Search Documents

By N. Cabrera

IN a recent paper Kuczynski' studied the rate at which the crack between a metallic plane and a spherical particle of the same material is filled up gradually when heated at temperatures near the melting point. If x is the radius of contact between plane and sphere (fig. I), Kuczynski shows experimentally that x5 = At [1] where t is the time. Assuming that the mechanism of transport of matter is the volume diffusion of vacant lattice sites, he is also able to prove Eq 1 theoretically. The constant A contains as a factor the self-diffusion coefficient of the metal and he shows that the values for this coefficient deduced from his experiments yield the same activation energy as that calculated by other methods, which is a confirmation of this point of view. Kuczynski has also considered theoretically the law of growth of x which would be expected if surface diffusion were the important mechanism. He suggests that x should then obey a law of the form x7 = At, and claims to be able to decide the mechanism involved from the observed law of growth., The purpose of this note is to prove this incorrect. On the contrary, when the mechanism is surface diffusion Eq 1 is also obeyed, but with a different constant A. Following Kuczynski, we suppose the bottom of the crack (surface A A) to have an average radius of curvature p. As a result of this curvature the concentration of adsorbed atoms in this surface, n(p) per cm2, will be smaller, and the concentration of vacant lattice sites in the neighborhood, N(p) per cm3, will be larger than the corresponding concentrations, n(w) and N(w), for a flat surface. For all practical cases we can write Thomson's formula in the form n(co)— n(P) N(P)—N(cc) _ 2a-a" n(oo) JV(co) kTp [2] where u is the surface energy of the metal and a the interatomic distance. 1. Let us now consider the mechanism of surface diffusion. We suppose the concentration of ad-

Jan 1, 1951

EDUCATION for the mineral industry was at first a single comprehensive curriculum, but it was early recognized that the main basis of mining is physics, while that of metallurgy is chemistry. The first school to offer curricula leading to degrees in mineral industry education in the United States (1853) had separate ones in mining and metallurgy. The Columbia School of Mines (the fist really successful one) had only a single curriculum when it opened in 1864, but within a few years had so reorganized its work that it offered curricula in mining, metallurgy, geology, chemistry, and civil engineering. Interest in the metallurgy or geology curricula was slight at fist, and for the next 30 years the great majority of Columbia students took the mining curriculum, probably partly because it contained nearly as much geology as the geology curriculum, practically all the metallurgy, and most of the chemistry, and partly because of the degree awarded for it. Other schools kept their mining curricula equally broad, and as late as 1900-1910 men were graduating as mining engineers who were practically as well prepared to make geology or metallurgy their life work as they were for mining. Gradually, however, the subject matter of mining geology and metallurgy became so enriched through research and development that separate curricula in them became worth while; their progressive development is the subject of another chapter. Mining curricula also began to be somewhat diversified, and schools in areas where coal mining was of outstanding importance began to offer options in coal mining, the earlier curricula having been chiefly aimed at metal mining. The petroleum industry began its meteoric rise about the same time as mineral instruction in this country, but little more of applied science attended its birth than had attended such ancient practical arts as copper and iron

