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By M. H. Harris

A solution has been obtained to the problem of calculating flow into a cased and perforated well. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. Computer experimentation indicated that the results are within 3 per cent of the exact solution. Computed results are presented as an apparent skin effect, on a series of dimensionless working curves. Productivity ratios can be rapidly calculated from these data for the wide range of wellbore and reservoir properties actually encountered in field practice. Any reasonable vertical unisotropy ratio can be included in the computation. Productivities can be calculated for wells perforated in a regular pattern, a single horizontal plane or a vertical line on one side of the casing. Solutions for asymmetrical perforation patterns can he easily obtained from the working curves. Solutions for flow into sells completed with a horizontal notch are also provided. Results show that productivity can be increased by extending perforation penetration. This is especially true for shallow penetrations. The highest productivity is obtained when perforations are arranged in horizontal planes, as opposed to a vertical line on one side of the casing. Four or five perforations in one plane will approach the maximum productivity. The effect of perforation hole diameter is small, and is rioticeable only in shallow penetrations. INTRODUCTION The perforating method of well completion has been successfully and widely used in most producing areas. In the past, the desired perforation results were achieved by simply shooting numerous large holes in the casing. A perforating scheme for an area, or particular well, was established by evaluating two types of experimental data: the well flow index and the productivity ratio.' 3 The well flow index test is a means of determining the relative flow capacity of perforations in a linear system. This test also gives information on the perforation size, shape and hole damage which can be expected under well-bore conditions. However, relative flow data from this test cannot be accurately tarnsformed into the radial wellbore system. Thus, no true indication of the productive capacity of a perforated well can be obtained from the well flow index test. A well productivity ratio is derived from electrolytic models built to simulate perforated wells. Available productivity ratio data 2,3 are limited in that all important variables are not extensively evaluated. For example, data are limited to well radii of 3 and 6 in., and to maximum perforation penetration of 1 ft. Practically no information is available on the pattern of flow into a perforation. The effect of various perforation patterns on well productivity has not yet been determined and the effect of perforation diameter has not been thoroughly studied. Also, it will be shown that this type of electrolytic model data is probably in error by as much as 10 per cent or more. Modern completion techniques such as limited-entry perforating, single-plane fracturing, steam and hot air injection and chemical consolidation of incompetent formations all rely on injection and/or production from a limited type of completion. These completions may consist of several high-capacity perforations or a horizontal notch which is equivalent to an infinite number of perforations in one plane. Proper design of these new completion techniques requires, in part, accurate estimates of a well's productive capacity. Data on perforated and notched well productivity have been determined in this investigation. Results are presented as a function of the pertinent variables. Equations describing the idealized system were solved by numerical analysis techniques on a high-speed digital computer. DESCRIPTION OF PROBLEM PRACTICAL APPLICATION The computed results can be applied to wells which meet several general specifications. An external drainage radius of the well must be known or assumed, but the well need not be drilled on a regular pattern. The well must be cased and cemented through the entire producing interval. And, the casing must be perforated with one or more horizontal planes of perforations. The perforation pattern itself must conform to three geometrical requirements. 1. The perforations in a plane must divide the plane into equal angular segments (Fig. 1). Four perforations per plane would be 90" apart. 2. Perforations in a plane must be directly above or beneath perforations in adjacent planes. For two shots per plane, perforations would lie in the BB' plane (Fig. 1). 3. Horizontal planes must have equal vertical spacing and be separated from the top and bottom of the formation by one half the spacing interval. Single planes of perforations should be in the middle of the formation. This is shown in Fig. 2 where h is the formation thickness in a single plane conlpletion or the spacnig interval in a multiple plane completion. The spacing interval at the top and bottom of the formation may vary somewhat without causing an appreciable error in the productivity calculation if the formation is reasonably thick and there are many horizontal planes of perforations. A special provision has been made to calculate the productivity ratios of wells with uneven spacing intervals, or for the case where a single plane of perfora-

Jan 1, 1967

By David B. Reger

New discoveries of gas in the southern counties featured the petroleum industry in West Virginia during 194;. Drilling for oil increased slightly over 1944 and a small increase of initial production resulted. Out of 28 wildcats drilled, there were 16 gas discoveries and 12 dry holes. No commercial oil was found in the 28 wells.

