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By C. A. Queener, W. L. Mitchell

In recent years bismuth telluride has received considerable attention, primarily due to its value as a thermoelectric material. Since there seems to be little dependence of thermoelectric effect upon crystal orientation1 many of those who have previously worked with this material have been unconcerned with knowing its crystallographic angles to any degree of accuracy. However, when one studies deformation modes, lattice stresses, or the aniso-tropy of mechanical properties of a material, knowledge of the interplanar angles and their relationships as depicted in a stereographic projection becomes essential. Lange2 originally published crystallographic data which described the structure of bismuth telluride as rhombohedral with the space group A more recent work by Francombe3 presented data which corroborated and refined the original findings of Lange. In addition, Francombe established that there is no coexistence of rhombohedral and hexagonal lattices in bismuth telluride as was suggested by Vasenin and Konovalov,4 and that the structure can be treated as a pseu do hexagonal structure with an axial ratio, c/a, of 6.95 for convenience of presentation and study. The interplanar angles and standard projections for several unalloyed hexagonal metals have been previously published,5-9 but the present work appears to be unique in that it presents data for a rhombohedral compound in pseudohexagonal form. As a pseudohexagonal structure, this material has an extremely large axial ratio as compared to the usual range of approximately 1.5 to 1.9 for the hexagonal metals. Since the interplanar angles are a function only of c/a, the angular relations between various planes for Bi,Te3 will be grossly different

Jan 1, 1965

By John Jermain Porter

THe value of any particular ore, coke, or limestone, for iron-making, depends upon its effect, first, upon the quality or value of the resultant product; and second, upon the cost of smelting. The factors under the first head are the percentages of phosphorus, manganese, and other elements, which remain in the pig-iron ; while those under the second head are the percentages of iron, carbon, or lime, the slag-forming constituents, which must be fluxed, and any other ingredients which give rise to variations in cost of fuel and flux. The first of these criteria of value is perhaps not capable of being reduced to a general formula embracing all cases, since it must vary to a great extent with market-fluctuations. For example, Bessemer pig is worth sometimes more and sometimes less than foundry-pig; and the premium paid for high manganese varies within wide limits. The second, or smelt-ing-value, however, can be expressed numerically with a fair degree of accuracy; and it is with this phase of valuation that the present paper is concerned. The utility of a means of comparing numerically the relative smeltiug-values of difierent ores, cokes, and limestones, is self-evident, although it may not have importance in Northern practice, where materials are largely standardized. On the other hand, there are, especially in the South, many furnace-managers who must use a great variety of materials of widely varying grade; and it is with special reference to this district, and in connection with the efficiency-methods which I have elsewhere proposed,' that the methods herein described were devised.

Jan 1, 1913

By Raymond B. Ladoo, C. A. Stokes

T is unfortunate that the word "economics" has -¦¦ come to mean, in the minds of many people, a sort of half-baked mixture of New Deal philosophy and bookkeeping. It may mean anything from mine cost keeping to the theory of gold as a monetary standard. As applied to the industrial mineral industries as a whole it means to us an integrated study of all of the technical, geographical, market, financial, and other factors which determine whether or not a given enterprise has a sound chance of making a business success. Of course it is impossible to generalize too freely in this large group of industries which go to make up the nonmetallic minerals. This group includes such dissimilar products as crushed stone and ca- pacitor mica, phosphate rock and spinning fiber asbestos, roofing granules and potash salts, borate minerals and monumental granite. Yet in many respects their economic problems are similar and, at the same time, far different from those of the metals and of petroleum and coal. These basic differences are almost never recognized by people outside the industries and are rarely appreciated even by metal mining engineers. But in many instances these economic factors are fully as important as, if not more important than, technologic problems. It has been a long fight to get an intelligent and wide-spread appreciation of sound technology in the nonmetallic mineral industries. The importance of the economic side of the problem has yet to be widely understood and appreciated. The problem was outlined in considerable detail by one of the authors some 18 years ago in a long series of articles* and he has since prepared numerous talks

