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By W. T. Cardwell

Physically absurd, triple-valued saturations appear in the straight-forward solution of the Buckley-Leverell equations for the displacement of oil by water or gas. From an engineering viewpoint, the triple value causen no difficulty. It is well known how it may be compensnted in order to obtain physically meaningful, numerical results. From a scientific viewpoint, the question still arises: What did the triple value mean? This paper explains how and why the triple value arose in non-capillary Buckley-Leverett theory. The discussion should serve as a background for the understanding and use of the modern method of characteristics in di.~pkzc(>ment theory. INTRODUCTION Displacement theory was introduced to petroleum technologists in 1 941 by Buckley and Leverett.' Their first equation, which they wrote down without derivation, was equivalent to the following: ?s/?t= - qr/F ?f/?r (1) where S = saturation of displacing fluid (a fraction) r = time q,. = total volumetric velocity of both the displacing phase and the phase being displaced (usually, but not necessarily, assumed to be a constant) F = porosity (a fraction) f - fraction of the total volumetric velocity that is the volumetric velocity of the displacing phase (assumed to he a function of S only x = distance. Buckley and Leverett called Eq. I "a material balance equation". Actually it is derived from both a continuity equation, or material balance equation, and Darcy's law. Buckley and Leverett jumped from their Eq. 1 immediately to their Eq. 2, which was the equivalent of the following: (?x/?t)x = qr/F df/ds = qr/F f'(s) (2) The jump from Eq. 1 to Eq. 2 involves apparently simple mathematics, but in that apparently simple mathematics lies a subtle point that is part of the key to the meaning of the triple value to be discussed here. Eq. 2 may be readily interpreted as saying that a point of constant saturation (on a saturation-vs-dis-tance curve) moves with a constant velocity that is proportional to the total volumetric rate, inversely proportional to the porosity, and is otherwise a function of the saturation itself. So that if one knows the derivativc with respect to saturation of the fractional flow function, f(S), for each saturation, one knows the velocity of each point of the moving saturation-vs-distance curve. The function f(S) can he determined experimentally and its derivative f'(S) can be calculated. It turns out that the experimentally derived f'(S) is not a monotonic function of S, but instead it has a definite maximum and declines away at both high and low saturations. This in turn means, in accordance with Eq. 2, that on a moving saturation-vs-distance curve, ccrtain intermediate saturations will travel faster than the saturations either higher or lower. The result is indicated in Fig. 1. In Fig. 1, the abscissas represent distances along a column of porous medium, which column is assumed to be uniform in cross-section perpendicular to the ab-scissal direction. The ordinates represent fractions of pore space occupied by the displacing phase, which may be either water or gas. It is assumed that the saturation is uniform over all planes perpendicular to the abscissal direction. The saturation is a function only of time and one space variable. Time variation of the saturation is represented by change in shape of a curve such as curve AGJ, which represents the initial saturation-vs-

By James K. Stanley

Preferred orientation, particularly in irons and low-carbon steel, is a phenomenon that is both of considerable importance and theoretical interest. At times it is a liability and at other times an asset. In deep-drawing operations, preferred orientation is extremely undesirable because it necessitates trimming operations and increases scrap loss. Furthermore, oriented metals are likely to crack more easily than randomly oriented material because the forming of symmetrical and unsymmetrical shapes out of preferentially oriented metals and alloys increases the probability of rupture in regions of high stress, owing to differential ductility.' In the electrical industry, on the other hand, preferentially oriented silicon irons are in demand for transformer application because of the improved magnetic permeabilities in the rolling direction.2 This phenomenon of preferred orientation in soft magnetic materials has been responsible for the tremendous improvement in transformer design and construction in recent years. Directional properties in metals have received a great deal of attention in the metallurnical -literature,3-9 in which much of the information reported about orientation has been obtained by conventional methods, mechanicai properties and X-rays. A wealth of data has been obtained and often at a great expenditure of time. The recent introduction of the magnetic torque measurements on ferromagnetic materials provides a very simple and rapid method of evaluating orientation. The judicious use of the method can supply important information, but it should be borne in mind that such studies must be supplemented by X-rays, optical methods,10 and etch and pressure figures" to get a rational understanding of the orientation phenomena. No claims are made that the magnetic torque of evaluating orientation will reveal the behavior of the metal in deep drawing. For this purpose the accepted tests for deep-drawing quality must be used. For a good drawing stock, which must have low impurities, desirable grain size, ductility, strength, hardness, good surface, random orientation, and good recrystallization behavior, it cannot be expected that any simple test will be satisfactory for appraising all the factors. The only factor on which the magnetic method can be used is orientation, which is, of course, of considerable importance. When directionality can cause a 10 to 15 per cent change in tensile strength and a IOO to 300 per cent change in tear length,12 it goes without saying that a reliable as well as rapid method for detecting these changes would be desirable. There are certain inherent advantages in testing orientation by the torque method: The method is rapid with the proper type of equipment; no elaborate preparation of specimens is required—it is only necessary to punch or machine a I-in. disk of the sheet material and insert it into the testing device.

