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By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By J. Quigley

As the outcrop mines in the West developed into underground operations, systems of ground support were gradually evolved. In the early coal mines there was little need for support except near the dirt line in portals, where stone masonry was common. Where the top was shaley or broken, native pine props with light cross bars and legs furnished enough support even in Utah's 25-ft coal seams. As depth of workings increased. roofs and backs of the same general nature as those near the surface became more and more unstable and required more and more support. Some coal airways show this tendency very clearly. From the surface down the same type of roof shows deterioration which an experienced eye can translate into a measure of depth under surface rather than change in rock characteristics. Rock bolts, developed by various companies and by the U. S. Bureau of Mines, have become an effective substitute for timber in sections of some metal and nonmetal mines formerly requiring escessive timber support, and further use of war surplus landing mats, chain link fencing, and a new punched channel developed by one of the steel companies has enabled other mines to operate deposits where costs of timber and lack of clearance for timber support would have prohibited mining. The block caving mines have made extensive use of reinforced concrete underground to achieve similar ends under difficult conditions. Steel sets are standard in many Bureau of Reclamation projects, although these are usually covered in with concrete to make the permanent structures the Bureau's reclamation projects require. But the use of steel in mining operations is limited and has been confined principally to the iron ore mines of Michigan, Wisconsin, and Minnesota. Some mines have installed used rail as posts, caps, and crossbars, but a rail section is not suited for load carrying, and used rails are generally brittle. having a tendency to fail without warning when overloaded. European mines were the first to reach the size of worked out areas and depths of cover resulting in major roof problems. The Europeans resorted to pack walls and masonry walls, in conjunction with timber arched sets. rail arches, and combination timber and rail and steel arches. The give in these pack walls and wooden blocking was supplemented by a hinge in the center of the arch. This design is called an articulated arch Through various refinements of this principle of the support giving graduallv with the load. Toussaint-Heintzmann developed the yielding or sliding arches, in which yield is accomplished by friction in the overlapping joints of the arch. This type has gained widespread acceptance in the Ruhr and Lorraine Basin and is being manufactured by Bethlehem Steel for sale in this country. In North America the anthracite mines in Pennsylvania, followed by certain iron ore mines in upper Michigan and Canada, were the first to employ these arches to any extent. The practice was later adopted by Kennecott at Ruth, Nev., and by others. Despite high initial cost, the use of these arches is growing in many parts of the country because of their suitability in heavy ground. In its present form of manufacture the yield-able arch consists of open U-shaped rolled section with heavy beads on the edge. The open edge of the U is placed toward the wall. The section nests in another section of the same dimensions, and an arch can be built up from rolled radii and tangents of various weights and lengths. Sections are fastened together by U bolts and saddles. The lap on the joint varies from 12 to 24 in., and ordinarily the bolts are tightened with a 1-in. drive air wrench. The arches are spaced with channel struts held by J bolts and saddles. Sections can also be obtained that are composed of various combinations of radii and tangents and true circles. The joints can be placed to bear against anticipated loads and asymmetrical loads imposed by dipping strata. In the arches now being manufactured clearance widths up to 19 ft are obtainable in weights of sections from 9 to 30 lb per ft. The circular cross sections are available in the same weights ranging from 8 to 16 ft diam. At present most of the arches sold are supplied only in carload lots. It is hoped that demand will grow so that distributors can stock various weights and sections to give small operators a chance to try this new type of rock support under their own particular conditions. Several excellent papers have discussed the properties of various sections now manufactured, the dimensions of the sets obtainable, and their application under widely differing conditions. The present article will describe the methods and results of a special use of the arches at Kaiser Steel mine No. 3. Sunnyside, Utah. Problem at Mine No. 3 : In 1953 Kaiser Steel Corp. laid out Sunnyside mine No. 3 to recover coking coal left by the previous operator, Utah Fuel Co.. below workings that had been abandoned in 1928. Two seams had been worked, the upper and lower, separated by 30 to 42 ft of rock. Approximately 10 million tons of coal had been extracted from this area some 3000 ft down the itch from the outcrop to a 1500-ft depth of cover. The mine had been opened by slopes in both upper and lower seams. Sometime in the late 1920's the lower slope

