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By W. Klement

By quenching liquid alloys, single-phase solid solutions are obtained in the ranges 0 to 42.0 at. pct Co-Au and 0 to 15 and 75 to about 100 at. pet Co-Cu. Metastable solid solutions are also found in multiphase 42.0 to 49.0 and 69. 0 to about 100 at. pet Co-Au alloys. fie inability to achieve complete solid solubiliiies in Au-co and cu-co alloys is rationalized by a conszderation of the rate processes during cooling and solidification. Trends in lattice distortion and shifts in the compositions of the melting-point minima and critical points are discussed for the binary alloys of copper, silver, and gold with some of the transition metals of the first long period. By rapidly cooling alloys from the melt, a continuous series of metastable solid solutions can often be obtained for components of similar crystal structure which normally form eutectic systems.' The eutectic system Au-Co, Fig. 1, and the peritectic system Cu-Co, Fig. 2, were investigated in order to determine the extent of the metastable solid solutions attainable with the present technique.* EXPERIMENTAL PROCEDURES Most of the alloys were prepared by melting weighed quantities of the elements (purity greater than 99.9 pct) under hydrogen in alumina crucibles by means of induction heating. After reweighing, the alloys were cast under argon into 1 mm diam wires. However, it was not possible to prepare some of the Cu-Co alloys with the requisite homogeneity (over about 1 mm3) in this way. For these alloys, reduced powders (purity greater than 99.9 pct) were mixed for 12 to 48 hr, pressed into compacts that were sintered at 1000º to 1050°C for 6 to 48 hr under hydrogen, and then furnace-cooled. Alloy charges of a few mm3, cut from the cast wires or chipped from the sintered compacts, were heated to 1550º to 1600°C in 30 sec in an alumina insert held within a graphite support and then ejected by a pulse of helium onto a lightly polished copper strip on the inner periphery of a rotating wheel. The

Jan 1, 1963

By Edward Steidle

It has been said that "the command of nature has been put into the hands of man before he knows how to command himself," and what we see about us gives particular emphasis to this observation. If this condition be granted, the vaunted boast of school and college, of the institution that had the training of this generation, and of its fathers, and of its grandfathers, the boast that education is a "preparation for life," stands exposed as a hollow claim, or as a ghastly, cynical conception of life, or else education has fallen far short of its intentions. It has been evident for some time that education was not meeting the fullest expectations of society. In recent years there has been a deal of speculation indulged in by both laity and faculty in regard to American education and American civilization, and some few and sporadic changes have been effected. Today, however, there is no longer time for mere hypothetical considerations; we are faced with certain definite facts and confronted with obvious conditions that will not wait for fine-spun theories. If educators do not put their house in order, someone else will do it for them. The trends in mineral industries education must be in harmony with this general realignment that is today visible on the educational horizon, and only as these trends are in conformity with this movement can they be called sound. Two questions, then, confront mineral industries educators: (1) What are the trends in mineral industries education, and (2) how do these trends correlate with the major educational movements of the day? Scope or Mineral Industries Education Before launching into these particulars, it might be well to define the scope of mineral industries education and to consider its present position. Mineral industries education embraces three main types of work: 1. Earth Sciences and Geography.—Geology, mineralogy, geography— courses basic to all mineral industries and to the humanities. 2. Mineral Engineering.—Mining, petroleum and natural gas—dealing with mineral producing industries. Application of earth sciences and all types of engineering to exploitation of natural mineral resources.

Jan 1, 1934

By Paul Tyler

FULLY a decade ago, demand for ground mica began to exceed supplies of scrap mica from manufacturing operations and of waste block from feldspar and sheet mica mining in the United States, with the result that in recent years the market has absorbed larger and larger quantities of mica recovered as a by-product from clay washing,1 as a joint product with kyanite,2 and by grinding schists. So far, only schists that contain a large percentage of mica have been utilized for making ground mica, but already there has been a good deal of wishful thinking with regard to recovering mica as an aid to the prospective working of low-grade gold ores and ores of certain base metals. With wet-ground mica selling at $60 to $100 a ton and even dry-ground mica worth over $20 a ton, many ores that could not be considered as otherwise workable under present conditions will show commercial possibilities if they can be made to yield even a relatively small percentage of salable mica. An interesting paper might be written on the coming role of industrial minerals as joint products of metal mines, It is largely a matter of mar-kets. Many years ago I watched the mess left behind the gold dredges in the mountains of Colorado and thought of the Denver sand and gravel operators who prided themselves upon their canniness in providing devices for catching gold merely as an incident to their regular business of selling what we miners classed as "tailings." Nowadays almost every milling or mining operation near settled communities finds use for at least part of its waste for road material or concrete aggregate and several eastern iron mines have gone into the crushed-stone business. Promoters now mention fertilizer "filler" as potentially salable at all the way from $1 to $10 a ton, or whatever is needed to cover costs of mining and treating the "ore" and leave the metal values as "clear profit." In emulating the pork packers in their efforts to utilize "everything but the squeal,"

