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By B. Fitch

This paper deals with the behavior of sedimenting suspensions. More particularly, it treats, in as organized a manner as possible, the body of knowledge, theoretical or empirical, by which one predicts the behavior of miscellaneous swarms of particles in suspension. Such knowledge is necessary for precise and economical design of equipment. While the behavior of a single spherical particle settling through an infinite sea of quiescent fluid is well understood, practical sedimentation processes are almost always concerned with particles of assorted sizes, densities, and shapes, in such concentration that there is profound particle interaction. Such swarms of particles are observed to settle in any of four markedly different manners. Which one they follow is governed by particle interaction. It is determined largely by the dilution of the suspension, and the relative tendency of the particles to cohere. TYPES OF SEDIMENTATION The relationship between the different modes of sedimentation is shown paragenetically in Fig. 1. The left side of the diagram represents particles having little tendency to cohere; the right side represents particles for which interparticle cohesion is large compared to the settling force. The vertical axis represents dilution. As seen in the diagram, sedimentation is divided into three broad fields or regimes. At high dilutions there exists a regime here named 'clarification.' Particles in clarification may settle either individually, or by collecting into separated floccules. Thus there are two different possible modes of settling in the clarification regime. It is characteristic c~f this regime that there will be no clear line of demarcation between settling suspension and a supernatant. Faster particles settle out ahead of slower ones. In batch tests there develops a gradation of both particle sizes and pulp density due to progressive depletion of the largest particles from any given pulp level.

Jan 1, 1962

By N. P. Goss

ASTERISM appearing in X-ray Laue dia-grams is an extremely sensitive index of changes in the internal structures of indi-vidual grains of polycrystalline metals. It indicates the existence of various forms of subboundary structure or subdivision within the grain. The present viewpoint is that the grain is made up of lattice blocks having substantially the same size and shape.1-4 When these blocks all assume exactly the same orientation, the crystal is perfect and asterism is absent. Cleaves and Thompson5 observed that the hardness of iron is virtually constant over a range of grain sizes. It is quite possible that the subboundary structure caused this, and that the latter is just as important as grain size itself. While the experiments reported here are not con-clusive, they do support this viewpoint. Metals can, under certain conditions, be prepared entirely free from asterism, but this preparation does not necessarily require long heating or slow cooling, as will be shown here. In this paper a distinction is made be-tween mosaic and distorted grain struc-tures but the difference is only a matter of degree. In a previous paper9 it was shown that the grains can become distorted even during heat-treatment. The block structure exists inherently, even in a perfect crystal; the size and shape of these crystallites, or lattice blocks, varies, depending upon a number of factors. Goetz, for example,7 has shown that a metal before crystallizing from the molten state must go through a paracrystalline phase with oriented groups of atoms about 10-14 to 10-15 c.c., or 10-5 cm. in size.

Jan 1, 1940

By N. P. Goss

ASTERISM appearing in X-ray Laue dia-grams is an extremely sensitive index of changes in the internal structures of indi-vidual grains of polycrystalline metals. It indicates the existence of various forms of subboundary structure or subdivision within the grain. The present viewpoint is that the grain is made up of lattice blocks having substantially the same size and shape.1-4 When these blocks all assume exactly the same orientation, the crystal is perfect and asterism is absent. Cleaves and Thompson5 observed that the hardness of iron is virtually constant over a range of grain sizes. It is quite possible that the subboundary structure caused this, and that the latter is just as important as grain size itself. While the experiments reported here are not con-clusive, they do support this viewpoint. Metals can, under certain conditions, be prepared entirely free from asterism, but this preparation does not necessarily require long heating or slow cooling, as will be shown here. In this paper a distinction is made be-tween mosaic and distorted grain struc-tures but the difference is only a matter of degree. In a previous paper9 it was shown that the grains can become distorted even during heat-treatment. The block structure exists inherently, even in a perfect crystal; the size and shape of these crystallites, or lattice blocks, varies, depending upon a number of factors. Goetz, for example,7 has shown that a metal before crystallizing from the molten state must go through a paracrystalline phase with oriented groups of atoms about 10-14 to 10-15 c.c., or 10 5 cm. in size.

