Search Documents

By M. G. Arthur

This paper is a theoretical analysis of fingering of water and coning of water and gas in homogeneous sand. Investigation of this idealized case illustrates the relative magnitude of the factors involved in actual conditions. The body of the report presents equations, example calculations, and charts that facilitate solution of such problems. Derivation of the equations introduced in this paper and a discussion of previously published equations are included in the appendix. Introduction Production of water from oil wells as a result of the pressure gradients established by flow of fluids through oil-~roducing sands is a common occurrence, which influences the cost of oil production, the degree of depletion and the efficiency of expulsion of oil from naturally occurring reservoirs. Control of water production and encroachment are important both in primary and secondary phases of of exploitation in order to produce oil and gas at lowest cost and in order to achieve the greatest ultimate recovery of the oil in the reservoir. Although many actual oil reservoirs present a multitude of variables that influence fingering and coning of water and gas, an inspection of the relationship and magnitude of the forces involved in the case of a homogeneous sand may indicate satisfactory methods of controlling water production. Application of equations relating the variables may indicate the geometric type of drainage that exists in a particular reservoir or in the vicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoir influenced by the well. Two geometric types of drainage are considered theoretically. The first is water fingering into an oil sand that is relatively thin compared with the lateral extent of the sand. This sand may represent the entire oil-producing reservoir or it may represent one interval in an oil reservoir, which is separated from other producing intervals by competent lithologic barriers to flow of fluids. For the condition of complete penetration of a well in such a sand body, it may be assumed that no flow occurs across bedding planes. A mathematical relation is developed between the limit of approach of a water finger to the well without being drawn into the well and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil well as the result of coning through bedding planes. The theory and graphical solution developed by Muskat' for the limit of approach of a water or gas cone to a well, without its entry into the well, related to the corresponding maximum pressure drawdown, is reviewed and amplified, Charts are presented, which facilitate graphical solution of the problem. A method is presented for the extension of this type of graphical solution to the case where gas and water coning occurs simultaneously~

Jan 1, 1944

By M. G. Arthur

This paper is a theoretical analysis of fingering of water and coning of water and gas in homogeneous sand. Investigation of this idealized case illustrates the relative magnitude of the factors involved in actual conditions. The body of the report presents equations, example calculations, and charts that facilitate solution of such problems. Derivation of the equations introduced in this paper and a discussion of previously published equations are included in the appendix. Introduction Production of water from oil wells as a result of the pressure gradients established by flow of fluids through oil-~roducing sands is a common occurrence, which influences the cost of oil production, the degree of depletion and the efficiency of expulsion of oil from naturally occurring reservoirs. Control of water production and encroachment are important both in primary and secondary phases of of exploitation in order to produce oil and gas at lowest cost and in order to achieve the greatest ultimate recovery of the oil in the reservoir. Although many actual oil reservoirs present a multitude of variables that influence fingering and coning of water and gas, an inspection of the relationship and magnitude of the forces involved in the case of a homogeneous sand may indicate satisfactory methods of controlling water production. Application of equations relating the variables may indicate the geometric type of drainage that exists in a particular reservoir or in the vicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoir influenced by the well. Two geometric types of drainage are considered theoretically. The first is water fingering into an oil sand that is relatively thin compared with the lateral extent of the sand. This sand may represent the entire oil-producing reservoir or it may represent one interval in an oil reservoir, which is separated from other producing intervals by competent lithologic barriers to flow of fluids. For the condition of complete penetration of a well in such a sand body, it may be assumed that no flow occurs across bedding planes. A mathematical relation is developed between the limit of approach of a water finger to the well without being drawn into the well and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil well as the result of coning through bedding planes. The theory and graphical solution developed by Muskat' for the limit of approach of a water or gas cone to a well, without its entry into the well, related to the corresponding maximum pressure drawdown, is reviewed and amplified, Charts are presented, which facilitate graphical solution of the problem. A method is presented for the extension of this type of graphical solution to the case where gas and water coning occurs simultaneously~

