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By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By F. R. Brotzen, D. L. Davidson

ALTHOUGH much effort has been devoted to the problem, the nature of plastic flow in bcc metals is still not fully understood. Some of the difficulties encountered stem from the scarcity of information on orientation effects and the uncertainty as to the glide system in these metals. In an attempt to provide some of this information, the present investigation was carried out, using zone-refined molybdenum single crystals deformed in tension and in direct shear. Considerable evidence exists to indicate that the primary slip system for molybdenum is (110) <111>.1,2 Figs. 1 and 2 indicate that this is, indeed, the case for direct shear at room temperature (see Ref. 3 for a description of the shear-testing equipment and procedure). Moreover, from Fig. 2, the shear stress on the (123) is lower than that on the (112). This would be the case if, as has been suggested,4,5 slip on these two planes is in reality com-

Jan 1, 1965

THE CHAIRMAN (A. F. LUCAS, Washington, D. C.).-The activities of the Petroleum and Gas Committee for the half year have brought gratifying results, as exemplified by 14 technical papers, brim full of novel and attractive issues in which we are all keenly interested. I beg to extend my hearty thanks to all members and authors who have responded to my appeal, and to all those who have endeavored to meet the growing demand which has resulted in the augmented production of this commodity which is so essential for the Nation&apos;s welfare, comfort and safety. As you well know, within the last few years, petroleum and its products have been used for numerous and novel purposes, so that we have become accustomed to their use in thousands of activities, and pleasures as well, but we should also note that we have been wasting and misusing these wonderful products, apparently believing that their sources are inexhaustible.

Jan 1, 1918

By B. L. Averbach, Morris Cohen, S. A. Kulin

The martensitic transformation can be initiated by elastic stresses at temperatures above M. in a steel containing 20 pct Ni and 0.5 pct C. Shear strains and normal tensile strains acting on a potential habit plane promote the transformation but compressive strains oppose it. THE strain sensitivity of the martensitic transformation has long been recognized. It is now well known that martensite formation can be induced by plastic deformation at temperatures below, and not too far above, the M, point.&apos; However, the exact role of elastic vs. plastic strains and of the concomitant stresses has proved to be a very elusive matter. Many investigators2-&apos; of the steel hardening reaction have made use of the stresses resulting from volume changes to account for such observations as the existence of retained austenite and its variation across the section of a bar, the change in the amount of retained austenite with quenching rate, and the self-stopping nature of the transformation when the cooling is stopped. The effect of applied strain as an independent variable has been studied in 70 pct Fe-30 pct Ni alloys by Scheil7 and McReynolds.8 Some data are also available for lithium and Li-Mg alloys,9 Cu-Zn,10 Cu-Sn and Cu-A1 alloys," and aus-tenitic stainless steels."-" It has been found that martensite formation can be induced isothermally, even at temperatures above M,, by mechanical deformation of the parent phase. The competitive nature of plastic yielding by slip and by the martensitic reaction has been depicted by Scheil.7 Basically, Scheil postulated that: 1—at temperatures not too far above M, (where austenite is less stable than martensite), a critical resolved shear stress (within the elastic range) is required to promote the transformation to martensite; 2—at and below M,, the austenite lattice becomes mechanically, as well as thermodynamically, unstable and shears over spontaneously into martensite without the application of external stress; and 3—at temperatures sufficiently far above M8, the critical resolved shear stress for martensite formation increases to a level above that required for slip, and plastic flow then supersedes the transformation when external stress is applied. Scheil&apos;s concepts were tested by McReyno1ds8 ho found no change in the elastic moduli (measured both statically and dynamically) of 71 pct Fe-29 pct Ni alloys in the vicinity of the M, temperature. Since the moduli did not approach zero or become negative on cooling to M,, it was concluded that the austenite lattice does not become mechanically unstable at M2, as postulated by Scheil. McReynolds also reported that M, is not raised by elastic stresses. Accordingly, plastic deformation was considered to stimulate the transformation by generating martensite nuclei in the distorted regions of the parent phase. The above issues with regard to the role of applied stress require clarification, if a basic understanding of the martensitic transformation is to be obtained. For example, in the reaction-path theory,&apos;"," it is postulated that strain embryos exist in the austenite that provide part of the activation energy for the nucleation process. These embryos are visualized to be regions of localized strain in which the atoms in the austenite lattice are displaced part way along the path to their ultimate positions in the martensite. Consequently, it would

