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By J. E. McDonald, J. G. Eberhart

A model is discussed from which the work of adhcslon .tor liquid transition metals on aluminum oxide surfaces can he calculated, A close-packed (00011 oxygen surface on A12O3 is assumed with two different types of surface sites: one type involving metal-oxygen bonds and the other man der Waals into actions. The work of adhesion is thus expressed as the sum of these two bonsding free energies. Calculated works of adhesion for nickel, titanium, chromium, and zirconium on sapphire agree well with the experimentally determined quantities. The model is extentled to the calculation of the work of adhesion and shear stress required to remove a thin metal film from a sapphire substrate and is in good agreement with experimental values. The obsewed dependence of the work of adhesion on the free energy of oxide formation of the metal is shown to also provide an interpretation of the tittle dependence of thin-film adhesion. THIS paper presents a model for the type of bonding which occurs across a metal-A12O3 interface. The model is used to explain the results of two types of experiments in which such an interface exists: 1) the adhesion of thin metal films on Al2O3 substrates and 2) the wetting of A12O3 by liquid metal drops. The adhesion of thin films to various substrates has been the subject of a variety of investigations.'-' Benjamin and weaver3 and Bowie,6 using the scratch test developed by Heavens,10 studied the adhesion of metallic films to glass substrates. Their observations for noble-metal film adhesion agree well with an adhesion model involving a van der Waals type of bonding between the film and the substrate. For films of metals whose free energy of oxide formation. ?F°f, has a negative value. Benjamin and weaver3 and Bowie6 found a time-dependent adhesion with an initial value that can be interpreted in terms of van der Waals interactions but a larger terminal value which was related to ?F°f, Karnow-sky and Estill7 deposited films on sapphire at elevated temperatures and noticed no time dependence of film adhesion but a similar correlation with ?F°f. Because of the kinetic problems associated with thin-film adhesion it is desirable to examine adhesion in an equilibrium system. The wetting behavior of liquid-metal drops on Al2O3 provides such a system. Systems of this metal-ceramic type have been studied extensively.11 Humenik and Kingeryl2 have measured the wetting of A12O3 (and other substrates) by several metals and have pointed out that the wetting ability of these metals increases with increasing values of -?F°f. It is thus seen that thin-film adhesion and metal wetting on A12O3 are both related to the tendency of the metal to react with the surface oxide ions of the Al2O3 substrate and, because of this, both phenomena should be explainable by an appropriate model for the metal-Al2O3 interfacial bonding. In the sections that follow, wetting and adhesion data on A2O3 are reviewed and a model is presented by which these phenomena can be interpreted. ANALYSIS OF WETTING EXPERIMENTS In an equilibrium system involving a liquid-metal drop on a solid Al2O3 substrate, the work of adhesion, WAD, is defined by the Dupre, equation as WAD = ?s + ?L -?sL [1] where ?s and ?L are the surface free energies of the solid substrate and the liquid drop, respectively, and ?sL is the interfacial free energy. The work of adhesion is the work required to separate a unit area of the solid-liquid interface into two surfaces. The work of adhesion is usually determined from a sessile-drop experiment in which yL and the contact angle, ?, are measured. The Young-Dupr6 equation is then used to calculate WAD Wad = ?L (1+ cos ?) [2] The literature of this subject has been examined and Table I shows work of adhesion data for various liquid metals as measured on A12O3 substrates. The standard free energy of oxide formation of the metal at the temperature of the wetting experiment, ?F°f . is also tabulated in kcal per g-atom of oxygen. The data is grouped according to the gaseous atmos-