Jan 1, 1946

By R. J. Cowan

IN the art of cementation a controversy has been going on for years as to whether solid or gaseous carbon is the active agent in carburizing steel. More recently opinion has crystallized into a compromise to the effect that carburizing is a gaseous cementation of steel in the presence of solid carbon. The importance of this theory has a particular bearing upon the work to be described. In the art of carburizing, use is commonly made of such words as "catalytic," "atomic," "nascent" and "activated;" in an attempt to describe the process. These words are used indiscriminately. For, instance, the gas is said to be "catalytic" and carbon to be "nascent," or vice versa. In using these expressions, investigators are confirming the acceptance in their minds of the active conditions of both gas and carbon in the cementation process.

Jan 1, 1931

By C. M. Wayman, M. Miyagi

COMPARED to many of the binary alloys of iron, Fe-Ir alloys have received very little tud.'' Virtually nothing is known about the Fe-Ir equilibrium diagram' except for a few details concerning the liquidus-solidus positions for dilute iron-based alloys. It is reported1 that the y to a transformation temperature in Fe-Ir alloys (up to 40 wt pct Ir) is composition-dependent, varying from -900°C for pure iron to 0" to 100°C for Fe-40 pct Ir in an almost linear manner. The y to a transformation appears to be reversible,' the transformation hysteresis width increasing with increasing iridium content. In a qualitative way, the composition dependence of the y to a (and vice versa) transformations appears similar to those in the widely studied Fe-Ni system. In that the y phase (in Fe-40 pct Ir) can transform at -1000C, it

Jan 1, 1967

By Irwin Roman

THE literature of geophysics as applied to the discovery of mineral deposits has been very extensive during the past few years,1 but there seem to be few references to the use of the method of least squares for obtaining better interpretations of the observed data .2 There seems to be a general reluctance among geologists and engineers to acquire the technique of least squares, in spite of the fact that a thorough knowledge of the theory is not necessary for the use of the method.

Jan 1, 1932

By James Douglas

This sketch of the history, geography and topography of the American transcontinental railways is based upon a paper read many years ago by the author before the American Geographical Society, and now re-cast, with numerous modifications and additions required to bring it up to date. It was intended primarily for the information of members and guests of the Institute from the East attending the California meeting; and, with that purpose in view, the Secretary of the Institute compiled;

Jan 1, 1900

By R. S. Bradley, B. K. Miller

The principal producing areas of fire clay in Missouri are: (I) the east central district, which includes Audrain, Callaway, Montgomery, Warren, and Boone Counties (Fig. I); (2) the St. Louis district, which includes St. Louis and St. Louis County; (3) the north central Ozark district, which includes Franklin, Gasconade, Osage, Maries, Phelps, and Crawford Counties. Most of the semiplastic‡ fire clay is found in Audrain, Callaway, Montgomery and St. Louis Counties, and in St. Louis. Flint fire clay is found in Callaway, Audrain, and Montgomery Counties and in most of the north centra! Ozark district. High-alumina diaspore clay is found only in the north central Ozark district, except a few deposits found in Montgomery County. This paper is concerned with the semi-plastic fire clay that occurs in the east central Missouri district near Mexico, Audrain County, Missouri, which is mined by the open-pit method as practiced by the A. P. Green Fire Brick Co. About one-fourth of the semiplastic fire clay in that district is mined in shaft mines, and three-fourths in open pits.