Jan 1, 1953

By W. J. Joslin

The frontal-advance equation can determine how the fluid withdrawal rate and subsurface operating pressure influence oil recovery from pressure-maintained reservoirs having characteristics favorable for efficient vertical segregation. For effective vertical segregation in formations having low dip angles, the requirements are: thick, massive sands, low viscosity oil and high vertical permeability with few discontinuous shale members. This approach has been successfully applied to the LL-370, which is a massive Eocene sandstone reservoir containing crude with an average gravity of 26" APT, a dip of only 3" and vertical permeability of ½ darcy. The average gas cap saturation was calculated for various rates of vertical gas-oil contact movement corresponding to a wide range of reservoir producing rates. This method also evaluated the effect of different pressure maintenance levels on oil recovery. Applicability of this procedure for calculating the present oil saturation in the LL-370 gas cap has been substantiated from field performance, where the oil saturation was computed by comparing oil recovery with the gas cap volume vacated. INTRODUCTION During the natural depletion history of the LL-370 reservoir, located in Lake Maracaibo, Venezuela, excellent vertical segregation resulted in the formation of a thin gas zone over a substantial portion of the oil-productive area. Subsequently, gas injection forced this thin gas-saturated zone slowly downward, reducing the oil saturation in the gas cap to a low value. The oil recovery has been raised considerably above earlier predictions where vertical segregation effects were under-estimated. In order to determine the maximum efficient producing rate and optimum operating pressure for this reservoir, a vertical gas frontal-advance analysis has been made through application of the fractional flow equation. LL-370 RESERVOIR CHARACTERISTICS The reservoir consists of a truncated monocline of massive. highly-permeable Eocene sandstone, called the B-b formation, covering an area of more than 13,500 acres. The original oil in place was 2.17 billion STB. Internal non-sealing faults subdivide the structure into four blocks called the B-6-x.6, 10, 11 and 13, which are effectively bounded by major faulting on the flanks, an unconformity updip to the west, and an immobile aquifer to the southeast. The producing formation occurs at an average depth of 5,250 ft subsea and has a closure of more than 1,500 ft. A typical producing section has a net oil sand thickness of 170 ft. Scattered throughout the section are a few randomly-positioned shale lenses which increase in thickness and areal extent downdip. The reservoir rock and fluid properties vary with depth. The permeability and produced oil gravity are 1600 md and 28" API at the top, compared to 300 md and 18° API at the water-oil contact. The productivity of updip wells is, therefore, much higher than the reservoir average. The reservoir oil was originally saturated at the crest, grading to a slight degree of undersaturation at the water-oil contact. There was no original gas cap; and material balance and the field performance indicate no water influx. Except for the northern B-6-x.6 block, the fluid and rock properties have already been published.&apos; Average LL-370 reservoir properties are shown in Table 1. RESERVOIR PERFORMANCE UNDER NATURAL DEPLETION Fig. 1 shows production performance from 1939 to date. Early development was gradual, with 30 wells pro-

Jan 1, 1965

G. F. LOUGhlin,* Washington, D. C.—With reference to Mr. Bain&apos;s paper: The scarcity of adequate geologic data on building stone reflects, among other things, a lack of interest on the part of geologists. It has been one of my duties to attend to matters relating to building stone and other structural materials that have come to the U. S. Geological Survey, but for several years my principal administrative and other duties in the Section of Metalliferous Deposits have prevented me from giving structural materials the attention that they deserve. I have felt that investigations relating to structural materials should be assigned to someone else, but thus far nobody with a sufficient interest in the subject has come forward; further, the specific calls for these investigations have been so few and far between that it has not seemed practical to draft any one for the job. The general situation is such that steady and substantial progress in the application of geology to the utilization of structural materials is not likely to be made unless someone with keen interest in the subject takes the initiative. If the start is once made, I know from experience that cooperation from the more progressive members of the quarry and building industries will be readily forthcoming. Mr. Sales&apos; suggestions are all constructive and most welcome. A thorough, detailed discussion of them might be as long as his manuscript, but could largely be summarized with the one word "amen" qualified by the alibi that a chronic shortage of funds and therefore of personnel has prevented us from carrying out some of his suggestions already. A few of them might call for an Act of Congress before we could undertake them, and one or two, such as the preservation of mine maps, with which I heartily agree, would call for much additional space as well as clerical and supervising help. Several items in Mr. Sales&apos; paper—for example, the question of balance between the scientific and more directly practical studies and the surveys or resurveys of the larger and smaller mining districts—have been covered in my contribution to the symposium. The suggestion of frequent reviews of progress in the study of ore deposits is excellent and can be followed without serious diversion from projects already on the Survey&apos;s program. Brief reviews by Survey men have been published in periodicals, and the contributions by several of them to the Lindgren Volume1 may also be cited as serving this purpose to some degree. The practice of publishing short papers by Survey men in outside journals rather than in Government reports is largely the result of experience and expedience. Our printing funds are limited, and considerable time must elapse between the transmittal of a paper and its publication. Time is saved therefore by sending papers to outside journals, and the editors of those journals are usually glad to receive them. Members of the Survey would doubtless prefer to have the products and byproducts of their official work appear in official Survey publications if conditions were more favorable. If we were left entirely to ourselves the balance between the more scientific and the more directly practical studies would be somewhat better than it is, but the