Jan 1, 1944

By James K. Stanley

Preferred orientation, particularly in irons and low-carbon steel, is a phenomenon that is both of considerable importance and theoretical interest. At times it is a liability and at other times an asset. In deep-drawing operations, preferred orientation is extremely undesirable because it necessitates trimming operations and increases scrap loss. Furthermore, oriented metals are likely to crack more easily than randomly oriented material because the forming of symmetrical and unsymmetrical shapes out of preferentially oriented metals and alloys increases the probability of rupture in regions of high stress, owing to differential ductility.' In the electrical industry, on the other hand, preferentially oriented silicon irons are in demand for transformer application because of the improved magnetic permeabilities in the rolling direction.2 This phenomenon of preferred orientation in soft magnetic materials has been responsible for the tremendous improvement in transformer design and construction in recent years. Directional properties in metals have received a great deal of attention in the metallurnical -literature,3-9 in which much of the information reported about orientation has been obtained by conventional methods, mechanicai properties and X-rays. A wealth of data has been obtained and often at a great expenditure of time. The recent introduction of the magnetic torque measurements on ferromagnetic materials provides a very simple and rapid method of evaluating orientation. The judicious use of the method can supply important information, but it should be borne in mind that such studies must be supplemented by X-rays, optical methods,10 and etch and pressure figures" to get a rational understanding of the orientation phenomena. No claims are made that the magnetic torque of evaluating orientation will reveal the behavior of the metal in deep drawing. For this purpose the accepted tests for deep-drawing quality must be used. For a good drawing stock, which must have low impurities, desirable grain size, ductility, strength, hardness, good surface, random orientation, and good recrystallization behavior, it cannot be expected that any simple test will be satisfactory for appraising all the factors. The only factor on which the magnetic method can be used is orientation, which is, of course, of considerable importance. When directionality can cause a 10 to 15 per cent change in tensile strength and a IOO to 300 per cent change in tear length,12 it goes without saying that a reliable as well as rapid method for detecting these changes would be desirable. There are certain inherent advantages in testing orientation by the torque method: The method is rapid with the proper type of equipment; no elaborate preparation of specimens is required—it is only necessary to punch or machine a I-in. disk of the sheet material and insert it into the testing device.

Jan 1, 1944

By John R. Green

Rotary kilns, varying in construction, are used in a variety of processes. Products differ and operating conditions vary accorcling to economic requirements. All of these variables influence the degree of instrumentation and type of control necessary or profitable to install. Products fired in rotary kilns are the results of combined temperature and time treatment and the interrelation of these two factors should be kept constantly in mind in the perusal of this paper. Measurements of Kiln Temperature The securing of proper temperatures within the rotary kiln, either of the charge or of the kiln lining in the high fire zone, are basic objectives of kiln operation; therefore the measurement of these high-temperature conditions merits first consideration. For these measurements, radiation pyrometers, properly designed and protected, have proved adequate, particularly where records ox automatic control are desired, while Optica1 pyometers may serve as portable indicators. Light-sensitive devices or photoelectric cells in this service are capable of producing records as well as certain forms of automatic control. High-temperature measuring devices for rotary-kiln work should have the measuring unit protected from dust, as a continued accumulation of deposit would lower the readings. Fig. 1 shows a typical application of radiation equipment to a rotary kiln, mounted far enough away from the sighting hole through the kiln hood to be protected From puffs or stingouts and with a sighting tube having a series of settling chambers, to prevent dust from reaching the lens. Although dust conditions inside the kiln itself usually fluctuate considerably and have their effect upon the readings at that moment, such effects are not cumulative and show as a continuous fluctuation in the temperature indicated, provided the radiation unit and recorder are responsive to such slight and rapid temperature fluctuations. The ambient temperature to which a measuring unit is subjected fluctuates from possibly 0" to over zoo°F., therefore these changes should have no effect upon the final reading or upon the life of the measuring unit. A very narrow sighting angle is desirable, so that measurement of temperature may be made as far as possible into the high fire zone without effect of the flame temperature. There should some sighting means on the measuring unit, so that the proper field may be viewed. Measurement of wall temperature taken at a point where the charge has just left the wall is less affected by dusting conditions than when taken elsewhere. Factors influencing Temperature Table I gives an outline of the factors that produce kiln temperatures and comments on the possibility of measurement and control. Of greater number and of varied influence are the factors that control when, where and how the heat is delivered to the kiln, the type of flame and the rate of

