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By J. C. Wilhoit, J. B. Cheatham

Although an oil well is a long cylindrical hole with an irregular bottom, it appears likely that the nature of the stress concentration at the bottom of the hole can be ascertained from an analysis of the stresses around a short cylindrical cavity with rounded comers and smooth bottom. Such a cavity is studied primarily because it leads more readily to a solution to the problem by the use of stress functions. In this paper the stress distribution around a short cylindrical cavity subjected to bit loading, overburden and drilling-fluid pressures is determined by means of an analytical solution which approximately satisfies the boundary conditions of the problem. From this solution the stresses at the corner of the hole are calculated to be about 35 per cent lower than comparable results obtained by photoelastic and relaxation analyses. This difference is apparently due to the large radius of curvature at the corner of the cavity in the present analysis. Since good agreement is obtained between the results of this analysis and the stresses calculated for a similar loading on a semi-infinite elastic solid, it is concluded that the bit action in the region near the center of the hole is not appreciably affected by the presence of the sides of the hole. INTRODUCTION Much has been written concerning drilling "under down-hole conditions" and pertaining to the stress distribution in the rock at the bottom of an oil well.1-5 For example, it is known that identical rocks can be drilled more rapidly at the surface than under subsurface conditions of pressure and stress.6 Information on the behavior of rocks under loading can be obtained from triaxial test data.7-9 From such tests it is found that rocks exhibit brittle failure when the confining pressure and pore pressure are equal, but the mode of failure may change to ductile as the difference between the confining pressure and the pore pressure is increased. Brittle failure implies that there is very little permanent deformation before fracture, whereas ductile failure indicates that permanent deformation takes place before fracture. Some rocks are ductile at differential pressures of 5,000 psi , but other rocks are brittle even at differential pressures of more than 50,000 psi. Cuttings embedded in mud at the bottom of the hole may act as a plastic mass which the bit teeth must penetrate in order to attack the virgin rock below. 10 During drilling, the mud pressure acts as the confing pressure, and in many cases the difference between the mud pressure and the formation pore pressure IS sufficiently low so that the rock most likely falls in a brittle manner. Very little penetratiori by the bit teeth may be required for brittle failure of the rock. For these brittle materials, the elastic stress distribution is of practical interest in determicing the possible effects of a given loading on failure. The penetration of bit teeth into ductile or plastic rock has been analyzed previously ll,12 and will not be considered further in the present work. During actual drilling, many teeth act at various points ovel an irregular hole bottom. In the present analysis a solution is obtained for an idealized problem of determining the elastic stress distribution caused by only one tooth acting alone at the center of a smooth hole bottom. It obviously is not proposed that any driller should put a special one-tooth bit on bottom, but it is hoped that extensions of the simpler problems can eventually lead to a better understanding of more complex actual drilling phenomena. To obtain a solution by the use of stress functions, a short cylindrical cavity with rounded corners and smooth bottom is studied. The solution to this problem should give an insight into the nature of the stress concentration at the bottom of an oil well which is in reality a long cylindrical hole with an irregularr bottom. After selection of the proper curvilinear co-ordinate system, the stress functions are expressed as series of Legendre polynomials. The coefficient of each term in the series is then determined to satisfy the boundary conditions at a finite number of discrete points on the boundary of the cavity with least square error. Results are compared with bottom-hole stresses obtained by photoelastic and relaxation analyses.

Charles T. Malcolmson, Chicago, Ill.:—Mr. Blauvelt's admirable paper is a valuable contribution to the literature on briquetting of coal in this country. It should have a special significance for those interested in the commercial development of the coal-briquette industry. I believe that the data included in Mr. Blauvelt's paper will be particularly useful because they represent costs taken from a briquette-plant in actual operation. There are several points touched on in Mr. Blauvelt's paper which may bear comment in the way of emphasis rather than of criticism. In the first place, he has stated a fact which becomes axiomatic to any one who has had any experience in the design, building, or operation of coal-briquette plants, and that is, that the press is only one factor in the successful opera-

Jan 1, 1911

By J. Richard Lucas

The coal industry, one of the great basic industries in the nation, plays a major role in the American economy. Coal is the principal fuel used in generating tremendous quantities of low-cost power so necessary to the nation. Two-thirds of the electrical energy and one-fourth of all energy consumed in the nation is produced from coal. Large-scale production of steel, cement, and chemicals is vitally dependent upon this natural resource. Because of extensive reserves and low mining cost, it is one of the few natural resources in which the United States is a significant exporter. During 1965 in excess of 500 million tons of coal were produced, almost 10% over the previous year; more than 50 million tons were shipped to foreign markets. The utility market gained approximately 8% during the year for a total of 242 million tons.