Jan 1, 1935

G. F. LOUGhlin,* Washington, D. C.—With reference to Mr. Bain&apos;s paper: The scarcity of adequate geologic data on building stone reflects, among other things, a lack of interest on the part of geologists. It has been one of my duties to attend to matters relating to building stone and other structural materials that have come to the U. S. Geological Survey, but for several years my principal administrative and other duties in the Section of Metalliferous Deposits have prevented me from giving structural materials the attention that they deserve. I have felt that investigations relating to structural materials should be assigned to someone else, but thus far nobody with a sufficient interest in the subject has come forward; further, the specific calls for these investigations have been so few and far between that it has not seemed practical to draft any one for the job. The general situation is such that steady and substantial progress in the application of geology to the utilization of structural materials is not likely to be made unless someone with keen interest in the subject takes the initiative. If the start is once made, I know from experience that cooperation from the more progressive members of the quarry and building industries will be readily forthcoming. Mr. Sales&apos; suggestions are all constructive and most welcome. A thorough, detailed discussion of them might be as long as his manuscript, but could largely be summarized with the one word "amen" qualified by the alibi that a chronic shortage of funds and therefore of personnel has prevented us from carrying out some of his suggestions already. A few of them might call for an Act of Congress before we could undertake them, and one or two, such as the preservation of mine maps, with which I heartily agree, would call for much additional space as well as clerical and supervising help. Several items in Mr. Sales&apos; paper—for example, the question of balance between the scientific and more directly practical studies and the surveys or resurveys of the larger and smaller mining districts—have been covered in my contribution to the symposium. The suggestion of frequent reviews of progress in the study of ore deposits is excellent and can be followed without serious diversion from projects already on the Survey&apos;s program. Brief reviews by Survey men have been published in periodicals, and the contributions by several of them to the Lindgren Volume1 may also be cited as serving this purpose to some degree. The practice of publishing short papers by Survey men in outside journals rather than in Government reports is largely the result of experience and expedience. Our printing funds are limited, and considerable time must elapse between the transmittal of a paper and its publication. Time is saved therefore by sending papers to outside journals, and the editors of those journals are usually glad to receive them. Members of the Survey would doubtless prefer to have the products and byproducts of their official work appear in official Survey publications if conditions were more favorable. If we were left entirely to ourselves the balance between the more scientific and the more directly practical studies would be somewhat better than it is, but the

Jan 1, 1935

By Leo L. Van Sambeek

An understanding of the creep and yield behavior of salt is required for the rock mechanics design aspects of solution mining. Most previous studies of salt behavior have been performed on small specimens of salt under homogeneous stress conditions; i.e., uniaxial and triaxial tests on specimens <0.002 m3. The corejacking test is a larger scale test (-0.75 m3) with inhomogeneous stress conditions that provides data on the structural response of salt. Interpretation of the responses from eight such corejacking tests provides verification of the requisite constitutive parameters required to predict salt behavior at different levels of stress and temperature. These constitutive parameters are not those studied in the usual laboratory test. Corejacking test results show almost inseparable elastic and plastic closures simultaneous with the corejack pressurization. Very rapid closure (on a relative basis) continues for a period of time after the pressurization. This rapid closure is shown to be both continuing yield deformation and creep deformation. After the period of rapid closure, the closure rate approaches a constant value. Numerical modeling of the corejack tests using a creep law containing both transient and steady-state creep functions does not provide results that agree with the responses measured in the corejack tests. Using an experimental design technique plus additional numerical modeling that includes yielding of the salt, results in identification of the significant parameters which allow agreement. The significance of the results from the study is demonstrated by comparing the postulated stability and creep response of a solution-mined cavern using the previous understanding of salt behavior and the understanding developed from this study.