Jan 1, 1941

By J. Hunter

DuXing 1942, Louisiana attained the rank of fourth among the great oil-producing states of this country. Its present prominent position is the result of an orderly and systematic program of exploitation with emphasis on conservation. Even before the functioning of M-68, the Federal spacing order, development and production in Louisiana were regulated by various acts of legislation, the most recent of which and by far the most effective is Act 157 of 1940. Under the authority of this act, it has been possible for the Department of Conservation to hold many public hearings and thereby to secure data and evidence regarding the feasibility of issuing rules and regulations for development of various oil and gas fields in the state. As a result of information compiled at such public hearings, many orders have been issued by the Commissioner of Conservation that have in most cases provided reasonable solutions to the problems that arise in the exploitation and development of fields in this state. Probably one of the most effective powers granted the Commissioner of Conservation in the state of Louisiana has been the authority to provide for fieldwide unitiza-tion and pooling of condensate fields. This has led to the erection of huge cycling plants in Louisiana, which permit the most efficient recovery of the liquid content of the reservoirs, and further conserve most of the gas reserve that undoubtedly will be of considerable future value. Many months have passed since various orders of the Department of Conservation were put into effect, and all are accomplishing their purpose; namely, the elimination of waste. Although the effectiveness of these orders provides considerable satisfaction to the members of the Department of Conservation, it is also a tribute to the members of the oil and gas industry in Louisiana, who, in addition to providing carefully prepared technical data, have also given unstinting cooperation and have thereby enabled the Department to cope intelligently with the many problems. Production On Dec. 31, 1942, oil and/or gas was being produced in 50 parishes, or 78 per cent of all the parishes in the state. Thirty-three of the parishes produced oil and gas, 12 produced oil, and 5 produced solely gas. This is indeed an enviable record for any state. However, it is reasonable to assume that eventually all parishes in the state of Louisiana will be productive. From a geological viewpoint, there is no apparent reason to assume otherwise—a point that a11 operators seeking oil and gas production in this state may well bear in mind. Twenty new fields were found during 1942—a rate of discovery that does not compare favorably with the 30 new fields found during 1941. The record of discoveries in Louisiana during 1942 is further disappointing when it is realized that 8 of the 20 new fields discovered were gas fields. During this period of war emergency, there are, of course, many

Jan 1, 1943

By J. Hunter

DuXing 1942, Louisiana attained the rank of fourth among the great oil-producing states of this country. Its present prominent position is the result of an orderly and systematic program of exploitation with emphasis on conservation. Even before the functioning of M-68, the Federal spacing order, development and production in Louisiana were regulated by various acts of legislation, the most recent of which and by far the most effective is Act 157 of 1940. Under the authority of this act, it has been possible for the Department of Conservation to hold many public hearings and thereby to secure data and evidence regarding the feasibility of issuing rules and regulations for development of various oil and gas fields in the state. As a result of information compiled at such public hearings, many orders have been issued by the Commissioner of Conservation that have in most cases provided reasonable solutions to the problems that arise in the exploitation and development of fields in this state. Probably one of the most effective powers granted the Commissioner of Conservation in the state of Louisiana has been the authority to provide for fieldwide unitiza-tion and pooling of condensate fields. This has led to the erection of huge cycling plants in Louisiana, which permit the most efficient recovery of the liquid content of the reservoirs, and further conserve most of the gas reserve that undoubtedly will be of considerable future value. Many months have passed since various orders of the Department of Conservation were put into effect, and all are accomplishing their purpose; namely, the elimination of waste. Although the effectiveness of these orders provides considerable satisfaction to the members of the Department of Conservation, it is also a tribute to the members of the oil and gas industry in Louisiana, who, in addition to providing carefully prepared technical data, have also given unstinting cooperation and have thereby enabled the Department to cope intelligently with the many problems. Production On Dec. 31, 1942, oil and/or gas was being produced in 50 parishes, or 78 per cent of all the parishes in the state. Thirty-three of the parishes produced oil and gas, 12 produced oil, and 5 produced solely gas. This is indeed an enviable record for any state. However, it is reasonable to assume that eventually all parishes in the state of Louisiana will be productive. From a geological viewpoint, there is no apparent reason to assume otherwise—a point that a11 operators seeking oil and gas production in this state may well bear in mind. Twenty new fields were found during 1942—a rate of discovery that does not compare favorably with the 30 new fields found during 1941. The record of discoveries in Louisiana during 1942 is further disappointing when it is realized that 8 of the 20 new fields discovered were gas fields. During this period of war emergency, there are, of course, many

Jan 1, 1943

By J. A. Herrick

FOR a long time, especially in Europe, heavy pieces of forgings, such as cannon, armor plates, marine shafting, etc., have been steadily augmented in size, more particularly since steel has been substituted for wrought iron. To keep pace with these forgings several, very large hammers have been, from time to time, erected. The most powerful and thoroughly appointed of all now in operation is that designed and built by Messrs. Schneider & Co. at their works at Creusot, and it is the design of this communication to give to the members of the Institute a concise description of this remarkable piece of mechanism, which I have taken from an article published in the Annales Industrielles. This hammer is rated nominally at 80-tons power, but its capacity is, in reality, far greater, as will be seen by the comparative figures given later. The complete plant, comprising the hammer, the cranes, the furnaces, and the building which shelters the whole, is distin-