Jan 1, 1965

By E. R. Shorey

FLOTATION-Mill operator's have recognized that slimes are detri-mental to the flotation concentration of zinc ores. The, presence of primary slime in many of the Wisconsin ores is largely responsible for the failures experienced in treating these ores by flotation. These failures have discouraged the adoption-of the flotation process by opera-tors in the Wisconsin zinc district. The removal of slimes by decantation seemed to be the obvious way to meet the problem of treating slimy or' clayey ores by flotation. To facilitate the removal of slime, it was decided to mix the ore pulp with sodium silicate, which acts to deflocculate the pulp.1 Deflocculation causes slime suspension, making it possible to separate the slime from the sands by decantation.2 Since the literature contains little definite information on the use of sodium silicate to deflocculate ore pulps, a series of tests was conducted to obtain the necessary information. Tests to determine the settling rates of sand and slime in deflocculated pulps were conducted on a dolomite-marcasite-sphalerite ore ground to minus 80 mesh (175 microns) and mixed with water to form a pulp. The deflocculator3 was Mallinckrodt 40° to 42.5° Bé. liquid sodium silicate (Na20 + 3.25Si02). .By microscopic analysis the suspended slimes4 were found to be minus 15 microns (approximately 1000 mesh).

Jan 1, 1934

By Robert Glass Cleland

IN gathering material for this book, I have made extensive use of the archives of Phelps Dodge, contemporary news- papers, and a wide range of secondary sources. Two manuscripts-one on the history of Phelps Dodge by Arthur Train, Jr., and John L. Lawler, the other a biography of William E. Dodge by Richard Lowitt-have been of the greatest value. I owe a particular debt to the authors whose names I have just mentioned. I have also gathered important information and obtained revealing points of view from conversations with many people. Personal visits to the company's mines and plants added knowledge and understanding that nothing else was able to supply. I am greatly obligated to the officers of the company, especially to Mr. Louis S. Cates, chairman of the board of directors, Mr. Robert G. Page, president, Mr. George R. Drysdale, vice-president of Phelps Dodge Corporation, and Mr. Walter C. Bennett, president of Phelps Dodge Refining Corporation, for their co-operation and assistance. Mr. Wylie Brown, former president of Phelps Dodge Copper Products Corporation, also supplied valuable data and deeply appreciated hospitality. In my visits to the Phelps Dodge properties, company representatives extended every hospitality and placed at

Jan 1, 1952

Frank Owen, El Perú Venezuela (communication to the Secretary): Mr. Cragoe's accurate description of the rich and extensive mines of the Frontino and Bolivia Co. is of much interest to those acquainted with Colombian mining. While the labor in that part of Colombia is, of course, admittedly far inferior to that of white miners, it is,. nevertheless, decidedly superior to that available in other parts of the republic, and in the northern mining regions of South America generally. The Autioquenos have been miners for several generations, and many of those employed at the Frontino Co.'s works have been brought up at the mines, which is a distinct advantage. The ground encountered in the surface-workings of that district being very treacherous, they are skillful timber-men, every miner being able to put in his own timber in tunnels, stopes, etc., so that, except for the main shafts, where sawn timber is used, special timber-men are not required. In the shallow workings it is the custom for a miner to come out of the mine into the thickly-wooded bush and select and cut the timber he requires, which he will then take into the mine and put in

Jan 1, 1899

By Alan English, M. F. Morgan

EXPERIMENTAL work on the concentration and agglomeration of low-grade iron ores was started many years ago at the Mines Experiment Station of the University of Minnesota by E. W. Davis and his staff. From these laboratory results and the work of 0. G. Lellep, consultant for the Allis-Chalmers Manufacturing Co., there were indications that the use of a downdraft continuous- grate furnace, patterned from a conventional-type sintering machine, would be practical. Consequently, a pilot plant was designed and constructed by the joint efforts of Allis-Chalmers Manufacturing Co. and Arthur G. McKee & Co. at Carrollville, Wis. Several years of work resulted in plans to build a large-scale pilot plant for commercial application. Such a pilot plant, built at Babbitt, Minn., by the Reserve Mining Co., was designed to produce 1000 tpd. Sufficient metallurgical and operating data were accumulated to permit the successful application to the design of a commercial plant of any desired capacity. Based upon this data, a pelletizing plant having a 3 ¾ million ton per year capacity was erected by the Reserve Mining Co. at Silver Bay, Minn. and started operation in October, 1955. Provisions were made in the design to permit future expansion to a capacity of 10 million tons per year.