Jan 1, 1940

The plan recently started for the organization of a Division of Re-search and Statistics in the American Petroleum Institute will probably shortly be consummated. It is proposed to expend $500,000 annually for this research work. The organization's work, as now outlined, pro-vides for a Technical Director, who is to be in general charge of all the work. He is to be assisted by Consulting Technical Experts, who are to be distinguished specialists in the industry and are to serve without pay. In addition, there is to be an advisory committee made up of one representative from the Bureau of Standards, Bureau of Mines, Geo-logical Survey, American Institute of Mining and Metallurgical Engi-neers, Society of Automotive Engineers, National Automobile Chamber, of Commerce, American Society for Testing Materials, American Chem-ical Society, and the National Research Council. This committee is to meet regularly to discuss the problems of the petroleum industry. An engineer and chief economist are to assist the Director.- The econ-omist is to be in charge of statistics, economic phases of the industry, and publicity. It is the intention to centralize in the Institute all infor-mation that may be required by the States or Federal Government, which would be of value to members of the Institute. This includes prices of crude oil, refined products, and natural gas. The engineer of the division is to coordinate the research work to be undertaken by, the subdivisions of production, chemical engineering, utilization, and special research. Systematic study is to be made of the

Jan 12, 1919

By Norris Johnston, Carrol M. Beeson

For many years the permeability of reservoir sands has been measured by flowing air through a cleaned and dried core sample. This differs from the true reservoir permeability in one important respect: the rock particles in the reservoir are surrounded by interstitial water, not air, and their physical shape and condition of hydration are greatly dependent thereon. Permeability as defined must be measured with a single-phase fluid. Since no means exist for removing the oil and gas from a core sample by simply flowing water through it, the sample must be cleaned and then resatu-rated with water before testing. The present discussion attempts to show that after the cleaning process a considerably different permeability is determined with salt or fresh water than is obtained with air. The postulate is made that the salt-water permeability is probably closer to the true reservoir permeability than is the measurement with air. This is discussed in relation to both physically possible and economically feasible measuremerits. Data On more than 1200 core samples are given to show the nature of the effects observed, and a plea is made for others to consider water permeability measurements as a routine necessity, eventually replacing air permeability in regions where the differences are great. Introduction Permeability is defined1 as a "a measure of the capacity of a porous medium to transmit fluids, when there is no interaction between the solids and the fluid." Darcy's law of liquid flow in porous media states: kA?P QµL/A?L [I] where Q represents milliliters of liquid of viscosity p centipoises passed per second through a porous medium of permeability k darcys and cross-sectional area A sq. cm. under a pressure gradient ?P/L atmospheres per centimeter, the flow being understood to be laminar or viscous, not turbulent. This equation defines the darcy. For the case of radial flow in a uniform sand, such as usually exists in the neighborhood of a well in an oil or gas sand, Darcy's law becomes:2 Here h is the net sand thickness in feet, Pe and Pw are pressures at the drainage radius4 and well radius, and re and rw are these radii, respectively. The productivity index3 is defined as the barrels of liquid produced per day per pound per square inch mean pressure differential between ferences and well bore, and is thus: By further definition, the specific productivity index is: or in terms of practical units, and allowing for shrinkage:

Jan 1, 1945

The dictionary defines 'jargon' as "barbarous or debased language ". This description does not suffice. Quiller-Couch has said, it is "a kind of writing which, from a superficial likeness, commonly passes for prose in these days, and by lazy folk is commonly written for prose, yet actually is not prose at all ". The two main vices of jargon, he says, are "that it uses circumlocution rather than short straight speech", like the Babu who reported his mother's death by saying: "Regret to inform you, the hand that rocked the cradle has kicked the bucket ". Its other chief vice is that "it habitually chooses vague woolly abstract nouns rather than concrete ones", like the newspaper statement, "He was conveyed to his place of residence in an intoxicated condition", instead of saying, "He was carried home drunk". Jargon is "an infirmity of speech", it is not journalese, but akin to it. "Like respect- ability in Chicago, jargon stalks unchecked in our midst" and renders much technical writing ridiculous. It deals in periphrasis instead of going straight to the point, it loves the abstract rather than the concrete, it dabbles in words of sound rather than of meaning. Avoid it, despise it, if you purpose earnestly to write well. "In literature as in life he makes himself felt who not only calls a spade a spade but has the pluck to double spades and redouble." * Jargon is rampant in technical publications. Catalogues and other advertisements are conspicuous offenders, but with these the critic is not concerned, except in so far as such 'write-