Jan 1, 1942

Jan 1, 1951

Jan 1, 1951

By Nicholas J. Grant, Raymond E. Cairns

A high-purity chromium, made by solid-state extrusion, and a series of molten, extruded, dilute alloys containing carbon, oxygen, nitrogen, and sulfur were studied to establish the effects of composition, cooling rate, grain size, strain rate, and prior strain on the transition temperature for brittle THE transition from ductile to brittle fracture with decreasing temperature remains of extreme interest especially among the refractory metals, such as tungsten, molybdenum, and chromium, which have relatively high transition temperatures. Fracture, yield stress, and hardness. Tension tests at a strain rate of 0.015 per min were generally utilized. Results are interpreted in terms of the quantity of each element retained in solid solution. Of these elements, chromium has been studied the least, but deserves additional attention because of its superior oxidation resistance for high-temperature use. In the past, impurity elements which have received attention are carbon, nitrogen, oxygen, and sulfur;'-' of these, nitrogen has usually been considered to be the most detrimental. Unfortunately, because of different levels of both specific and total impurity content, and because of the many different test and evaluation techniques used, a clear, definitive picture of brittle fracture in chromium has not been forthcoming. However, many

Jan 1, 1964

By B. K. Miller, R. S. Bradley

The principal producing areas of fire clay in Missouri are: (I) the east central district, which includes Audrain, Callaway, Montgomery, Warren, and Boone Counties (Fig. I); (2) the St. Louis district, which includes St. Louis and St. Louis County; (3) the north central Ozark district, which includes Franklin, Gasconade, Osage, Maries, Phelps, and Crawford Counties. Most of the semiplastic‡ fire clay is found in Audrain, Callaway, Montgomery and St. Louis Counties, and in St. Louis. Flint fire clay is found in Callaway, Audrain, and Montgomery Counties and in most of the north centra! Ozark district. High-alumina diaspore clay is found only in the north central Ozark district, except a few deposits found in Montgomery County. This paper is concerned with the semi-plastic fire clay that occurs in the east central Missouri district near Mexico, Audrain County, Missouri, which is mined by the open-pit method as practiced by the A. P. Green Fire Brick Co. About one-fourth of the semiplastic fire clay in that district is mined in shaft mines, and three-fourths in open pits.

Jan 1, 1942

By H. Le Chatelier

Jan 1, 1894

By M. E. Wadsworth, R. L. Pearson

THE dissolution of UO, in carbonate solutions can occur only il the tetravalent uranium is oxidized to the hexavalent state. The carbonate system is of particular interest because it provides a means whereby the oxidized uranium may be dissolved by forming the complex ion UO,(CO3)3-1. In the presence of oxygen the over-all reaction may be written UO+1/2O,4CO3T+2HCO2UO,(CO4)11+H2O [1] UO, was used in this study because it could be obtained in high purity and also because it is representative of the most refractory of the primary uranium minerals. The mineral ulrichite is the natural counterpart of the synthetic UO, used. The kinetics of the leaching of UO, should be similar for any of the uraninite type minerals. A pressurized system was used not with the hope it could be extended to commercial systems as a primary purpose but simply to provide the means whereby important temperature and pressure parameters could be varied for the evaluation of the kinetic processes. The importance of such pres-

Jan 1, 1959

By H. B. Pulsifer

ABOUT 15 varieties, or modifications, of the best magnesium available were prepared and subjected to etching tests, then examined for microstructure. Of the 30-odd etching reagents that were tried, nearly half, mostly ammonium salts, etched the metal satisfactorily. The surfacing and etching of magnesium is shown to be a very simple and quick operation. The density and hardness of magnesium were determined. The most interesting new observations relate to the finding of the hexagonal etch figures, the crystal laminations, and the fact that the metal is plastic, cold, when restrained or quickly deformed. Under slowly applied pressure cold metal deforms slightly, then shears to fracture without plastic flow: The chief structural features of magnesium are presented in two reduced photographs and 30 photomicrographs.