Jan 3, 1958

By N. M. Saum, W. T. Caneer

Uranium may be in short supply due to the predicted energy needs in the coming years. As a result of this, a new surge of uranium exploration is underway accompanied by the refinement of numerous exploration techniques. One such technique is the monitoring of radon gas in surface soils and rocks as a guide to subsurface uranium deposits. The Colorado School of Mines Research Institute became involved in radon studies in 1967 on a project for the Atomic Energy Commission. Since that time the Institute has conducted numerous radon surveys for a large number of companies which have been active in uranium exploration. The objective of this paper is to relate the techniques utilized by the Research Institute and the results of some of the studies performed. Most of the studies performed by the Research Institute were related to roll front, sandstone-type uranium deposits. However, we have performed radon studies in various other types of rock. For those who may not be familiar with the application of radon "sniffing" in soils and rocks, a brief descriptive background should be given. The following question may be asked-why use radon as a guide to uranium mineralization? Some of the answers to this question are:

Jan 5, 1974

By R. L. Templin, D. A. Paul

The modulus of elasticity is defined as the ratio of stress within the proportional limit to corresponding strain. This property, as thus defined, is a constant for each kind of material; and in tension or compression is usually designated by the symbol E. The modulus of elasticity serves as an index of the stiffness of a material or a measure of its ability to resist change of shape under stresses not higher than the proportional limit. In view of the frequency with which the modulus of elasticity is used in engineering calculations, it is surprising to note the uncertainty that exists as to authentic values, and the marked lack of published information relating to the variation of the constant E within individual alloy systems. A value of 10,000,000 Ib. per sq. in. has been quoted as representative of aluminum and its alloys. This value has been found to be approximately corrcct for pure aluminum and aluminum alloys in which the total percentage of the alloying elements is low, but seriously in error in the case of alloys that contain relatively large amounts of the alloying elements. a National Metals Handbook. b Intcrnatiunal Critical Tables. '' Aluminum Co. of America. " Based on density of alurminum (2.70). c Smithsonian Pliysical Tables.

Jan 1, 1931

By I. L. Box

IN planning retreatment of tailings, the material to be retreated should be thoroughly investigated, tak- ing into consideration the total tonnage, the blende content, the specific gravity of the different particles, and the grinding necessary to liberate the mineral. The tailing pile is surveyed by making a closed trav-erse around the outer edges, locating the stations at points from which a considerable portion of the pile is visible. From each of these points the pile is sur-veyed by stadia and a contour map made. The yardage is then calculated from the contour interval and the area inclosed by the contours obtained with a planim-eter. A party of three men can survey an average tailing pile in one and one-half, days. In calculating tonnage it is assumed that 22 cu. ft. of tailing in place equal one ton. Sampling is done by the use of an auger with casing to prevent the hole from caving. These holes may be bored 12 to 15 ft. deep by hand, but to penetrate the entire pile some kind of power is applied to drive the casing and raise or lower the auger. The latter method is more expensive but the increased cost is more than compensated for by the value of the information obtained.

Jan 7, 1928

By G. L. Oldright

THE economic manufacture of sulfuric acid by the ordinary chamber process usually involves production on a large scale and a plant that is costly to construct. The nature of sulfuric acid makes it costly to transport any great distance. For these reasons, the metallurgist has not found it feasible, at times, to beneficiate ores amenable to leaching, and a. need exists for a local process that will produce acid cheaply on a small or large scale. To leach ores containing residual sulfides, an oxidizer, such as ferric sulfate, is needed in solution. Precipitation with scrap iron is one of the cheapest methods of removing some metals from solution, giving a plant of low first cost and supplying a source of cheap ferrous sulfate. The other ingredient needed for the process is SO2 roaster gas; the addition of which, as, described below, will give both ferric sulfate and sulfuric acid. Where roaster gas is a waste or obnoxious, product, the expense. for materials is still further lessened. The use of ferric sulfate and sulfuric acid as a solvent lends itself, well to the utilization of scrap iron as a precipitant, and the stages of the process fit in well together as an economic whole.