Jan 1, 1938

By Carl Floe

A NUMBER of proposals have been made for the hydrometallurgical recovery of copper from flotation concentrates, but as yet no process has been developed that has demonstrated an ability to compete with the present smelting methods under ordinary conditions. The treat-ment of copper concentrates by hydrometallurgical methods is in general similar to that used in the present electrolytic zinc process and involves roasting, leaching with H2S04 solution, separation of solutions, control of impurities and electrodeposition. While many of these steps are simpler and more readily carried out for copper than for zinc, a number of inherent difficulties have prevented the general adoption of the process. To compete with smelting, the following problems must still be con-fronted, although many solutions for their have been proposed: (1) con-duction of the roast in such a way that leaching will give an extraction of copper comparable to that obtained by smelting; (2) regulation of the ferric iron content of the solutions during electrolysis; (3) disposal of the excess acid regenerated from the sulphates formed in roasting; (4) eco-nomical recovery of the precious metals from the leach residues. The roasting problem is largely one of preventing the formation of copper ferrites, CuO.Fe2O, and Cu20.Fe2O3, which are quite insoluble in dilute sulphuric acid. These ferrites are apparently formed' to a small extent even at low temperatures and above 650° C. their formation is rapid1. While it is possible to carry out laboratory roasts in such a way that less than 5 per cent of the total copper is present in the insoluble ferrite form, a closer temperature control is required than can readily be obtained in industrial furnaces. The flash" roasting effects and consequent high temperatures that occur as the calcine falls from hearth to hearth in the ordinary multiple-hearth roaster are probably largely responsible for the inevitable formation of some ferrites. The result is that in a commercial plant the extraction of copper would not average more than 90 per cent in a single 10 per cent H2SO4 leach. This is

Jan 1, 1937

By B. H. Dunshee

This paper is not intended to be a technical discussion of square-set framing as used in mines, but merely a short description of the different kinds of framing that have been used in the Butte mines, and what has been decided upon, after years of practical experience, as being the best, taking into consideration the physical condition of the veins and country rock, and also the supply of timber available for mining purposes. Butte is, essentially, a square-set district. Virginia City, Nev., was the first mining camp to use this method of timbering, and to Philip Deidesheimer, who went to the Ophir mine in 1860, is given the credit of solving the problem of square-set framing, where large bodies of ore were stoped and the timbers were supposed to hold the ground from caving without any filling. That he did his work well is shown by the fact that the main features of his framing are in use to-day. In the Butte mines the conditions are such that this method of timbering is generally used. We do not, of course, depend upon the timbers any more than is necessary. The worked-out stopes are filled with waste rock as close behind the miners as possible and not interfere with mining operations. The waste rock is obtained from development work on the different levels or from the surface. In the earlier days of mining in Butte there were numerous independent companies and naturally there were different ideas as to the best way to frame the square sets, although the general features were the same. Timber was abundant for mining purposes and the common practice was to use sawed lumber, generally 10 by 10 in. or 12 by 12 in. square. Some of the mines used for girts 6 by 10 in. or 8 by 12 in. timber, depending upon whether they used 10-in. square or 12-in. square timber for posts and caps. This avoided the necessity of framiug the ends of the girts, and also required less timber for the