Jan 1, 1960

By D’Arcy A. Shock

In this year's review, the concept of solution mining has been expanded to include total solution as well as the technology of leaching, or partial solution methods. Leaching methods continue to make strides in the processing of metallic minerals, particularly in copper and uranium production. No quantitative data are available on the increase of leach operations; however, it is known that there were more systems installed in 1969 and that the estimated 15% of U.S. domestic production of copper produced in 1968 was by leach methods.1 While the number of publications appearing during the year were few,2,3 there were special sessions in this field at the AIME Annual Meeting and SME Fall Meeting in 1969 and more scheduled for these meetings in 1970. Significant areas that should be mentioned are: the continuing interest in bacteria to convert sulfide sulfur to acid thus reducing reagent costs in both copper and uranium sulfide ores, the exploration of leaching agents other than common mineral acids or alkaline solutions,4,5 kinetic studies of leach mechanisms and the development of microfractures for increased leach solution penetration by use of chemical or atomic explosives.6,7

Jan 1, 1970

By E. W. Johnson, M. L. Hill

The dijfusiuity D was determined at 25° to 780°C- from hyd?-ogen evolution rates. Anomalous evolution from air-melted iron was att~zbztted to residual hydrogen, which is interpreted as a hydrogen compound that decomposes at a strongly temperature-(Ieperzdent rate above 500°C. Above 200°C, D = 0.0014 cm2sec-1 exp (-3200 cal per g atom/RT). Below, 200°C the diffusivity is anomalously low and represented by D = 0.12 cm2sec-l exp (-7820 cal per g atom/RT). It is postulated that at low temperatures the hydrogen in the metal is "trapped" with an energy 4.8 kcaL per g atom below- that of the interstitial hydrogen. 1 HE purpose of the present experimental study was to determine the diffusivity of hydrogen in a-Fe over an extended temperature range. As certain anomalies were encountered, attempts were made to understand the anomalies themselves. This research was in progress both before and after a determination of the diffusivity of hydrogen in nicke1.l The latter system was found to exhibit none of the anomalies of hydrogen in iron, and its description was far simpler. The experiments on nickel also

Jan 1, 1961

By D. B. Crouch, D. A. Poulter

The engineering and metallurgical assessment of the McLaughlin Project ore body concluded that an open-pit mine and cyanide leach mill process would be feasible, producing both waste rock and residual mill tailings. As a part of the planning and permitting process, site selection studies were conducted for the tailings and waste rock disposal. The site selection process began with a regional identification of potential disposal sites and proceeded through 1) regional screening, 2) elimination of sites with obvious fatal flaws, 3) qualitative ranking of site evaluation criteria, 4) quantitative ranking of sites, 5) field investigation, 6) evaluations of field data, and 7) selection of preferred sites. Based on this approach of site rankings and field evaluations, tailings and waste rock disposal sites were selected and recommended for the preliminary design phase of the permitting and project development process. The site selection study provided the documentation necessary to justify the use of these sites for waste disposal and enabled Homestake Mining Co. to anticipate and integrate environmental concerns with agency requirements into the planning process.

Jan 1, 1986

By G. Beghi, G. Piatti

THE authors examined the problem of the gradual transformation of Al2O3 from the transition phases normally encountered in SAP (r -x-n)1-3 to the stable a phase. This phenomenon is well-known at temperatures above the melting point of aluminum,3"6 whereas in this paper the transformation was studied at temperatures lower than the melting point of the aluminum matrix.