Jan 1, 1942

By John R. Green

Rotary kilns, varying in construction, are used in a variety of processes. Products differ and operating conditions vary accorcling to economic requirements. All of these variables influence the degree of instrumentation and type of control necessary or profitable to install. Products fired in rotary kilns are the results of combined temperature and time treatment and the interrelation of these two factors should be kept constantly in mind in the perusal of this paper. Measurements of Kiln Temperature The securing of proper temperatures within the rotary kiln, either of the charge or of the kiln lining in the high fire zone, are basic objectives of kiln operation; therefore the measurement of these high-temperature conditions merits first consideration. For these measurements, radiation pyrometers, properly designed and protected, have proved adequate, particularly where records ox automatic control are desired, while Optica1 pyometers may serve as portable indicators. Light-sensitive devices or photoelectric cells in this service are capable of producing records as well as certain forms of automatic control. High-temperature measuring devices for rotary-kiln work should have the measuring unit protected from dust, as a continued accumulation of deposit would lower the readings. Fig. 1 shows a typical application of radiation equipment to a rotary kiln, mounted far enough away from the sighting hole through the kiln hood to be protected From puffs or stingouts and with a sighting tube having a series of settling chambers, to prevent dust from reaching the lens. Although dust conditions inside the kiln itself usually fluctuate considerably and have their effect upon the readings at that moment, such effects are not cumulative and show as a continuous fluctuation in the temperature indicated, provided the radiation unit and recorder are responsive to such slight and rapid temperature fluctuations. The ambient temperature to which a measuring unit is subjected fluctuates from possibly 0" to over zoo°F., therefore these changes should have no effect upon the final reading or upon the life of the measuring unit. A very narrow sighting angle is desirable, so that measurement of temperature may be made as far as possible into the high fire zone without effect of the flame temperature. There should some sighting means on the measuring unit, so that the proper field may be viewed. Measurement of wall temperature taken at a point where the charge has just left the wall is less affected by dusting conditions than when taken elsewhere. Factors influencing Temperature Table I gives an outline of the factors that produce kiln temperatures and comments on the possibility of measurement and control. Of greater number and of varied influence are the factors that control when, where and how the heat is delivered to the kiln, the type of flame and the rate of

Jan 1, 1942

By Dewitt T. Ring

Lack of reliable detailed production figures for earlier years, together with the loose nomenclature in reference to producing horizons and the application of the term "field" without any definite meaning or restriction, has made it impossible to gather statistical data suitable for the Institute's form. In common with all other producing areas in the United States, Ohio has felt severely the economic ills of the entire industry during the past year. With overproduction, not only of crude but also of refined products, going on throughout the country, the price structure as a direct consequence has weakened on Ohio oils. Valuable crude is being sold at a big loss today because producers arc willing to, and do, sell more than the market can absorb. The axe hangs heavy over the heads of Ohio producers, and will until something constructive is done to keep supply in proportion to demand. This not only applies to Ohio but to the entire industry. Production of Pennsylvania grade in Ohio was under 50 per cent proration, which has been in effect since Oct. 1, 1937. Three price cuts since February have lowered the posted price from $1.70 to $1.18, a 30 per cent reduction; other grades were less drastically reduced. Pipeline storage facilities were limited; many producers were faced with the problem of providing their own storage or the risk of ruining their wells. If they wanted to pull and abandon wells, there was no market for junk equipment. Many employees have been cut to half time and in a number of instances their services entirely dispensed with. Summary of Production and Drilling Both oil and gas production in the state during 1938 showed a definite decline over the previous year. (A table showing production by years from 1876 through 1937 was published in Vol. 127 of the Transactions.) The total production of crude oil in the state for 1938 was 3,357,914 bbl., as compared with 3,654,000 bbl. in 1937, a decrease of 7.1 per cent. At

Jan 1, 1939

By M. Van Siclen

THE outstanding fact in connection with dust disease in the United States at present is the growing recognition of its seriousness by state officials and by the more progressive operators of mining, metallurgical and allied industrial plants. The same may perhaps be said of labor in some of its better organized centers, but the average independent non-union workman continues, as of yore, to suffer the toll of disability and even of death from dust inhalation without realization of the source of his ill-being. Progress in the betterment of the handling of sufferers from dust disease and of the conditions creating dust hazards in mining and allied industries is pursuing a course similar to that of the now widespread campaign against accidents, in which the risk is more obvious, more severe, and was naturally recognized sooner. The coming on of dust disease is generally relatively slow and its immediate effects not infre-quently masked by or attributed to other diseases. Marked exceptions to this general rule have occurred in districts where the dust is particularly pernicious, such as the Rand and Joplin; yet such exceptions, unhappy in themselves, opened the eyes of medical men, and of those in other localities charged with the responsibility for the welfare of industry, to the much more widespread if less spectacular hazard existing from the inhalation of dust in all rock-excavating operations and all industrial operations creating inorganic dust, whether it be crushing and grinding, sand-blast-ing, granite-cutting, or what not. Advancement to date in the United States in prevention and treat-ment has been slow, yet the record shows that quantitative methods for determining the degree of hazard and means for decreasing it were being developed as far back as 25 years ago; and that more rapid progress may be looked for from now on. In 1908, in this country, F. L Hoffman?(1) discussed the mortality from consumption in dusty trades, especially brass foundries; and in 1913 E. R. Hayhurst(2) described the effects of inhalation