Jan 1, 1951

By Koichi Kashida, Mayumi Someno, Kazuhiro Goto

The present work has two objectives: first to develop an experimental method which would give some new information on the micromechanism of the reduction of oxides by gases at elevated temperature; second to clari,fy the intermediate phases of the W-0 system, formed during the reduction. A Galvanic cell with the solid electrolyte , ZrO2 . CaO, was imbedded in powders of W03, CuO, or Fe20s with two measuring electvodes and with a reference electrode. The change of the intraparticle gas composition was measured at An oxygen concentration cell consists of two electrodes separated by an electrolyte through which the transference of electrical charge is accomplished predominantly by the migration of oxygen ions. Many works have been reported on the oxygen con- 600" to loo@ C during the reduction by the gas mixture of hydrogen and argon. The intraparticle gas composition changes stepwise with time. The electromotive force of such temporary interruption corresponds to the equilibrium electromotive force of two solid phases formed during the reduction. The intermediate phases of W-0 system, which are formed in a large quantity during the reduction by hydrogen, are W0 2 W02.72 and WOz. The micromechanism of the reduction of oxides by gases is discussed. centration cells with the solid electrolyte of solid solution of zirconia and lime, since Kuikkola and wagnerl demonstrated the possibility of determination of standard free energy of formation of oxides by an electromotive-force method with the Galvanic cell. One of the present authors (K.G.) and his coworkers have applied the cells with the solid electrolyte of zirconia and lime to the following measurements:

Jan 1, 1969

By G. F. Loughlin

The subject of this lecture might well have been assigned to an economist or banker rather than to a geologist, but, as it was deliberately assigned to me, it is to be treated from a geologist's viewpoint. The term precious metals ordinarily includes the platinum group as well as gold and silver. Platinum, like silver, has had a great decline in price during the last few years, but has not been a medium of exchange and therefore has aroused comparatively little comment. Its relation to price level is like that of commodities in general, and will be dismissed without further comment. Of the two precious metals used as mediums of exchange gold, because of its adoption as the basis of most monetary systems and because of its threatened shortage in the near future; has been a subject of general concern to governments, financiers, and economists; silver, on the other hand, which has flooded the market of late has brought forth cries for help, direct or indirect, from producers and to a less extent from the largest users, especially China, whose purchasing power has been greatly curtailed, but it fails to arouse the interest that gold does. Many predictions have been made by economists, bankers, and others regarding future supply of gold and its effect on prices but the differences among these predictions are about as many as the number of prophets. Since gold is the standard by which the value of commodities as a whole is to be measured, it would seem that the greater the ratio of gold supply to commodities the higher the price level and vice

Jan 1, 1932

By J. C. Williams, M. J. Blackburn

MANY aspects of the formation of the metastable w phase in titanium-transition metal alloys have been described in several recent papers.1-4 These papers have reviewed earlier work on the w phase and have further defined most of the important features related to the formation of this phase, e.g-., its crystal structure, composition, and morphology. There are, however, several important points regarding formation of the w phase in titanium alloys which have been described in less detail. Two of these are the relationship between lattice misfit and w phase morphology and the influence of lattice misfit on the mode of formation of the equilibrium a phase. In this communi- cation we will present transmission electron microscopy results relevant to these two points. The alloys used in this study were prepared by non-consumable electrode arc melting, each 30-g button being remelted a minimum of twelve times. The alloy compositions we have studied are listed in Table I. Thin foils were prepared using standard techniques described elsewhere. Two distinct c' phase morphologies have been reported in earlier papers. The phase is ellipsoidal in the Ti-Mo3 and Ti-Nbl system and cubical in the Ti-V3 system. Results of the present study show that the w phase is also cubical in Ti-Mn, Ti-Fe, and Ti-Cr alloys as illustrated in Fig. l(b) to (d). Fig. l(a) shows the ellipsoidal morphology in Ti-MO3 for comparison purposes. It was suggested in an earlier paper3 that the w phase morphology may be controlled by the lat-

