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By E. C. Barfield, D. G. McCarty

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) develop a representative numerical model of the reservoir and (2) employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially (I) calculating the pres-' sure distribution in the reservoir and (2) tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional .flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restrains and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the highspeed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. INTRODUCTION One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-

By Charles A. Ashburner

' I. Natural-Gas Explorations. The rapid development of the natural-gas* industry in Western Pennsylvania, and the great economy which results from its use, both for manufacturing and domestic purposes, has led to an inquiry as to the occurrence of this gaseous mineral in all thickly populated and large manufacturing centers of the United States. Natural-gas springs are to be found in almost every State in the Union, and in many States gas has been obtained in wells sunk either for water, oil, or gas, or in search of solid mineral deposits. The occurrence of natural gas is, however, not dependent upon mere chance, as is popularly supposed, but upon the existence of special geological phenomena; this fact is now recognized by professional men and by many practical men concerned either in the exploration for or in the use of this gas. The desire among our leading manufacturers, to emulate Pittsburgh, has led to the sinking of many wells in many localities, in search of natural gas. Some of these wells are now being located and drilled under the direction of professional experts, but many more have been, and are still being located by "quack " explorers, who often depend upon spiritualistic communications, or the diviningrod, or by intelligent persons, who are ignorant, however, of the geological and physical conditions under which gas has already been found. My attention has recently been directed to a number of these exploring operations where holes have been drilled, and, after failing

Jan 1, 1887

By Arthur Dwight

ARTHUR SMITH DWIGHT, president of the American Institute of Mining and Metallurgical Engineers, was born in Taunton, Mass., on March 18, 1864. He is descended on both sides from early settlers, one of whom was Richard Warren, of the "Mayflower." His forebears included Col. Benjamin Church, Tim-othy Dwight, and the Rev. Jonathan Edwards, third president of Princeton College. Mr. Dwight was graduated in 1882 from the Poly-technic Institute of Brooklyn, N. Y., and three years later from the Columbia School of Mines, with the degree of Engineer of Mines. In 1914, he received the honorary degree of Master of Science from Columbia. On leaving Columbia in 1885, he went to Pueblo, Col., and for thirteen years was associated with the Colorado Smelting Co. Beginning as assayer he rose to be general superintendent. When he gave up the latter position he became connected with several large companies in the mining and smelting of lead, copper and the precious metals in the Rocky Mountain region. This work occupied him from 1897 to 1906, and six years of that time were spent in Mexico. He was general manager of the Greene Consolidated Copper Company at Cananea, Mexico, in 1906, when trouble first developed against the régime of Diaz. A general uprising was planned to seize the mines, and with money and supplies so obtained, carry the revolt through the interior. Mr. Dwight turned his industrial organiza-tion into a military unit almost over night, stemmed the tide of revolution, and had the situation well in hand before the arrival of troops. In the fall of 1906 he returned to New York and began practice as a consulting mining and metallurgical engineer. He next developed important metallurgical patents for the roasting and agglomeration of fine ores, known as the Dwight and Lloyd sintering process, now extensively used ail over the world.

Jan 3, 1922

By L. D. Rickets

The principles on which an art is founded are usually few and necessarily basic in nature, but he who wishes to achieve the power to select his aides and give success to important undertakings that may be entrusted to him in the future must ordinarily undergo years of drudgery in order to gain the experience that will enable him to distinguish such fundamentals through the haze of reenforcing detail that clothes and tends to disguise them. This especially applies to those who would dream dreams that may come partly true. Professor Henry B. Cornwall of Princeton was a graduate of Freiberg with mining experience in Mexico. He was my friend and mentor during my college life. In 1883 I finished my postgraduate course and had two offers of work to consider. His advice is very clear in my mind today. It was essentially as follows: I know something of the mines of Mexico and have crossed through the mountains of the West. The West possesses a vast area of mountain and valley. California has long had its gold mines, the Comstock and Gilpin County followed and now comes the discovery of Leadville. I believe the West, will become a great mining country. You can choose now to teach here or go to the mountains. Were I in your place I would go West and identify myself with mining.

