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By M. King Hubbert, David G. Willis

A theoretical examination of the fracturing of rocks by means of pressure applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid be of the penetrating or non-penetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical with the injection pressure less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should be horizontal with injection pressures equal to or greater than the pressure of the overburden. Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden. These conclusions are compatible with field experience in fracturing and with the results of laboratory experimentation. INTRODUCTION The hydraulic-fracturing technique of well stimulation is one of the major developments in petroleum engineering of the last decade. The technique was introduced to the petroleum industry in a paper by J. B. Clark,' of the Stanolind Oil and Gas Co. in 1948, and since then its use has progressively expanded so that by the end of 1955 more than 100,000 individual treatments had been performed. The technique itself is mechanically related to three other phenomena concerning which ah extensive literature had previously developed. These are: (1) pressure parting in water injection wells in secondary-recovery operations, (2) lost circulation during drilling, and (3) the breakdown of formations during squeeze-cementing operations, all of which appear to involve the formation of open fractures by pressure applied in a wellbore. The most popular interpretation of this mechanism has been that the pressure had parted the formation along a bedding plane and lifted the overburden, notwithstanding the fact that in the great majority of cases where pressures were known they were significantly less than those due to the total weight of the overburden as determined from its density. Prior to 1948, this prevalent opinion had already been queried by Dickey and Andresen,2 in a study of pressure parting; and by Walker,"' who, in studies of squeeze cementing, pointed out that the pressures required were mostly less than those of the overburden, and inferred that the fractures should be vertical. J. B. Clark,' in his paper introducing hydraulic fracturing, and later Howard and Fast," and Scott, Bearden, and Howard," also of Stanolind, postulated that the entire weight of the overburden need not be lifted in producing horizontal fractures, but that it was only necessary to- lift an "effective overburden," requiring a correspondingly lower pressure. Hubbert,7 in discussing the paper by Scott and associates, pointed out that the normal state of stress underground is one of unequal principal stresses; and in tectonically relaxed areas, characterized by normal faults, the least stress should be horizontal. Therefore, in most cases, fracturing should be possible with pressure less than that of the overburden and, moreover, such fractures should be vertical. Harrison, Kieschnick, and McGuire,8 also on the expectation that the least principal stress should be horizontal, argued strongly in favor of vertical fracturing. Scott, Bearden, and Howard6 observed that, when

Jan 1, 1958

By A. H. Geisler, R. F. Mehl, C. S. Barrett

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1'2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y' are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y' and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y' is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By R. F. Mehl, C. S. Barrett, A. H. Geisler

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1'2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y' are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y' and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y' is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By T. B. Counselman

Continuous countercurrent decantation calculations have always been a headache to the cyanide man (and the chemical engineer) because of the simultaneous equations involved. These are tedious to solve, and there is considerable opportunity for mathematical error. This paper presents a shortcut method for making these calculations, which has been in successful use for twenty years by the author, and which is particularly valuable in selecting the best of several possible flowsheets, or evaluating the effect of various assumptions.

Jan 2, 1950

By G. Rinelli, A. M. Marabini, V. Alesse

Salicylaldehyde, a chelating agent for tin, has been found to function as a collector for the flotation of cassiterite. Infrared and nuclear magnetic resonance studies clearly show that salicylaldehyde can form a chelate compound in bulk and at the surface. Results are also given for the flotation of a tin ore with this reagent.

Jan 1, 1976

By A. Bleier, E. D. Goddard, R. D. Kulkarni

The influence of the collector structure on the amine (RNH2, R=alkyl) flotation of quartz has been systematically investigated using a modified Hallimond microflotation cell. This study focuses on the effect of varying chain length, branching in the alkyl group R, polyfunctionality of the collector molecule, and alkyl substitution on the nitrogen atom. In addition, adsorption at the solution/air interface and electrokinetic results for the solid/solution interface were employed to further elucidate the role ad the interrelation of the structural parameters in the flotation process. Estimates of an electrical double layer attractive energy between the bubble and the solid particle are made.

Jan 1, 1976

By S. K. Kawatra, R. A. Seitz

The use of inferential particle sizing for closed wet grinding circuit control has been practiced for several years. This paper presents a review of some inferential sizing equations developed for pilot and industrial plants using regression analysis. An analytical development is then presented showing how the general inferential sizing model arises from the nature of the classifier model. The relation between the general sizing model and the individual equations is then discussed.