Jan 1, 1933

By J. J. Sense

10.2-1. Equipment Scheduling. In any earth-moving operation, more profit may be earned or lost by equipment scheduling than by any other single facet of the project. Many now-defunct earth movers would have survived the cost-profit squeeze had they followed an efficient, cost saving, equipment scheduling program. The ideal program would have every item of the equipment fleet working all of the time. In practice for many obvious reasons, principally mechanical conditions, operating conditions, and human nature-this ideal situation is not possible. The cost-conscious organization strives to keep as many pieces of equipment of the fleet working efficiently as much of the work day as possible. Operating efficiency requires the minimum equipment to move the predetermined tonnages in the prescribed period of time. In the case of a shovel-truck operation this would mean the scheduling of the minimum shovel and truck shifts to excavate and transport the necessary tonnage to the processing plant or waste dump. To accomplish this goal, the operator must work from the predetermined production established by the requirements of the plant, stripping ratio, mine plan, etc. This production schedule may be in terms of tons or yards per year, per month, or per hour, but must eventually be translated into tons or yards per ma- chine per unit of time. In this regard, the reader is referred to Sections 8.0, Excavation and Loading, and 9.0, Haulage and Transportation. The trend to larger and faster, and as a result more costly, equipment requires that the operator consider every possibility to keep the equipment operating around the clock, seven days per week. In some areas seven day operation may not be feasible economically, because of premium pay for Sunday work. Mine labor agreements are generally written without premium pay penalties for weekend work, and such scheduling is possible and most often desirable.

Jan 1, 1968

By R. W. Raymond

The western public domain acquired by the United States through trcaties, as the result of conquest or purchase, was invaded after Marshall's re-discovery of gold in California, by an overwhelming multitude of prospectors and miners from all parts of the world. he mineral lands of the whole Pacific slope were practically unsurveyed. Congress, disgusted with the experiment of leasing mineral lands, which it had tried for 40 years, and abandoned in 1847, enacted no laws for the management of these public mineral lands, and the pioneers made their own laws governing mining titles. These local regulations applied at first to gulch-mining in the auriferous river-beds only; and they constituted a simple and practical system. adapted to the needs and means of primitive communities—significantly called " camps." They had the means of measuring distances, but not angles; they knew no property except personal property in the form of pickaxes, pans, supplies, camp-equipage, horses or mules, and mining rights. The earliest codes which they developed expressed what might be called the law of the lariat. With the lariat they measured the distance assigned to each miner along the gold-bearing gulch—a double portion to the discoverer, and a single portion to his successors, in the order of their coming. With the lariat, they hung, after such due process of law as was available, the rascal who stole a horse, or a bag of gold-dust, or a mining claim, or killed another man without giving him fair notice and a chance to defend himself. In these pioneer codes, adopted in mass-meetings and enforced by the same authority, two features concern us most: 1. They measured mining property by one dimension only. So many feet of the gulch, held by one man, meant a distance into either bank, and a distance in depth, extending as far as gold might be found.

Jan 1, 1915

By John Primrose

Tube stills having demonstrated their usefulness for refining operations, the later developments in their design have been in the direction of improved thermal efficiency. The earlier designs operated with low furnace temperatures and large volumes of furnace gas because the fuel was burned with much excess air. It was quite possible to provide sufficient heating surface to lower the temperature of the flue gas to within 150" of the temperature of the inlet oil, or when inlet-oil tempera-tures were high to have the flue gas escape at 300" or 350" F. by using the heat remaining in the flue gas from the still to preheat the air supplied for combustion. But even so, the thermal efficiency was low because of the large quantity of air used for combustion. The large quantity of excess air was required to burn the fuel in the furnace at a temperature low enough to prevent overheating the furnace walls and overheating of the oil. Supplying heat to the tubes of the heating surface at a rate beyond the capabilities of the oil to absorb, except with a considerable difference between the temperature of the inside of the tube and oil passing through, would result in overheating the tubes and the oil in contact with them. For these reasons it was very necessary in the older types of tube stills to burn the fuel with large quantities of excess air, resulting in low thermal efficiency despite the low flue-gas temperature. Neglecting loss by radiation, the thermal efficiency could be improved only by burning the fuel with less excess air, but it was necessary to accomplish this without upsetting the furnace temperature conditions existing when large quantities of excess air were used. There are several methods of bringing this about, such as controlling the furnace temperature by returning a proportion of the flue gas to the furnace, or by exposing direct to the fire a heat-absorbing surface so located and proportioned that sufficient heat will be absorbed by radiation to prevent excessive furnace temperatures.