Jan 1, 1932

By C. H. Mathewson

MICROSCOPIC rnetallography has been exploited quite well enough to bring about a very general understanding that the typical metal or alloy is composed of minute crystalline particles blended into a coherent microstructural mosaic. One does not have to be a specialist in metallography to realize that the properties of such an aggregate are essentially a summation in appropriate form of individual effects derived from the shape, size, placement or orientation and cohesive characteristics of the component particles. It is clearly of great importance to consider the various forms of discontinuity which may occur at the boundaries between these crystalline particles. When a number of particles each possessing the same orderly arrangement of atoms are brought together into a close-fitting system of purely haphazard contacts, not unlike a handful of snowflakes compacted into a snowball, the particles are said to possess random orientation. There are no generally accepted views concerning the arrangement of the atomis or the constitutional reaction between atoms where one crystal meets another, but these contact regions are characterized by strength rather than weakness and it is customary to require the presence of many rather than few boundaries in preparing metal for useful service. Under certain circumstances all of the particles in a metal may be nearly alike in orientation. Other general tendencies of orientation may be associated with particular forms of mechanical and thermal treatment. In contrast with these cases of fortuitous or statistical diversity of orientation, we often find adjacent particles united along a plane which possesses a grouping of atoms belonging equally well to both structures. This, of course, determines a fixed relationship between the two orientations and it is always possible to derive one from the other by some form of rotation or reflection prescribed by the symmetry of the crystal structure under consideration. Particles united in this manner are known as twin crystals although the term refers to the form of association rather than the number of individuals concerned.

By W. A. LaVenue, W. M. Houston

Pebble phosphate mines of Florida have been established from south of Hardee County to north of the Georgia state line, a distance of over 200 miles. Mining has been carried out on an ever-increasing scale since 1885, but phosphate deposits that can be mined on the economical standards of today, are confined in a roughly circular area about 30 miles in diameter, generally within Polk and Hillsborough Counties, in the central part of the State. The phosphate deposit, which is in the Bone Valley formation of Pliocene age, is covered by Pleistocene terrace deposits of unconsolidated quartz sand. The matrix is composed of approximately 1/3 clay slimes, 1/3 silica sand and 1/3 phosphate pebbles. The phosphate usually occurs as rounded pebbles, ranging in size from about 1 in. down to approximately 400 mesh. The phosphate may vary from well-defined hard pebbles to soft weathered rock. The color and character of the phosphate will range from smooth buff pebbles to black and white "salt-and- pepper rock." The screen size distribution varies considerably between locations; the recoverable phosphate may extend down to the 400-mesh size in some areas, while in others the phosphate may cut off sharply at about 35 mesh.

Jan 11, 1962

By J. E. Burke

RECENT investigations have elucidated many of the phenomena of the grain growth process, but have also revealed some conflicting and unexplained results. Beck and his co-workers1,2,3 have shown that grain growth continues with continued heating at one temperature until the average grain size approaches the thickness of the specimen, Plotting the logarithm of the average grain diameter, D, against the logarithm of the annealing time, t, they find the straight line relationship given by the equation: [D=Ktn [11] with possible small deviations at short annealing times. K and n are constants at constant temperature. On the other hand, Walker4 finds that, in alpha brass, the rate of growth falls off more rapidly than indicated by Eq I after long annealing, so that an equilibrium grain size is approached. Burke5 showed, using Walker's data, that time and temperature for grain growth are apparently related through an activation energy, H, according to the relationship: [t, Hr i '_ III t„ = R \T, - ~) [2]] where t1 and t2 are the annealing times necessary for the average grain size to increase from Do to D at temperatures T1 and T2 and R is the gas laws constant. In the case quoted, H had the value 60,000 cal per mol. The apparent validity of this relationship, at least up to 700°C, and the approximate value of H were later confirmed by Beck.' The results obtained by Beck, Kremer, Demer and Holzworth2 for aluminum and aluminum-magnesium alloys could not be satisfied by such a relationship, since the slope of the isothermal curves increased with increasing temperature. These data indicate and Beck, Holzworth and Hu6 later demonstrated experimentally that the only apparent factor controlling the rate of grain growth at constant temperature is the grain size. While many of the phenomena have been elucidated, a reasonably quantitative explanation of the process is lacking. There exists uncertainty even as to the primary driving force for grain growth, although there is a considerable body of indirect evidence that the interfacial energy of the grain boundary is responsible.7,8,10 Making implicit use of this assumption, several authors14,15 have pointed out that grain boundaries should migrate toward their center of curvature. Harker and Parker' have advanced this concept furthest, and show that one can expect grain boundary migration to occur only when the grain faces are curved, or when they meet at non-equilibrium angles. When the face is curved toward a grain A, for example, the atoms in the surface of grain B, on the other side of the boundary, are on the average more surrounded by the atoms of their lattice than the atoms on the surface of grain A. Because of thermal motion, the atoms at the interface will sometimes be attached to grain A and