Jan 1, 1967

By R. Neilson Clark

THE discovery of a thin pay streak, yielding carbonates of copper, native silver, and perhaps chloride of silver, was made on the 9th of April, 1874, within the trachytic belt which forms part of the Sierra Mojada. The discoverer named it the Humboldt Mine. On the 2d of May, 1874, another discovery was made, in a northwest direction from the Humboldt, at about five hundred feet distant, this was named the Pocahontas Mine. After some exploration these two discoveries were proven to be on the same vein. To the southeast of the Humboldt a claim had already been taken up, called the Virginia; and to the northwest of the Pocahontas, one called the Southeast Leviathan. On these last two this same vein has been found and worked. This paper will therefore treat of the Humboldt-Pocahontas vein, as worked on these four claims, to wit: beginning at the northwest, the Southeast Leviathan, the Pocahontas, the Humboldt, and the Virginia claims. Since the spring of 1874, there has been sunk on this vein a total of twenty-seven hundred and fourteen feet of

Jan 1, 1879

By J. J. Reed

The mines of southeast Missouri's Lead Belt have been in operation since 1864, almost 100 years. During this period about 10 pct of the total ore available has been left in place as pillars, and this now represents the best ore reserve left to the older mines. St. Joseph Lead Co. has been investigating various plans of pillar recovery for several years. The example to be described is only one possible approach under a specific set of conditions. Conditions vary greatly in the different areas within the Lead Belt, and the same approach would be entirely inadequate in certain other areas, but there are important sections where this system is clearly applicable. Horizon mining is practiced in the Lead Belt, and stopes may vary from 10 ft to well over 100 ft high. Fig. 1 is a plan view of 6100 stope, the area to be discussed. For these mines this is a small stope, only 10 to 12 ft high. Before any plans were drawn up for pillar recovery, three independent estimates of the pillar grades were made by the mine superintendent, the mine captain, and the mine geologist. After these results were averaged, pillars indicated to be of economic grade were marked for removal as shown. At this stage several alternatives were considered: 1) retreat with caving, 2) concrete replacement pillars, and 3) systematic bolting and retreat. A retreating system with caving was not chosen because the roof was known to be too bad even to permit loading a blasted pillar before caving would begin. Concrete replacement pillars would have been too costly and would have required a large crew, bulky materials, and unwieldy equipment. Systematic bolting was chosen as being most acceptable for the following reasons: 1) Limited area and spans were involved. 2) Only minor modifications to the jumbo would be required for bolting. 3) Only a two-man bolting crew would be needed. 4) Only compact bolting materials would be required. 5) The bolting plan could be modified to allow

Jan 1, 1960

By Lo-Ching Chang, K. M. Goldman

The kinetics and mechanism of transfer of a constituent across a slag-metal interface are fundamentally important because many metallurgical processes involve the existence of a slag phase and a metal phase. Industrial processes seldom proceed to equilibrium, and information of the rates and modes of reactions are therefore often of greater practical importance than equilibrium data. A study of the kinetics of sulphur transfer across a slag-metal interface under reducing conditions will contribute a great deal toward a better understanding of desulphurization in the blast furnace process. The general principles existing in the transfer of a constituent, such as sulphur, across a slag-metal interface can be extended to similar transfer phenomena in other metallurgical processes. The present paper will demonstrate how such studies will lead to fruitful results from both the practical and theoretical standpoints. EXPERIMENTAL METHOD The apparatus used was, simple. A graphite crucible 15/8-in. id, a wall 1/8-in. thick, and a depth of 4 in., was packed in an outer fused silica tube with powdered magnesia. The crucible assembly was rotated at a speed of 235 rpm inside an in- duction coil. A charge of 250 g of Armco ingot iron was introduced into the graphite crucible and melted by induction heating. The melt was held at a desired temperature for 3-5 "'in., aftcr which 7.5 g of granular ferrous sulphide was added and the bath was held for another 3-5 mi11. A metal sample was then taken by means of a fused silica tube and a rubber suction bulb. Immediately after the metal sample was taken, 30 g of a prefused and crushed slag were introduced. The slag reached the ternperature of the furnace in 1 to 1 1/2 min. Slag