Jan 2, 1966

By T. M. Drown, P. W. Shimer

The precipitation of phosphoric with titanic acid, by boiling an iron solution which had been reduced to the ferrous condition by sulpharetted hydrogen or sulphurous acid, was first noticed by E. H. Bogardus in 1874.* Since that time, as far as we are aware, not much has been published on the relation of these two acids to each other, and to silicic acid, in the ordinary course of analysis of iron ores. The following investigation may perhaps aid in clewing up some of the obscure points in the analysis of titaniferous ores. THE DETERMINATION OF PHOSPHORUS. From two to five grams of the finely powdered ore are weighed into a beaker and treated with about 50 c.c. of hydrochloric acid (sp. gr. 1.12), evaporated to dryness, and heated ih an air-bath for

Jan 1, 1882

By N. Mao

This paper presents the results of a research effort to develop a technique for estimating in situ stresses by measuring stress-induced velocity anisotropy around a borehole. Relevant parameters required to make the estimate were identified and measured in the laboratory on a 35.6 cm (14.0 in) cube of Nugget sandstone with a 10.2 cm (4.0 in) diameter hole, under biaxial loading. Two pairs each of radially and tangentially polarized transducers were placed inside the hole with displacement directions either parallel or perpendicular to the principal stress directions. With this configuration, relative travel times were measured by both a pulsed phaselocked loop technique and a cross correlation of digitized waveforms. The biaxial velocity data were used to back-calculate the applied stress. The standard deviation of the differences between the calculated and applied stresses is 0.62 MPa (90 psi) for a stress level up to 8.63 MPa (1250 psi).

Jan 1, 1984

MARCEL R. DALY (written discussion+).-I have read with great interest Mr. W . Van Der Gracht's discussion of my paper and I fail to see where his theory contradicts mine on any fundamental point. My contention is that petroliferous accumulations are generally coincident with diastrophic deformations, synchronous with them and essentially a result of them. This implies that the causes which have led to the distortion of the strata, whatever these causes may be (thrusts, torsion, etc.), have also led to the concentration and accumulation of the hydrocarbons existing in the strata at that time. It is in this respect that both set of phenomena may be said to be related in space and in time and that we may speak of an identity of causes. It is evident that no concentration of the hydrocarbons could take place where these hydrocarbons would not exist. But whenever they do so exist, deformation will tend to concentrate them; and whenever they are found to be concentrated (or accumulated) the cause of their accumulation will have to be traced directly to distortion. I have tried to show, in some previous papers,' the probable sequence of such a mechanical process in the simple case of a series of parallel, superposed, horizontal and homogeneous layers, individually uniform in thickness, but variable in composition and resistance; and I have pointed out that the general results so obtained would harmonize with some striking features recognized in the field. But I have also stated that conditions being much more complicated in nature than in the theoretical instance considered above, a complex superposition of effects would. have to be expected as a general rule, though the leading principle would remain the same. Mr. Van der Gracht admits that the motion of the primary oil, when it has been formed, and its accumulation in adequately porous containers, if any, that would be mostly found on the front edge of the original geosynclines, would be due to the action of the mountain-building forces. Our agreement on this point seems to be complete. But Mr. Van der Gracht wants also the formation of the bituminous matter in its primary form to be coincident only with the earliest phase of the uplift, viz., after the slow geanticlinal upheaval has been completed, and the accumulation

Jan 3, 1918

At the Second Pan-American Scientific Congress, meeting in Washington, D. C., from Dec. 27, 1915 to Jan. 8, 1916, the following special topics will be discussed in each of the four sub-sections of Section VII, of which Hennen Jennings is Chairman: A. Mining.-The mining law of each country and the changes that may be made to aid the development of mineral resources. History of the mining industry in each country with reference to the beginnings of that industry. The development of the Patio process. Bibliography of mining. B. Metallurgy.-Present methods of concentrating ores and the development of concentration methods. International relations in the exchange of ores and metals. Bibliography of metallurgy. A. and B. Mining and Metallurgy.-Development of hydro-electric power for mining and metallurgy, the amount probably available, and specific benefits from its utilization.