Jan 8, 1925

By P. N. Ivanov

The world experience shows that the tremendous potentialities of the computers and other technical means in improving management efficiency are not fully utilized. One of the causes is the tendency to solve the problems of management automation divorced from the management methods and schemes which demand continuous improvement in view of the steady progress of the social production. It may be safely affirmed that making decisions on management improvement divorced from management schemes or on both divorced from management automation problems cannot lead to success. The grave and sometimes unsuperable difficulties encountered in management automation arise from copying traditional management methods and schemes without solving the problems which exist both in management and automation fields. The system solution of management problems has unquestionable advantages and is not proposed for discussion. What is proposed to discuss is the difficulties emerging in developing a methodology of the system approach to management improvement and automation. Though aware of the fact that the questions proposed for discussion are not new, we think it advisable to briefly review them, first because they fall in the "chronically unsolvable" category, and, secondly, as it will enable us to illustrate the method of solving them in the framework of the proposed system approach.

Jan 1, 1977

By Theodore Simons

The rapid and comparatively recent development of flotation has opened so fascinating a field for study and research that the older processes of gravity concentration no longer receive the attention they deserve. The early work of Munroe1 and Richards,2 and the more recent contributions by Clevenger and Coe,3 Laist and Wiggin,4 Ammon,5 Bardwell,6 Crowfoot,7 and Hayden8 to mention only some which have appeared in our own Transactions-and by Schulz,9 have furnished so much data that to offer something new seems a difficult task. It is still possible, however, to present known facts from a different point of view, and, with this in mind, the writer has undertaken to express basic principles of gravity concentration in terms of simple mathematics and mechanics; the conclusions thus reached will be found to correspond, in general, with those obtained by experimental methods. Rittinger, in his classic Aufbereitungskunde (1867), reached analogous conclusions by way of intricate higher mathematics, for which reason his interesting investigations have remained a sealed book to most of us. The writer hopes that a more elementary treatment of the subject, based in part on Rittinger's methods, may, arouse new interest in the study of basic principles.

Jan 7, 1922

By Alden Greninger

ALTHOUGH the crystallography of lattice transformations has been studied extensively during the past few years, these studies have been limited, with few exceptions1,2, to specimens in which the transformed lattice appears as a, segregate phase. A realization of the technical importance of the segregation mechanism, especially in the formation of martensitic structures and in age-hardening phenomena, has undoubtedly stimulated research in this direction. In the crystallographic studies of segregation, the general problem has been to relate the orientation of the parent crystal to that of the segregate crystals. The technique has been complicated by the fact that it has been necessary to deal with the presence of as many as 24 ideal segregate orientations within one parent lattice; furthermore, the segregate lattices are invariably scattered (seldom less than ±2°, often as much as 15° or 20°) about these ideal positions. It is probable that a more complete picture of phase transformations may result from a study in which complete lattice relationships between individual grains are evaluated, thereby providing an additional param-eter which, when it is necessary to work with multiple segregate-orienta-tions, cannot be evaluated. The present paper presents the results of such a study, ? wherein a peritectic reaction is made use of to produce the transformed lattices.

Jan 1, 1937

By Arthur A. Brant

Let us start back as far as possible, to the beginnings of this universe, some 5 billion or more years ago. This is a time interval that can be crudely underestimated by the moon-earth tidal friction effects that have increased the length of the day by about 1/1000 second per century-from a 5 to 7 hour day to its present 24-and have moved the moon away at 5 inches per year to its present 240,000 miles. The oldest stony meteorites from interplanetary space give an age dating of some 4.6 billion years, approximating the time of formation of our earth. Further, certain stars pulsate, the period of pulsation being related to their absolute brightness. Measuring apparent brightness and comparing, gives the distance away. Thus Hubble and Shapley of Harvard, from 1925 on, were able to show that the universe reached as far as our telescopes could scan. The Doppler shift of the hydrogen red lines could only mean that the nebulae, or galaxies, were moving away at velocities increasing with their distances, by 180 km/ sec velocity increase for every million light year's distance. In short, the universe is expanding like an exploded bomb.