Jan 1, 1944

By Thomas W. Dawson

The H. C. Frick Coke Co. has used belt conveyers for handling coal for the last eighteen years but, until recently, only for small tonnages and over short distances. The first installations were outside the mines for distributing coal to various parts of plants. A belt conveyer was put in service at Colonial No. 4 Mine in November, 1906, to carry coal from the main hoisting shaft to a storage bin serving two blocks of beehive ovens on the other side of the valley; it was in constant service until the Colonial No. 4 ovens were abandoned less than a year ago. This conveyor was in an overhead gallery that spanned our sidings and yard tracks and the main line of the Pennsylvania Railroad. It was a crude installation, from the viewpoint of present conveyor engineering practice. It had no mechanical feeding device, the coal simply ran through a gate in the side of a bin on to the belt; but one belt on this conveyor lasted eleven years. This conveyor is about 300 ft. long center to center of pulleys. It operated at a speed of 250 ft. 'per min-and carried about 400 tons per day. On this basis, the belt life of eleven years means that not over a million and a quarter tons was carried by the belt. whi1e: this is not a large tonnage, the cost per ton was much less than by any previous method in use for supplying coal to ovens located at a distance from the main shaft. The next belt conveyor was installed at Bridgeport Mine in 1907. It carried about the same daily tonnage as the first, delivering from the hoisting shaft to a coke-oven bin. Very few data were kept on this conveyor. It also operated until the coke ovens at the plant were put out of blast and the coal taken to the Clairton byproduct plant by river. In 1916, work was started to equip the Bridgeport, Palmer, Gates, and Ronco mines to load their entire output on the river for transportation to the Clairton byproduct plant, which was then being built. These mines were all operating at that time and had a large area of coal available for river shipment. The Monongahela Railroad was located between the hoisting shaft and the river at each of these plants and, therefore, had to be crossed at each location to deliver coal to the river. After careful study, it was decided to transport this coal from the hoisting shaft to the river at each of these plants by belt conveyors.

Jan 1, 1925

The Institute is custodian of funds for support of numerous gold medals and prizes and has representatives on boards awarding still others. Details regarding the Institute Awards are given below. The Institute is represented on the boards of the John Fritz Medal, the Hoover Medal and the Washington Award, in connection with the three national societies of Civil, Mechanical and Electrical engineering; and, also, in the case of the Washington Award, with the Western Society of Engineers. The Institute is represented with these four societies on the committee in charge of the Alfred Noble Prize.

Jan 1, 1937

By Thomas D. West

The fact that iron expands when heated, until fusion takes place, and that molten iron is consequently less dense than solid iron of the same grade, is now universally admitted. It was proved by the extensive experiments of Mr. Thomas Wrightson, reported in the Jownal of the Iron and Steel Institute (1890, No. 1, p. 72, and 1891, No. 1, pp. 75, log), and, in a manner, is illustrated in heavy founding by the shrinkage 'of the molten metal, which must be " fed " in order to obtain solid castings. This decrease in volume requiring " feeding" while the metal is still liquid I call " shrinkage," applying the term " contraction" to the decrease in volume which takes place after solidification, while the iron is cooling to atmospheric temperature. The light-work founder, not having the opportunity to make heavy castings, in which shrinkage can be observed, is apt to confound the two; but they are in fact distinct, and are separated by an act of expanion, which takes place at the moment of solidification. The fact of this expansion was first practically demonstrated by Mr. John R. Whitney, of Philadelphia, Pa., whose experiments are recorded in the National Car and Locomotive Builder of May, 1889. Experiments recently made by the writer indicate that there is a constant relation between this expansion and the preceding shrinkage and forcibly demonstrate the necessity of " feeding " a casting to make its interior solid. This is a matter with which all makers and users of castings have experienced difficulty. The founder being heretofore unable to define correctly the principles involving the urgent necessity of " feeding " has failed to impress the moulder with its importance in making sound castings.