Jan 1, 1949

By K. M. Goldman, Lo-Ching Chang

The kinetics and mechanism of transfer of a constituent across a slag-metal interface are fundamentally important because many metallurgical processes involve the existence of a slag phase and a metal phase. Industrial processes seldom proceed to equilibrium, and information of the rates and modes of reactions are therefore often of greater practical importance than equilibrium data. A study of the kinetics of sulphur transfer across a slag-metal interface under reducing conditions will contribute a great deal toward a better understanding of desulphurization in the blast furnace process. The general principles existing in the transfer of a constituent, such as sulphur, across a slag-metal interface can be extended to similar transfer phenomena in other metallurgical processes. The present paper will demonstrate how such studies will lead to fruitful results from both the practical and theoretical standpoints. EXPERIMENTAL METHOD The apparatus used was, simple. A graphite crucible 15/8-in. id, a wall 1/8-in. thick, and a depth of 4 in., was packed in an outer fused silica tube with powdered magnesia. The crucible assembly was rotated at a speed of 235 rpm inside an in- duction coil. A charge of 250 g of Armco ingot iron was introduced into the graphite crucible and melted by induction heating. The melt was held at a desired temperature for 3-5 "'in., aftcr which 7.5 g of granular ferrous sulphide was added and the bath was held for another 3-5 mi11. A metal sample was then taken by means of a fused silica tube and a rubber suction bulb. Immediately after the metal sample was taken, 30 g of a prefused and crushed slag were introduced. The slag reached the ternperature of the furnace in 1 to 1 1/2 min. Slag

Jan 1, 1949

By W. J. Rude

LARGEST of the known commercial deposits of pebble phosphate are those found in Polk County, Florida. The phosphate bed, commonly known as the matrix, will consistently average 6 to 9 ft. in depth, and is found under 3 to 60 ft. of over-burden. The phosphate pebbles, white and black in color, varying greatly in grade, are found imbedded in a matrix of sand and clay; and range in size from the fines to pebbles 1 1/2 in. in diameter, although the average coarse size is approximately 1/2 in. in diam¬eter. On some of the washers all material under 14 mesh is lost. High-grade phosphate (75 per cent plus of bone phosphate of lime, CasP2Oa) is generally soft, the pebbles breaking up during the mining operation and in pumping; low-grade phosphate, 67 to 69 B.P.L., is black in color with hard pebbles with no loss encountered in pumping.

Jan 1, 1941

Because common salt, sodium chloride, is necessary to all animal and much plant life, it is probably the most widely used of all mineral commodities, except for water. Nevertheless, of the total salt consumed, only 7% is used for food, including animal food. Two-thirds of the total is used as chemical raw material, principally for making such basic chemicals as chlorine, caustic soda, and soda ash. Other uses are for road thawing (16%) and water softening. Some 162.5 million tons of salt were used, worldwide, in 1972 (Table 15.4F.1). Production is from bedded salt deposits, salt domes, and evaporation of brines, including solar evaporation of seawater. Production is worldwide from at least 20 countries, of which the United States, China, USSR, the United Kingdom, and West Germany are the leaders. Consumption increases about 7 % annually. Reserves are plentiful: Other important sodium salts are soda ash (sodium carbonate) and salt cake (sodium sulfate). Soda ash comes mainly from the Solvay process (70% ) , which uses salt, limestone, and ammonia as raw materials. A large and growing portion of United States production is from mining large bedded deposits of trona, a natural hydrated sodium carbonate and bicarbonate found in Wyoming, and from brine evaporation in California. Soda ash is used for glassmaking, phenol, soap, detergents, and bleaches. Half of the United States salt cake used is a byproduct from rayon manufacturing. The other half comes from brines and playa lakes in California, Texas, and Wyoming. Salt cake is used mainly for papermaking. ACKNOWLEDGMENT Appreciation is expressed to William B. Dickson, president, Salt Institute. [ ]