Jan 1, 1928

By Dewitt T. Ring

Lack of reliable detailed production figures for earlier years, together with the loose nomenclature in reference to producing horizons and the application of the term "field" without any definite meaning or restriction, has made it impossible to gather statistical data suitable for the Institute's form. In common with all other producing areas in the United States, Ohio has felt severely the economic ills of the entire industry during the past year. With overproduction, not only of crude but also of refined products, going on throughout the country, the price structure as a direct consequence has weakened on Ohio oils. Valuable crude is being sold at a big loss today because producers arc willing to, and do, sell more than the market can absorb. The axe hangs heavy over the heads of Ohio producers, and will until something constructive is done to keep supply in proportion to demand. This not only applies to Ohio but to the entire industry. Production of Pennsylvania grade in Ohio was under 50 per cent proration, which has been in effect since Oct. 1, 1937. Three price cuts since February have lowered the posted price from $1.70 to $1.18, a 30 per cent reduction; other grades were less drastically reduced. Pipeline storage facilities were limited; many producers were faced with the problem of providing their own storage or the risk of ruining their wells. If they wanted to pull and abandon wells, there was no market for junk equipment. Many employees have been cut to half time and in a number of instances their services entirely dispensed with. Summary of Production and Drilling Both oil and gas production in the state during 1938 showed a definite decline over the previous year. (A table showing production by years from 1876 through 1937 was published in Vol. 127 of the Transactions.) The total production of crude oil in the state for 1938 was 3,357,914 bbl., as compared with 3,654,000 bbl. in 1937, a decrease of 7.1 per cent. At

Jan 1, 1939

By Joseph E. Pogue

Any mechanism, either natural or artificial, for regulating the functioning of a given unit in the general economy must operate toward the maintenance of equilibrium if it is to survive. The petroleum industry, concerned as it is with the production of a natural resource of specialized character, is surrounded not only by the economic factors common to other industries but by an extra set of unique elements centering about the fugitive character of crude petroleum under conditions of competitive development. The term equilibrium, therefore, so far as the oil business is concerned, involves a combination of economic and physical factors: the first set having to do with supply, demand, costs, profit margins, purchasing power, and the like; and the second, with underground pressures in oil pools, efficient rates of extraction, and all other aspects of engineering that may be summarized by the familiar term "conservation." The two categories, in fact, are not as clearly divided as the foregoing statement would imply, for in practice it will be found that the economic and physical aspects have a pervasive interaction and interrelationship. If the development of the petroleum industry in the United States is examined from its inception in 1859 down to the present, it will be found that, beginning about 11 years ago, a new mechanism for regulating the production of crude petroleum made its appearance. Prior to this recent period, the production of this raw material was determined by competitive forces operating without outside restraints. At present the output of crude oil is subjected to supervision by regulatory bodies in most of the oil-producing states, which impose upon the operators certain conditions having to do with the manner and rates of production. Thus, in the space of a decade, the mechanism for producing crude oil has changed from an automatic to a designed procedure called proration. And in its short history this method has been marked by a rapid evolution in its nature and incidence, with progressive changes still under way.