Jan 1, 1897

By A. G. Suydam

Ancient as is the art of producing copper, so ancient is one of its eternal problems: refractories. Looking backward, in the light of present knowledge, clouded though it be, one cannot avoid a sense of profound respect for the patience, acumen and courage of those who have wrought so successfully despite difficulties, a more accurate understanding of which seems merely to accentuate. The problem of refractories arises from the necessity for constructing containers in which to bring natural ores into thermal solution in order to effect reduction and separation of the valuable metal content and free it of undesirable contamination while producing a waste slag. The very forces known to produce thermal solution of sufficient liquidity are necessarily destructive of exposed refractory linings in proportions varying inversely with thermal conductivity, directly with the porosity and ease of fluxing of the refractories used, and directly with the temperatures employed. Beyond this, mechanical forces are set up within the refractory lining incident to rapid heating or cooling, shrinkage at high temperatures, and unequal or excessive loading, that frequently pass the elastic limit, causing spalling or distortion. The effects of these forces are often accentuated by the necessity of providing at the same time as hot a bath and as cool a container as are consistent with fuel economy. Evolution in the Use of Refractories Clay Brick.—Fireclay and clay refractories had to yield wherever they were in contact with slags rich in basic oxides, first because of the combining power of those oxides with free silica and secondly because of the tendency of alumina to form either aluminates or alumina-silicates of varying complexity. Of no less importance, the incipient fusion point was low as compared with good clay brick of today, while the brick lacked strength at high temperatures. Expansion was slight, therefore it was difficult to make and maintain tight walls, roof, or bottom. However, the spalling tendency was low because of some of these properties and clay brick have retained their place in roasting furnaces, boiler furnace linings, and in the upper walls of some of the reverberatory types such as some refining, anode and wire-bar furnaces. They have served often and most efficiently for hot patching.

Jan 1, 1934

By William F. Ward

One often reads of the rich placer gravels in many of the citnoe-trav-elqd rivers of South America. The apparent richness of these gold-bearing gravels impresses the traveler, and in fact he may see batea after batea showing enough colors to figure over a dollar per cubic yard. These workings are called "playas" from the Spanish word playa, meaning shore or beach. Many workings have been reported in tropical rivers, but to my knowledge no dredge has made a success in such deposits. Investigation generally shows that the area of richness is limited and especially that the depth of the rich concentration is hardly ever more than a few inches. The Cauca river in Colombia, South America, is noted for its many rich playas. This river rises near .Popayan in the southern part of Colombia, flows north through a narrow valley between parallel mountain ranges and empties into the Magdalena river near Maganque. , The airline distance between source and mouth of this river is only about 500 miles. The rainfall is large and the lower Cauca appears to be about the size of the Missouri river in the United States. From its mouth up to Valdivia, in the State of Antioqua, it is navigable. Above Valdivia is a narrow gorge, above which the river is again navigable for some distance. The part of the Cauca where the play a panning is most noticeable is from Valdivia down to where the Nechi river enters the Cauca, a distance along the river of about 100 miles. The current in this part is swift, so that the stern-wheel river steamers make the trip with some difficulty. In the course of my work in this section of Colombia I have had the opportunity to make a study of several of these play a workings and will give in detail the conditions observed. The Island"Playa" The richest of the island playas is about 40 miles below Valdivia and a little below the old town of Caceres. The shape of the river and the location of the deposit are shown in Fig. 1, which indicates the condition at low water. The river at this place is about 600 ft. wide and the island about 75 ft. wide by 300 ft. long. The island is made up of coarse pebbles, some of which are as big as a man's head. In times of high water this island is under several feet of water and in a swift current. When the river lowers the current is still fast enough to prevent sand or silt from covering the coarse pebbles.

Jan 1, 1915

By E. F. Loiseau

(Read at the Philadelphia Meeting, February, 1878.) UNTIL June, 1868, it had not been attempted, either in this country or abroad, to manufacture by mechanical means, from anthracite coal-dust, artificial fuel for domestic use. Several attempts had been made to utilize coal-waste by converting it into a fuel for manufacturing purposes, but none of the processes were original, and they were merely applications of the well-known European processes and machinery, slightly modified by American ingenuity and mechanical skill. With one exception all those attempts have been failures. The great difficulty in the application of European processes and machinery has always been the limited production, and the excessive cost of the manufactured product, as compared with the cost of mining and preparing the ordinary anthracite coal for the market. The only serious and intelligent attempt to manufacture, on a large scale, artificial fuel for manufacturing purposes, has been made by the Anthracite Fuel Company, whose works are erected at Fort Ewen, near Rondout, New York. This company, organized under the auspices of the Delaware and Hudson Canal Company, had to go through the usual course of difficulties, breakages, and disappointments, which seems to be the lot of every new industry. Thanks, however, to the energy and perseverance of Mr. L. L. Crounsse, a gentleman of means, from Washington, D. C., the enterprise succeeded, and it is to-day established on a permanent basis. In order to increase the production, and to reduce its cost, the Anthracite Fuel Company was compelled to change most of its plant, and to erect more powerful machinery, producing lumps of a larger size, almost twice the size of the lumps made previously by the same company. This increase in the size of the lumps has been resorted to in Europe as well as in this country, in order to increase