Jan 1, 1931

By M. P. Tixier

In several log interpretation methods, water saturation is evaluated by use of the ratio of the readings of a short spacing resistivity device and a long spacing resistivity device plus information on the mud filtrate and connate water resistivities, which is often derivable from the SP. These methods are valid over a certain range of conditions, usually specified by moderate invasion and R.. greater than R,. Since these methods involve no explicit evaluation of the formation factor, F, the saturafiion so found may be used in the standard Archie equation to derive a computed formation factor which, as a check, may be compared with the formation factor known from other independent measurements. Discrepancies in the two values of formation factor generally indicate that the ratio method is not within its range of applicability. If the computed F is too low, the corresponding S, is too low; if the computed F is too great, the corresponding S, is too great. By means of this "porosity balance" check, and some knowledge of the probable conditions of invasion, the interpretation can often be improved. The poqosity balance check is discussed for the cases of the Induction-Electrical Log Interpretation Method, the Rocky Mountain Method, and the R.,/R, Method. For the first method, a discussion is also given for the case of shaly sands. INTRODUCTION Al though many logging tools are available to obtain a practical value of porosity, the only logging method reflecting the water saturation is electrical logging. Water saturation is commonly computed from electrical log data by means of the basic Archie formula, Where F is the formation factor, R, the resistivity of the formation water, and R, the true resistivity of the formation. One difficulty in this procedure is a possible error in the evaluation of R, from the logs— for example, in the case of very deep invasion. There is no possibility, inherent in the procedure, which would provide a check of the accuracy of R, and, hence, of the computed saturation. Other approaches have been proposed which are based essentially on the ratio of the readings made with two dzerent devices: one device, with a short radius of investigation, provides a value close to the resistivity of the invaded zone; the second device, with a long radius of investigation, gives a value close to the true resistivity of the bed. By these methods, the determination of saturation is made independently of any direct knowledge of the formation factor. Therefore, if the formation factor (or porosity) is known from other sources (core analysis, neutron log, MicroLog . . .), it becomes possible to take advantage of this additional information in order to check the value of saturation derived from these latter methods. Inasmuch as this proposed check procedure relies on a knowledge of the value of formation factor or porosity, it has been deemed appropriate to call this verification a porosity balance. The purpose of this paper is to discuss the principle and the application of the porosity balance, depending on the method of interpretation being used. Basis of the Method There are in existence three interpretation methods by means of which the water saturation can bc found without a knowledge of the formation factor (or porosity). As just stated, they are based on the fact that the ratio of the two resistivities (one measuring the resistivity close to the hole, the other measuring the resistivity far from the hole) is independent of the formation factor since it affects the two resistivity measurements in the same way. Chronologically, the resistivity ratio methods are: (1) the Rocky Mountain Method, which has been used since 1943 and was explained in a paper in 1949;' (2) the R../R, Method or Shaly Sand Method, presented in 1954, which permits the calculation of the water saturation in both clean and shaly sands2; and (3) the Induction-Electrical Log Method, presented in 1957 for the interpretation of the induction-electrical log combination." Each method requires certain definite conditions in order for the interpretation to be reliable. The porosity balance method will let us know whether these conditions are fulfilled. In clean formations we know that the fundamental Archie relation (Eq. 1) must always be verified. This relation can be rewritten:

By E. V. Potter, H. C. Lukens

INTRODUCTION IN general, during all electrowinning processes, large volumes of gas are liberated at the cathodes of the electrolytic cells. Most of this gas escapes from the electrolyte, but much of it may be absorbed or entrapped in the metal being plated. In many cases, this is not objectionable, but since it is liberated when the metal is heated, it is a potential source of trouble where the metal has to be heated or melted. Since this gas is principally hydrogen, in escaping from a melt it may cause minor explosions and scattering of the molten metal, while in other cases it has been reported to make the metal rise in the molds when cast. Therefore such metals would be more generally useful if all or most of the gas were removed before they were used. In an earlier investigation' the gas content of electrolytic manganese was determined and methods found for removing most of it without detrimentally affecting the properties of the metal. In this paper results of a similar investigation on electrolytic chromium are presented. APPARATUS The apparatus used in these investigations is essentially the same as that used in the manganese work' and is shown in Fig I. It consists of sample chamber A, vacuum or pressure gauge B, volume gauge C, vacuum pump D, hydrogen container E, auxiliary gas chamber F, and furnace G. The pressure in the system is measured by the mercury manometer B. Changes in ' gas volume are measured by volume gauge C which is essentially another mercury manometer in which . the volume of the mercury column is large and can be varied by raising or lowering the well H. In this apparatus the tube had a volume of 100 cc for a 61 cm length. Larger changes in gas volume can be accommodated by auxiliary containers attached to the system at F. The sample is heated by furnace G, the temperature of which is regulated within ± 5°C by an automatic controller. The only change in the apparatus was the sample container which was made smaller because of the chromium metal's containing more gas than the manganese metal and a smaller sample was used. METHOD The measurements were made as follows: The complete system when cold was evacuated and refilled with H2 until all the air was removed. It was then refilled with H2 to the desired pressure, as indicated on manometer B. The temperature was then raised to the desired value and as gas was either liberated from or absorbed by the sample, the height of well H was changed to alter the volume of the system so as to keep the pressure constant. In determining rates of liberation of gas, volume readings were taken at convenient time intervals depending on the rapidity with which the gas was liberated. In determining total volumes, the specimen was held at constant temperature and pressure until

Jan 1, 1948

By E. V. Potter, H. C. Lukens

In general, during all electrowinning processes, large volumes of gas are liberated at the cathodes of the electrolytic cells. Most of this gas escapes from the electrolyte, but much of it may be absorbed or entrapped in the metal being plated. In many cases, this is not objectionable, but since it is liberated when the metal is heated, it is a potential source of trouble where the metal has to be heated or melted. Since this gas is principally hydrogen, in escaping from a melt it may cause minor explosions and scattering of the molten metal, while in other cases it has been reported to make the metal rise in the molds when cast. Therefore such metals would be more generally useful if all or most of the gas were removed before they were used. In an earlier investigation1 the gas content of electrolytic manganese was determined and methods found for removing most of it without detrimentally affecting the properties of the metal. In this paper results of a similar investigation on electrolytic chromium are presented. Apparatus The apparatus used in these investigations is essentially the same as that used in the manganese work1 and is shown in Fig I. It consists of sample chamber A, vacuum or pressure gauge B, volume gauge C, vacuum pump D, hydrogen container E, auxiliary gas chamber F, and furnace G. The pressure in the system is measured by the mercury manometer B. Changes in gas volume are measured by volume gauge C which is essentially another mercury manometer in which the volume of the mercury column is large and can be varied by raising or lowering the well H. In this apparatus the tube had a volume of 100 cc for a 60 cm length. Larger changes in gas volume can be accommodated by auxiliary containers attached to the system at F. The sample is heated by furnace G, the temperature of which is regulated within 5°C by an automatic controller. The only change in the apparatus was the sample container which was made smaller because of the chromium metal's containing more gas than the manganese metal and a smaller sample was used. Method The measurements were made as follows: The complete system when cold was evacuated and refilled with H2 until all the air was removed. It was then refilled with H2 to the desired pressure, as indicated on manometer B. The temperature was then raised to the desired value and as gas was either liberated from or absorbed by the sample, the height of well H was changed to alter the volume of the system so as to keep the pressure constant. In determining rates of liberation of gas, volume readings were taken at convenient tirne intervals depending on the rapidity with which the gas was liberated. In determining total volumes, the specimen was held at constant temperature and pressure until