Jan 1, 1948

By W. G. Jeffery, James F. McDivitt

THE FRAMEWORK Consider where you, the reader, would place the emphasis m your answer to the following questions on mineral supply. Do you think of the mineral resources of developing countries in terms of the contribution which they can make to world mineral supply or in terms of the contribution they can make to development of the country? Do you look upon developing countries as a source of minerals for world industry or as a potential enormous market for minerals? If you are from a developed country it would be surprising I£ you did not emphasize the first alternative in each case, but it is also possible that simply raising the questions will call for some mental adjustments, because usually we do not think in these terms. If you are among the two-thirds of the world's population which comes from developing countries, you might well emphasize the second alternative. And to a growing extent during the reaming decades of the 20th century this is where emphasis must be placed. Increasing amounts of the world's mineral production come from countries which are in the early stages of development. Mineral consumers of the world look to these regions for continuing supplies of material to help meet their ever-growing needs; the producing countries look to mineral exports as one means of stimulating and financing their economic development-this seems a happy and fortuitous relationship. But due to the complexities of world mineral supply, it is a relationship which is fraught with potential confusion and misunderstanding. That this is so is not surprising when one considers that many of the producing countries are new countries which are urgently trying to find the path along which they can move towards development; that the direction of the path is by no means clear because various theories of economic development, as a planned and deliberate process, are relatively recent in origin and none are well understood; and that the very concept of the less developed countries (LDC's) is a relatively new one. To further complicate the situation there has never been a clear under- standing of the full role which minerals play in economic development, either in the case of those countries which are already classed as developed, or in the case of countries which are in the process of development. Before embarking on an investigation of some aspects of the relationship between minerals and developing countries, it seems wise to establish broad terms of reference, which may not be totally valid but which will at least give an initial direction for a journey with no clearly definable goal. First it can be noted that the world has been divided somewhat arbitrarily into a group of countries that are termed developed or advanced and a group of countries which

Jan 1, 1976

By John H. Hollomon

IN recent papers, O'Neill,1 Vivian,2 and Zener and Hollomon3 have reviewed some of the information concerning the relations between stress and strain during plastic deformation. Since further information has been obtained since these reviews were published, this paper attempts to further coordinate and amplify the knowledge concerning the plastic deformation of metals in simple tension. Ordinarily the results of tensile tests of metals are presented as graphs in which the load divided by the original area is plotted as a function of the percentage of elongation measured over some specified gauge length. The interpretation of graphs of this sort is limited, since the stress required to deform the metal at any stage of the deformation is actually the load divided by the instantaneous rather than the original area. Furthermore, each increment of the deformation is performed on metal that has been previously deformed, and, as pointed out by Ludwik,4 the strain could be more effectively defined: [e = In A t][I] where a is the strain and Ao and A are, respectively, the original and instantaneous areas. The results of the tensile tests can be more effectively presented and interpreted if the stress* (load divided by actual area) is plotted as a function of the strain as defined above. A schematic curve of this type is presented as Fig. I. In a previous paper,6 the concept of Ludwik7 concerning the flow and fracture of metals was successfully employed to explain some of the puzzling results of notched-bar impact tests of steel. It appears that the use of this concept is very fruitful and should be kept in mind in any study of the deformation characteristics of metals. Ludwik considered that a flow stress-strain curve of a metal was essentially a locus of points that described the stress required for plastic flow of an infinite number of specimens, each with a different strain history determined by the preceding part of the flow curve. Each of these specimens can also be considered to have a fracture strength. Unfortunately (or fortunately depending upon the point of view), all the specimens, except the one deformed to the fracture strain, flow and do not fracture. Even though the metals do not fracture, the concept of a fracture-strength curve seems