Jan 1, 1985

By R. F. Shurtz

This note calls attention to a contradiction in current eatistical theory and to corresponding difficulties in practice. These are significant concern in evaluating almost all ore deposits. The theoretical contradiction is that the commonly used spherical model for the semivariogram is not consistent with the usual definition of a "regionalized variable" as a mathematical function, the direct study of which "is excluded because its spatial variability is usually extremely erratic, with all kinds of discontinuities. . ." (Journel and Huijbregts, 1978). Specifically, this means a grade function that is too "rough" for interpolation to be useful. The practical difficulty is that the spherical semivariogram interprets the data upon which it is based in a manner that is, more often than not, demonstrably inconsistent with reality. This is attributable to the widely disregarded interaction between the sample pattern and the grade function. Each sample pattern "blurs" the grade function in its own particular way. It is as though the grade structure of the deposit were seen through a lens of poor resolution or reflected in a warped mirror, such as those found in amusement parks. The fitted spherical model embeds this sometimes dangerously blurred and distorted image in the Krige regression. A full analysis of these inconsistencies is to be presented later but, in the meantime, it seems urgent to communicate their effects so that those engaged in estimating ore reserves may be on guard. The spherical semivariogram has a sill and can be replaced by the corresponding covariogram. The equation of the spherical covariogram in normalized form, that is, variance and range both equal to one, is represented as: [ ]

Jan 1, 1984

By D. R. Mitchell

This paper discusses some of the fundamental physical and chemical characteristics of coal in Illinois that affect its preparation for the market. At the present time preparation consists almost entirely of sizing and hand-picking. The washing of coal has almost entirely disappeared from the state. This is a rather startling fact when one considers that in the year 1908 Illinois outranked all other states in the quantity of coal washed and a few years later, in 1912, 85 washing plants were reported. Two reasons are apparent for this change. One, which is probably the most important, is that immense areas of comparatively clean coal were opened; the other is that many of the early washing plants were inefficient, so that washed coal was looked upon with disfavor in many trade centers. Objectives of Operators Some of the outstanding preparation aims being given due consideration by operating men are: 1. The greatest possible production of lump and domestic sizes which bring in the market at least $1 per ton more than the fine sizes or screenings. 2. Efficient screen sizing with as little breakage as is consistent with economical operation. 3. The removal of extraneous ash and sulfur. 4. Utilization of low-priced screenings. 5. Suppression of dust in domestic coal shipments. Preparation Underground To get the greatest possible production of the larger sizes, preparation must start at the face. Improvements in blasting and loading have increased the sizes larger than 2 in. by as much as 20 per cent. at some mines. Tiffany and McKitterickl report the results of an investigation they made at a mine in southern Illinois in which, by a carefully controlled

Jan 1, 1931

By Charles Albert Ashburner

Natural gas has been known to exist for many years in the St. Lawrence Valley, between Quebec and Montreal, and more partirularly in the vicinity of Louisville and Three Rivers, 74 and 94 miles respectively northeast of Montreal, and 98 and 78 miles respectively southwest of Quebec; the distance from Montreal to Quebec along the St. Lawreuce River being about 175 miles. It was not until 1880 that any practical explorations were begun with the hope of finding gas in sufficient quantities for commercial uses. In this year Messrs. Piret and Genest, of Three Rivers, sank a well near St. Maurice to a depth of 50 feet, where solid rock was encountered. A similar well was drilled through the glacial and allavial drift, in the same district, in 1883, by the Messrs. Renaud Freres and Dubois, to a depth of 70 feet before solid rock was encountered. In this latter well a strong flow of gas was obtained. The gas was an outflow from a very limited reservoir in the porous glacial gravel, which had been filled from the gas resulting from the decomposition of vegetable remains, which had been buried in the gravel at the time of its deposition. Subsequently, other wells were sunk in the same way, with the hope of getting gas in commercial quantities from similar reservoirs. Commercial Gas.—By gas in commercial quantities I mean gas in such quantity that, if utilized with proper care and economy, it would generate steam at a cost below the cost at which the same duty could be obtained from the use of coal or wood at current prices, and that

Jan 1, 1890

By Albert H. Chester

During the summer of 1875 I visited some of the iron mines of Houghton County, Mich., and was quite interested to observe the progress made there within a few years. Working in open pits is gradually giving place to underground work in most of the mines where this system is practicable. In some cases, as in the Lake Superior Mine, the body of ore is so irregular, and the deposit so liable at any time to be pinched out, or nearly so, that it. has been found impractical, if not impossible, to lay out any plan for systematic underground work. But in many other mines the deposit is so regular in character, that the work can be laid out in shafts at regular intervals, and a series of 60 feet levels. The Michigammi Mine, opened in 1872, and first worked in 1873, is arranged on this plan, though some quarrying is still done. But the men are being put at overhead stoping as fast as it can be got ready for them, and before long it will all be worked in this way. The New York Mine is undergoing a similar change to the pillar system, and several others have either been changed, or it is about to be done. My principal object in visiting this region was to obtain samples from some of the important mines, so as to be able to answer the question: "What is the average percentage of iron in the Lake Superior ores?" Most iron furnaces work on mixtures of ore, so that it is impossible to tell, from their records, just the percentage in each one.