Jan 1, 1949

By Glenn Alvey

THE measure of value of an oil property is approximated by the length of time it takes to "pay out;" viz., the time required for it to return the original investment. This time varies in different fields. In the Appalachian and Mid-Continent fields, a good investment pays out in about four years; in California, it requires a slightly longer time; and in the Gulf field about two years. The two principal methods for establishing these values are based on acreage, as in California, and on production, as in the Appalachian field. The method of establishing values based on production1 was worked out in the Appalachian fields and approximates the value remarkably well in some fields; but it is a rule of thumb and should be used intelligently. Briefly, the method is as follows: An arbitrary number of dollars (called the barrel-day price) multiplied by the number of barrels of settled daily production of the property gives the value.. In its crudest application, the barrel-day price is determined by the "$10 to $.01" rule, which means that the barrel-day price is one thousand times the prevailing price of oil. For instance, with oil at $3.50 per bbl. the barrel-day price would be $3500 per bbl. This rule, however, is not strictly applied, for the, barrel price is varied according to whether or not the wells "hold up." But when a barrel price for a district has been fixed it is quite general to raise or lower the price with the fluctuation in the price of oil; here the" $10 to $.01" rule is used extensively. However, the prospective purchaser takes into account tangible equipment upon the property, the extent to which the drilling program has been carried out, whether or not the wells are "shot" or natural, depth of wells, spacing of wells, paraffin trouble, etc.

Jan 1, 1921

By Howard L. Hartman

6.1-1. Introduction. Of necessity, the first of the unit operations conducted during the exploitation phase in surface mining is production drilling. It precedes blasting, with which it is associated as the two unit operations employed to break or fragment consolidated material (usually rock) in place. The purpose of production drilling is to provide the cavity for placement of the explosives. So far, no alternative to blasting has been devised for fragmenting very resistant rock in situ, although some forms of excavation (ripping, bucket wheel) are suitable without prior blasting for softer rock, such as weathered shale or mudstone, decomposed sediments, etc. For the vast majority of surface mines, however, drilling and blasting are pre- requisite to excavation and essential to the production cycle. Drilling is also used in surface mining for purposes other than providing blastholes. It finds application during exploration for obtaining samples and during development for drainage, slope stability, foundation testing, etc. Only in the exploitation phase of surface mining, however, are unique or specialized drilling methods and equipment employed; and the discussion in this Section is directed primarily to that application of drilling. Drilling is the most common means of rock penetration, the operation of placing a directed hole in rock. Closely akin to drilling for exploitation purposes is the cutting or freeing of dimension stone in quarrying. This operation, usually termed channeling or sawing, also takes the form of directional penetration of rock; but instead of producing a cylindrical hole, it yields a kerf or cut. The material thus freed from the solid is both a shaped and sized product, an objective of vital importance in the dimension stone industry. In sawing, holes are sometimes drilled to insert tools, but this drilling is a minor part of the sawing operation and employs conventional methods. Cutting, as a unit operation for freeing stone in quarrying, may be considered equivalent in purpose to drilling and blasting in other forms of surface mining.