Jan 1, 1880

By Marcel R. Daly

The writer has devoted a number of years to practical operations and to the study of geology in the oil fields. In consequence, he has been brought to investigate the theories advanced to account for the accumulation of oil and gas in commercial deposits. It is the result of these investigations and his personal conclusions that he wishes to sum up in this paper. The writer is an advocate of the organic origin of petroleum found in pools. He has been led to believe that the present theories of oil and gas accumulations are incomplete and, in certain respects, incorrect, although they may embody certain elements of truth; that the forces that are called upon to explain the movement are only secondary forces in the process, and insufficient, by themselves, to cause this movement; and that the phenomenon of accumulation is of much larger order than heretofore admitted and bears an intimate relation with the general as well as with the local deformations of the crust and is a direct consequence and a mechanical effect of these deformations to which the term " diastrophie " has been applied. As a complement to this theory, the writer offers a new interpretation of the "rock pressure" and of the mechanism of the "sealing up" of this pressure in oil and gas pools. The Anticlinal Theory The theory most generally accepted to account for the accumulation of hydrocarbons in commercial deposits is the anticlinal or structural theory. This theory, the principles of which have been laid down by I. C. White, Orton, Winehell and others, and which has since been modified and perfected, is too well known to need a detailed statement. A clear interpretation of it may be found, in the paper of W. T. Griswold, in Bulletin No. 318 of the United States Geological Survey, and the reader is

Jan 1, 1917

By John Norton

FOR many years the copper-bearing steels have been of considerable interest to the metallurgist because of their corrosion-resistant properties. More recently the discovery of their definite age-hardening characteristics has focused attention on them again. In a recent paper, Smith and Palmer(1)? have given an admirable description of the behavior of a considerable number of steels of this type and a study of their results suggests two questions, of a more or less fundamental sort. In the first place, it has been plainly shown that the hardening effect of added copper does not increase up to the maximum solubility of copper in iron as given by earlier investigators, but reaches its greatest value considerably below this point. This fact suggests that either the solubil-ity is not, so great as previous investigators have stated, or that the age-hardening mechanism is not the simple precipitation phenomenon that has been postulated. In the second place, the nature of the aging mechanism in this partic-ular system should be determined. Recent developments in the study of age-hardening processes have shown that the increase of hardness is often, but not always, accompanied by precipitation and the action of a particular system is not predictable on the basis of its components or type of phase diagram. It would be of considerable interest to study the aging of the iron-rich iron-copper alloys in detail. One would like to know whether the aging mechanism is different at high and low aging tempera-tures, and whether the extreme sluggishness of the system may perhaps represent some new type of aging process.

Jan 1, 1934

By R. M. Hays

Prior to use of this model siphon finisher, the only means of evaluating metallurgical performance of the siphon finisher was by pilot plant studies. These are costly and require large quantities of material. A model siphon finisher and a test procedure which permits the evaluation of siphon finisher metallurgical performance has been developed. Metallurgical results between the model siphon finisher and pilot plant or commercial units show fairly good correlation. The upgrading of magnetic taconite concentrates by hydraulic concentration has been practiced for several years. In the 1940's, Braund1 used a multistage upflow classifier to upgrade magnetized magnetic concentrates. In present taconite plants, the SiphonSizer, marketed by Dorr-Oliver, Inc., has been particularly suitable for upgrading magnetic concentrates. When the hydraulic SiphonSizer is used to upgrade the concentrates in the finishing portion of the overall flowscheme, the unit will be called a siphon finisher to distinguish this application from classification. Prior to this work the only means of evaluating the metallurgical performance of the siphon finisher was by pilot plant studies which are costly and require large quantities of material. Therefore, it was desirable to develop a model siphon finisher and a test procedure which would simulate siphon finisher performance and require only small samples of material. This model would permit the evaluation of small samples such as drill core samples and be useful in evaluation of commercial siphon finisher design and performance. THE SIPHON FINISHER The siphon finisher, as shown in Fig. 1, is a tank equipped with a system of water jets which distribute the hydraulic water uniformly across the bottom of the vessel with an energy release for agitation in the teeter bed. The feed to the siphon finisher is intre duced through a feed well in the center of the unit. The silica and middling particles overflow a peripheral weir into the overflow launder. The magnetite fraction is discharged by a siphon or a modulated discharge valve. The siphon or the discharge valve is usually operated automatically by a float assembly which is responsive to the depth of the teeter bed. Various interface sensing devices have also been