Jan 1, 1878

By E. F. Loiseau

Until June, 1868, it had not been attempted, either in this country or abroad, to manufacture by mechanical means, from anthracite coal-dust, artificial fuel for domestic use. Several attempts had been made to utilize coal-waste by converting it into a fuel for manufacturing purposes, but none of the processes were original, and they were merely applications of the well-known European processes and machinery, slightly modified by American ingenuity and mechanical skill. With one exception all those attempts have been failures. The great difficulty in the application of European processes and machinery has always been the limited production, and the excessive cost of the manufactured product, as compared with the cost of mining and preparing the ordinary anthracite coal for the market. The only serious and intelligent attempt to manufacture, on a large scale, artificial fuel for manufacturing purposes, has been made by the Anthracite Fuel Company, whose works are erected at Fort Ewen, near Rondout, New York. This company, organized under the auspices of the Delaware and Hudson Canal Company, had to go through the usual course of difficulties, breakages, and disappointments, which seems to be the lot of every new industry. Thanks, however, to the energy and perseverance of Mr. L. L. Crounsse, a gentleman of means, from Washington, D. C, the enterprise succeeded, and it is to-day established on a permanent basis. In order to increase the production, and to reduce its cost, the Anthracite Fuel Company was compelled to change most of its •plant, and to erect more powerful machinery, producing lumps of a larger size, almost twice the size of the lumps made previously by the same company. This increase in the size of the lumps has been resorted to in Europe as well as in this country, in order to increase

Jan 1, 1879

By D. M. Spratt, O. R. Bell

In Australia's remote northwest are located the operations of Cliffs Robe River, one of the world’s largest iron ore projects. initial project cost was $US300 million and required the construction of a deepwater port, two towns for 3000 people, a 105 MW power station, and 170 km of railroad, all in harsh, arid country over 1300 km from the nearest industrial center. The ore occurs as goethite cappings on scattered mesas and averages 57% iron. All aspects of the project are reviewed from pre-operational research, through project construction to current operation.