Jan 1, 1968

P. W. BRIDGMAN.-Owing to a misunderstanding, I did not see Dr. McAdam's and Dr. MacGregor's remarks on my paper on Flow and Fracture (Metals Technology, December 1944, Pp. 32-38), until after their publication. Both Dr. McAdam and Dr. MacGregor speak of my analysis for the stress distribution at the neck of a tension specimen as containing several assumptions; in particular, that the strain is uniform across the section of the neck, that there is no hoop tension at the periphery, and that the plasticity conditions of von Mises hold. As far as the mathematics goes, the situation is no different in this problem of plastic flow than in a conventional problem of elasticity. That solution is unique which satisfies the boundary conditions on the stresses, the stress equations of equilibrium, and in addition the constitutive equations connecting stress and strain in the elastic case, or a corresponding set of equations, of which the von Mises relations are a special form, in the plastic case. In the particular case of the necked tension specimen I have found that there is a solution satisfying the boundary conditions, the stress equations of equilibrium, and the von Mises plasticity conditions in which the strain is uniform across the section, and there is no hoop tension at the periphery. This is therefore the solution, and the uniformity of strain and vanishing of hoop tension at the periphery are to be described as discoveries, over which the operator has no control, rather than as assumptions. The only part of the solution that can properly be described as an assumption is the von Mises plasticity condition. With regard to this it is to be noted that the condition is needed only in a much weakened form, for the analysis uses the condition only at the neck, where the strain is approximately constant. Thus, in the extreme case referred to in a footnote of my paper (p. 37, Met. Tech. Dec. 1944) the actually measured strain across the section varies from 2.4 to 2.6. Obviously it is a much weaker assumption to postulate that the von Mises condition holds in the strain range 2.4 to 2.6 than to assume it to hold for the entire range of strain from o up to 2.6, which would be necessary if the solution applied to the entire tension specimen rather than to the immediate region of the neck only. Furthermore, it is to be commented that under the special conditions of this problem the von Mises condition becomes identical with the maximum shearing-stress criterion of plastic flow; this amounts also to a weakening of the restrictions imposed by the von Mises condition. Dr. MacGregor refers to actual experiments of his own in which the strain was found not to be uniform across the neck. It is to be emphasized, however, that these were experiments on bars of rectangular section, and that the nonuniformity established was a nonuniformity around the perimeter, not a nonuniformity from the surface toward the axis. My method of solution applies only to a circular cross section. It can be said that the solution that satisfies the boundary conditions, etc., would definitely not be expected to demand a uniform strain for noncircular sections. In discussing my results, Dr. McAdam uses a definition of "flow stress" different from mine, so that the immediate applica-

Jan 1, 1945

By Edmund Shaw

In the year just past there were produced in the United States about 170,000,000 tons of sand and gravel. Much of this was pit-run material used for gravelling roads and as railroad ballast on lines that did not carry heavy traffic. But more than half of it was marketed as washed and sized, or graded, material. The methods used for preparing sand and gravel for the market have long been used in ore dressing and, as in ore dressing, depend on differences in the specific gravity of two substances or in the size or weight of particles. But many changes in the design and operation of plants and machines have been necessary. In ore dressing, the concentrate is only a small part of the feed; in sand and gravel washing, it is much the larger part of the feed. In addition, such close work as is needed when concentrating a metallic ore is not needed when washing gravel; the ability to put through a large tonnage is more important, and sizing, which is only a preliminary process in ore dressing, is an end to be attained. Rock crushers are found in most sand and gravel plants and they are used to break up the larger pieces from the deposit (known as boulders and cobbles) which are removed by a scalping screen. The crusher discharge is usually sent back to the scalping screen, the perforations in this screen setting the maximum size of the finished product. Washing Washing is to prepare sand and gravel so that they may be used as aggregates in concrete and wall plaster and in various processes in which impurities would harm the product. At one end of the scale of washed materials may stand ordinary concrete sand, which in some states may contain as much as 3 per cent, of clay and still be used in highway concrete construction. At the other end will stand the silica sand used for making plate glass, which must be washed so clean that the impurities that can be removed by washing do not exceed a few hundredths of a per cent. The methods and machinery that would produce one of these