Jan 1, 1968

By Blamey Stevens

The object of this paper is to show how igneous intrusion is governed by definite mechanical laws. A distinction is made between dikes and fissures, and the various characteristics of intrusions are explained on an exact scientific basis. The modification of rock-stresses by intrusion is then considered and extensive isostress regions are recognized. Finally, a complete classification of intrusions is constructed covering all possible cases. The generalizations of observed data, taken from Geikie's Text-Book of Geology, confornl to the laws of intrusion herein stated, and the deductions based upon these lams. No authority, however, is quoted for the type which I hare named a corrugated intrusion. Its existence is a necessary deduction from the laws of intrusion, and even the entire absence of examples in technical publications cannot disprove its reality. In all probability, corrugated fissures would have remained undiscovered, but for the nrorking of mineral veins. As intrusions of tabular form are seldom worked for commercial purposes, it has been left for theory to anticipate the discovery of corrugated dikes. In the light of these laws of intrusion and the corresponding laws of fissures,' there seems to be a remarkable uniformity of stress-distribution in rocks at moderate depths. This renders possible the mathematical calculation which should help us to approximate exact science in this and kindred branches of applied geology.

Jan 1, 1911

By W. C. Hagel

Previous inuestigators have repovted unusually low H* and Do values for self-dzf@szon in certazn bcc metals, e.g., chromium nnd y -uvanium. It has been postulated that this is nn experimental crl -tetion for the existpnce of a four -atom ring meclzanzsm, mid there could be. zmpovtant theoretrcal Implicatlons. By utilizing a precise sectioning technique with Cr51 as the tracer, self-dzffi-lsion measurements in large grains of 99.99-pct Cr were extended from 1200° fo 1600"C. A least- squares analysis of the data yields that D 0.280 exp (-73,20U/RT) cm2 sec-'. These AH* and Do unlues are not anomalous; there is little reason to believe that n vacancy mechanism is not opevatiue. Apparent differences at lower temperatures may result from preferential diffusion along short-circuititing paths and/or sample contamination. WITH continued technological effort, chromium and chromium-base alloys should ultimately become useful high-temperature structural materials. Accurate measurements of self-diffusion coefficients in the pure metal are necessary for a quantitative understanding of sintering, grain growth, creep, and other related rate processes. However, two conflicting determinations have been reported.* Using an Since careful diffusion studies normally yield Do values ranging from 0.1 to 10 cm2 sec-l, the Paxton-Gondolf results require independent experimental corroboration before an undue amount of speculation arises to explain the apparent anomaly. As discussed by Nowick6 and clearly shown by Hoffman and Turn-bull7 for self-diffusion in silver, a low AH* and Do can arise from preferential diffusion along grain boundaries or other short-circuiting paths. The most reliable data come from high-temperature measurements where volume effects predominate. Following a precise sectioning technique developed for determining silver diffusion in the intermetallic compound AgMg8 and cation diffusion in the corundum oxide Cr2O3,9 the purpose of this study was to measure true volume diffusion in high-purity, large-grain samples at higher temperatures than considered previously. Another point of interest is the frequent proposal10-12 that chromium undergoes an allotropic transformation between 1375" and 1800°C where the diffusion data might then show a discontinuity. I EXPERIMENTAL 1) Sample Preparation. The highest purity (99.997 pet) Cr currently available is produced by reduction of chromium tri-iodide. Three pounds of the resulting crystal bar were shipped in a sealed container with a complete chemical analysis from the vendor.* In conformity with the procedure used for