Jan 1, 1916

By John S. Alexander

DURING the past few years the block coal of Indiana has been talked about and written upon to such an extent, that almost every one at all interested in such subjects, has been made acquainted with the area and geographical position of the field, the quality and peculiar properties of the coal, the thickness of the veins, the manner of mining, etc. The writer, therefore, taking for granted that to those present all this is familiar ground, desires more especially to call attention to the position this coal takes in the market, and at those points of consumption where it is brought in direct competition with rival fuels. Chicago, thus far, has been the chief consumer of Indiana block coal, the distance from the mines at Brazil, via Terre Haute and the 25

Jan 1, 1873

By D. T. Peters, J. C. Bisseliches, J. W. Spretnak

The pain boundary relaxation phenomenon in high-purity copper, 0FHC copper, and a precipitation-hardenable alloy o-fCu-2 uit pct Co has been studied by internal ,friction and elastic aftereffect techniques. The data were analyzed by assuming the broad distribution of relaxation times observed obeys a lognormal distribution law which enables calculation of the relaxation strength. Grain size had no effect on relaxation strength, although the peak width increased with increasing grain size and decreasing temperature. A double grain boundary peak was produced in high-purity copper by annealing to produce secondary recrystallization. The activation energy measured for 99.999 pct Cu is 37.5 * 3 kcal per mol and 46.5 kcal per mole for OFHC copper. A small peak in the Cu-Co alloy at about 220°C at 1 cps was deduced to be the grain boundary peak. Its height increased and its activation energy decreased with increasing aging time. Except for erratic peak positions the observations were consistent with the theory of pain boundary sliding. BEFORE the mechanism of the grain boundary internal friction peak in metals can be satisfactorily explained, the detailed characteristics of the relaxation process must be documented. Of interest are the effect of grain size on relaxation strength, the high-temperature background, and peak width and position. The effect on the grain boundary peak of a precipitate at grain boundaries and of the change in distribution of the particles with aging time must also be explained by any existing or forthcoming theory. The model which has received the most attention was proposed by KG' and zener2 and proposes that the anelastic strain results from sliding of adjacent crystals at grain boundaries. The sliding is limited by the interlocking of grain corners. It follows, according to this model, that the relaxation strength is independent of and the relaxation time is proportional to the grain size. The proportionality between grain size, D, and relaxation time, t, has been confirmed by K&' and Bisseliches . In this case, the internal-friction peaks of various specimens can be superimposed by plotting Q-' as a function of the parameter vD exp H/RT where v is the frequency and H the activation energy. However, the data of Starr et 01.' and Leak6 fit better to a parameter containing D to an exponent near two. A meaningful relationship is not always deducible from the shift of peak temperature with grain size. KG7 demonstrated that a twofold variation in grain size obtained by varying the amount of cold work followed by identical recrystallization anneals will cause a peak shift that is too large to be accounted for even by an exponent of two. Since the decreased grain boundary area existing with a larger grain size is exactly compensated for by an increased sliding distance, the relaxation strength should not decrease with increasing grain size. The height of the internal-friction peak has generally been observed to be rather insensitive to grain size as long as the average grain diameter does not approach the specimen diameter. Exceptions have been reported by Koster, Bangert, and Lang8 for copper, and by Leak6 for iron. The observations for copper could well have been confused by the presence df 0.3 pct0. The possibility that the peaks may simply be increasing in width with increasing grain size and that the relaxation strength, which is proportional to the area under the peak, may remain constant was not examined. his point has been checked in this investigation using high-purity copper. Atomic mechanisms to account for damping by sliding at grain boundaries have been proposed by KG7 and Mott. KG predicts the activation energy to be identical to that for self-diffusion. Mott's "island" model suggests the activation energy is nL where n is the number of atoms in an island and L is the latent heat of fusion per atom. Other authors have felt that a value equal to the activa-