Jan 1, 1970

By C. H. G. Bushell

The author maintains that selectivity in flotation depends in part on differences in rates of flotation. The rate of flotation should be directly proportional to the frequency of particle-bubble collisions. In this paper, it is suggested that floatable particles of the mineral must be distinguished from nonfloatable particles. Success in flotation is entirely a matter of selectivity. All minerals can be made to float. The problem is to make one mineral float and leave the others in the tails. For a typical ore, with all minerals naturally hydro-philic, a collector which is adsorbed by only one mineral and not at all by the others would give perfect separations. The hydrophobic, collector-coated mineral would separate cleanly from the remaining minerals. In practice, no such highly specific reagents are known. All standard collectors adsorb on most minerals to some extent, and selectivity then becomes a matter of extent of adsorption rather than adsorption on some minerals and not on others. Flotation is therefore a compromise process: if enough reagent is used to float all the desired mineral, the concentrate will be low grade; conversely, high grade concentrates can be attained only at low recovery. With many minerals coated with collector to varying degrees, selectivity appears to depend in part on each mineral floating at a different rate. The study of flotation kinetics is therefore a basic requirement to quantitative understanding of the process. REVIEW OF PREVIOUS THEORIES Before a particle enters the froth it must strike a bubble and adhere to it. Flotation rate will therefore depend on the number of particle-bubble collisions

Jan 1, 1962

By Robert L. Zook, Bernard J. Olup, James J. Pierre

Coal refuse slurry impoundments are dams constructed of coarse coal refuse to impound fine refuse (slurry) and water (25 to 30% solids). Both products are waste from coal preparation plants. A number of these structures in West Virginia, Pennsylvania, and Kentucky were investigated to determine embankment stability. During the investigation a variety of embankment designs were encountered. The investigation determined the soil and geological characteristics of the embankments and the sites. This was accomplished by a test drilling and monitor installation (observation wells and piezometers) program, geologic study, and large-scale mapping which allowed subsurface profiles of the embankments to be constructed. The laboratory testing program concentrated on textural classification of the coal refuse, permeability, and determining strength parameters to be utilized in the stability analyses. For the stability analyses, the modified Fellenius slip circle, simplified Bishop slip circle, and analysis for translational failure were utilized. In all stability analyses hydrostatic pressure and seismic acceleration probability were considered. This investigation indicated that 62% of the embankments analyzed were in a stable condition. The coal seam, the type of roof rock, and the gradation of the refuse influence the degree of compaction obtainable and the permeability of refuse. The shear strength of coal refuse appears to be controlled by its composition, moisture content, degree of compaction, amount and grain size of fines present. This investigation demonstrated these embankments should not be treated as pure state-of-the-art dams consideration must be given to the particular properties of coal refuse and the total refuse disposal system. Refuse dam slurry impoundments generally lack the site selection phase that is standard practice with siting most other types of dams.

Jan 1, 1976

By D. A. Belforti, M. P. Lepie

Spectroscopically pure copper was melted on sapphire plaques in a zydrogen atmosphere. The surface tension of the liquid metal was determined using the sessile drop technique. Measurements were made by direct observation with the aid of a specially const,mcted telescope. The value obtained, 1268 dynes per cm, is compared to that found in the literature. THERE is at this time considerable interest in the use of ceramics for vacuum tubes. The crystalline material is superior to the more conventional glass in mechanical strength, chemical inertness, dielectric properties, ability to withstand high temperatures, and so forth. However, ceramics are much more difficult to seal hermetically with metals than are the glasses. For this reason an investigation was undertaken to determine the wetting and adhesion of metals to ceramics. The sessile drop technique offers a convenient means at elevated temperatures for measuring liquid surface tension, wetting angle, density, spread- ing coefficient, and work of adhesion. Thus, from the contour of a drop of liquid at rest on a solid surface one can obtain a quantitative evaluation of the degree to which the two substances will bond. To this end a special apparatus was constructed so that various molten metals could be observed. Standardization of the apparatus was done initially by measuring the surface tension of copper since this is well documented in the metallurgy literature. Although there are many methods available for the measurement of surface energy,'+ the sessile drop technique has been used most extensively for molten metals and ceramics.5"' Fig. 1 illustrates the dimensions to be measured. From these values, the surface tension of the liquid can be obtained using the Bashforth and bdams' equation and tables.