By C. S. Yust, Lida K. Barrett

The change in shape of the void in a sirzterir~g copper mass has been investigated as a juntction of&apos; density. A serial sectioning&apos; technique was used to eoaltrate the irregular shape of the void at two levels qf density. A measure of the void size and configuration, the proximity number, is defined and used to describe the progress of void removal. The process of. void removal deduced front the observations of this study contrasts with current sintering models in that it takes into account the irregularity of structure of a sintering mass and demonstrates that isolated Porosity does not occur first as spherical pores, but as large, definitely nonspherical sections of the void void volume. The process of sintering, about which there is much practical and theoretical knowledge, has evaded a direct and thorough analysis despite the intensity with which it has been studied for 60 years or so. This is due, of course, to the complex structure of a sintering mass and the inability to observe directly the development of a fully dense solid from the initial particulate arrangement. Extensive theoretical analyses have been based on the adoption of one or another of several model systems, that is, by visualization and analysis of some sort of regular assembly or arrangement of geometric "particles" approximating the conditions of a sintering mass. It seems appropriate at this time to try to examine experimentally in some detail the extent to which a sintering mass of irregular particles dlffers from these models. Many models deal with neck growth and the initial stage of sintering and follow the direction established by ~ucz~nski&apos; in 1949 for the sintering of spheres to flat plates. Recently Johnson and cutler2 have adapted these models to sintering of powder masses. coble3 has presented a mathematical model for sintering that applies to the middle and final stages of the process. These papers, without exception, assume a regular geometry, generally spheres in contact in a regular array. Rhines~ and coworkers, however, are studying the sintering process by applying a model based on the topological concept of genus which permits them to consider an irregular structure. whites has described the various models with the exception of that of Rhines et al., and the assumptions on which they are based and their shortcomings. The present paper examines the geometric changes that occur in the powder mass during sintering by examination of the void. The method is to analyze a series of partially sintered structures and to propose from this analysis the sequence of events which occur in the removal of the void space as a sintering mass progresses from a collection of individual particles to a solid body. The irregular nature of the stacking of particles and of the particles themselves will be taken into account. The significant points derived from this study are: first, accurate reconstructions of the irregular void shapes are presented; second, it is clearly established that closed porosity occurs first as widespread volumes of interconnected porosity, definitely nonspherical in shape; and third, a new factor, the proximity number, is defined, which serves in this paper as a tool for describing the void shape changes observed, and which will be used in a later paper as part of the basis of a mathematical model for sintering. While the specific material studied is copper, the observations are thought to be relatively general as indicated by comparison of the results with partially sintered structures in other materials presented in the literature, both metallic and nonmetallic. EXPERIMENTAL PROCEDURE Four series of specimens representing progressive stages of the sintering process were prepared by sintering high-purity copper powder for various time periods. A relatively large particle size was used so that the void-solid interface could be readily distinguished at low magnification. In three series of specimens a loose stacking of particles was obtained by pouring powder into an alumina mold and lightly tapping the mold. The green density of such compacts was approximately 40 pct of theoretical density. Two of these three series utilized irregularly shaped particles in the size range -230 +325 mesh, one series sintered in vacuum and one in hydrogen at 950°C. The third series of loosely stacked particles consisted of spherical particles in the size range -270 +325 mesh, sintered in hydrogen at 950°C. A fourth series was prepared from compacted irregular particles sintered in hydrogen at 950°C. The specimens for this series were formed by lightly pressing the irregularly shaped particles in a steel die; the green density of the pressed pellets was approximately 60 pct. The irregularly shaped particles used in this study are shown in Fig. 1. The density of these particles, measured by a toluene picnometer technique, is 98.2 pct of theoretical density. Each particle is highly convoluted, and in some instances appears in cross section to contain internal porosity. The density measurement, however, indicates that completely enclosed porosity is very small so that the individual particles have a highly irregular surface but are essentially fully dense copper. Therefore, most of the void space that appears in two dimensions to be isolated within the particle is actually at the particle surface and connected to the external void in the dimension not included in the plane of the cross section. The void space that appears as void surrounded by the par -ticle or within folds in the particle w~ll be r~fc\r?