Jan 1, 1938

By W. A. Walker, G. W. Ostroot

An increase in the number of deep wells being drilled where extreme bottom-hole temperatures are encountered, and the anticipated drilling of wells where temperatures in the range of 500°F or higher may occur, has brought about a comprehensive investigation of cementing materials and of the techniques involved in their proper usage at these elevated temperatures. Included are developments in cements, retarders, weighting materials and other cement additives which make it possible to formulate a variety of compositions to help resolve the cementing problems of these extreme well conditions. The problems associated with the selection and testing of cements are discussed, and a resume of field results is included. Previous studies on strength retrogression indicate that caution should be exercised in the selection of a cementing composition for use in high-temperature wells. It now appears that, by the addition of silica flour as a stabilizing additive to certain cements, compositions covering a wide range of slurry densities can be designed to meet extreme well conditions without strength retrogression. Improvements in cement retarders make it possible to produce a four-hour thickening time at static temperatures up to 500°F. This temperature is considerably higher than conditions presently being encountered in drilling and completion work. Inert weighting materials, used to produce 20-lb/gal or heavier cement slurries, are reviewed. INTRODUCTION As the search for oil continues, the number of wells being drilled to depths of 10,000 ft or below has continued to increase over the past decade. During 1959, there were 50,893 wells drilled in the United States for a total of 209 million ft of hole. Of this total, approximately 4.45 per cent were drilled below 10,000 ft and 0.30 per cent below 15,000 ft, with a record depth of 25,340 ft recorded (Table 1). With the drilling of this record-shattering hole comes the question, "How deep can wells be drilled?".' Limitations with respect to equipment (surface and subsurface), cementing materials and techniques would cause some concern; however, a panel of experts have agreed that the U. S. oil industry has the equipment and know-how to drill a 50,000-ft hole. The greatest deterrent would be the 700°F temperature they would anticipate encountering at this depth. Although the number of wells drilled under what is generally considered hot-hole conditions (230°F and higher) has been relatively high, each well often presents distinctly individual problems and requires separate consideration and selection of special materials, techniques and equipment. At the present time there are over 30 additives and special cements available for use in "tailoring" a cementing composition for a specific well. It is not uncommon to use three or four different additives with the basic cement to produce the desired slurry characteristics. A generally accepted procedure is to make laboratory tests on selected cementing compositions prior to pumping them into wells deeper than 12,000 ft, or where static temperatures are in the range of 260°F or higher. In some instances, it is recommended that laboratory tests be made where less severe well conditions are encountered. Prior to selecting a cementing composition for a particular well, key personnel representing the operator, drilling contractor and service company should meet to determine that each individual is acquainted with every detail which might influence cementing results and to discuss the execution of the job. For cementing hot-holes, a number of factors must be evaluated before proceeding with the operation. Consideration must be given to the following. 1. Thickening time—The slurry must remain fluid for a sufficient length of time to allow displacement down the casing and up the annular space in a primary cementing job or, in squeeze-cementing, adequate thickening time for both the build-up of a satisfactory squeeze pressure and the reversing out of excess cement. The thickening time of standard retarded cements will often be too short under extreme temperature conditions, thus involving special formulations and requiring laboratory tests to determine the proper amount of additional retarder to obtain the desired pumpability.

PRESIDENT E DEGOLYER, District 0 NEW YORK, N Y PAST PRESIDENTS J V. W. REYNDERS, District 0 NEW YORK, N Y SAMUEL A TAYLOR, District 3 PITTSBURGH, PA FIRST VICE-PRESIDENT GEORGE OTIS SMITH, District 4 WASHINGTON, D C TREASURER CHARLES F. RAND NEW YORK, N Y SECRETARY H. FOSTER BAIN NEW YORK, N Y

Jan 1, 1923

By William G. Pariseau

There are important phenomena in rock and soil mechanics that cannot be explained in terms of theories of homogeneous, isotropic materials. Subsidence of strata about mine openings is an example. In-situ stress measurements in nonisotropic sedimentary and metamorphic rocks is another. Patterns of joints, faults, fractures, and similar geologic features impart directional mechanical properties to rock masses that are locally isotropic or anisotropic. On the geologic scale, the nonhomogeneity of composite rock masses may, in certain instances, be dealt with as homogeneous anisotropy. The mechanics of large rock masses can, therefore, be expected to involve considerations of anisotropy. The source of the anisotropy is not relevant. Once the scale of observation is selected and the material is defined accordingly, the analysis of stress and deformation proceeds without regard to the numerical values of the material constants. There are also important phenomena in rock and soil mechanics that cannot be explained in terms of linear elasticity, theory. For the mechanical description of anisotropic geologic materials capable of deforming beyond the limit of purely elastic strains, a plasticity theory is required. The purpose of this chapter is to present a plasticity theory for anisotropic rocks and soils. The proposed theory is based on the work of Hill in anisotropic metal plasticity and represents an extension of his work so as to include anisotropic geologic materials. The point of departure from metal plasticity theory begins with the inclusion of the normal stresses as linear terms in the yield condition, which plays a central role in plasticity. Once the yield condition is established, the plastic strain increments are obtained immediately through the principle of normality. For practical applications, some simplification of the three-dimensional theory is re-

Jan 1, 1972

By J. E. Clennell

It is a common observation that the improvements introduced in practice since the first announcement of the cyanide process have been almost entirely mechanical. Although .a good deal of study land research has been devoted to the chemical problems [involved, the results obtained appear trifling in comparison. Few of the suggested modifications in the chemical treatment have come into practical use and those only in limited fields. Nevertheless, if we study the recent history of the cyanogen compounds from a somewhat broader standpoint, we shall find that considerable additions have been made, not only to our knowledge of their chemical properties, but also to their applications for industrial purposes. The present review of these advances naturally falls into two divisions: (1) processes involved in the treatment of ores; (2) manufacture of cyanides and other related compounds. Part I. Advances in the Chemistry of Ore Treatment by Cyanide In the attempt to extend the scope of the process, various ores have been encountered which contain gold and silver in such forms that they will not yield satisfactorily to ordinary methods of cyanide treatment. In some cases the difficulty is due to the excessive action on the solution of base metals present in the ore; in others, to the occurrence of minerals such as dyscrasite (the native alloy of antimony and silver), or a supposed oxidized manganese compound containing silver, which are either altogether insoluble in or very slightly attacked by cyanide. A particularly troublesome case is that of the so-called "graphitic" ores, containing carbon in some form which has the property of precipitating gold and silver already dissolved. Other efforts have been directed to improving extraction by electrolysis of working solutions, and by addition of various chemicals with or without electrolysis; to the diminution of cyanide consumption by "re-