Jan 1, 1945

By S. S. Raymond, C. R. Hayward

In reheating quenched steel to remove part of the hardness, the softening effect has generally been considered to be a function of temperature and time. The temperature effect is well known, and long before pyrometers were heard of the blacksmith was able to do a good job of tempering, by rule-of-thumb methods and experience in judging temperatures. Modern conditions, which demand steel that will withstand the severest tests, require that the heat treatment be carried out with every possible precaution to secure the best results obtainable. Pyrometers and heat-treatment furnaces of many types are on the market and improvements are continually being made so that it is now possible to regulate the temperature in heat treatment very accurately. There is still a question regarding the time that the steel should be subjected to treatment. It is customary with all operators to insure the desired temperature throughout the specimen and it is generally supposed that a longer treatment of a hardened steel produces a further softening but there are few published figures showing the exact effect of time of treatment at constant temperature. A search of the literature disclosed several brief statements that the tempering effect was a function of both time and temperature, but in no case were any figures given. The opinion is very generally held that the well-know tempering colors are accurate indicators of the degree of tempering. This is disputed by Brearley (The Heat Treatment of Tool Steel, page 102) who states: It has been said that the result would be the same in respect to both hardness and other properties whether the colors were obtained by a shorter heating at a higher temperature or a longer heating at a lower one. This, to say the least, is a very doubtful conclusion, and is certainly not borne out by mechanical tests on oil-hardened and tempered motor car steels which, after tempering for periods varying from 15 min. to 2 hr., show no very great bifferences. The present investigation had for its object the obtaining of some definite data regarding the effect of time, which might serve as a guide to those engaged in the heat treatment of steel. The Rhode Island Tool Co. cooperated by furnishing the steel and machining the test specimens.

Jan 1, 1917

By Jack A. Simon, M. E. Hopkins

GENERAL GEOLOGY Coal is defined as a combustible rock that originated in the accumulation and physical and chemical alteration of vegetation. Coal can be ignited and burned like the wood that was man's earliest fuel, but coal gives more heat than the same amount of wood and has many industrial uses. Unlike wood, coal is not generally found on the surface of the ground but is mined from the solid rock of the earth. Before taking up the occurrence, formation, and the unique character of coal in the rock sequence, let us briefly consider the general character of all rocks in the crust of the earth. Relatively little is known about the very earliest history of the earth, although a number of logical theories have been developed. Manned exploration of the moon and the rocks returned to earth continue to provide some answers to questions concerning the earth's origin and history. The period of earth history with which we concern ourselves here begins after great areas of water had evolved on earth and substantial land areas of once molten (igneous) rock existed. Weathering and other processes that attacked the surface of the rocks reduced them to small particles. Water provided by rainfall transported this material, ultimately, to large bodies of water where it was deposited. Thus was initiated the geologic sequence of sedimentary rocks that lie above the once molten igneous rocks. The crust and upper mantle of the earth are made up of several large plates along which differential movement (primarily horizontal) takes place. Such movements, although small, are occurring today. These horizontal movements are accompanied by vertical movements causing important changes in the relative position of the continents and oceans. Low-lying coastal swamps with favorable climates are ideal locations for coal accumulation and burial by river-borne sediments, and large areas