Jan 1, 1964

By Alvin Kaufman

ANTHRACITE mining in the United States is concentrated in a 480 sq mile section of north- eastern Pennsylvania. The producing area is broken up into four fields, known as the Northern, Southern, Eastern Middle and Western Middle fields. These areas represent intricately folded coal measures in synclinal residuals left by erosional forces. Destruction by erosion has eliminated some 95 pct of the original coal. However, discounting the 5 billion tons removed to date, 8 billion tons are believed to be still recoverable.

Jan 3, 1953

The Committee appointed by your Board of Directors to nominate Officers for the Institute for the year 1915 invites the participation of all members in the nominations. The suggestion of names for the various offices will be appreciated and given full consideration when making the selection of candidates which this Committee will recommend. The officers to be elected at the annual meeting in February, 1915, are: One officer, known as Director and President. Two officers, known as Director and Vice-President. Five officers, known as Director. The attention of members is called to Articles V and VII of the Constitution, and to By-Law XIII, which reads as follows:

Jan 6, 1914

By Thomas E. Howard

Tunneling is at the threshold of a new era. An exciting new technology is becoming available. And, supplying the increasing quantities of minerals required by a growing and socially advancing world population, together with providing the subsurface facilities attendant to the rapid urbanization of the more developed countries of the world, will require underground excavation during the next decades on a scale that would have seemed fantastic a few years ago. It is estimated that world mineral consumption will increase fivefold by the year 2000. Projections for the United States indicate that domestic consumption of nonfuel minerals may increase two to three times by the end of the century. Meeting these requirements will entail opening up many new underground mines, even if present trends toward surface mining continue. And, at least in the United States, new factors that are becoming increasingly important may modify these trends. We are depleting our shallow easy- to-find and easy-to-mine mineral deposits; and, if we are to avoid becoming dangerously dependent on imports, we must turn more and more toward deeper deposits that are not amenable to surface mining. Growing public concern with environmental quality is apparently leading toward increasingly stringent regulation of surface mining which also will tend to make underground mining economically more attractive. The world market for underground construction is also growing rapidly. The most conservative projections indicate that in the United States alone more than $7.0 billion will be spent on excavation for underground facilities during the next ten years. And these estimates do not include any of the bold, imaginative new applications for underground excavation that have been proposed, such as extensive underground power transmission, the Chicago Deep Tunnel plan, and the Northeast Corridor Transportation project. There can be little doubt then that the market for tunnels for conventional applications is increasing rapidly and that the trend will continue. It

Jan 1, 1970

By John C. McDonald

This report is a continuation of an earlier one with a similar titlell to which the reader is referred for such details of procedure as do not appear here. A brief summary will be given of the objects and methods of the research at this time. It was pointed out in the previous paper that properties of magnesium alloys, as reported by different workers, often differ. This was thought to be due to differences in the preparation of the specimens tested. The ideal way to compare alloys would be to prepare each of them in so many ways that reasonable assurance would exist that the best properties of each alloy had been developed. The alloys would then be compared on the basis of these properties. The treatment actually given the alloys of these studies is necessarily a compromise with completeness. Nevertheless, enough treatments have been given so that a considerable degree of assurance exists that the properties obtained are representative of the alloy as such, and not merely of the manner in which it was worked and heat-treated. Procedure The alloys were cast in the form of cylindrical ingots, which were extruded into bar before being rolled. Some of the ingots were made in 2-in. diameter molds whereas all of the alloys of the previous paper were cast in 4.in. molds. For the larger ingots, the extruded bar was 2 by 0.140 in.; lor the 2-in. ingots, it was I by 0.100 in. Preliminary work indicated that strip rolled from both sizes of the bars would have substantially the same properties. The bar was rolled at some temperature in the range 400' to 800°F., for a total reduction of 50 per cent. The temperature and reduction per pass were so selected that no cold cracking occurred, but were such as to leave the metal in a semihard condition. The hot-rolled metal was annealed at several temperatures in the range 400' to 800°F.; it was also cold-rolled, and given solution and aging treatments. Two standard test bars corresponding to each treatment were pulled in tension, and the average was obtained. Twelve treatments, in all, were given each alloy. The properties of the annealed specimen having the highest percentage of elongation were selected to represent the alloy in the annealed condition. The properties of the cold-rolled specimen having the highest yield strength were selected to represent the alloy in the cold-rolled condition. These properties were then plotted against percentage composition by analysis. Smooth curves were drawn among the points, thus graphically averaging the results over the entire range studied. The percentage of elongation in the cold-rolled state was not plotted, since it was always low, and varied in an irregular manner with composition. Alloys Studied Magnesium-calcium Alloys.—Fig. I presents the results on the alloys of the rnag-