Jan 1, 1916

By W. Mitchell, B. H. Bergstorm, C. L. Sollenberger

A unique compression testing machine was constructed to load individual 1/8 to I-in. spheres of glass, etc., at rates from 100 to 100,000 lb per min. During loading the applied load was continuously plotted us the deformation of the sphere-platen system. The load-deformation curve conforms to the theory of elasticity. The spheres were surrounded by steel retaining rings or by gelatin (to prevent secondary fracture). The product size modulus was determined from screen analyses. The data shows: 1) Energy input per unit mass is inversely proportional to the product size modulus (or directly proportional to the surface area per unit mass). 2) Increased loading rates slightly increase the energy input per unit mass required for fracture without affecting the preceding relationship. Theory and experiments show that much of the input strain energy is transformed into kinetic energy of fragments at fracture, this being a reason efficiencies based on "surface energies" are exceedingly small. This large kinetic energy component is usually dissipated as heat but may be partially reclaimed because impact of fragments against the surface of steel retaining rings causes additional comminution. There are currently several theories of crushing, all of which can be derived from the general energy equation of Gillilandl as was pointed out by Mitchellet al in 1954'and more recently by Rose and Sullivan. If the exponent of the equation dE-x-"dx is assigned values of 2,1, or 3/2, one obtains by intergration between suitable limits, the equations of Rittinger, kick,' and Bond,' respectively. Other investigators prefer to let the exponent be a variable parameter. To help resolve the controversy, the Allis-Chal-mers Research Laboratories set up a series of carefully controlled experiments in which the level of energy input required to induce the comminution of a single particle by slow compression loading was very accurately measured. The energy input requirement, in conjunction with the size analysis of the fragments produced at fracture, yielded an accurate energy-product size relationship for the conditions studied. APPARATUS The experimental apparatus was designed to apply a compressive load on opposite sides of an "ideal particle." Spherical shapes were chosen, because point contact loading is typical of the mechanics of conventional crushers. The bulk of the experimental data was obtained with glass spheres because glass is a fairly homogeneous, brittle material for which the properties follow definite statistical distributions. The spheres ranged from 1/8 to 1-in. diam. The compressive load was applied to the specimen at a uniform rate by a loading mechanism (Fig. 1) which acted through a system of levers. The uniform rates, ranging from 100 to 100,000 lb per min, were obtained by metering water into a bucket suspended at the end of the secondary level. Point contact was made with the sphere through tungsten-carbide platens. This latter material is extremely hard and has a high modulus of elasticity, thereby having a minimum of distortion when loaded. The actual load on the sphere was measured independently of the lever system by a load cell, Fig. 2, which was designed so that the voltage output of the load cell would be proportional to load. The deformation of the specimen was indirectly measured by a pair of transformers which were attached to opposite edges of the upper platen. The cores of the transformers, which were attached to the lower platen, moved relative to the transformer so that the voltage output was proportional to the deformation of the sphere-platen system. The load was plotted against the deformation on an X-Y recorder. The area under the curve, as shown on Fig. 3, was proportional to the energy input of the