Jan 1, 1982

By A. N. Holden

A DISLOCATION mechanism has been described by Cottrell' by which metals can yield locally, I. form Liiders bands, giving rise to a characteristic stress-strain curve with a sharp yield point and appreciable strain at constant or decreasing stress. It is undoubtedly the best mechanism that has been suggested to date." In its present development, however, the dislocation mechanism provides a more satisfying explanation for the sharp yield point than for the extensive localized flow occurring at the lower yield stress. The primary objective in this paper is to extend the dislocation mechanism to account for localized cataclysmic flow by a dislocation collision process and to give experimental evidence to support such a process. Only the yielding of iron containing carbon -will be discussed, although other metal-solute systems are known to behave similarly. Cottrell Mechanism In brief, Cottrell explains the yield point in the following way: The dislocations in iron which must propagate to produce slip usually lie at the center of local concentrations of carbon atoms, since segregation about these dislocatlons relieves some of the local stress resulting from them. A dislocation surrounded by a "cloud" of carbon atoms is thus anchored, and a higher stress is required to set it in motion than to move a free dislocation. Considering all available dislocatlons to be anchored in this fashion, the iron exhibits a yield point when the first dialocations break free and move through the lattice causing slip. This first breaking away of a dislocation enables other dislocations to break loose by "interaction" and the process becomes a cataclysm producing local deformation or Luders bands. The yield point in the stress-strain diagram for iron is absent in freshly deformed material, but returns gradually with time; the phenomenon is one aspect of what is called strain aging. The rate at which the yield point returns following straining depends on the temperature of aging. According to Cottrell the rate of return of the yield point in strained iron is limited by the rate of diffusion of carbon at the aging temperature, the mechanism is onr: of reforming the solute atmospheres around carbon-free dislocations that had stopped moving coincident with the removal of stress. If the specimen is retested immediately after straining and unloading, carbon will not have had time to diffuse to, and re-anchor, dislocations and the yield point will not occur. The carbon diffusion limitation for the rate of strain aging apparently applies if the criterion for strain aging is either the change in hardness" or the change in electrical resistance" of the strained speci- men with aging time. The possibility exists, however, that the yield point actually returns to strained iron at some rate other than that deduced from hardness or electrical resistance data. Therefore, as a preliminary experiment, the rate of yield point return in a rimmed sheet steel strained 6 pct in tension was measured at 27°, 77°, and 100°C. A plot of yield-point elongation for each of these temperatures against aging time appears in Fig. 1. The aging process is described by curves which rise to a plateau value of elongation that seems independent of temperature, but at a rate that depends on temperature. Very long times lead to a further rise in the yield-point elongation above the plateau value. However, if the later increase in yield-point elongation is ignored and the log of the time to reach half the plateau value of elongation is plotted against 1/T, a straight line results for which an activation energy of about 25 kcal pel- mol may be assigned. Within the accuracy of this sort of experiment this is approximately the activation energy for the diffusion of carbon in iron (20 kcal per mol), and the carbon diffusion limitation suggested for the yield-point return on strain aging is valid. The Cottrell mechanism thus explains in a qualitative manner the occurrence of a yield point in iron and its return with strain aging. It fails, however, to explain some of the other experimental observations that have been made of the yielding behavior of iron. For example, it is known that the yield point in iron becomes less pronounced with increasing grain size. Annealed single crystals of iron have very small yield-point elongations .if indeed they have any,' compared to a polycrystalline steel. If the only requirement for a yield point is that the dislocations in the lattice of the annealed. material be anchored by carbon atoms, the difference in the behavior of single crystals and polycrystals is not explained. That a dislocation mechanism may be entirely consistent with little or no yield point in an annealed single crystal will become apparent later when dislocation interaction is discussed. Strain aging produces a definite yield point even in single crystals. This accentuation of the yield-point phenomenon in single crystals after strain

Jan 1, 1953

By Daniel Houdouin

Data is frequently collected in mineral processing plants in order to evaluate operating performance or to model process units. Metal concentrations, circulating loads, products flow rates, classifiers efficiencies, flotation units recoveries, grinding mill efficiencies are typical parameters calculated from plant data. The validity of these calculations depends strongly upon the reliability of the data used for that purpose. The objective of this paper is to illustrate that flowrates, efficiencies and rate parameters of mineral processes are more reliable when calculated from balanced data rather than from raw data. Using variance-covariance matrices of balanced data produced by automatic mass balance packages (including flow rates, concentrations, percentage of solids and size analyses), variances of separator efficiencies (flotation or classification) and of mill grinding rates are derived. The variances are compared with those of variables calculated from raw data. The advantage of using balance data is illustrated with real data from flotation, grinding and classification units.

Jan 1, 1984

By J. W. Snavely

WITH all the advantages of handling bulk materials by means of belt conveyor also go some problems, one of the most persistent being that of cleaning. When sticky materials are being carried; the build-up of material on the return idler rolls results in difficulty of belt training. Much attention has been given to the problem of cleaning conveyor belts, and a great variety of cleaning devices have been developed. Even the best involve troublesome maintenance, and none can completely remove the fine particles imbedded in the belt cover, which cause rapid wear of the return idler rolls, and at the same time, of the belt cover as well.