Jan 4, 1964

By Ingvar Janelid

DURING the last ten years, in the effort to save manpower and costs, methods of drilling and blasting in Sweden have changed and developed in a revolutionary manner. These developments have been accompanied by extensive alterations in methods of tunneling and in mining technique. Since the end of the 1940's there has been a 100 pct change-over in Sweden to the use of tungsten carbide tipped drill steel. Both investigations and practical results have shown clearly that a tungsten carbide chisel bit fastened directly on the drill steel is the most economical for Swedish conditions. This applies to drill steel up to the longest size it is practical to handle. In terms of drilling footage, durability of the drill steel and the tungsten carbide bit is generally the same. In this respect, therefore, a detachable bit offers no advantage over integral steel. Transportation of integral steel to the grinding plant, instead of detachable bits only, involves heavier work, but this is counteracted by placing grinding plants closer together or by grinding at the working place itself. The drilling rate with integral steel is higher, the trouble of changing bits is avoided, and the difficulties which always arise with joints are eliminated.

Jan 6, 1954

By S. M. Moos, R. E. Dugger

In reviewing available vacuum filtration equipment in this paper, several types of filters have been included which are probably not familiar to operators in the mining industry. However, it was felt that these units might be of interest in the event that an application should arise for the filtration of a product in the future that does not exist today. In addition, exposure of our industry to equipment used in other industries might have a tendency to be thought provoking and perhaps lead to the development of equipment and/or applications in our industry which do not necessarily exist at this time. Most innovations in filtration equipment have been confined to the improvement or design change of components and accessories, particularly reflecting the availability of materials of construction that have been developed. Recent developments in the application of horizontal belt filters have been innovative. The application of this unit as a substitute for or an adjunct to thickeners in a CCD circuit can certainly be innovative and perhaps provide a basis for reduction in capital and operating costs in this area. For example, mill tails are generally pumped at the highest possible density that will adequately flow. Tailings ponds and dams with their attendant design requirements are based upon this estimated water volume.

Jan 10, 1979

By J. T. Crawford

COAL-CLEANING plants using the launder process generally wash the fine coal (minus 3/8 or minus 5/16-in.) separately in a plant consisting of washing launders or troughs placed one below another and sometimes supplemented by additional washing equipment such as tables and jigs. The coal and its associated impurities enters the feed end of the top launder, with a current of push water. As the material moves along the impurities, being heavier than coal, settle toward the bottom of the launder and are drawn off, with some coal, through "free discharge" boxes to the launder below. These boxes were given their name because their discharge falls freely; that is, it does not discharge into a water seal. Thus the impurities are progressively concentrated in the lower launders until box products are sufficiently free of coal to be discharged to refuse. The overflows of the upper launders go to clean coal while the overflow of the lowest launder, and perhaps that of the one immedi-ately above, is usually recirculated to the plant feed. Thus the bulk of the clean coal is removed rapidly and the impurities are concentrated more slowly. The chief purpose of this paper is to present the cleaning data of such a plant under different operating conditions.