Jan 1, 1961

By L. A. Rapport, J. R. McCord, W. P. Drews, K. H. Coats

Water movement about an oil or gas reservoir can be predicted provided an aquifer influence function is known. This function is generally determined from an electric analyzer study or by fitting an idealized mathematical model to field data. A prohlem arises in determining that influence function which best reproduces field data and satisfies certain smoothness requirements, without making any idealizations concerning aquifer geometry and heterogeneity. This study shows the problem to be solvable through the linear programming technique and presents applications to one oil reservoir and two gas storage reservoirs. In addition, a theorem is stated and proven which confirms influence junction smoothness requirements heretofore accepted on physical intuition and establishes additiotzal smoothness constraints formerly not recognized. INTRODUCTION The pressure decline accompanying production results in water encroachment into oil and gas reservoirs situated adjacent to aquifers. The importance of this water movement derives from the significant dependence of production rate upon reservoir pressure and of pressure, in turn, upon water encroachment. Pressure and rate of water movement are uniquely related through an "influence" function which may be in the form of reservoir pressure response to a unit water encroachment rate or of water movement caused by a unit reservoir pressure drop. This influence function reflects the heterogeneity and geometry of the aquifer and is therefore particular to each reservoir. If the influence function is known, then reservoir pressure may be predicted from a production rate schedule, or vice-versa, with the aid of the material balance equation which relates water influx to reservoir production and pressure. The problem of determining this influence function for a given reservoir has been approached in three different ways. Van Everdingen and Hurst calculated and tabulated certain influence functions pertinent to idealized mathematical models which satisfy simplifying assumptions such as aquifer homogeneity and elementary reservoir-aquifer geometries.' Other studies developed additional tables for a variety of elementary reservoir-aquifer geometrical con- figurations and demonstrated their validity and utility.:' Hicks, et al. described the use of an electrical network to determine an influence function giving "best" match of field history and allowing prediction of future performance.' Finally, Hutchinson and Sikora5 and Katz, Tek and Jones attempted to develop a calculation method for deriving the influence function directly from field data with no idealizing assumptions concerning aquifer geometry and homogeneity. They encountered difficulties with inaccuracies in field data and with satisfaction of well-known smoothness requirements of the influence function. This study is concerned with the determination of influence functions from field data and, more specifically, treats the following problem: given field pressure-production data of arbitrary accuracy, how does one determine the influence function which, subject to satisfaction of known smoothness requirements, gives best agreement with field history? A rigorous solution to this problem is ohtained through linear programming as described below. Example applications to one oil and two gas storage reservoirs are presented. In addition, a theorem is proved which confirms influence function smoothness requirements heretofore accepted on physical intuition and establishes additional smoothness requirements formerly not recognized.

Jan 1, 1965

By Charles C. Russell

Pressures developed by the coal during the coking process have been responsible for serious trouble to many companies that operate or build by-product coke ovens. The insidious nature of this trouble is indicated by the fact that oven operators, unless they have ascertained the characteristics of the coals they use, cannot determine the existence of dangerous pressures until after the damage has been done. A rather popular misconception is that ease of pushing of the charge at the completion of the coking period indicates that no dangerous pressure has been developed, but this is far from the truth; pressures developed during the coking period are often completely dissipated by the shrinkage of the charge in the completion of coking, and so any criterion based on the ease of pushing is futile. However, methods of testing coals are available that will definitely distinguish the dangerous coals from those that are safe, and such methods have been brought to a high degree of certainty. The operator should take no risk that involves either a lack of knowledge of the behavior of coals during coking or the failure to believe that certain of the coals or coal mixtures can cause damage to the oven structure. This merely tends to minimize the problem and leads to claims that coking coals of all kinds may be carbonized with no danger of damage to the oven structure provided some particular kind of byproduct oven is used. This lack of appreciation of the true situation is in itself one of the main factors leading to damage of coke-oven structures. Coals that develop more than a certain safe pressure cannot be used in by-product coke ovens without causing damage to the side flue walls. The following paper presents a highly certain method for the measurement of the pressures developed during the carbonization of coal—a method that is the culmination of many years of work on the problem in which a number of methods for the purpose were investigated and used. While actual pressures found may appear to be small when expressed in pounds per square inch, the number of square inches in each oven wall is so large that the total pressure on the oven wall becomes an enormous load.

Jan 1, 1940

By C. L. Berrien

Many fires have occurred in the mines of Butte in recent years, and while all have been of a serious nature, simply because they were mine fires, six of them have been especially dangerous in respect to loss of life and property, and the expense of extinguishing or controlling them. It is not my intention to discuss the relative merits of methods used in fighting these different fires because the conditions under which they occurred varied in each case, and it was not always advisable to expend the large sum of money necessary to actually extinguish them if they could be bulk-headed off from the rest of the mine. It is needless to say that everything possible has been done to check all fires at the beginning, but without success in some cases; and it has then become necessary to bulkhead all connections to them, in which state several now exist. The mine fires of Butte, or fires in any mine, may be divided into two classes, namely: Those occurring in accessible workings, and those occurring in inaccessible workings; because these two conditions govern to the greatest extent the methods of fighting fires. Accessibility and inaccessibility in the case of mine fires concern not only new open workings and old closed workings, respectively, but also the condition of the ventilation in and about those places. When a fire is accessible at the start it should not be difficult to confine it to a small area and extinguish it in a relatively short time, but when it is impossible to actually reach a fire in old filled, abandoned workings, or there is no opening by which the gases may be conducted away from the fire zone, then the time consumed in changing those conditions permits the fire to increase to such an extent that it is a long, hard fight to overcome it. These different conditions have been met in Butte, and of the six fires of serious proportions the Steward mine fire and the High Ore-Modoc mine fire were in new accessible workings and were extinguished in a month or so. The Anaconda mine fire, the Leonard-Minnie Healy mine fire, the West Colusa mine fire, and the Mountain View mine fire, were all inaccessible. The Anaconda mine fie started about 25 years ago and though safely bulkheaded is still active. The Leonard-Minnie Healy

Jan 1, 1916