Jan 1, 1968

By L. F. Stutzman, George Thodos

The friction factor plot presented by Cornell and Katz4 and developed for the flow of fluids through consolidated formations has been directly adapted for handling fluid flow problems involvitrg both linear and radial flow. In this adaptation the friction factor plot is used directly for the solution of problems and thereby eliminates the use of conventional equations which are specific to laminar (Darcy) or turbutent flow. This upproach overcomes the disadvantages inherent in the use of these conventional equations. It eliminates the necessity of checking the type of flow occurring in order to identify the specific equation which must be used. In radial flow problems, because of the increasing mass velocity of the fluids as they approach the wellbore. the type of flow may no longer remain laminar. Consequently, it is necessary to use more than one equation in a problem and to identify the range over which each equation should be applied. Finally, in practice it has been found that much of the flow of gases through consolidated media occurs in a range that is neither laminar or turbulent. For this transitional region, no convenient equations are available. The method and presented friction factor plot are appficahle to both liquids and gases. INTRODUCTION The flow of fluids through unconsolidated media in packed beds has been treated extensively by a number of investigatorsl,2,3,5,7,8 Most of these studies present friction factors as a function of modified Reynolds number similar to those developed for conventional fluid flow through pipes. These friction factor plots are presented for linear flow; however, Elenbaas and Katz have extended these concepts to apply to radial flow. All of these studies on unconsolidated materials require a knowledge of packing properties such as sphericity. porosity, and particle diameter. Sphericity and particle diameter cannot be defined at the present time for consolidated formations such as those commonly found in gas or oil reservoirs. As a result many investigators have not utilized friction factors and Reynolds number in the study of fluid flow through consolidated media. However, Cornell and Katz4 present a plot (Fig. 1) for the flow of fluids through consolidated porous media, in which the friction factor defined as: The turbulence coefficient, P, is related to the formation permeability, K, as presented in Fig. 2. Three different types of flow may exist in the flow ot

Jan 1, 1957

By J. J. Gilman, T. A. Read

S URFACE effects in the cleavage of brittle crystals have been known for some oftime,1, 2 but our knowledge of surface effects in the plastic deformation of crystals is of relatively recent origin. In 1936, Roscoe9 eported his observations comparing oxidized and clean cadmium crystals. He found that cadmium crystals 1/2 mm in diam when covered by an oxide film less than 1200 atoms thick had critical shear stresses about twice those for clean crystals. This effect is anomalous in that it cannot be caused by the inherent shear strength of a normal oxide film. Either an interaction between the film and the crystal causes the large increase in strength, or the oxide film has an abnormal mechanical strength. Several authors since Roscoe have studied surface effects in crystal plasticity. A complete review of the literature will not be presented, but most of the results may be summarized as follows: 1—The critical shear stress for slip is increased markedly by very thin oxide films on zinc4 and cadmium crystals;" &apos; also, the entire stress-strain curve is raised by an oxide coating;3,4 both effects increase with decreasing specimen radius. 2—Surface active substances such as oleic acid destroy the hardening effect of oxide films.4, 6-8 The time required for the reduction of the hardening effect to begin increases with the viscosity of the solvent4~ 3—There has been dispute in recent years about the effects of surface active substances themselves on plastic deformation. Rehbinder, Lichtmann, and Maslenikov9 state that surface active substances reduce the strength of metal monocrystals markedly and increase the number of slip lines per unit length at a given strain. The effect varies with orientation for tin crystals being smallest for x, = 0, largest for x, = 45", and intermediate as x, + 90°.10 Several workers claim to have disproved the results of Rehbinder&apos;)"." but Rehbinder and Lichtmann9 have defended themselves and Masing with his collaborators" has confirmed some of Rehbinder&apos;s results. 4—Immersion of metal specimens in electrolytes such as sodium chloride reduces their strength12,13&apos; and subsequent cathodic polarization increases the strength reduction. For noble metals, the strength reduction occurs for both anodic and cathodic polarization," increasing with increasing polarizing voltage. 5—Electroplated copper coatings effect the creep rates of zinc monocrystals. Poly crystals are not affected." 6—Immersion in dilute acid destroys the hardening effect of an hydroxide film. When an acid solution is applied to a steadily creeping crystal, the creep rate jumps to a very high value and then drops gradually to a steady value which is higher than the initial steady rate.*&apos; " If the hydroxide film to be removed is very thin (about 100A thick), the creep rate does not change measurably, but a small rapid strain-increment is observed when dilute acid is applied." 7—Crystal plasticity depends on specimen dimensions. This was observed by Lichtmann and Ven-stroml" for monocrystalline tin and by Andrade and Kennedy" for polycrystalline lead. 8—Immerson of copper crystals in mercury has no effect on their stress-strain curves.&apos;" 9—Bombardment of creeping cadmium crystals with a particles which penetrate the surface to only 0.005 mm may increase their creep rates as much as five times.&apos;&apos;&apos; The experiments which will be described in this paper pertain to: (a) the effect of a crystal&apos;s shape on its plastic deformation, and (b) the effect of metallic surface films on plastic deformation. For the work pertaining to (a), crystals of zinc, tin, and lead were grown which had various shapes. These were tested in simple tension. Macroscopic rotations about the tension axis which are unpredicted by the classical theory of slip were observed, and serrated edges were observed in tin crystals. For the work pertaining to (b), the effects of evaporated and electrodeposited films of copper, nickel, gold, and zinc on the mechanical properties of zinc, tin, and lead crystals were determined. The films influenced both slip and twinning of the crystals in creep and tensile tests. Experimental Details Chemically pure zinc, tin, and lead were used in this investigation. The zinc was 99.999t pct pure;