Jan 1, 1927

By John Wulff, David A. Stevenson

The rates of solution of copper, nickel, and three copper-nickel alloys in liquid lead were studied at 527° and 727°C under dynamic conditions. The relative velocity at the solid-liquid interface was varied from 8.65 to 125 cm per sec. Analysis of the data for the pure metals indicates that the solution rate is transport corztrolled at lower velocities, but a transition to mixed control occurs at higher velocities, higher temperatures, and higher percent saturation. 1 HE present work concerns the effect of relative velocity at a solid-liquid interface on the dissolution kinetics of pure solid materials in liquid metals. This general problem is of interest in electrode kinetics, in electrolytic processes, and more recently in the field of liquid metal corrosion. Considerable work has been done on dissolution kinetics in aqueous environments because of the obvious importance to electrolytic processes.1,2 In purely metallic systems investigation has been more limited. There are, of course, extensive data from loop tests which are used in an engineering evaluation of liq- uid metal corrosion. Here, however, the dissolution process is complicated by several interdependent processes. In general, one of two factors is considered to be rate limiting in the dissolution process: the transport of material from the solid-liquid interface into the bulk liquid, or an activation process directly at the interface. A number of studies of the dissolution rates of solid metals in liquid metals under static conditions have been published.3- Since the attendant hydrodynamic conditions imposed by thermal gradient convection and concentration gradient convection are difficult to analyze, it is doubtful if a clear interpretation of the experimental findings of these papers in terms of the mechanism involved in the dissolution process can be made. A clearer picture of the dissolution process is provided by

Jan 1, 1962

By J. L. Rodda

THE desirability of a uniformly sized abrasive for metallographic polishing has probably been recognized in a general way for a long time. Certainly all metallographers have recognized the damage that can be done to a polished surface by a piece of grit, especially if one of the softer metals, such as zinc or aluminum, is being polished. It is to be doubted, however, whether many metallographers have had any adequate idea of the particle size of the abrasives they were using or of the range of sizes encountered in any given grade of abrasive. At any rate, the descriptions of abrasives for metallographic work found in the literature are generally very meager. It was with the idea of securing an abrasive with a limited range of particle size that a study of this problem was commenced. Commercial abrasives, even when recommended for metallographic work, are made up of particles of varying sizes. One such abrasive contains some particles so fine that they remain in suspension for days and other particles so coarse that they settle at the rate of 3 in. per minute. It is evident that the coarsest particles are over 100 times the diameter of the smallest ones, or over 1,000,000 times the volume. The hopelessness of avoiding scratches under these conditions is evident. Vanderwilt1 has described a laboratory method for grading abrasives in which the elutriator is used. Le Chatelier's method, described by Goerens,2 also makes use of an elutriator. However, the elutriator is too slow for this purpose and requires too delicate a control for the range of sizes desired. The method of stirring up the abrasive in water, allowing it to settle for as given time, then drawing a measured depth off the top of the suspension, has been finally adopted as the simplest proce-dure. The largest particle in a given portion is. then determined by Stokes' law:3

Jan 1, 1931

By A. W. Fahrenwald

PRACTICALLY all fine grinding is done in a ball mill or some modification of a ball mill. Millions of tons of material are ground each year. The cost varies from, say, a minimum of 10 c. to a maximum of 35 c. per ton. It is thus obvious that even small improvements, which may result in increased grinding efficiency, would be welcomed by mill operators. A review of literature shows that various phases of the subject have been studied independently by many investigators. Also, it is now a subject of investigation at various laboratories in the United States and in foreign countries. Notwithstanding this extensive investigation, ball milling still remains a subject of some speculation. This paper presents the results of an experimental study of some of the factors entering into ball mill grinding.