Jan 1, 1984

By A. V. Henry

THE kaolins of the southeastern United States were known to civiliza-tion as early as the latter part of the eighteenth century-and yet the GEORGIA PRODUCTION UNITED STATES PRODUCTION IMPORTS Fig. 1.-KAOLIN PRODUCTION AND IMPORTS. commercial history of Georgia kaolins may be said to begin in the year 1900. The U. S. Bureau of Mines reported for that year a production of 6885 tons of "miscellaneous" clays in Georgia. A comparison of these figures with those of 1934, when the production rose to 284,556 tons (65 per cent of the domestic production), indicates the growing economic and technologic importance of this raw material. Fig. 1 clearly shows that a part of the increase is due to a normal growth in the use of kaolinitic clays and a part is due to replacement of clays formerly imported.

Jan 1, 1937

By H. J. Beattie, G. C. Gould

J. B. Seabrook' recently published properties of a low-alloy Ni-A1 age-hardening steel known commercially as "Nitralloy-N". He mentioned three possible mechanisms of age hardening, viz. order-disorder in the matrix, order -disorder in a precipitate, and a precipitate that goes in and out of solution reversibly without losing coherency. The following results indicate that the last - mentioned of these mechanisms is the cause of age hardening in Nitralloy-N. The reversibility of the age hardening with a sub-critical solution temperature was demonstrated strikingly by Seabrook, whose results are reproduced in Fig. 1. Aging for 22 hr at 975°F (525°C) can reharden the fully-tempered martensite to its original as-quenched hardness of R, 45. A Nitralloy steel was obtained from Seabrook' with the following analysis:

Jan 1, 1962

By W. F. James, Richard Murphy, S. N. Kesten, A. H. Lang

The paper is a summary of information on Canadian deposits of uranium and thorium up to the end of 1948, prepared by geologists of Eldorado Mining and Refining Ltd. and by the specialist on uranium deposits for the Geological Survey of Canada. The paper contains a history of Canadian uranium and thorium discoveries, a working classification of the deposits, fairly detailed descriptions of the Eldorado mine and of properties in northern Saskatchewan, and shorter accounts of several other discoveries.

Jan 2, 1950

By W. D. Forgeng, B. F. Decker

IT has been known for almost a century' that silicon and nitrogen combine when heated to a high temperature. Three nitrides have been reported, SiN, Si3N,, and Si,N, containing 33.3, 40.0 and 42.9 pct nitrogen by weight, respectively. The existence of SisN, is well established but that of Si,N, and SiN is doubtful. The first systematic study of the reaction between silicon and nitrogen was made in 1910 by Weiss and Engelhart" who determined the rate at which silicon absorbed nitrogen at temperatures from 1250°C to

Jan 1, 1959

By William K. Callaway

Cominco American has operated the Magmont Mine for 16 years as a traditional open stope room and pillar mine. Diminishing ore reserves and the discovery of high grade ore zones over 90' in thickness caused consideration to be given to hydraulic sandfilling as a method of ground support to increase pillar extraction and mine life. This paper will review the results of sandfill testing. Plans for underground experiments, and operational plans for the future will also be discussed.

Jan 1, 1984

By C. Richard Tinsley

As discussed in the economics section of this article, the main processing consideration is whether manganese will be recovered, as this has major implications for reagent consumption. Nodule processing can be classified into three sections; smelting, roasting, and leaching. Many patents have been issued for various stages of these techniques. Since extensive laboratory and pilot plant testing is continuing, it is certain that some companies are close to full-scale commercial processes. Published data does not include all of the possible concepts for nodule treatment. In fact, one may suspect that published flowsheets are those that have been rejected or have since been extensively modified.

Jan 4, 1975

By H. S. Hanna, C. Rampacek

The problems and limitations encountered in the Physical beneficiation of the Appalachian Red Iron Ores are discussed. Two major problems are identified - the high phosphorus content and the fine dissemination or encapsulation of mineral impurities in the iron-bearing minerals. A process that combined extreme fine grinding techniques with magnetizing roasting or flotation-separation methods is suggested. By these methods, concentrates assaying 60-61 % Fe, exceeding the widely accepted upper limit of 56% Fe set for these ores, were produced with 75-90% iron recovery. Moreover, it was shown that the phosphorus content of these concentrates could be reduced from 0.25% to 0.03% phosphorus by acid leaching. A brief discussion on production costs based on current and future developments in iron ore processing is given.