Jan 1, 1914

By C. S. Blair

The development of a geological department as an integral part of the Tennessee Coal, Iron & Railroad Co. in the Birmingham district, Alabama, in 1908 was an innovation probably unique for any mining organization south of the Ohio River. At that time a few of the oil companies were starting geological departments, but there were no geologists among the larger industrial organizations. The Tennessee Coal, Iron & Railroad Co. had been a substantial producer of pig iron for many years and was just getting a start in the manufacture of steel products from the pig iron. It had large acreages of coal land, ore land and timber land, but there was lacking the detailed knowledge of the possible mineral resources of much of its territory, and this territory at that time covered an area in the neighborhood of 500,000 acres in the states of Alabama, Tennessee and Georgia. Those responsible for the operations of the mining properties, not being familiar with the kind of help that might be expected from geologic work, were decidedly skeptical of the utility of the work. Therefore it was necessary to develop cooperation with the mining organization, by not infringing upon its functions, and by developing the work in such a manner as to demonstrate to the mining department its practical utility. In the first instance the man responsible for a mining operation is apt to assume the attitude that the geologist is a blockader, because the geologist, unfortunately, is obliged to point out difficulties in the carrying out of mining operations in the way originally planned. He points out the dangers of mining out one coal or metal seam at the ultimate expense of an upper or lower seam, and he develops structural features, such as faults and folds, which call to the attention of the mining operator difficulties in his future operations, which the latter had not anticipated. Eventually, however, the value of having these data became apparent to the Tennessee Coal, Iron and Railroad Co., and the operators not only welcomed the geological work and cooperated fully in its acquisition of essential information, but reached the point of asking assistance and advice; and complete coordination of the two activities has existed for many years.

Jan 1, 1935

By C. S. Blair

The development of a geological department as an integral part of the Tennessee Coal, Iron & Railroad Co. in the Birmingham district, Alabama, in 1908 was an innovation probably unique for any mining organization south of the Ohio River. At that time a few of the oil companies were starting geological departments, but there were no geologists among the larger industrial organizations. The Tennessee Coal, Iron & Railroad Co. had been a substantial producer of pig iron for many years and was just getting a start in the manufacture of steel products from the pig iron. It had large acreages of coal land, ore land and timber land, but there was lacking the detailed knowledge of the possible mineral resources of much of its territory, and this territory at that time covered an area in the neighborhood of 500,000 acres in the states of Alabama, Tennessee and Georgia. Those responsible for the operations of the mining properties, not being familiar with the kind of help that might be expected from geologic work, were decidedly skeptical of the utility of the work. Therefore it was necessary to develop cooperation with the mining organization, by not infringing upon its functions, and by developing the work in such a manner as to demonstrate to the mining department its practical utility. In the first instance the man responsible for a mining operation is apt to assume the attitude that the geologist is a blockader, because the geologist, unfortunately, is obliged to point out difficulties in the carrying out of mining operations in the way originally planned. He points out the dangers of mining out one coal or metal seam at the ultimate expense of an upper or lower seam, and he develops structural features, such as faults and folds, which call to the attention of the mining operator difficulties in his future operations, which the latter had not anticipated. Eventually, however, the value of having these data became apparent to the Tennessee Coal, Iron and Railroad Co., and the operators not only welcomed the geological work and cooperated fully in its acquisition of essential information, but reached the point of asking assistance and advice; and complete coordination of the two activities has existed for many years.

Jan 1, 1935

By Paul M. Tyler

FULLY a decade ago, demand for ground mica began to exceed supplies of scrap mica from manufacturing operations and of waste block from feldspar and sheet mica mining in the United States, with the result that in recent years the market has absorbed larger and larger quantities of mica recovered as a by-product from clay washing,1 as a joint product with kyanite12 and by grinding schists. So far, only schists that contain a large percentage of mica have been utilized for making ground mica, but already there has been a good deal of wishful thinking with regard to recovering mica as an aid to the prospective working of low-grade gold ores and ores of certain base metals. With wet-ground mica selling at $60 to $100 a ton and even dry-ground mica worth over $20 a ton, many ores that could not be considered as otherwise workable under present conditions will show commercial possibilities if they can be made to yield even a relatively small percentage of salable mica. An interesting paper might be written on the coming role of industrial minerals as joint products of metal mines. It is largely a matter of markets. Many years ago I watched the mess left behind the gold dredges in the mountains of Colorado and thought of the Denver sand and gravel operators who prided themselves upon their canniness in providing devices for catching gold merely as an incident to their regular business of selling what we miners classed as "tailings." Nowadays almost every milling or mining operation near settled communities finds use for at least part of its waste for road material or concrete aggregate and several eastern iron mines have gone into the crushed-stone business. Promoters now mention fertilizer "filler" as potentially salable at all the way from $1 to $10 a ton, or whatever is needed to cover costs of mining and treating the "ore" and leave the metal values as "clear profit." In emulating the pork packers in their efforts to utilize "everything but the squeal,"