Jan 1, 1963

By Charles McElroy White

IT is indeed an honor to have been asked to participate in the program which celebrates the seventy-fifth birthday of the American Institute of Mining and Metallurgical Engineers. This great organization has occupied an important place in the professional and industrial life of this country-of the world. Its members have explored the far reaches of our globe and have played a great part in the discovery, extraction and utilization of the mineral resources upon which our civilization so largely depends. These engineers, together with the restless prospectors, on the one hand, and the scientists, on the other, have literally been the advance scouts of our modern way of life. As such, we owe them a deep and lasting debt of gratitude. May I, therefore, wish many happy returns to the American Institute of Mining and Metallurgical Engineers and express the hope that it may long continue to be of great service, as it has been in the past. The subject assigned to me-Iron Ore and the Steel Industry-is, indeed, important, as one considers the future of our world. I shall give as few figures as possible. Pertinent statistical data are included in the tables in this chapter, which, I think, will prove interesting. Many studies of iron-ore reserves have been -published and are available; hence I shall limit myself mainly to an interpretation of these figures. The statistics data are from standard sources, including the Lake Superior Iron Ore Association, the American Iron and Steel Institute, the United States Bureau of Mines, the United States Geological Survey, the United

Jan 1, 1947

By H. F. Yancey, M. R. Greer

At the annual meeting of this Institute held two years ago a new method1 of estimating the grindability of coal was described, based on experimental work carried on by the Bureau of Mines at its Northwest Experiment Station. Since that time, several organizations concerned with the testing or utilization of coal as pulverized fuel have adopted and used the method in determining the grindability of several hundred samples of coal. In addition, a series of comparative tests of this method and three others has been carried out in five laboratories under the auspices of Committee D-5 of the American Society for Testing Materials. As a result the Committee has recommended that the Bureau of Mines method, designated as the "ball-mill method," and the Hardgrove method2, previously advanced, be accepted as tentative standards3. Since the ball-mill method was originally developed and published, an opportunity has been presented to apply it to a larger number of coals and to study intensively some of the principles upon which the method is based. This paper presents a résumé of these further studies and includes a comparison with the Hardgrove-machine method. Trial runs were also made with another procedure recently proposed—the C.I.T. roll-test method4. Principles of Methods In the ball-mill method, the relative amounts of energy necessary to grind coals to the same fineness are determined by the number of revolutions of the mill required to reduce 80 per cent of the feed (500 grams of 10 to 200-mesh coal) fine enough to pass a 200-mesh screen. This is a

Jan 1, 1936

By John E. Conley

The production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.' The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnstonr2 Smyth and Adams,3 Ralston et al.,4 Furnas,6 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894" to 898' C. The dissociation of dolomite and magnesite, although studied by several investigators,4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (I) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1942

By Ronald W. Utley

INTRODUCTION The ''Do's and Don'ts" of installing equipment in a comminution circuit begin during the study stage of a proposed project, continue through preliminary engineering, detail engineering, procurement, the actual placement of equipment at the job site, and end with turnover to the owner. Equipment supplied for a modern comminution circuit will be high quality, rugged machinery designed according to appropriate manufacturing standards for long hours of trouble-free service. However, certain precautions and procedures must be observed in plant design and layout, equipment handling, installing and servicing in order to obtain optimum performance. This chapter contains general installation "DO'S and Don'ts" for the major equipment in the circuit. •Primary Gyratory Crushers •Rock Breakers (Hammer) •Belt Conveyors •Apron Feeders •Weigh Belt Scales •Secondary Crushers •Vibrating Screens •Grinding Mills •Mill Liners •Open Gear Sets •Speed Reducers •Electric Motors •Cyclones •Slurry Pumps Some questions will not be covered in this chapter, or may not be applicable to the actual equipment purchased, as requirements do vary from manufacturer to manufacturer. Additional specific information can be obtained by contacting the manufacturer's local representative or the factory. All inquiries should be accompanied by the following information: •Unit size and type of equipment •Manufacturer's shop order number (after order placement) •Serial number (after manufacture) DO'S 8 DON'TS FOR INSTALLATION OF ALL COMMINUTION CIRCUIT EQUIPMENT Installation By Design DO obtain tables of weights and clearances from manufacturer. DO obtain WR2 forces from manufacturer to determine that the foundation is adequate. DO determine compression strength of foundation soil and/or rock. DO obtain manufacturer's recommended typical foundation drawings. If substantial alteration to manufacturer's drawings is required, check with the manufacturer before proceeding.