Jan 1, 1976

By R. R. Wilson, Robert Henderson

The Cassidy Colliery operated by the Granby Consolidated Mining Smelting & Power Co., Ltd., is situated about 9 miles in a southerly direc tion from the city of Nanaimo on Vancouver Island. The coal seam worked, which is called the Douglas bed, outcrops in the western part of the property, dipping easterly, and is opened by a slope 7 by 14 ft. in the clear, and is timbered by 12 to 14-in. framed sets of timber, 4 ft. center to center. A separate manway provides for a traveling road and at the same time forms an intake airway. The general average of the dip of the seam at Cassidy is 18º, and varies in thickness from 1 to 25 ft., averaging about 8 ft. The main slopes follow straight down the dip a distance of 4845 ft. At the bottom of the main slope two rock tunnels were driven a distance of 1500 ft. to the south, cutting through a fault, and opening up an area in the same seam which is known as No. 7 South Section. The coal is found in this section at a vertical depth of 1560 ft., and is very soft and friable. The immediate roof is a strong, sandy. shale overlain by massive sandstone while the floor is a light-colored shale, hard when freshly exposed. It does not soften materially on exposure. In the folding of the coal measures a great thrust caused a movement along the coal seam as indicated by the slickensided nature of the coal. The floor has buckled and this has rolled and squeezed the coal so that with rare exceptions it shows no normal bedding but curved slip planes, which frequently start at right angles to the floor, curving upward and then in the direction of the dip. As such planes are slickensided it is probable that there is a coating of clay which is more or less impervious to gas. Outbursts of Gas and Coal Outbursts of gas and coal have occurred in this mine previous to 1921, but not until June 14 of that year was a complete record kept of them. No outbursts occurred above the fourth levels, or, in other words, until a vertical depth of about 900 ft. was reached. Since that time quite a

Jan 1, 1927

By M. P. Tixier, A. Poupon, M. E. Loy

Simple qualitative methods are explained for identifying those shaly sands in a well that are most likely to contain oil. A need for more precise measurement of the variables that enter shaly sand analysis is indicated. Field examples are given to illustrate the methods. A theoretical discussion of the quantitative interpretation of shaly sands is given as a basis for discussion and as a guide for the future. While not generally capable of practical application at the present time because of the lack of sufficient accuracy of the electric log data, these methods may become more feasible in the future as the result of the improved logging methods now being introduced. INTRODUCTION Experience has shown that for porous formations containing only a negligible amount of clayey material, reliable information on the fluid saturation and porosity of the reservoir rocks can usually be derived from the electrical logs. The interpretation is based on empirical formulae relating the true resistivity of a porous formation to its lithologic character, to the resistivity of the interstitial water, and to the proportions of water and hydrocarbons in the pores.' If the resistivity of the interstitial water is not known, its approximate value can be derived from the SP curve.2,3 The porosity can usually be determined to a good approximation from a MicroLog, or a MicroLaterolog.4,5 When the reservoir rocks contain an appreciable percentage of clayey material, an additional factor is introduced into the analysis. In a clean formation, the matrix is an electrical insulator, so that the ability of the formation to conduct current is due only to the conductivity of the electrolytes in the pores; in a shaly formation, the shale constitutes a part of the rock matrix able to conduct current, and influences the resistivity of the formation. On the other hand, the spontaneous emf's and the circulation of the SP currents are also responsive to the presence of the shaly material. All other factors being the same, the deflection of the SP curve opposite a shaly permeable formation is smaller than the deflection which would be observed if the formation were clean. The effects of the presence of shale on the resistivity and on the SP curves in a shaly formation are functions of the amount, of the specific resistivity, and of the geometrical distribution of the shaly material within the formation. The presence of shale therefore constitutes an important complication in electrical log interpretation. It is easy to realize, for example, that the presence of a large amount of clayey material in a sand may have such a predominant effect that the resistivity of the sand will not change very much, whether the pores are entirely filled with connate water, or contain a high saturation of hydrocarbons. Important research projects have been undertaken to investigate the influence of shales and to find a way to allow for this influence in the interpretation of a log. The problem of the SP in shaly sands was analyzed mathematically by H. G. Doll"' for the case of sands with shale laminations. Formulae expressing the resistivity of shaly formations were proposed by Patnode and Wyllie8 and de Witte.9 Other quite interesting theoretical and experimental results have been published by various authors.l0,ll,12,l3,14 The purpose of the present paper is to discuss an approach to electrical log interpretation in shaly sands. This approach is based partly on some of the theoretical and experimental data available in the literature and partly on observations made on actual field logs. Comparatively simple methods for qualitative and semi-quantitative analysis are described. These methods depend principally upon information provided by the electrical logs.