Jan 1, 1938

By Leland Wemple

PREVIOUS to 1915, zinc refining had not become a general practice among the zinc smelters in the United States. Such refining as had been carried on was confined chiefly to remelting very high-leaded zinc, such as third-draw metal from the retort furnaces, and slab dross, and hard spelter from galvanizing pots. In this remelting operation, the lead and iron were settled out and the refined spelter obtained graded fifth class, i.e., Prime Western. Owing to the presence of lead in most zinc ores, the bulk of the spelter produced by direct smelting is of this Prime Western grade. Careful selection of ores of low lead content gave purer grades of spelter, i.e., Brass Special and Intermediate; and smelters which could secure ores carrying practically no lead produced high-grade spelter. Thus, in general, the grade of spelter produced by any smelter was pre-determined by the purity of the ore it could obtain. The needs of the warring nations of Europe for enormous quantities of cartridge and other high-grade brass resulted in such a demand for the purer grades of spelter that the available supply of lead-free and low-lead ores could not produce the quantity required. Prime Western grades went begging, so to speak, while high grades sold at times from 5 to 15 c. per pound over the Prime Western market. The great demand, coupled with the wide market margin, which permitted the inherent costs and losses, resulted in the conversion of the lower grades into higher grades by processes of refining. These conditions also accentuated the development and size of the electrolytic plants, which were being worked out at the time this increased demand for pure grade of metal occurred. The electrolytic process, where available, produces a higher grade of spelter from impure ores than does the fire process; a large portion of those impurities in the ore, which by the distillation process would be carried into the spelter, are removed in the leaching of the ores and the purification of the solutions. The refining process, adopted at a number of smelters for the purpose of converting low-grade spelter into "grades suitable for brash was that of redistillation.

Jan 11, 1917

By Karl Fetters

IN the process of making steel in the open-hearth furnace the refining of the metal during the working period of the heat is largely accomplished through the agency of the slag. From the birth of the process until the present day steelmakers have recognized the importance of the slag in determining the composition of the metal and the quality of the product. The general relationships between slag composition and metal analysis have long been known, at least in a qualitative or approximate fashion. For examples, the iron oxide content of the slag is higher on lower carbon heats; the more basic slags are higher in iron oxide for a given carbon content; certain amounts of iron oxide and lime are required for phos-phorus removal and a high lime-silica ratio is needed if the sulphur content of the metal is to be diminished. In recent years a number of quantita-tive relationships involving these and other variables have been developed through plant and laboratory studies by numerous investigators in this country and abroad. The direct comparison of laboratory and open-hearth data involves the question of the degree to which each approaches the conditions of chemical equilibrium, a question which, from the open-hearth standpoint, we are scarcely yet in position to answer. And, although a considerable body of dependable equilibrium data has been obtained in the laboratory, this work has not yet been extended to cover the ranges of slag composi-tion encountered in basic open-hearth practice. In the present study we shall not attempt to draw comparisons between data from the two sources; nor do we attempt to draw conclusions as to the approach to chemical equilibrium in the open-hearth furnace. Many of the operating variables that are likely to be erratic or unrecorded during the earlier stages of the heat become more consistent and are more readily subject to observation and control during later stages. For example, undigested lime or ore gradually goes into solution, the rate of carbon drop levels off, and the temperature of the metal is brought under control. For these and other reasons a greater degree of self-consistency is likely to be found among data obtained during the