Jan 1, 1981

By W. F. Hosford, E. W. Kelley

By testing polycrystalline specimens from textured plates which had Previously been used to provide materials for growing single crystals, it has been possible to relate the plastic anisotropy of textured materials to the deformation behavior of single crystals. The deformation studies have been conducted at room temperature on textured polycrystalline magnesium and binary Mg-Th and Mg-Li alloys. Variously oriented specimens of the textured materials were deformed in plane-strain compression and in uniaxial tension and compression. The stress-strain curves are similar in their general jorm of anisotropy and stress levels to those obtained on single crystals of the same alloys. The degree of anisotropy is lower, however, in the polycrystalline materials and correlates with the intensity of the basal texture. Yield loci for the textured materials appear reasonable in terms of the deformation mechanisms, and deviate sharply from the form predicted by the Hill analysis for aniso-tropic material. A N earlier study1 of single crystals has shown that magnesium and magnesium alloys with thorium and with lithium deform at room temperature primarily by basal slip, {10i2) twinning, and (1011) banding. The (10i1) banding mode is a combination of {10ll) twinning followed by (1012) twinning and basal slip within the doubly twinned material.2, 3 Magnesium with lithium can also deform by {1010)(1210) prism slip.1'4'5 Still other deformation modes have been reported for magnesium6-11 but these are considered to play a minor role in room-temperature deformation. In a polycrystalline material, plastic deformation must occur in the individual grains through the operation of one or more of the various deformation modes. Because the critical shear stress for basal slip is very low compared to the activation stresses for the other deformation modes,' basal slip accounts for much of the deformation in the polycrystalline aggregate. However, since there are only two mutually independent basal slip systems, and because five independent systems must be active for an arbitrary shape change in any material,'' modes other than basal slip must account for some of the strain. The deformation of textured magnesium, like that of other hcp metals, must be controlled by the same mechanisms observed in single crystals. In strongly textured material, the form of the anisotropy should be similar to that of single crystals, and the degree of anisotropy should depend on the intensity of the texture. EXPERIMENTAL PROCEDURE The anisotropy of deformation was investigated through the use of plane-strain compression tests, as well as uniaxial tension and compression tests. Materials. Test specimens were cut from the three textured plates of magnesium which had previously been used to provide material for single crystals.' These plates, furnished by Dow Chemical Co., had been reduced about 80 pct during the process of being hot-rolled to their final 1/4-in. thicknesses. The plates had the three respective compositions, pure magnesium, Mg-0.5 wt pct Th (0.49 pct Th by spectro-graphic analysis), and Mg-4 wt pct Li (3.84 pct Li by chemical analysis). Impurities other than iron were less than 0.0005 pct Al, 0.01 pct Ca, 0.001 pct Cu, 0.0006 pct Mn, 0.001 pct Ni, 0.003 pct Pb, 0.001 pct Si, 0.001 pct Sn, and 0.01 pct Zn. Iron was 0.001 pct in the pure magnesium, 0.002 pct in the Mg-0.5 pct Th, and 0.014 pct in the Mg-4 pct Li. The textures of the three plates were determined by X-ray diffraction utilizing only the reflection technique out to an angle of 50 deg from the sheet normal. The resulting basal pole figures are presented in Figs. 1, 3, and 5. Grain sizes in the plates were ASTM number 4 in the pure magnesium and number 7 in each of the alloys. Plane-Strain Compression Tests. Plane-strain compression specimens approximately $ in. thick by 4 in. wide by $ in. long were prepared for each of the three compositions. These specimens were prepared in a manner similar to that used for the single-crystal specimens of the earlier study.' All polycrystalline specimens were stress-relieved at 500°F for hr as the final step in their preparation for testing. The testing procedure was identical to that used for the single crystals, involving compression in a channel and using 2-mil Teflon film as a lubricant. The specimens were tested in six orientations of interest, these being the six combinations of the rolling, transverse, and thickness directions of the material serving as loading, extension, and constraint directions in the plane-strain compression test. Each of the six orientations was assigned a two-letter identifying code. These are combinations of the letters (thickness direction), R (rolling direction), and T (transverse direction) with the first letter signifying the loading direction and the second letter the extension direction. For example, ZR specimens were compressed in the thickness direction while extension was permitted to operate in the rolling direction of the textured material. To facilitate comparison of the present work with that of the single-crystal study1 the orientations used for single crystals are given in Table I along with the polycrystalline orientations that most nearly correspond. To insure reproducibility, at least three duplicate