Jan 1, 1955

By John H. Hollomon

In a recent paper,' a very early suggestion by Ludwik2 concerning the nature of the mechanical behavior of metals has becn reexamined and extended. In essence it was suggested that there exists, at least under certain conditions, a mechanical equation of state; that the stress required for flow depends upon the instantaneous values of the strain, strain rate, and temperature, and not upon their past values. It is proposed that under these circumstances thc stress does not depend upon past history of these variables, but is like the temperature of a gas that depends only upon the instantaneous values of the pressure and volume. This notion has not been applied to present-day studies of metals, though it is especially applicable to the study of creep. It is the purpose of this paper to analyze the significance and possible range of applicability of this idea and to determine how it influences the accepted ideas concerning creep. Stress-strain Relations It is wcll known that the stress-strain curves of metals are influenced by both train rate and temperature. For a fixed strain rate and temperature there is associated with each metal a stress-strain curve. If either the strain rate or temperature is changed a new stress-strain curve will be characteristic (Fig. I). A much more genera1 relation between the effects of these variables is possible, however. Consider the stress-strain curves of Fig. I determined at

Jan 1, 1947

By John H. Hollomon

In a recent paper,' a very early suggestion by Ludwik2 concerning the nature of the mechanical behavior of metals has becn reexamined and extended. In essence it was suggested that there exists, at least under certain conditions, a mechanical equation of state; that the stress required for flow depends upon the instantaneous values of the strain, strain rate, and temperature, and not upon their past values. It is proposed that under these circumstances thc stress does not depend upon past history of these variables, but is like the temperature of a gas that depends only upon the instantaneous values of the pressure and volume. This notion has not been applied to present-day studies of metals, though it is especially applicable to the study of creep. It is the purpose of this paper to analyze the significance and possible range of applicability of this idea and to determine how it influences the accepted ideas concerning creep. Stress-strain Relations It is wcll known that the stress-strain curves of metals are influenced by both train rate and temperature. For a fixed strain rate and temperature there is associated with each metal a stress-strain curve. If either the strain rate or temperature is changed a new stress-strain curve will be characteristic (Fig. I). A much more genera1 relation between the effects of these variables is possible, however. Consider the stress-strain curves of Fig. I determined at

Jan 1, 1947

By John C. Calhoun, Frank T. Bethel

The application of a method for analyzing pressure build-up curves to determine the effective permeability in the Spraberry is presented. Sixteen upper Spraberry wells of the Driver area arc analyzed and show variations in the in-place effective permeability of 2 to 183 md. Since these value- are much larger than the .5 md. or less reported for the matrix rock. a large part of the vertical fractures noted in Spraberry cores- must be considered native to the formation. The effectiveness of the well fracture treatment in connecting the well bore to the native fracture system is analyzed by comparison of the effective permeability as determined from the PI test to that obtained from a pressure build-up curve. These results show that the fracture treatment is sufficiently effective in connecting tile well bore to the native fractrure system to yield a flow capacity within about 50 per cent of that dictated by the native fracture system About two-thirds of the wells show some degree of local blockage. INTRODUCTION Fractured reservoirs have been known in the past.' However, during the past two years the Spraberry formation has directed the attention of the petroleum industry to a study of the performance of a fractured reservoir. The large variation in the number of fractures noted in Spraberry cores rile large variation in the producing ability of offset well.. the dramatic effect of well treatment on well ,productivity. the unknown quantity of oil stored in the fractures and matrix rock. and the unknown oil to be recovered were part of the initial Spraberry puzzle. In this type reservoir where the well treatment is an important factor in determining the productivity. it i- particularly desirable to determine the in-place flow capacity of the drainage area at distance* far removed from the well bore. This value. when compared to the flow capacity obtained from a PI measurement, will show the effectiveness of the well treatment (completion. fracture treatment, acidization. etc. in establishing a flow capacity in the vicinity of the well bore equal to that in the more remote region. The object of this paper i.; to show the application of a method of pressure build-up analysis for this purpose in studying the Upper Spraberry formation in the Driver area. STATEMENT OF THEORY The theoretical basis for the application of a pressure buildup curve to show the effective permeability of the rock at distances far removed from the well bore has been presented in detail in earlier publications.', in the previous development it was shown that pressure build-up behavior of all wells could be reduced to the same dimensionless build-up curve of Fig. 1. This mean.; that the bottom hole pressure of a well after hut-in will rise in such a manner that a plot of pressure against the logaritllm of time yields a straight line. The slope of this linp can be rlzed to calculate the effective permeability as expressed by the following equation: where: effective oil permeability md oil production rate prior to shnt in. STB/I) In practice the flow which occurs into the well bore after shut in and the variation in flow capacity in the immediate vicinity of the well bore usually cause the early part of the build-up curve to be unsatisfactory in the determination of permeability. In general the effect of these factors on the straight line section will become negligible after a time when the of the following equation is equal to 0.1. and the preferred section Of the curve for use in defining the slope lie-