Jan 1, 1940

By Walter W. Bradley

(Three, papers included, in this discussion are classified as Mining Geology and also as one of the following-A, Metal Mining: B, Milling and Concentration: L, Geophysics. These papers are TP 2255, TP 2092 and TP 2038.) CONTENTS [PAGE Review of Fluorescence as Applied to Minerals, with Special Reference to Scheelite. (TP 1967 by J. W. VANDERWILT, Min. Tech., March 1946. Discussion by WALTER W. BRADLEY) I Geologic Interpretation of Magnetic Exploration on the Mesabi Range, Minnesota. (TP 2038 by R. B. H. JONES, Min. Tech., July 1946. Discussion by ROBERT B. SOSMAN) I A Technique for Photographing Difficult Subjects through a Petrographic Microscope. (TP 2092 by DONALD W. SCOTT, Min. Tech., Nov. 1946. Discussion by HORACE WINCHELL) 2 The Search for Concealed Deposits-a Reorientation of Philosophy. (TP 2146 by SAMUEL G. LASKY, Min. Tech., May 1947. Discussion by T. M. BRODERICK)3 Occurrence of Lead-zinc Ore at Iron King Mine, Prescott, Arizona. (TP 21 go by H. F. MILLS, Min. Tech., July 1947. Discussion by HUGH M. ROBERTS)3 Geologic Relations and New Ore Bodies of the Republic District, Washington. (TP 2197 by LAWRENCE B. WRIGHT, Min. Tech., July 1947. Discussion by AUGUSTUS LOCKE and J. A. RICHARDSON) 4 San Manuel Prospect. (TP 2255 by H. J. STEELE and G. R. RUBLY, Min. Tech., Sept. 1947. Discussion by L. KENNETH WILSON, ELDRED D. WILSON and the author) 5] Review of Fluorescence as Applied to Minerals, with Special Reference to Scheelite WALTER W. BRADLEY*-AS I recall, the first portable units for ultra-violet light of practical use with scheelite were developed at the Nevada-Massachusetts Tungsten Mine at Mill City, Nevada, and were used underground. Ultra-violet lamps are also installed there in the mill, above the gravity-concentration tables, for control observations. Geologic Interpretation of Magnetic Exploration on the Mesabi Range, Minnesota ROBERT B. SOSMAN*-When artificial precipitated magnetite is oxidized at a temperature in the vicinity of 100°C, the oxide is converted into a chocolate brown ferric oxide of the formula Fe2O3, free from ferrous iron, yet possessing the same magnetic susceptibility as the original Fe3O4. This form of Fe2O3 is variously called "ferromagnetic ferric oxide," " maghemite," or "gamma ferric oxide," and has been found as a natural mineral. If a body of magnetite in the Biwabik were to oxidize to this form, the oxidized and leached ore body might successfully conceal itself from Mr. Jones' survey by this ferromagnetic pretense. So far, gamma ferric oxide has not been found on the Minnesota iron ranges. I thought I had found some in the Hibbing pit in 1940, in a strongly magnetic specimen of soft ore differing in color from the prevailing hematite

Jan 1, 1947

By Frank Ruskey, Richard G. Burdick

Many problems associated with potential hazards in a proposed mining area may not be adequately appraised because of the complexity of trying to evaluate them in terms of production requirements. Frequently, encountered hazards have to be dealt with by day-to-day operational schemes that require the miner to either force a way through them or avoid them by blocking off the area in which the hazards are known to exist. These considerations, after the mine is in full production, can be costly to the mine operator and can increase the danger to the miners. A hazard-evasion computer program for mine planning that will appraise proposed mine layouts on the basis of existing or potential hazards has therefore been developed. The program is intended for use during the planning phase of a mine, where it should assist the mining engineer in making decisions in mine design, With the output from this program, the mining engineer should be able either to corroborate his judgments made on the basis of mining experience or to find unanticipated solutions to design problems. The program tests hundreds of possible solutions to a mining layout, and by sorting out the 10 best (based on a criteria of minimum-abandoned-coal) limits the number of choices that need to be considered and appraised for applicability to a given mine scheme.