Jan 1, 1926

By E. H. Dix

The purpose of this paper is to introduce the subject of Stress-Corrosion Cracking at the Joint Symposium of the American Society for Testing Materials and the American Institute of Mining and Metallurgical Engineers. In this Symposium we are concerned with spontaneous cracking which results from the combined effect of high, prolonged stress, and corrosive attack. Stress-corrosion cracking may be considered a specific phase of the more general subject of the effect of high constant stresses in accelerating the rate of corrosion of metal products. The kindred subject of corrosion fatigue in which the life of a metal part under repeated stresses is reduced by corrosive attack is not a part of this Symposium. Likewise "creep," the failure of a metal part by high constantly applied stress, in the absence of a corrosive environment, is not to be included. How- ever, corrosive influences may have more effect on creep failures than is sometimes realized. The penetration by molten metals such as often occurs during tinning or soldering operations, or by mercury, frequently causes cracking when the part is stressed. Strictly speaking this is not stress-corrosion cracking. However, the committee has decided that this phenomenon should be included in the Symposium. The penetration by molten metals such as often occurs during tinning or soldering operations, or by mercury, frequently causes cracking when the part is stressed. Strictly speaking this is not stress-corrosion cracking. However, the committee has decided that this phenomenon should be included in the Symposium.

Jan 1, 1945

By Stewart Coleman, Thomas W. Moore, H. D. Wilde

It is recognized that in the early days of the petroleum industry oil was produced with practically no scientific or fundamental knowledge of the laws and principles governing its extraction from the ground. Only a few, if any, of those exploiting the oil resources made any effort to collect accurate scientific information. There was little need for it, for as is frequently the case where the supply of a natural resource appears inexhaustible and is greater than the demand, large profits were possible from merely skimming the surface with little regard to the efficiency or thoroughness with which the oil was obtained. With this policy in force, great quantities of gas were wasted and when the reservoirs ceased producing by natural means they still contained a large fraetion of the oil originally in them. The present tendency in the industry is toward conserving existing oil reserves. In order that greater percentages of the oil present in the ground may be recovered, efforts are being made to improve production methods and to rework depleted fields. If the production methods are to be improved intelligently it is essential that the fundamental laws be known and understood, consequently large amounts of money and effort are being spent in gathering data that will serve to define and interpret these laws. A great deal of attention is being focussed on the study of the motion of oil through an oil-bearing sand, the forces that cause it to move and the factors that affect its motion. It is recognized that one of the important factors is pressure, but its quantitative effect is not known. In a given field the rate of production declines with time and so does the rock pressure. Furthermore, a comparison of different fields shows, as a

Jan 1, 1930

By L. C. Morganroth

From a geological standpoint, but scant attention has been paid to fire-clay beds. Only within the last few years have they been the subject of individual investigation, prior to this time having been considered only in their relation to coal seams. While the relative importance of coal and fire clay is still immeasurably in favor of coal, yet an industry as large as that of fire clay is entitled to a measure of attention. A discussion of the Carboniferous clays is practically a discussion of the clay beds in the Appalachian basin, since more than 90 per cent. of these clays mined are from this region. The clays are confined to the northern end of the basin, or the States of Pennsylvania, Ohio, Kentucky, Maryland and West Virginia, ranking in importance about in the order named. The clay deposits of the Carboniferous period have been divided into two classes; those found in the Pottsville conglomerate series of rocks, ' and all those that are found in the formations above, for the reason that the clay beds above the Pottsville series all resemble each other in properties, composition and appearance, and all are distinctly different from the bed found in the Pottsville formation. The bed of clay found in the latter formation is unique in that flint clay is practically restricted to it. (A variety of flint clay is occasionally found in these upper deposits but this is in such small amounts as to be negligible.) Carboniferous clays occur between stratified rocks; sandstones, limestones, etc., in the same manner as coal veins. They are often accompanied by a coal vein although where the clay is of a workable thickness, the coal is generally too thin to work. The clay beds are sometimes known by the name of the coal seam at which horizon they occur. Clay beds may be from a few inches up to 20 ft. in thickness. They may consist of all soft clay, all flint or both soft and flint. The Carboniferous clay beds of Pennsylvania are the most important of any of the clay beds found in the country, and are among the oldest ones worked. We know more about this clay geologically for the reason