Jan 1, 1953

By L. C. Campbell

The purpose of any accident-prevention program is the curtailment or entire elimination of injuries and fatalities. It is a job that is never finished in the coal-mining industry. Day by day, on shift and off shift, men are exposed to injury and death in varying numbers. Seldom is it possible to lock up at the end of the shift and leave a mine plant in the care of a sleepy watchman, as can be done at most manufacturing plants. Even on off shifts there are maintenance and supply crews, coal cutters, pumpers and ventilation men exposed to danger. The prevention program of The Koppers Coal Co. recognizes two primary facts: First, no program can be successful without the full support of the management and complete knowledge of the job at hand on the part of every supervisor. Second, and equally important, is the full cooperation of every employee in observing the safety rules and practices set up by the management. Conscious day-to-day concern for his safety by the individual worker is the longest stride toward a good safety experience. How to accomplish the education of the individual worker and supervisor for safety is the problem of The Koppers Coal Co., as it is the problem of all coal companies. Safety Rules A simply stated set of Safety Rules and Practices for the government of employees is the starting point with The Koppers Coal Co. There are but 13 of these rules, which are short, easily understood and followed by a campaign of education and inspection. Each employee receives a set of these Safety Rules and Practices and signs a receipt for them, which is bound in at the back of the booklet, and this receipt becomes a part of his employment record. These rules and practices are as follows: Introduction The following rules have been compiled for the safety of employees and are established according to rules number one and number two of the official bulletin

Jan 1, 1940

By L. C. Campbell

The purpose of any accident-prevention program is the curtailment or entire elimination of injuries and fatalities. It is a job that is never finished in the coal-mining industry. Day by day, on shift and off shift, men are exposed to injury and death in varying numbers. Seldom is it possible to lock up at the end of the shift and leave a mine plant in the care of a sleepy watchman, as can be done at most manufacturing plants. Even on off shifts there are maintenance and supply crews, coal cutters, pumpers and ventilation men exposed to danger. The prevention program of The Koppers Coal Co. recognizes two primary facts: First, no program can be successful without the full support of the management and complete knowledge of the job at hand on the part of every supervisor. Second, and equally important, is the full cooperation of every employee in observing the safety rules and practices set up by the management. Conscious day-to-day concern for his safety by the individual worker is the longest stride toward a good safety experience. How to accomplish the education of the individual worker and supervisor for safety is the problem of The Koppers Coal Co., as it is the problem of all coal companies. Safety Rules A simply stated set of Safety Rules and Practices for the government of employees is the starting point with The Koppers Coal Co. There are but 13 of these rules, which are short, easily understood and followed by a campaign of education and inspection. Each employee receives a set of these Safety Rules and Practices and signs a receipt for them, which is bound in at the back of the booklet, and this receipt becomes a part of his employment record. These rules and practices are as follows: Introduction The following rules have been compiled for the safety of employees and are established according to rules number one and number two of the official bulletin