Jan 1, 1941

By John C. McDonald

This report is a continuation of an earlier one with a similar titlell to which the reader is referred for such details of procedure as do not appear here. A brief summary will be given of the objects and methods of the research at this time. It was pointed out in the previous paper that properties of magnesium alloys, as reported by different workers, often differ. This was thought to be due to differences in the preparation of the specimens tested. The ideal way to compare alloys would be to prepare each of them in so many ways that reasonable assurance would exist that the best properties of each alloy had been developed. The alloys would then be compared on the basis of these properties. The treatment actually given the alloys of these studies is necessarily a compromise with completeness. Nevertheless, enough treatments have been given so that a considerable degree of assurance exists that the properties obtained are representative of the alloy as such, and not merely of the manner in which it was worked and heat-treated. Procedure The alloys were cast in the form of cylindrical ingots, which were extruded into bar before being rolled. Some of the ingots were made in 2-in. diameter molds whereas all of the alloys of the previous paper were cast in 4.in. molds. For the larger ingots, the extruded bar was 2 by 0.140 in.; lor the 2-in. ingots, it was I by 0.100 in. Preliminary work indicated that strip rolled from both sizes of the bars would have substantially the same properties. The bar was rolled at some temperature in the range 400' to 800°F., for a total reduction of 50 per cent. The temperature and reduction per pass were so selected that no cold cracking occurred, but were such as to leave the metal in a semihard condition. The hot-rolled metal was annealed at several temperatures in the range 400' to 800°F.; it was also cold-rolled, and given solution and aging treatments. Two standard test bars corresponding to each treatment were pulled in tension, and the average was obtained. Twelve treatments, in all, were given each alloy. The properties of the annealed specimen having the highest percentage of elongation were selected to represent the alloy in the annealed condition. The properties of the cold-rolled specimen having the highest yield strength were selected to represent the alloy in the cold-rolled condition. These properties were then plotted against percentage composition by analysis. Smooth curves were drawn among the points, thus graphically averaging the results over the entire range studied. The percentage of elongation in the cold-rolled state was not plotted, since it was always low, and varied in an irregular manner with composition. Alloys Studied Magnesium-calcium Alloys.—Fig. I presents the results on the alloys of the rnag-

Jan 1, 1941

By A. J. Shaler, J. Prieto Isaza, J. Wulff

Tantalum metal has a number of unique properties which give it widespread application in modern technology and in research. In electronic apparatus involwing high temperatures in vacuo some of the refractory metals 6ecome brittle. Tantalum retains its ductility at elevated temperatures, and this property, together with its low vapor pressure and its ability to absorb gases, make it important in this field. Its chemical inertness in the presence of acids, halogens, and other corrosive media, makes it useful in chemical apparatus and in neuro and orthopedic surgical applications. As an addition to tungsten carbide in steel-cutting grades of cemented-carbide tools, the carbides of tantalum and of its sister element colum-bium have found considerable use. The present-day method1 of manufacturing tantalum is to sinter a powder compact of the metal in vacuo. Because tantalum-columbium alloys are difficult to work and since tantalum ores almost always contain columbium, the two metals must be separated chemically, the products of the separation being generally in the form of potassium tantalum fluoride and potassium columbium oxyfluoride. These salts are used in fused-salt electrolytic baths from which coarse metallic powder is deposited as a sponge at the cathode. Finer powder can be made from the coarse product or from tantalum scrap by first submitting it to an embrittling heat treatment in hydrogen and then crushing it. The fine hydrogen-containing powder may subsequently be degassed in vacuo at a high temperature. Prompted by the success of others2,3 in the magnesium reduction of titanium and zirconium halides; one of the authors undertook4 an investigation of the thermochemistry of the reaction between solid magnesium and gaseous tantalum penta-chloride, a subject which had not previously been studied. He found that the heat of formation of tantalum pentachloride is approximately 364,250 cal per mol at temperatures lower than the melting point of magnesium. A value of 83 units was found for the standard entropy at these temperatures. With these values, it was shown that magnesium and tantalum pentachloride are capable of reacting exo-thermically at temperatures less than the melting point of magnesium, and that no great violence is to be expected when these substances are heated together. The exothermic nature of the reaction indicated that the Drocess should be efficient and should not require much externally applied energy. Tantalum pentachloride is not commonly made commercially, and any process using it therefore involves the subsidiary problem of producing and handling this substance. A series of experiments was carried out in which dried chlorine saturated with carbon tetrachloride was passed over heated tanta-