Jan 1, 1953

By A. E. Bellis

THERE is a wide difference of opinion among rifle experts in the matter of barrel steel, and the relative importance to the life of the barrel of the steel's composition, heat-treatment, structure, and physical properties. In order to promote discussion, which it is hoped may lead to the discovery of the source of 'some of the traditional beliefs on the subject, the results of some tests are presented here, with data on heat-treating, physical tests, and erosion. The detailed metallographic study of this steel is given in another paper.1 The conclusions from these tests should be capable of wider application than their direct bearing on the barrel-steel problem. The Government specifications for barrel steel for model 1903 rifle (Springfield) call for carbon 0.50 to 0.60 per cent., manganese 1.00 to 1.29 per cent., silicon under 0.25 per cent., sulfur under 0.06 per cent., phosphorus under 0.08. per cent. The minimum physical requirements are: Tensile strength,- 110,000 lb. per sq. in. (7733 kg. per sq. cm.); yield point, 75,000 lb. per sq. in (5472 kg. per sq. cm.); elongation, 20 per cent.; reduction of area, 45 per cent. Material fulfilling these requirement's gives practically no failures when proof-fired, with charge of 70,000 lb. per sq. in. pressure, which is 40 per cent. in excess of the service charge. The turning and drilling operations show up any seams or laps such as accidentally occur even in- the best heats of open-hearth steel, so that' faulty stock is practically all eliminated before proof-firing. These physical requirements are met either by rolling billets at, a proper temperature clown to the form of tapered barrel blanks or by heat-treating bars that have been upset to enlarge the breech section. The transformation temperature of this steel, on heating, is around 1350° F. (732° C.), varying somewhat with the composition and the rate of heating. The actual treatment of the barrel blanks, as carried out by different