Jan 1, 1976

By K. A. Jackson, J. D. Hunt

The discussion by Tammann and Botschwar of the transition from eutectie grouth to denrdritic plus eu-tectic growth is reviewed and applied to metallic eutectic systems. Using expevimental data on the geowth rate of the Pb-Sn eutectic, and an extrapolalion of dendritic growth rate in tin and Sn-Pb alloys , qlcantitatice prerlictiotls of the extent of the eutectic region in tin-vich Sn-Pb alloys are made. There are no experimenta1 measuvements available for detailed comparison with these predictions. EUTECTIC structures form over a small range of compositions. The theory of lamellar growth presented by Jackson and Hunt' indicates that it is in principle possible to have eutectic growth over almost the complete range of compositions between the two solidus lines. This does not occur in practice. Alloys far from the eutectic composition grow dendritically followed by a eutectic as shown in Fig. I. The transition from a eutectic to a dendritic plus eutectic interface cannot be predicted from constitutional undercooling arguments because constitutional undercooling always exists ahead of the eutectic interface.' Reasonable predictions can, however, be made using arguments originally put forward by Tammanl. and Botschwar.3 These and later workers'"*6 carried out extensive experimental investigations of the extent of the eutectic range in organic materials. They concluded that the structure formed, eutectic or dendrites plus eutectic, depended on which structure grew faster at the given undercooling. This is, of course, equivalent to the structure which grows with the smallest undercooling at a given growth rate. In this paper, we will discuss these ideas briefly and then apply them to predict quantitatively the range of eutectic growth in tin-rich Pb-Sn alloys. The temperature dependence of the growth rates of dendrites and eutectic for a typical metal alloy of eutectic composition is shown schematically in Fig. 2(a). The growth rate for the eutectic increases more rapidly with undercooling than those of the dendrites because of the short diffusion path maintained in the eutectic, see Fig. 1. For an alloy off the eutectic composition on the A-rich side, the growth rates shift as shown in Fig. 2(b). The liquidus temperature of the a phase increases, that of the 3 phase decreases, and the temperature of zero growth rate for the eutectic does not change. The curves, particularly the dendritic ones, change shape as well, but for our purposes the principal effects occur because of the change in liquidus temperatures.3-6 In an isothermal system, only a dendrites will grow above TE, Fig. 2(b). If the temperature is below TE, and both phases have nucleated, a dendrites will grow ahead of the eutectic at

Jan 1, 1968

By Rex W. Woods, Morris Muskat

A leastmsquare analysis procedure has been developed and applied for the study of the deviations in estimations of oil in place as given by the material-balance equations. The data used were those obtained from field observations on the Jones sand in the Schuler pool, Arkansas, and the Monroe dolomite in the Reed City pool, Michigan. Possible effects of water intrusion were taken into account by expressing the cumulative water influx in terms of various functions previously proposed in the literature. Formulas were developed and values calculated for the minimum deviations and minimal percentage deviations in the calculated volumes of oil in place from the average values, as could be obtained by suitable choice of the water encroachment and initial gas-cap volume parameters. The results show that the fluctuations in these calculated volumes are very insensitive to the values chosen for the rate of water intrusion and initial gas-cap volume, and hence cannot be safely used in discriminating between spurious values for these parameters and such as actually pertain to the producing reservoirs. Moreover, the exact form of the water-intrusion function seems to have but little effect on the fluctuations in the computed oil in place. Accordingly, it is concluded that the material-balance method does not of itself provide a satisfactory criterion for determining the basic physical unknowns of producing reservoirs or in making conclusive decisions regarding the production mechanism, unless independently established geological control data are available for eliminating unreasonable values for the reservoir parameters, even though they may still satisfy the material-balance formulas. If, however, from core or logging data the initial oil in place and the gas-cap volume can be established in advance, the material-balance formulas can be inverted to find the water intrusion. Moreover, by determining by such calculations the water-intrusion coefficient, the iuture production performance can then be predicted by the aid of the materiaI-balance formulas for specified operating conditions. This type of application may be of particular value in predicting the results of Pressure-maintenance operations. Introduction The evaluation of the forces acting upon an oil reservoir is a problem of considerable interest to the operator as an aid in determining the proper method of operation for the reservoir to obtain an optimum recovery of oil. In many pools, the nature and magnitude of the forces acting upon the reservoir remain unknown until an appreciable amount of ultimate recovery is obtained. To be of value to the operator, a reliable interpretation of reservoir performance should be available in the early life of the pool to permit an optimum plan of operation. Progress has been made in an understanding of reservoir behavior and the importance of the different factors involved. The material-balance method of estimating oil in place has been proposed as a tool in analyzing reservoir-performance problems.l The solution of such problems by this method ordinarily involves two or more unknown values relating to the nature of the reservoir, and the results

Jan 1, 1945