Jan 1, 1983

By L. S. Castleman, L. L. Seigle

IN a recently reported investigation, J. B. Clark and F. N. Rhines1 used a diffusion couple technique to determine the number of intermetallic phases which should be present in the Al-Mg equilibrium phase diagram. Their method was an application of the following generally accepted principle. If a diffusion couple made up of two metals is annealed at a given temperature for a long time, all the phases of the binary system which exist under equilibrium conditions at the diffusion temperature will form intermetallic layers. It is important that the diffusion temperature be high enough and the diffusion time be long enough to permit the nuclea-tion of all thermodynamically stable phases at the interface of the couples and their growth to observable thicknesses. These simple time-temperature criteria are at times difficult to satisfy, and it is the purpose of this note to point out a situation in which this is the case. The authors are currently studying diffusion bonding in the Al-Ni system." It is well established

Jan 1, 1958

By Raymond E. Zimmerman

Abstract-The Swirl Cyclone developed in Japan, although based upon the same principles as the standard cyclones for heavy-media or water-only cyclones for cleaning coal, is novel in that it is invested with the apex on top, discharging rejects at the top, and clean coal at the bottom. It also uses a variable air vent tube for controlling the vortex. Tests conducted indicate that its efficiency is not only as sharp as standard cyclones but it also performs using a much coarser grain magnetite, promising higher magnetite recovery. The author describes the results of tests conducted in Japan on a very difficult coal.

Jan 2, 1978

By H. I. Smith

WHEN Spain established colonies on the North American continent, some of her land grants, in what is now the United States, reserved to the Crown deposits of gold, silver, and mercury. Later mineral rights were reserved under some of the English Crown charters involving land in the eastern part of North America, with provisions for the payment of royalties thereon to the Crown. Reservation of mineral deposits to the United States Government was instituted by an ordinance of Congress on May 20, 1785, which applied to such deposits in the Northwest Territory, then north of the Ohio River and east of the Mississippi River, and provided that there should be reserved "one third of all gold, silver, lead, and copper mines, to be sold or otherwise disposed of as Congress shall hereafter direct." Little was known then of the mineral resources of the country; the Great Lakes copper region had just come into the possession of the United States by treaty and much of the western mineral land still belonged to France and Spain.

Jan 4, 1954

POSITIONS VACANT No. 255. A company manufacturing malleable iron fittings in Connecticut needs a manager for its steel department. Experience with converter is essential. No. 256. A prominent mining company in Central America wishes a shift boss for its mill and cyanide plant, who is technically trained, experienced, and can speak Spanish. He should he sufficiently expert to be able to take entire charge of the mill in case of emergency. Salary $150 per month on a two years' contract, with additional allowance for board, lodging and transportation expenses. No. 257. A Mexican copper mining company in the State of Puebla needs an engineer on surveying and mapping and drafting in connection with field construction. Healthy locality. Salary $150 per month.

Jan 1, 1918

By T. F. Adams, L. G. Margolin

The Bedded Crack Model (BCM) is a constitutive model for brittle materials. It is based on effective modulus theory and makes use of a generalized Griffith criterion for crack growth. It is used in a solid dynamic computer code to simulate stress wave propagation and fracture in rock. A general description of the model is given and then the theoretical basis for it is presented. Some effects of finite cell size in numerical simulations are discussed. The use of the BCM is illustrated in simulations of explosive fracture of oil shale. There is generally good agreement between the calculations and data from field experiments.

Jan 1, 1982

By Charles O. Thompson

In 1867 the city of Worcester walled in the Mill Brook for its main sewer. This stream, one of the important affluents of the Blackstone River, flows through the city in a southwestenly course from Salisbury Fond, and along its valley a considerable part of the heavy manufactories of the city are placed. At two points, a mile apart, a sufficient fall occurs to be turned to account for motive power, and at many points it was the right and practice of the riparian proprietors, prior to 1867, to use the water for steam and other manufacturing purposes. But the

Jan 1, 1881