Jan 1, 1969

By H. M. Howe

The tenacity with which a bad name adheres to a process is well illustrated by the prevalent belief in the irregularity of the product of the Bessemer converter. We have been lately told by an eloquent member that lack of uniformity is the name of Bessemer steel, and that uniform soft steel can only be made in the Clapp-Griffiths Bessemer converter. Yet I believe that, however irregular the percentage of carbon in Bessemer steel may have been formerly, to-day it is well-nigh completely under control. Indeed, the results of a large number of analyses that I' have studied go to show that the

Jan 1, 1887

By Lincoln F. Elkins

The Spraberry Trend Field of West Texas was discovered in January, 1949. Drilling of 2.234 wells and production of some 45 million bbl of oil by January, 1953, indicated this to be an important field which will ultimately cover more than 400,000 acres. In addition to being the world's largest field in areal extent, the Spraberry has presented many problems in well completion and operation and has demonstrated unique reservoir performance characteristics. The pay section consists primarily of a few fine grained sandstone or siltstone members in a thousand-ft thick section of shale, limestone. and siltstone. Since porosity averages only 10 per cent and nearly all permeabilities are less than 1 md, conventional core analysis does not delineate the "pay" section. Mercury injection was used as a capillary pressure test adaptable to rapid routine use to select those intervals having low enough connate water saturation to contain commercially significant oil saturation. In the central area of the field this "pay" amounts to 16 ft of Upper Spraberry and 15 ft of Lower Spraberry sands. An interconnected system of vertical fractures, observed in cores, provides the flow channels for oil to drain into the wells hut most of the oil is stored in the matrix since the void volume of fractures is estimated to be less than 1 per cent of that in the sand. Initial potentials of wells range up to 1.000 B/D after fracture treatment which should be compared with estimated capacity of 5 to 10 B/D if oil had to flow into the wells through the sand itself. Without exception initial pressures of later drilled wells were significantly lower than initial pressures of earlier drilled nearby wells in a large area some 6 miles long. This means the earlier drilled wells had drained fluids from areas much greater than their 40-acre proration units. Since most of this performance occurred while the reservoir pressure was above the. saturation pressure it was analyzed by the compressible fluid flow theory. This analysis gave calculated initial presrilres which agreed within 30 psi of measured pressures of 60 per cent of wells in the area using 16-md permeabilitv corresponding to a fracture system substantially that indicated by cores and using combined compressibility of rock and its contained oil and water corresponding to the core analysis data. The most important feature of this analysis was the very close agreement between effective compressibility of the rock and its contained oil and water from the field performance and that from the core tests, because it meant there are no "islands" of low permeability reservoir rock left untapped in the inter-well area and thus no additional wells are necessary to insure that at least one well penetrates each "reservoir." Twenty-five of forty-four 40-acre spaced wells on three contiguous sections were wed in a four-month inteference test. Six shut-in well. were tested monthly for oil production. productivity index. gas-oil ratio and pressure buildup, and seven shut-in wells were tested for decline in reservoir pressure. Tests on 12 regularly producing wells gave comparative data for interpretation of shut-in test wells. Reduction in reservoir pressure, decline in productivity index. and increase in gas-oil ratio were found to be substantially the same in the shut-in test wells as those in the comparative regularly producing wells, meaning that the producing wells were depleting the

Jan 1, 1953

By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

The greatest mining center in the state of Utah is the incorporated town of Bingham about twenty-five miles southwest of Salt Lake City. The principal industry of this vicinity, prior to the early fall of 1863, was lumbering and the first saw-mill in the state was built near the mouth of Bingham Canyon. Early in the fall of that year. George B. Ogilvie discovered gold and shortly afterward the first mining district in the state was organized. Some writers place the discovery of gold in the canyon in the late fifties. If this be so, however, the matter was kept extremely quiet because no mining was engaged in until after Ogilvie's discovery. Bingham was a placer mining camp, producing about one million dollars' worth of dust and nuggets from placers up and down the canyon and in Bear Gulch until early in the seventies, or about ten years after the discovery of gold, when a large body of argentiferous lead ore was discovered and soon after heavy shipments were made from a half dozen or more properties.