Jan 1, 1916

By R. D. Carter

Methods are presented for calculating the performance of multiwell gas reservoirs. These methods account for two-dimensional, unsteady-state flow of a non-ideal gas through a heterogeneous formation. The performance can be obtained for gas reservoirs with known physical properties and configuration subjected to specified development and production schedules. These methods may prove helpful in optimizing the exploitation of gas reservoirs. The numerical solrrtion procedures given for this non-linear problem are extensions of known techniques for the linear diffusion equation. Two of these procedures are based on a new difference equation given by Saul'ev. Limitations and advantages of these procedures are discussed. An example solution is presented and is used to compare the calculation methods. INTRODUCTION Li planning the operation of a multiwell gas reservoir, it is desirable to predict its performance for each alternate development and producing schedule under consideration. This paper presents three numerical procedures that can be used to calculate such gas reservoir performance using a digital computer. These methods account for two-dimensional transient flow of a non-ideal gas within the reservoir. Extension of these methods to three-dimensional flow is possible. The paper is divided into three parts. The first describes the problem for which a solution is wanted and three numerical procedures that can be used to obtain solutions. The second discusses the information necessary to set up a problem. This part will be of greatest interest to the field engineer. The third gives data and results for an example problem. PROBLEM AND SOLUTION METHODS In the following development, a gas reservoir is regarded as a sealed, porous, permeable, heterogeneous body in which a single, non-ideal gas phase is flowing. Flow is permitted in the x- and y-horizontal directions, but is considered to be negligible in the vertical or z-direction. The reservoir can be tapped by one or more wells. Methods to be described provide a basis for calculating the complete performance of the reservoir, including rates and cumulative production from the wells, and pressure distribution and decline in the reservoir. If the isothermal flow of a non-ideal gas obeying Darcy's Law occurs in two dimensions in a region R, the governing equation in this region is:

Jan 1, 1967

By Samuel Hoyt

THE hardness of annealed copper has been given in the literature and is easily obtained by any of the standard methods of hardness testing. It is not our intention to correct published values or to add to them, but to describe tests of two bars of annealed electrolytic copper in which the methods of Meyer's analysis were employed. MEYER'S ANALYSIS OF BALL INDENTATION TEST The ball indentation test is probably the most valuable hardness test we now have but, as it is carried out in the Brinell or Rockwell test, the result may be seriously in error without the operator suspecting such to be the case. This condition results from the isolated and uncontrolled nature of the measurement. The accuracy depends on the accuracy of the equipment and the care and skill used in the operations; there is nothing in the impression diameter, which is all that is measured, to indicate the presence of error. Meyer's analysis supplies a control of the measurements that goes far toward eliminating unsuspected errors. The principles of this work maybe obtained from elsewhere.1 As this subject has not received the attention of this Institute, it may be well to summarize the more important points as follows.

Jan 2, 1926

By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953

By Walter White

THE measurement of the reading of a thermoelement is the measurement of an electromotive force extraordinarily small compared to those generally used in commercial work. Of the various possible methods of measuring such a quantity, the most advantageous is always a delicate galvanometer. Since a galvanometer measures current, it is necessary to adopt some scheme by which its current reading shall indicate electromotive force. There are two general methods of doing this. One is to use the delicate galvanometer as a "direct reader," that is, to let the electromotive force of the thermoelement furnish the power and produce the current measured. If the resistance is constant the reading will, after a suitable calibration, give the electromotive force of the thermoelement which, by means of a table or of a suitable scale in the galvanometer itself, will FIG. 1.-SIMPLIFIED POTENTIOMETER. POTENTIAL DROP ACROSS THE PART PIN or CIRCUIT OF BULL CELL BALANCES THAT OF THERMOELEMENT TC WHEN GALVANOMETER G READS ZERO. give the temperature. The other method, that of the potentiometer, is to balance the electromotive force of the thermoelement by means of another electromotive force, using the galvanometer to tell when the balance is made. The usual way of getting this other electromotive force is to have a battery, the "bull" cell, send a current through a series of resistances, which 'may in a special case be the resistance of a single wire. The fall of potential along this circuit will then, by Ohm's Law, be proportional to the resistance; the potential difference between any two points, proportional to the resistance between the two points. This is represented in Fig. 1, where M and N are the two points in the circuit AZ of the battery. If M or N, or both, is movable so that the resistance

Jan 9, 1919