Jan 7, 1919

By B. H. Bergstram, C. L. Sollenberger

When glass spheres are crushed by slow compression loading, the outer lune-shaped fragments resulting from the fracture consistently fly outward at high velocity. About 45 pct of the strain energy fed into the sphere-platen system reappears in the form of the kinetic energy possessed by these fragments. These measurements were obtained from high-speed photographs. This kinetic energy can be utilized for addtional comminution if the fragments are allowed to impact against a suitable structure. Comminution theory has advanced considerably in recent years by the study of this unit operation under laboratory conditions. Some of the parameters have been isolated, but the experimental measurements of the pertinent quantities, such as energy, particle size, etc., are still only made prior to and after the conclusion of a fracture sequence. The catastrophic fracture process itself has not been adequately studied from a comminution point of view. It has recently been suggested by Gilvarry that the fragments which result from the free crushing of a single glass sphere by slow compression contain a considerable amount of kinetic energy after fracture. This kinetic energy, if properly directed, possibly can be partially utilized to cause additional fracture. In this paper a hypothesis will be presented which suggests that this kinetic energy is necessarily present and that its dissipation is the process by which a large part of the thermal energy imparted to the crushed product is generated. Evidence supporting the existence of kinetic energy and its utilization for secondary fracture will also be presented. THEORETICAL A previous paper4 has shown that the load-deformation curve of a system composed of an elastic sphere gripped by a pair of parallel platens, can be predicted by a consideration of the theories of Hertz as summarized by Timoshenko.' The deformation A, of one half of the system is given by which states that the deformation is a function of the mutually applied load, P, the radius of the sphere, R; and the respective physical properties of Poisson's ratio, v, and Young's modulus of elasticity, Y. The shape of experimental load-deformation curves conform to this relationship. The energy input to the sphere-platen system, can be predicted from the integral of the load acting through the appropriate distance, dA. Since dA can be evaluated in terms of P from the derivative of Eq. 1, this integral can be integrated between limits of 0 and P. The test sphere, however, is loaded at not one but at two points of contact, i.e., at both ends of a diameter, and hence the total energy input, E, is twice the energy input at each end, or The energy input to the system calculated from this equation corresponds to the energy computed from the measured area under the load-deformation curve. Timoshenko, considering the impact of two perfectly elastic spheres, has shown that the inter-penetration distance A is given by - m f (D (^ * ^t w as modified for the special case where one sphere is of infinite radius, i.e., its surface is a plane; where M is the mass of the finite sphere of radius R, and V is the velocity of approach at the start of an impact and also equals the final velocity of separation for perfectly elastic bodies. Because A is also a function of the load and the elastic properties, as shown in Eq. 1, the velocity, V, can also be calculated in terms of the elastic properties and maximum load, P, or

Jan 1, 1961

By R. S. Craig, W. E. Wallace, G. S. Kamath

The destruction of long-range order in Mg-Cd, has previously been thought to occur as a second order process. In the present work a variety of X-ray diffraction techniques are employed to show that in this case and in Mg-Cd alloys containing frorn 20 to 33 1/3 at. pct Mg the process more nearly resembles an ordinary first order phase transformation. It is found that the ordered alloy, which occurs as a single phase at lgw temperatures, transforms with increasing temperature into a Cd-enriched disordered (P) phase and an Mg-enriched ordered (a) phase. The interval over which these two phases coexist under apparently equilibrium conditiovs extends from 25" to 87°C content. At 33 1/3 at. pct Mg the two-phase region has disappeared. Measurement of the long range order parameter, s, for the ordered phase in MgCd, (from superlattice line intensities) shows that it disorders only very slightly before it is transformed into the p form. Kinetic experiments reveal that when the a phase is formed frorn the p phase by suitably quenching so as to suppress phase segregation, the transformation is essentially complete and the a phase has acquired its equilibrium value of S in less than 1 min. In an earlier investigation carried out in this Laboratory1 the rate of disordering of the MgCd3 superlattice was determined over an extensive range of temperature. The process was found to be first order and the rate constant, k, was established. At the lowest temperatures studied k was found to increase exponentially with temperature. At higher temperatures, however, it passed through a maximum and for the 100 deg interval below the point at which the superlattice was destroyed k was observed to decrease with increasing temperature. The various theoretical treatments1-3 of order-disorder phenomena lead to a negative temperature coefficient for k near the superlattice critical temperature but this region for MgCdB seemed unusually wide. Detailed analysis of the point indicated' that either the long-range order parameter, S, for MgCda varied with temperature in an anomalous way or the disordering in this instance is more complex than in the cases which have been treated theoretically. The original objective in the present work was simply to determine S vs temperature for MgCda to ascertain whether the disordering was in conformity with theoretical expectations.2° In an early stage of the work it was noted, however, that under equilibrium conditions ordered (a) and disordered (0) phases coexist in MgCd, over a considerable range of temperature. Since on thermo- dynamic grounds the coexisting phases must differ in composition, the investigation was enlarged to permit the compositions of the two phases in MgCd3 to be determined and to establish the extent of the two phase regions for alloys containing from 20 to 33 1/3 at. pct Cd.

Jan 1, 1963