Jan 1, 1962

The Hanna Coal & Iron Corp, pilot plant at Randville, Mich , is handling about 250 tons of low grade Michigan core daily Ore is obtained from an ,open pit near the plant Operating alone In the area, the project was first announced about a year ago Construction began June, 1951 and actual testing started about the first of the year A paper presented by Plant Superintendent Elton P Geist at the Upper Peninsula AIME spring technical session, described the plant and outlined the present flow sheet A two-step beneficiation scheme is presently being used It utilizes both flotation and gravity methods After crushing and grinding to 28 mesh, the ore is passed over Humphrey spirals, making a coarse iron concentrate Tailings from the spiral concentrate are then reground and floated to produce iron concentrate and a final tailing Geist stressed that the present flow sheet is tentative and one of several possible variations Testwork is continuing at the plant and future work will determine the method of agglomeration to be used

Jan 1, 1952

SINCE you have asked me many times in particular how those mirrors are made that are commonly called spheres,* and even though I have told you at other times, I do not wish to omit writing of it here again in detail, so that you may have as complete information as I can give you, both in order to satisfy you fully and because it belongs among the subdivisions of the subject that I have proposed. Concerning this, I first tell you that it was an ancient discovery, and in those times as today was celebrated, and worthily so. For the effects these mirrors produce are miraculous things incomprehensible to me, and the more I think about it the more I am bedazzled with wonder, nor do I know how to explain by theory of perspective the causes demonstrated by their effects. Marvelous indeed is the beauty of their shining clearness, but much more so is the fact that (according to the shape that the craftsman has chosen to give them) they reflect back the shadow of the things

Jan 1, 1942

cation received from Brigadicr General Thos. G. Hanson said: "It is my painful duty to communicate to you the fact of the loss of your son, Martin F Bowles. About 11 o'clock on the night of September 3, Lieutenant Bowles, with Lieutenant Joseph B. Keckler, 355th Infantry, in command of a reconnoitering patrol of our troops, encountered the enemy. In the ensuing engagement your son received a rifle bullet through his heart. His death was instantaneous and painless. His remains were intcrred with full military honors on the 4th of September." He was promoted to First Lieutenant, but his commission did not reach him before his death. He was president of the Missouri Mining Association, Missouri School of Mines, for the year 1916-17.

Jan 1, 1920

By P. G. Beckett

THE problem of handling the large quantities of water encountered in the Old Dominion mine presents many features of interest. In the present paper are discussed the probable sources of water, the pumping equipment, the increased flow into the mine in the early part of 1915, culminating in the flooding of the 18th and 16th levels in March of that year, and the difficulties that were met with during the high-water period. I. PRELIMINARY The Old Dominion mine, situated 1 mile north of the town of Globe, Ariz., has long been one of the prominent copper producers of the State, and until the opening up of the copper schist deposits in the neighboring mines of Miami, was responsible for the greater part of the copper output from the Globe district. As the gradual exhaustion of its orebodies near the surface led to the downward development of the mine, more water was encountered in the western portions directly underlying the dacite formation until the drainage problem became a serious factor in the operation of the mine and in the economical extraction of the ore. A heavy inrush of water on the 10th level of the mine in 1906, preceded by still earlier water difficulties, rendered imperative the immediate installation of a pumping equipment capable of handling large flows of water. While the Old Dominion has been recognized as a wet mine since its early clays and one in which the complete control of the water situation was of paramount importance in the development of the lower levels, it is chiefly in the last nine years, since the installation of the increased pumping equipment, that the mine has developed and handled large quantities of water.