Jan 1, 1940

By I. Cornet

With the greatly expanding use of magnesium during the war, it appeared necessary to the War Metallurgy Committee that the notch sensitivity of magnesium alloy extrusions be further investigated and the influence of various factors upon notch sensitivity be noted. Accordingly, the National Defense Research Committee of the Office of Scientific Research and Development placed a research contract with the University of California, supervised by the War Metallurgy Committee. The work discussed herein was done under "Restricted" Project NRC-21, reported in Dec. 1943~; it has been released for publica-tion by the O.S.R.D. Scope of the Investigation The notch sensitivity of various magnesium alloy extrusions was determined under axial tension, and also under several conditions of nonaxial tension. Hardness, grain size and other metallographic features were observed; stress-strain data were obtained, and the chemical compositions of the alloys were determined, in order to correlate these quantities with thc notch sensitivity. Notch sensitivity under axial tensile load was determined for a few specimens which had been cold worked to various degrees by tensile prestraining. Magnesium alloy extrusions studied included Dowmetal 0, X, J, and A(. For comparison, extrusions of aluminum alloy 24s-T, cast bars of aluminum alloy 122-T2, and cast bars of magnesium alloy C were also tested. The specified chemical composition of these alloys is given in Table I. All bars tested were within specification limits of composition. Investigation of thc tensile notch sensitivity of various magnesium alloy extrusions, under conditions of axial and eccentric load, showed little or no correlation with stress-strain or other conventional data. Since the many uncontrolled variables present might mask significant relationships, one alloy was selected for intensive study. Magnesium 0 alloy extrusions were subjected to experimental heat treatments, and the ,Changing hardness, tensile strength, microstructure, and notch sensitivity observed. Experimental Techniques and Procedures Tensile Testing Bars used for axial loading were machined with % in.- and with 34-in. minimum diam1 and included specimens with 60" V notches (Fig I and 2). Each V-notched specimen was roughed out carefully and then finished with a honed tool. These Y-notched bars were sampled frequently, sectioned, polished, and examined at 500 X magnification to control

Jan 1, 1949

By E. C. Bain, E. S. Davenport

When annealed carbon, or low-alloy, steels are suitably heated the ferrite (alpha iron solid solution) and the carbide, of which they are composed, react together to form a single solid solution of carbon (and other elements) in gamma iron (austenite). This reaction may begin only at a certain minimum temperature called the eutectoid temperature. The first ferrite and carbide thus to react together do so in definite proportions known as the eutectoid composition. With further heating the original constituent that is present in excess is dissolved in the austenite until exhausted. Whether the excess constituent be ferrite (hypoeutectoid steels) or carbide (hypereutectoid steels) the procedure is much the same, and upon slow cooling the homogeneous austenite expels the excess of either (proeutectoid ferrite or carbide) until the eutectoid composition is reached. Thus the reaction upon heating is strictly reversed upon cooling and accordingly an equilibrium diagram of this process may be constructed. Such an equilibrium diagram concerns itself only with the temperatures involved and with the proportions and compositions of the phases developed under conditions that suffice to permit equilibrium. Specifically it has no concern for the type or mode of distribution of these constituents nor with any extra-equilibrium conditions such as undercooling, which is almost universally encountered in metals. Actually, however, of great importance is the sluggishness toward equilibration caused by the not inconsiderable time involved in diffusion. Thus instead of the theoretical transformation point AF, we find for a certain rate of heating or cooling the use of the designations Ar and Ac (transformation temperature found on cooling and upon heating). These figures obviously have no particular meaning except as measured and expressed for a definite heating or cooling rate, and represent the apparent temperature displacement caused by an inadequate time allowance. In this paper are presented the results of a study of the time required for the transformation of austenite to ferrite and carbide at a variety of temperatures and also of the time required for the reaction austenite? martensite at the temperatures at which this reaction occurs instead of

