would be difficult to reconcile these results on any other basis than that the diffusivity of atoms probably controls creep of iron in some very direct way. No other published data on other allotropic metals appear currently available for further checking such a possible correlation between i and D. Thallium transforms from a hexagonal close-packed (a) structure to a body-centered-cubic (ß) structure at 230°C (503°K) and the self-diffusivities of the two structures have been determined by shirn.10 His results are plotted in Fig. 1 where it will be noted that Dß/Da = 25 at the transition temperature. It would appear desirable, therefore, to determine the creep rates of polycrystalline a and ß thallium at the transition temperature, as well as determine

Jan 1, 1959