Jan 4, 1916

By Rudolph Emmel

The mines operated by the South American Development Co. are located in the Zaruma mining district of southwestern Ecuador. They are near the old mining town of Zaruma, which is the only important city in the canton of the same name. The district is situated in the upper end of a valley lying between two spurs of the Cordillera, one of which may be considered the Coast Range and the other an intermediate range. The mining camp proper, known as Portovelo, and the plant are 2.4 km. south of Zaruma, on the north bank of the Amarillo River, a tributary of the Tumbes River, which flows southwestward through Peru to the Pacific. Portovelo is difficult of access; it is reached from Guayaquil by means of river steamers and muleback. 'Embarking at Guayaquil, the route is down the Guayas River, across the Jambeli Canal, and up the Santa Rosa River to Santa Rosa, a distance of 177 km. From Santa Rosa, the road or trail follows the Santa Rosa River, then across the summit of the Coast Range into Portovelo, a distance of 74 km.—a two-day trip on muleback. The mining property of the South American Development Co. comprises 297 lode claims and 142 placer claims. The combined lode claims cover an area, roughly rectangular in shape, 9000 m. long from north to south by 4000 m. wide; the northern edge of the rectangle is about 3000 m. north of the central plaza of Zaruma. Mineral lands in Ecuador are held by virtue of an annual tax per claim paid to the central government, no surface rights being included. HiSTOry The Zaruma mine has been worked by white men since 1549, probably before that it was worked by Indians. The followers of Pizarro, led by traces of gold in the sands of the Tumbes River, followed that stream to its source, worked the gold veins that they found and established the city of Zaruma. Among the mines worked by them were th Sesmo, Leonora, Viscaya, and Mina Grande. Only the soft ores at the outcrop were

Jan 1, 1925

By C. E. Birchenall

DaVIES and Richardson1 have measured composition changes for Mn1-Owith variation in the equilibrium partial pressure of oxygen at 1500°, 1575°, and 1650°C, where 6 is the deviation from the simple stoichiometric ratio. No trend in this relationship with temperature was observed, so these remarks apply to the whole temperature range. The experimental values and their spread are shown by the bounded straight-line segments in the figure. Davies and Richardson assume that the stoichiometric oxide shows Frenkel disorder, given by the equation Mn2+Mn2+ + Mn" [1] where Mn2+ is a normal lattice ion which moves into an interstitial site (Mni2+) leaving a vacancy (Mn,"). The superscript dashes indicate that there is an excess charge on the anions surrounding the vacancy. Schottky disorder, in which a perfect crystal acquires equal numbers of cation and anion (Ov") vacancies according to leads to equations of exactly the same form in the analysis below. In view of the neutron diffraction results of Roth,2 which shows extensive Frenkel disorder in Fe1-o, Eq. [I] seems more appropriate. The deviations from stoichiometric composition, MnO, result from the addition of oxygen according to In effect Davies and Richardson ignore the variation of Mn3+in constructing equilibrium constants. This approximation might not appear to be very serious if the excess positive charges are really free posi- tive holes (P+) and if the intrinsic conductivity is high as a result of the reaction where e- is a conducting electron. However, the calculations of Buessem and Butler3 indicate that the partition functions of the free charges make a large contribution to the equilibrium constant, and this approximation would not be a desirable one. Furthermore, Morin4 shows that the positive holes are probably localized in MnO and therefore are described better by the mass action principle than by a degenerate gas model. Davies and Richardson's considerations require that activity corrections be applied beyond a 6 value of about 0.005. It is proposed to show here that the dissociation pressure curve can be calculated reasonably well over the whole composition range studied without activity corrections by choosing appropriate equilibrium constants for reactions 1 and 2. As stoichiometric composition The mass action constant, Ks, for reaction [I.] and the equilibrium constant, K,, for reaction [2] are given by where the concentrations which do not change significantly have been absorbed into the constants. The brackets denote concentrations. The deviation from stoichometric composition is given by gardless of [Mni2 ]. Substituting Eq. [7] in [6]

Jan 1, 1961

By T. R. Armstrong

Total crude oil production in Mexico in the year 1941 is estimated at approxi- mately 41,000,000 bbl.; a daily average of 112,700 bbl. and a decrease of about 5 per cent as compared with the daily average of 120,000 bbl. produced in the year 1940, and nearly 11 per cent decrease as com-