Jan 1, 1930

By I. Cornet

INTRODUCTION WITH the greatly expanding use of magnesium during the war, it appeared necessary to the War Metallurgy Committee that the notch sensitivity of magnesium alloy extrusions be further investigated and the influence of various factors upon notch sensitivity be noted. Accordingly, the National Defense Research Committee of the Office of Scientific Research and Development placed a research contract with the University of California, supervised by the War Metallurgy Committee. The work discussed herein was done under "Restricted" Project NRC-21, reported in Dec. 1943 1; it has been released for publication by the O.S.R.D. SCOPE OF THE INVESTIGATION The notch sensitivity of various magnesium alloy extrusions was determined under axial tension, and also under several conditions of nonaxial tension. Hardness, grain size and other metallographic features were observed; stress-strain data were obtained, and the chemical compositions of the alloys were determined, in order to correlate these quantities with the notch sensitivity. Notch sensitivity under axial tensile load was determined for a few specimens which had been cold worked to various degrees by tensile prestraining. Magnesium alloy extrusions studied included Dowmetal 0, X, J, and M. For comparison, extrusions of aluminum alloy 24S-T, cast bars of aluminum alloy I22-T2, and cast bars of magnesium alloy C were also tested, The specified chemical composition of these alloys is given in Table I. All bars tested were within specification limits of composition. Investigation of the tensile notch sensitivity of various magnesium alloy extrusions, under conditions of axial and eccentric load, showed little or no correlation with stress-strain or other conventional data. Since the many uncontrolled variables present might mask significant relationships, one alloy was selected for intensive study. Magnesium 0 alloy extrusions were subjected to experimental heat treatments, and the changing hardness, tensile strength, microstructure, and notch sensitivity observed. EXPERIMENTAL TECHNIQUES AND PROCEDURES Tensile Testing Bars used for axial loading were machined with 3/8 in.- and with 1/4-in. minimum diam, and included specimens with 6o° V notches (Fig I and 2). Each V-notched specimen was roughed out carefully and then finished with a honed tool. These V-notched bars were sampled frequently, sectioned, polished, and examined at 500 X magnification to control

Jan 1, 1948

By W. Randolph Van Lewis

In determilling the relative rate and in fi~lding the point where different inlpurities containecl in copper-matte are eliminated during the process of a converter-blow, the follo~ving results were obtainecl : A converter was selected which was starting on its sccolld charge. The first charge after lining had finished its copper " hot," and conseqaently no copper was adhering to the sides of the lining. All the copper and granulated slag from the previous charpc mcrc dumped, thus removing ally possibility of " salting " the matte to be tested. The coliverter worked fast and well during the entire test. Periods of ten minutes were selected. The converter mas brought from the stack to secure each sanlple of matte to be

Jan 1, 1904

By Henry M. Howe

Preparing the Metals.—Ordinary silver wire was hard-drawn to No. 23 Brown and Sharp gauge; it was cut in two, and one piece was carefully annealed in the ordinary way. The wire was prepared by Messrs. Guild and Delano, jewelers, Boston. The Ansonia Brass and Copper Co., Ansonia, Conn., kindly furnished me with some hard-drawn copper wire No. 31, A. W. G., and some of the same wire after annealing in the ordinary way.

Jan 1, 1885

COMMITTEES Committee on Arrangements DAVID H. BROWNE, Chairman LAWRENCE ADDICKS THOMAS T. READ P. E. BARBOUR BURR A. ROBINSON GEORGE D. BARRON F. T. RUBIDGE KARL EILERS E. MALTBY SHIPP LOUIS D. HUNTOON BRADLEY STOUGHTON H.A. MEGRAW EDWARD B. STURGIS ARTHUR L. WALKER

Jan 4, 1917

By Dorsey Hager

One of the most interesting fields in North America was discovered, early in 1922, near the towns of Sunburst and Kevin, Toole County, Mont. This field produces oil from the Jurassic beds, which heretofore have been of but little importance as oil producers, and promses to be the

Jan 1, 1923

By Dorsey Hager

One of the most interesting fields in North America was discovered, early in 1922, near the towns of Sunburst and Kevin, Toole County, Mont. This field produces oil from the Jurassic beds, which heretofore have been of but little importance as oil producers, and promses to be the