Jan 1, 1949

Notice is hereby given that all members whose dues are paid for the year 1917 will be supplied with a copy of the Volumes MV and LV. Volume LVI has been delayed by the fact that our printer, like almost every other industrial society, has taken up war work and is under great pressure in addition thereto. Volume LVI will be sent before the end of the year, to members whose dues for the year 1917 are paid.

Jan 12, 1917

Mr. Address Member ,is hereby proposed by the undersigned; as a Associate Junior Member of the American Institute of Mining Engineers. Signatures of three Members or Associates. Place of birth Year of birth Education, when, where and how acquired, with degrees, if any. A technical education is not requisite for membership. Dates Please give record of experience on following page with dates; for example, in the form used by "Who's Who In America" and similar publications.

Jan 5, 1917

By Edmund Newton

THE steel industry of the United States has depended in the past almost wholly upon imports for its supplies of manganese. Many of the important domestic sources yield ores leaner in their natural condition than the foreign ores the steel industry has been accustomed to use. To make them available, therefore, either' the ores must be concentrated or the practice of the steel industry modified. Roughly 25,000 T. annually of high-grade manganese ores are used for dry batteries, for chemical purposes, and in other ways; while approximately 750,000 T. are required for making steel. By present practice, every ton of steel takes an average of about 14 lb. (1.8 kg.) of metallic manganese. This is generally added to the steel in the form of an alloy, the standard alloys being the 80-per cent. ferro-manganese and the 20-per cent. spiegeleisen. During the year 1917 286,000 T. of ferromanganese and 193,291 T. of spiegeleisen were made in this country, the former largely from imported ores; and 45,381 T.

Jan 2, 1919

By Robert R. French

Beneficiation of low-grade nonmetalliferous mineral deposits by electronic color sorting is currently undergoing a period of rapid development. For those deposits in which the specific gravity, strength, soundness, and electric and magnetic properties of the ore and gangue are similar, the possibility of separation by color, reflectivity, or fluorescence offers hope for the utilization of much poorer quality ore than previously thought possible. For those ores in which consistency of color is required or for which a dry process is preferred, the electronic color sorter is particularly adaptable. Tests performed late in 1966 and reported herein are the result of the continued interest in the dry beneficiation of gypsum and the development of higher capacity color sorting machines. The ore used was a discarded fraction that consisted of – 1 ¼ -in, to + 3/8 -in. ore containing 63.1 to 71.4% (average 67.7%) gypsum. This material was contaminated by various amounts of both carbonate rock and shale, but no pretreatment was performed other than screening to closer size limits before electronic color sorting.

Jan 4, 1969

By James Aston

INDICATIVE of the practical importance of the achievement of James Aston , recipient of the Robert W. Hunt Medal for 1930, is the following prosaic item from the financial columns of a recent issue of a New York newspaper. "According to private advices from Pittsburgh, production costs of the A. M. Byers Co. for 1929 were reduced about $5 a ton by the use of the Aston process for making wrought iron pipe. A greater saving is anticipated for 1930, when more of the company?s requirements will be produced by the new method."

Jan 1, 1930