Jan 1, 1982

By H. F. Yancey, M. R. Greer

At the annual meeting of this Institute held two years ago a new method1 of estimating the grindability of coal was described, based on experimental work carried on by the Bureau of Mines at its Northwest Experiment Station. Since that time, several organizations concerned with the testing or utilization of coal as pulverized fuel have adopted and used the method in determining the grindability of several hundred samples of coal. In addition, a series of comparative tests of this method and three others has been carried out in five laboratories under the auspices of Committee D-5 of the American Society for Testing Materials. As a result the Committee has recommended that the Bureau of Mines method, designated as the "ball-mill method," and the Hardgrove method2, previously advanced, be accepted as tentative standards3. Since the ball-mill method was originally developed and published, an opportunity has been presented to apply it to a larger number of coals and to study intensively some of the principles upon which the method is based. This paper presents a résumé of these further studies and includes a comparison with the Hardgrove-machine method. Trial runs were also made with another procedure recently proposed—the C.I.T. roll-test method4. Principles of Methods In the ball-mill method, the relative amounts of energy necessary to grind coals to the same fineness are determined by the number of revolutions of the mill required to reduce 80 per cent of the feed (500 grams of 10 to 200-mesh coal) fine enough to pass a 200-mesh screen. This is a

Jan 1, 1936

By John E. Conley

The production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.' The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnstonr2 Smyth and Adams,3 Ralston et al.,4 Furnas,6 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894" to 898' C. The dissociation of dolomite and magnesite, although studied by several investigators,4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (I) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1942

By John Conley

THE production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.1 The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require addi-tional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnston,2 Smyth and Adams,3 Ralston et al.,4 Furnas,5 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894° to 898° C. The dissociation of dolomite and magnesite, although studied by several investigators, 4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (1) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1939

By M. Baeyertr

Since 1915 many papers and books have covered industrial applications of X-rays from various angles. Two of the more recent are a paper by Fink and Archer, which describes in detail the technique of radiography, and a paper by Clark2, which embraces the whole field of X-ray metallogmphy. This paper, therefore, is confined to work of the X-ray Laboratory of the Western Electric Co., which naturally divides into two categories: radiography and diffraction patterns of various types. Radiography Radiography is the field in which the application of X-rays has had most general appeal among the industries which produce or use metals and alloys. Equipment permitting the examination of heavy sections of metals less permeable than aluminum or other light alloys requires apparatus capable of generating hard X-rays over a considerable period of time. The equipment used in the work presented in this paper is practically identical with that described by Fink and Archer in their paper on radiography in industry and is easily capable of penetrating 1/8 in. of lead. Radiography is used in two major groups of problems: (1) in the development of cquipment and tools and (2) in studies of materials. So far there has been no instance in which the use of radiography for routine inspection is justified. This is partly due to the fact that the manufacture of telephone apparatus involves the production of many identical parts by standardized procedures and equipment that has had development and trial before being put on a regular production basis. It is during this stage of development of equipment and tools that radiography has been used to particular advantage.