Jan 12, 1951

By C. R. Garr, A. R. Troiano

FLAKING or hair-line crack formation has been a major problem confronting the producer of large alloy steel forgings.' Today it is generally conceded that hydrogen in one or more forms in alloy steel sections is a requisite for flaking. Hence an obvious remedy is a thermal cycle that reduces the hydrogen content to some low level. In practice, this generally means holding the material at some subcritical temperature for a period of time depending on the size of the ingot or forging. Another method that will suffice in some cases is to cool large forgings slowly, i.e., bury in ashes. In practice, this hydrogen bake is sometimes accemplished inadvertently by a series

Jan 1, 1958

By C. P. Proctor, J. T. Crawford, John Griffen

TROUGH washers were among the earliest methods used for concentrating ores; they are referred to by Agricola about the middle of the sixteenth century as already being used while the hand- operated jigging sieve had only recently come into use. For cleaning coal the trough washer apparently was first used in France and Belgium about 184.1. The early trough washers were intermittent and the refuse at least was shoveled out by hand. The invention of a continuous jig washer, by a Frenchman, Berard, in 1848, acted as a stimulus to coal washings in jigs and retarded progress in trough washing in the nineteenth century. Chapman and Mott 1 describe a number of trough washers developed in England and on the Continent from 1850 to 1900, such as the Bell and Ramsay, Ramsay, Bell and Green, Wunderlich, Scaife, McLellan, Lodge, Elliott, Blackett, and Murton. The later of these removed the refuse mechanically, either intermittently or continuously, but in ways that interfered with stratification. THE RHEOLAVEUR A Belgian engineer, Antoine France, is responsible for the development of means to remove refuse materials continuously from a trough washer, while preserving stratification and preventing the loss of coal with the refuse. The methods and equipment devised, which have become known throughout the world as rheolaveur, were initiated at the St. Nicholas mine near Liége, Belgium, about 1912. This installation consisted of two units to wash 20 to 8-mill. (3/16 to 5/16-in.) and 8-mm. to 0 (5/16-in. to 0), each having only two superimposed inclined troughs. The first few "Rheo" boxes on the top trough removed refuse directly and the remaining Rheo boxes discharged impure refuse to the lower trough for rewashing. On the lower trough the first few boxes removed refuse and the following boxes removed a middling product used for boiler fuel or other purposes. The overflow of both troughs was joined to form the washed coal product.

Jan 1, 1950

By H. W. Graham

AS these annual occasions in honor of Henry Marion Howe continue through the years, there is progressively less likelihood that the lecturer will have had personal knowledge of Dr. Howe. The present speaker is one of those who unfortunately had no opportunity to come under the inspiring presence of this great metallurgist. A review of Howe's work shows it to cover a comprehensive range of interests and to evidence an impressive richness of detail. Not only was Howe at home in the laboratory, but he was familiar with the processes of iron and steel making and had a real understanding of them writings include much that is descriptive of processes with a wealth of material that is becoming of increasing historical value. He recorded his studies of the theoretical aspects of processes and published at least two process classifications, one in 1890 that was lengthy and somewhat theoretical, and a second in 1906 that was more of a practical listing. Wide as Howe's field of interest was, it is significant of the circumstances of his time that he gave little consideration to raw materials or to their effect on iron and steel making processes. In 1933, Waterhouse, Howe lecturer for that year, presented a descriptive summary of the major steelmaking processes, and in 1946 Joseph discussed the blast furnace process. Otherwise Howe lectures have not dealt with processes as major subjects. In today's lecture, with no effort to describe the mechanical arrangements of iron and steel making facilities, it is proposed to examine the essential technological elements of the processes, to explore the inter-relation of these elements, and particularly to seek recognition and understanding of those factors which determine why certain processes are or are not used. The discussion of this lecture will deal with the major well-known large tonnage processes, with only such attention to processes of minor tonnage and special character as may be warranted for explanation by contrast. Subject to the errors of generalization and the short- comings of condensation involved in presentation limited to a single hour, it is proposed to examine broadly but intensively those operations which convert raw materials into steel. It is an innovation for a Howe lecturer to discuss the raw materials of the iron and steel industry, but the changing circumstances of passing years intensify the influence of raw materials on processes and require the metallurgist to be alert for the process adjustments that may become advisable or mandatory. For a half century the metallurgical processing of iron and steel has followed a surprisingly straight path, but this does not necessarily mean that there are no curves in the road ahead. Ages ago primitive man came to know iron in its metallic form, not only by the

Jan 1, 1947

By Roderick K. Davey

Introduction in any business, it is essential that we select those alternatives which are not only technically feasible, but will be the most profitable to the business m terms of corporate objectives Some of the studies and activities requiring support of financial analysis to select the alternatives which most closely satisfy the management objectives and technical considerations are as follows 1 ) Cutoff grade determination. 2) Ore reserve estimation. 3) Production forecasts (long- and short-term) for an operating mine, development of a new mine, or expansion of an existing mine. 4) Evaluation of haulage alternatives. 5) Evaluation of equipment.