Jan 1, 1942

By T. R. Armstrong

Total crude oil production in Mexico in the year 1941 is estimated at approxi- mately 41,000,000 bbl.; a daily average of 112,700 bbl. and a decrease of about 5 per cent as compared with the daily average of 120,000 bbl. produced in the year 1940, and nearly 11 per cent decrease as com-

Jan 1, 1942

By H. A. Wahl

This paper presents methods of designing hydraulic fracture treatments in formations saturated with slightly compressible liquids. Howard and Fast describe the fluid-loss control resulting from the viscosity and compressibility effects of the reservoir fluid in terms of a fracturing fluid coefficient. However, for horizontal fractures, this coefficient is applicable to infinitely thick reservoirs. These methods of evaluating fluid loss from horizontal fractures during treatment differ from previous methods in that: (I) formation thickness is incorporated in the velocity function describing the rate of fluid loss to the formation; and (2) for a given thickness the relative position of the fracture to the horizontal boundaries of the reservoir or any interrnediate permeability barrier is incorporated in the design procedure. This theory is applied to several actual and hypothetical field cases. The results of these calculations demonstrate that the eflect of formation thickness on fluid loss from horizontal fractures may result in fractures several times larger than predicted by other methods. INTRODUCTION Hydraulic fracturing has been the dominating well-stimulation technique during the last decade. From the time it was commercially available, fracturing has had a very favorable success ratio compared to other stimulation methods. However, numerous wells that were successfully stimulated remained economic failures. Only in the last few years has the oil industry recognized the importance of designing treatments for each well which will yield the maximum profit. This implies that for a given set of treatment conditions the size and general physical characteristics of the fracture can be determined. One of the outstanding contributions in the field of fracture design was presented by Howard and Fast.' In their paper, three flow mechanisms that control fluid loss from the fracture to the formation are defined: (1) viscosity effects of the fracturing fluid, (2) viscosity and compressibility effects of the reservoir fluid, and (3) wall-building effects of a treated fracturing fluid. The rate of fluid loss to the formation adjacent to a fracture is shown to be a function of time. For each flow mechanism the velocity function v(t) is expressed as a constant or fracturing fluid coefficient divided by the square root of time. This form of v(t) can be used in the Carter equation, as developed in the Howard and Fasc paper, to estimate the areal extent of fractures. This equation may be written as In the following sections the effect of formation thickness on fluid loss from horizontal fractures is evaluated when the controlling flow mechanism is the viscosity and compressibility of the reservoir fluids. The major assumptions inherent in the Carter equation are brought out in subsequent mathematical developments. THE EFFECT OF RESERVOIR FLUIDS ON FRACTURE EXTENSION When a fracture treatment is performed using a fracturing fluid identical to the reservoir fluid, the only flow mechanism controlling fluid loss is the viscosity and compressibility effects of the reservoir fluids. In developing a fracturing fluid coefficient for this mechanism, Howard and Fast considered a segment of the formation bounded by a unit area on the fracture face and extending to infinity in the direction of leak-off as shown in Fig. 1(a). The direction of leak-off z is normal to the fracture face. The equation governing the linear isothermal flow of fluid into this segment is where a = Eq. 2 is a form of the diffusivity equation. It is derived from the equation of continuity, Darcy's law and Eq. 3

By Joseph A. Gill, Ernest A. Curth

The Government and Leeco concluded a cost-sharing agreement in 1976 to demonstrate longwall mining of a thin coalbed, 1 m or less, in a mine near Hyden, Ky. A premining investigation laid the groundwork for mine design and equipment specifications. Four- legged shields, a face conveyor, a stage loader and an in-web shearer were selected to operate on a 183 m face. Lengwall mining began in 1979 and initially was slowed by low mining height and equipment problems. A rock mechanics program provides early warning capability and criteria for future mine design. Monitoring of surface effects is included.

Jan 1, 1981