Jan 1, 1931

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958

By M. Mortada

Nonsteady-state flow of slightly compressible liquids in porous media of non-uniform properties has been the subject of a number of recent studies. Most of these studies considered one-dimensional flow in systems with cylindrical geometry and with the properties of the porous medium varying with radial distance only. A. Houpeurt' studied the problem in its general form by examining the solutions of the differential equation, In Eq. 1, the permeability k and the porosity + are arbitrary functions of radial distance. Houpeurt concluded that, except for special forms of the functions k and the problem is not well suited for mathematical treatment, but lends itself to high-speed digital computation. Carslaw and Jaeger' discussed the solution of Eq. 1 for the case in which the permeability varies as a power of the radial distance. P. Albert3 studied analytically the pseudo steady-state solutions in systems of finite radial extent and non-uniform properties. He also obtained some numerical solutions for nonsteady-state flow using a high-speed computer. William Hurst4 examined the interference pressure drop due to a point sink located in an infinite system consisting of two permeability regions in series. In this case, the permeability changed at a radial distance r from the point sink. INTERFERENCE BETWEEN OIL FIELDS IN A NON-UNIFORM AQUIFER The interference pressure drop for oil fields located in an extensive aquifer of uniform properties is discussed in a number of places in the literature. This work considers the interference pressure drop for oil fields located in a non-uniform extensive aquifer comprising two regions of different properties as shown in Fig. 1. Region I of the aquifer extends from which is the radius of Oil Field A, to ar,,, where a>1. It has permeability k,, porosity +, and effective compressibility c,. Oil Field B is located in Region II which extends from ar, to infinity and has different properties from those of Region I, but the same formation thickness h. Region II has permeability k2, porosity and effective compressibility c2. The choice of this type of aquifer should not imply that it is of frequent occurrence. It is chosen primarily to illustrate the effects of non-uniform aquifer properties on oilfield interference. It is of interest to point out that a non-uniform radial aquifer in which both the permeability and the porosity are inversely proportional to the radial distance can be treated in a manner similar to a linear aquifer of uniform properties. The situation where only the permeability varies as the inverse of the radial distance is also amenable to analytical treatment. Both aquifers behave quite differently from a radial aquifer with uniform properties so far as the water influx and the interference pressure drop are concerned. METHOD OF SOLUTION The expression for the interference pressure drop in Oil Field B due to a constant rate of water influx in Oil Field A is developed in the Appendix. This is accomplished by the simultaneous solution of two partial differential equations describing the pressure in Regions I and 11. The two differential equations are solved subject to the following conditions: (1) at r,, the pressure gradient is constant; (2) at ar the pressure and

By R. K. Agarwal

In this paper, a new technique developed to analyze two-dimensional nonhomogeneous models is described. A simple three-layered medium with a circular hole centrally located in the intermediate layer is considered. The layered sheet is loaded uniaxially perpendicular to the stratification. The Young's modulus of the intermediate layer is lower than that of the outer layers. The stress distribution around the circular hole in a stratified medium is significantly different when compared to the case of a continuous homogeneous medium. The distribution depends upon the ratio of the height of the intermediate layer and the hole diameter. A comparison of stress distribution and procedures for preparation and testing of the model are given. The potential of the technique is outlined. In the process of applying the techniques of stress analysis to problems of rock mechanics, the recent discernible trend has been to postulate highly idealized models of physical situations. As new techniques have been developed, more complicated models have been conceived to simulate mote accurately the physical environment to which the analysis results are eventually applied. In this investigation, a new technique is developed to analyze two-dimensional nonhomogeneous models. The technique is used to determine the stress concentration around a circular hole in a soft material overlain and underlain by a hard material. In mining practice, such situations arise commonly in coal deposits and frequently in bedded or vein-type metallic mineral deposits. DEFINITION OF THE PROBLEM A plate, consisting of three layers with a circular hole in the intermediate layer, is loaded uniaxially, Fig. 1. The variable in the experimental investigation is the height of the intermediate layer, H. The diameter of the hole, D, is kept constant. The stress concentration factors around the periphery of the hole, for various values of H/D, are evaluated using the technique of photoelasticity, Table I. TECHNIQUE OF EXPLORATION Photoelastic analyses of composite models have hitherto been limited to the study of lap and butt joints between glued metals and dissimilar materials.1-3 In mining, Haber and Oudenhoven used composite models to study the stress distribution around a circular hole in two-layered media and the behavior of elastic liners in shallow underground openings.4-5 They used the stress freezing technique devised by Dally et a1.6 The procedure used in this investigation is outlined below: Casting of Layer A: Flat sheets of plastic were cast in a silicon-coated mold using Araldite 502 with hardener 951 in the ratio of 100:8 by weight. After

Jan 1, 1969