Jan 1, 1979

By Charles Larkey

NUMEROUS papers have been published on the use of graphic methods to determine the best curve to be used in estimating the production decline of oil wells but, as far as the writer has been able to ascertain, nothing has been published dealing directly with the subject as to how curves may be worked out mathematically, which will conform most closely to the production data under consideration in any given instance; hence the writer has endeavored to show by means of a few concrete examples just how such appli-cation can be made. Among valuation engineers, two types of curves are in current use for the representation of the decline in production of oil wells. One may be represented by the equation, y = krx, sometimes known as a percentage curve, for the reason that the production for any period is multiplied by a constant rate or percentage to obtain the production for the succeeding period. This curve appears as a straight line on semi-logarithmic cross-section paper. The other curve may be represented by the equation, y = kxn, and is shown as a straight line on logarithmic cross-section paper. In each of these equations, y represents the number of barrels produced over a given period of time, and x the successive periods of time. The other letters are constants to be determined for each well or group of wells considered in arriving at the most probable curve to represent the rate of production for a given property; from which the underground reserves may be estimated by extrapolation, or the extending of the curve beyond the last known period of production to show the most probable production values for the future.

Jan 7, 1923

By T. R. Cass, M. R. Achter

A technique for measuring the creep and rupture strength of nickel specimens bonded by sintered oxide layers has been developed for the investigation of the role of grain-boundary oxide in the oxidation strengthening of nickel during creep at 817 °C. Prom the inverse dependence of the rate of bonding on the thickness of the starting oxide, it is suggested that the rate of diffusion of Ni++ through NiO is the controlling process at the start of sintering. Cornparisons of the creep and rupture strength and of the microstructure of sintered couples with conventionul creep specimens suggest rupture in nickel is prevented by load-bearikzg, ikltergranular layers of oxide. A number of recent investigations have shown that at high temperature and low stress the creep-rupture strength of nickel and nickel-base alloys may be much greater in air than in an inert gas or vacuum.'-7 For example, at 817°C and 2500 psi, nickep failed in vacuum in 48 hr but not in air after 4000 hr, and a Ni-Cr-A1 alloy5 at 1038°C and 3000 psi failed in vacuum in 4 hr but not in air after 731 hr. Fig. 1 is a typical creep curve in air for materials experiencing this pronounced environmental strengthening. A common feature of these curves is the entry into a third stage of accelerating creep, concurrent with the for-

Jan 1, 1962

By C. A. Wert

THE solid solubility of cementite in a-iron has been investigated a number of times and there is now general agreement on the solubility of about 0.018 wt pct at the eutectoid temperature, 720°C. With decreasing temperature, the solubility falls off so rapidly and to such a low value that no data obtained by standard metallurgical methods are available below 500°C. Using a new technique, however, Dijkstral has obtained apparently accurate solubilities down to 400°C; which data agree well with previously measured solubilities in the 600" to 700°C temperature range.' The present paper has in part the purpose of extending his work to still lower temperatures. Earlier work of Low and Gensamer3 on iron has established that the presence of a relatively small amount of carbon can play a tremendous role in affecting the mechanical properties. In particular they found that the yield point remained high as they reduced the amount of carbon in the iron; the yield point dropped only after the carbon content had fallen to something less than 0.003 wt pct, the point where their carbon analysis failed. It seemed desirable to the present author to see if some means could not be found to extend this part of their work. This investigation has then the additional purpose to determine the range of carbon concentration in which the major change occurs. Solubility The method used in the present work to measure small percentages of carbon in a-iron utilizes internal friction. Since this method may not be fa-miliar to the reader, the following explanation will be given (a part of this procedure is from unpublished results of Dijkstra): It is known that the internal friction associated with the diffusion of

Jan 1, 1951