Jan 1, 1923

By R. A. Burton, J. T. Hansford, D. A. T. Donohue

Substantial evidence indicates that many petroleum producing horizons contain naturally occurring, ordered fracture systems and that within a particular geologic zone, vertical fractures induced in wellbores often will be directed along a particular compass direction. Both conditions will seriously alter the fluid displacement behavior within reservoirs. In this study the effect of induced fracture orientation and length on sweep efficiency is determined for a five-spot pattern. In general, it is assumed that all wells are fractured and directed along the same compass direction. Using the electrical analog to steady state, two-dimensional fluid flow in porous media, boundary conditions are obtained from which flood fronts are tracked numerically. The numerical computations require a particle tracking routine for approximating flood front histories. It is shown that recovery is sensitive to the length and orientation of fractures for the pattern studied. with the proper design of fracture-pattern systems, recovery can be enhanced considerably. INTRODUCTION Hydraulic fracturing introduced in 1949l gave the industry a rather inexpensive means of increasing the fluid injection or production capacity of wells. It has been used with particular success to increase the production rate of wells completed in tight formations, such as in western pennsylvania2 where producers have fractured in depleted or near-depleted fields and observed economic responses. Once the natural energy declines in such a reservoir where all wells have been fractured, waterflooding is generally suggested as means of further increasing recovery. Of the dual objective sought in waterflooding — high injectivity and high breakthrough sweep efficiency — the former condition can be obtained if all wells in the flood pattern are fractured; the latter condition should depend on the nature of the fracture system. Considerable theoretical work has been published on the nature of fractures induced in boreholes.3-5 Although discussion persists concerning the possibility of forming a horizontal fracture at a given point within the wellbore, it is generally conceded that only vertical fractures will develop below a given depth, i.e., where the fracturing Pressure is less than the overburden load. Given the fact that fractures will be vertical in most cases of interest, it is also important to know whether there is order to fracture orientations within a given geological region. Kehle has suggested that in tectonically relaxed areas of uncomplicated geology, the stresses are fairly uniform and all fractures in the region should be parallel.5 Dunlap arrived at a similar conclusion in a theoretical investigation of localized stress conditions surrounding the borehole.6 He concluded that most vertical fractures are propagated in a preferred azimuthal direction. Fraser and Pettitt, in extending these theoretical suggestions to a specific field case, used an impression packer to record both a vertical fracture and the orientation of this fracture in the wellbore of a well in the Howard Glasscock field, Tex.7 Use of this information enhanced the waterflood recovery of the field. Anderson and Stahl also used impression packers on three fractured wells in the Allegheny field. N. Y.. and found that the fractures were oriented more or less along the same compass direction.8 Orientation of the fractures in this manner depends on the stress condition within the formation during fracturing. Elkins and Skov have demonstrated that a natural, oriented, vertical fracture system exists within the Spraberry field? Heck suggests

Jan 1, 1969

By R. T. DeHoff

Saltykov's meihod for the determination of the size distribution of spherical particles from measurements made on random plane sections is extended to particle shapes which are not equiaxed. The analysis permits the deterrrzination of the size distribution of aggregates of ellipsoidol particles provided all particles have tlze same shape. V ARIOUS solutions to the problem of the determination of the size distribution of spherical particles from measurements made on random plane sections have appeared in the literature since the original solution was first published by Scheill in 1934. Solutions have been offered utilizing measurements of the diameter1y2 or area3'4 of circular sections that result when a test plane is passed through an aggregate of spherical particles, and the length of intercept5y6 that results when a test line is passed through the aggregate. To the best of the knowledge of the author, no method has been proposed which permits the determination of the size distribution of particles that are not equiaxed. The purpose of this paper is to develop a method which permits the determination of the size distribution for a specific class of particle shapes which cover awide range of axial ratios; namely, ellipsoids of revolution. In the interests of simplicity, it is necessary to limit consideration to aggregates of particles which are all similar in shape; that is, the ellipses which, by rotation about one of their axes, generate the particles, all have the same axial ratio. The size distribution, which is to be determined by the analysis, is arbitrary. It is also assumed that the section, or sections, upon which the measurements are made represent the average of all possible sections through the structure. This ideal condition can be approached as nearly as may be desired by observing a sufficient area of sections taken at random positions in a randomly oriented aggregate, and in random positions and orientations in an aggregate that has one or more axes of orientation. SIZE DISTRIBUTION FOR PROLATE ELLIPSOIDS Consider an aggregate of cigar shaped, geometrically similar particles (prolate ellipsoids), dispersed in an opaque matrix. Let the size of each particle be specified by the length of its minor axis, By Fig. 1, and the shape, q, be defined by the ratio of its minor to its major axis, B/A. Let the index, j, refer to dimensions of ellipsoids in a particular size class, and the index, i, to dimensions of an ellipse resulting from the intersection of a test plane and a particle. The size of such a section is specified by the length of its minor axis, b. Let the particles be arbitrarily divided into k size classes, and let the increment of size between each class be A, where A = &,$, B,,,being the minor axis of the ellipsoids in the largest size class. Since all sections are represented on the test plane, the minor axis of the largest of the sections observed, results from the intersection of the test plane with an ellipsoid in the largest size class at its center, and is therefore equal to Bmax Thus the increment, A = The final result will consist of the k numbers which represent the number of particles in each size class per unit volume of aggregate:

Jan 1, 1962