Jan 1, 1931

By L. L. Oriard

In order to predict the influence of blasting on slopes, one must first understand the action of explosives, the manner in which rock is broken or displaced, and how seismic waves are transmitted, and the nature of these seismic waves. In this paper, the author describes the action of high explosives on rock masses, beginning at the source of the explosion, extending through the zone of rupture to a distance where only elastic waves of low energy persist. The paper describes the relationships between explosives charge quantities and distances, including the character and intensity of the seismic waves in various types of terrain. In looking at the analysis of slopes subjected to seismic waves, it has been common practice to assume a simplified model in which the anticipated acceleration is applied horizontally to the slope as an equivalent static force, or a model in which there is a rigid base subjected to mechanical shaking. Such models do not accurately portray blasting activity taking place within or near the slope in question. In dealing with blasting effects, it is important to under- stand seismic wave types, wave lengths, attenuation and transmission paths, as well as vibration intensity. In most cases, those slopes that are the least stable under static loading will also be the least stable under dynamic loading, although there may be rare exceptions. Thus, the more that is known about a slope statically, the better will be the assessment of it dynamically.

Jan 1, 1983

By W. H. Emmons

Most mineral deposits change as they are followed downward on their dips. Some of these changes are due to primary arrangement; different ores were precipitated at different depths when the deposits were formed. Other changes are due to weathering or secondary enrichment. The chief changes resulting from weathering, in the main, are understood and standard changes are recognized. The processes are relatively simple. They take place at ordinary temperatures and pressures and can be duplicated in the laboratories. Moreover, there are thousands of deposits available for study, because the processes take place near the surface where the development of mines is begun. The changes due to primary arrangement of the deposits of the metals are not so well understood. Deposition has taken place at higher temperatures and our knowledge of the chemistry of the processes leaves much to he desired. Very few experimental data are available. The deposits, moreover, offer fewer examples because many mines are not developed to depths where the changes can be studied and a change to unprofitable material usually results in stopping work. Most students of ore deposits now accept, as confirmed, the hypothesis that nearly all lodes and related deposits were formed by solutions originating in intrusive igneous masses. Outward from these masses, the deposits at many places are grouped in zones and the arrangement noted from the intrusions outward are commonly the reverse of the changes noted from the surface downward in a single lode. A study of the changes in groups of deposits, from the parent intrusion outward, will throw light on the changes to be expected in a single lode downward. Recause the changes in series of deposits from the intrusive outward may all be observed near the surface, where more data are available, it is possible to increase the number of examples many fold and to apply the statisttical method of study with greater confidence of avoiding error. It is not everywhere possible to identify the parent igneous body to which a group of ore deposits are related. Several kinds of criteria are available; certain groups are superior to others. By applying the

Jan 1, 1924

By James Aston

THREE years ago the writer presented a paper on the trend of development in the wrought iron industry,1 wherein was described a process in the development of which he has been a factor, which at that time had passed through several years of progressive experimental development but which had not then been put upon a commercial scale of operation. The present paper deals with two years of observation and experience in the commercial operation of a plant by the A. A Byers Co. at Warren, Ohio. It will not enter into the controversial field of the relative merit of wrought iron and steel in various classes of service, nor will it elaborate upon the characteristic services or fields of utility to which wrought iron is particularly adapted. It is sufficient to state that the wrought iron industry is upon a substantial basis and that the material finds service in pipe, where its advantages are in superior corrosion, fatigue, welding and threading qualities; in bar iron for staybolts, engine bolts, and rivets, demanding maximum service against corrosion and fatigue; in plates for corrosion service; and in chains, because of welding and shock-resisting characteristics. In short, ability to withstand the stresses of shock and vibration, or the ravages of corrosion, to hold protective coatings, and to give maximum efficiency in welding, are its features of relative superiority. If these features were not well recognized, the wrought iron industry would have shrunk to insignificance in the face of high costs and acknowledged limitations in manufacture. To charge that this industry is built upon a structure of assumption, psychology, and improperly weighed evidence is an impeachment of the integrity or belittling of the powers of observation of users through many centuries of service experiences.

Jan 1, 1929