Jan 1, 1925

By G. A. Croes, N. Schwarz

The dimensionless groups, to which the variables that govern the displacement of oil from reservoirs by liquids can be combined, are derived. Three types of displacement are considered, viz. cold-water drive, hot-water drive and solvent injection. The derivation of the dimerzsionless groups is carried out by means of the relevant basic equations (in-spectional analysis). The resulting sets of groups are afterwards completed by means of dimensional analysis. The form of the groups is given in such a way that they can be adapted to suit the various boundary conditions that are encountered in practice. The physical meaning of the groups is discussed. They have all been brought together on a chart, from which their mutual relation and their corresporzdence to related dimensionless groups in common use in other engineering sciences can be read off. The limitations of dimensionally scaled model experiments as a useful tool for studying liquid flow in porous media, as occurring in oil reservoirs, are discussed. The use of models to study fluid mechanics has an appeal for everyone endowed with natural curiosity. What active boy has not played with ship and airplane models, or crude models of dam and drainage systems Even in the most advanced technical engineering, such models play a fundamental and indispensable role. "And yet in few departments of the physical sciences is there a wider gap between theory and practice, between scientific knowledge and the state of art, than in the use of models to study hydrodynamic phenomena." Garrett Birkhoff1 INTRODUCTION Laboratory displacement experiments are extensively used to investigate, directly or indirectly, the production behavior of petroleum reservoirs. Such experiments are representative of the reservoirs as a whole, if they are carried out with models that are "properly scaled." The performance of oil reservoirs is governed by the values of a number of variables, which can be combined to dimensionless groups. Two general methods are available for the derivation of these groups. In the first of these, dimensional analysis, combination of the variables is done essentially by trial and error. Its only premise is knowledge of the complete set of relevant variables. In the second method, inspectional analysis, the dimensional homogeneity of the equations describing the behavior of the system to be studied is used. The resulting dimensionless groups can be divided into: (a) independent (variable) groups, such as dimensionless length, time, etc.; (b) dependent groups, giving the dimensionless form of the variables, such as recovery and pressure, that can, at least in principle, be measured during an experiment; (c) similarity groups, which are independent constant groups, such as ratio of length to height of the reservoir and ratio of

Jan 1, 1957

By R. Venkateswar, G. C. Sresty

Size measurement is important in characterization of fine particles. Commonly employed size measurement techniques such as sieving, microscopy, and sedimentation are discussed in this paper. Operating principles, advantages and limitations of these techniques are discussed based on the published information and working knowledge with several of these instruments at the authors' laboratories. A brief description of the recently developed equipment for fine particle characterization is also included. At the end of the paper, a rationale is presented for selection of the size analysis equipment based on specific requirements.

Jan 1, 1980

By Joseph N. Morrison

A comprehensive solution is offered to the problem of dust emissions at belt conveyor transfer points. Details of enclosure design are discussed and a straightforward procedure for calculating required dust control exhaust volume is presented. Many design variables are taken into account which heretofore have been commonly ignored or inadequately considered. These include belt widths, belt speeds. enclosure openings, material flow rate, material bulk densities, material lump sizes, height of material fall, material temperature, and ambient air temperature. All of these questions are handled by means of a "fill-in-the-blanks" type of calculation form, permitting quick, reliable solutions by relative "non-experts."

Jan 1, 1972

By Zavis M. Zavodni, Carl D. Broadbent

During the past 15 years, rock mass structural properties have become acknowledged as the focal point for rock slope design. Re- search into the methods for measuring and incorporating structure into the design effort has taken many directions and has produced a variety of useful techniques. Among the findings at Kennecott has been the realization that structure-controlled instability can be categorized as regressive or progressive depending on the relative geometries of slope and structure and on the strength characteristics of the structures. It was further identified that a failure condition can initiate as regressive and in time become progressive should external stimuli increase or structure characteristics be altered due to extensive displacements. The transition point has been shown to be a useful indicator of the expectable collapse time. This paper defines three fundamental failure types as dictated by structure and offers discussion on the practical value of such a classification to slope design and failure control. Several prominent examples of failures typifying the categories of structure- controlled instability are discussed. An application of f allure prediction based on the regressive-to-progressive transition point is described.

Jan 1, 1983