Jan 1, 1940

By E. D. Cockrell, E. P. Hayes

The figures herein presented show that during the year 1938 drilling in the Texas Gulf Coast continued at a slightly lower rate than during 1937. In 1938 there were 21 new oil fields added to the Texas Gulf Coast; also numerous extensions and new sands in old fields. This report for 1938 cannot be compared with the report for 1937 in Volume 127 of the Transactions, because the area covered by this report is less than that covered last year. The cross-hatched area on Fig. 1 shows the limits of this report. Of the new fields, Cordele, in Jackson County, Eureka Heights and Fairbanks, in Harris County, Francitas, in Jackson County, LaRosa, in Refugio County, and League City, in Galveston County, have the greatest promise of prolific production. The 1938 production for the Gulf Coast area was 92,530,467 bbl. as compared to 94,019,355 bbl. for the same area in 1937. This shows a decrease of 1,488,888 bbl. during 1938, regardless of the increase due to the 21 new oil fields. This decrease was caused mainly by the Saturday and Sunday shutdowns (68 days during 1938) and by cut in allowables. The 68 shut-down days amount to approximately 18.6 per cent of the 365 days possible for production. The decrease in the 1938 production amounted to approximately 1.58 per cent. Therefore there was actually a potential increase in the year&apos;s production. During the past year, 1637 wells were completed as oil wells, 68 as gas wells and approximately 461 dry holes, as compared to 1672 oil wells, 83 gas wells and 448 dry holes in 1937 on the Texas Gulf Coast. Total wells drilled were 2166 in 1938 and 2203 in 1937. Condensate. sands in old fields and new fields are continuing to increase in importance from the standpoint of retrograde condensation and pressure maintenance. The following fields had major extensions during the year 1938 from the standpoint of increased areas of old sands and new deeper sands:

Jan 1, 1939

By E. D. Cockrell, E. P. Hayes

The figures herein presented show that during the year 1938 drilling in the Texas Gulf Coast continued at a slightly lower rate than during 1937. In 1938 there were 21 new oil fields added to the Texas Gulf Coast; also numerous extensions and new sands in old fields. This report for 1938 cannot be compared with the report for 1937 in Volume 127 of the Transactions, because the area covered by this report is less than that covered last year. The cross-hatched area on Fig. 1 shows the limits of this report. Of the new fields, Cordele, in Jackson County, Eureka Heights and Fairbanks, in Harris County, Francitas, in Jackson County, LaRosa, in Refugio County, and League City, in Galveston County, have the greatest promise of prolific production. The 1938 production for the Gulf Coast area was 92,530,467 bbl. as compared to 94,019,355 bbl. for the same area in 1937. This shows a decrease of 1,488,888 bbl. during 1938, regardless of the increase due to the 21 new oil fields. This decrease was caused mainly by the Saturday and Sunday shutdowns (68 days during 1938) and by cut in allowables. The 68 shut-down days amount to approximately 18.6 per cent of the 365 days possible for production. The decrease in the 1938 production amounted to approximately 1.58 per cent. Therefore there was actually a potential increase in the year&apos;s production. During the past year, 1637 wells were completed as oil wells, 68 as gas wells and approximately 461 dry holes, as compared to 1672 oil wells, 83 gas wells and 448 dry holes in 1937 on the Texas Gulf Coast. Total wells drilled were 2166 in 1938 and 2203 in 1937. Condensate. sands in old fields and new fields are continuing to increase in importance from the standpoint of retrograde condensation and pressure maintenance. The following fields had major extensions during the year 1938 from the standpoint of increased areas of old sands and new deeper sands:

Jan 1, 1939

By Paul M. Tyler, Oliver Bowles

The extensive employment of nonmetallic minerals antedates the use of metals, but only within the last two decades has the production of nonmetals begun actually to keep pace with the complicated activities which characterize the so-called Machine Age. The economic changes ushered in by the Industrial Revolution were reflected first in an increased demand for metals and for fuels. In the modern sense, therefore, the nonmetallic mineral industries are new and afford new opportunities for engineer and economist alike. A certain amount of caution is indicated, therefore, before attempting to apply ready-made formulas to the problems of these industries. Economics is not an exact science. In the field of production technology where the number of variables is fairly well known, the principles of economics are readily applicable, but as the student proceeds through the province of marketing into the unexplored regions of psychology and sociology he must distinguish carefully between scientific reasoning and purely metaphysical speculation, even when the latter masquerades as economics. The present paper attempts to prove no preconceived theorems and is designed primarily to stimulate careful thinking on sundry neglected phases of these industries. An attempt is made to differentiate the general problems into single aspects which afford promise of being comprehended separately; also, some fundamental statistical data are presented, but merely to indicate a method of scientific approach applicable to more intensive studies. Definition Before discussing the economics of the nonmetallic mineral industries, it is appropriate to consider what we mean when we say "nonmetallic minerals." This term, inasmuch as it is merely a negative description, is somewhat loose and ambiguous and gives rise to questions in regard to minerals that, like chromite or bauxite, are alternatively classed either as nonmetallic or as metallic minerals (or ores). The chrome ore used to make ferrochrome for steel manufacture is undoubtedly metallic in character; similar material destined for use as a refractory in the same

Jan 1, 1934