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By Jean Howard

THERE are two mechanisms by which secondary crystals can develop in bcc alloys, namely 1) impurity inhibition and 2) strip-thickness inhibition. This paper reports some studies of each mechanism; the alloys were Si-Fe, A1-Fe, Cr-Fe, Mo-Fe, and Ge-Fe, as well as iron itself. All the alloys, which were of interest as part of a program of work on soft magnetic materials, were made by a powder-metallurgy process, using carbonyl iron (Grade MCP) as the starting material. Earlier phases of the work have already been published. Work described previously1 shows how the oxygen content of the sintering. atmosphere can be used to produce silica in the material which acts as a grain-growth inhibitor. Since then it has been found more convenient to make use of the oxide in the iron powder to control the silica content of the material. The compacts are sintered in vacuum which allows a direct reaction to take place between the iron oxide and the silicon. Details are given elsewhere.4 By this method, and by suitable adjustment of the rolling schedule, material with cube-on-edge secondary crystals has been produced in thicknesses from 0.1 to 0.001 in. in iron containing from 2-1/2 to 4-1/2 pct Si. It was also found possible to process 6-1/2 pct Si-Fe to 0.001 in. This was achieved by refinement of the sintered-compact grain size by using fine-particle silicon (i.e., <200 mesh). The brittleness of the material necessitated hot rolling to 0.020 in., from which thickness cold rolling was possible. If the conditions of sintering and the cold-rolling schedule were correct (i.e., as given elsewhere4 for 3-1/4 pct Si-Fe) secondary crystals of (110) [001.] orientation could be developed. The size of the secondary" crvstals" could not be

Jan 1, 1965

By John V. Beall

New York was bathed in pale winter sunshine and, surprisingly, coatless weather. The time was the AIME Centennial and 100th Annual Meeting. From advance peeks into the fabulous schedule of events we were well aware that the Centennial Committee, New York Host Section and AIME staff&apos; had pulled out all the stops, laying on the best of everything, but the weather gimmick was the frosting on the cake. The Formal Greetings Session on the first morning, Joe Alford confided, was the greatest AIME experience of his life. Without doubt the honor bestowed on AIME by the greetings and felicitations of the presidents of the world&apos;s leading professional engineering societies was the greatest moment in AIME history-save one. That one exception was in 1928, when 1920 AIME President Herbert C. Hoover was elected President of the United States.

Jan 1, 1971

By William E. Bonini, Eugene A. Hickok

IN the course of an investigation directed toward expanding ground-water facilities in Essex and Morris counties, New Jersey, the Board of Water Commissioners of the city of East Orange authorized a seismic-refraction survey1 for the purpose of delineating bedrock topography below unconsolidated overburden. Results of the survey were highly satisfactory and led to the preparation of a comparatively detailed bedrock contour map. Knowledge of the bedrock depth and configuration was an important aid in selection of sites for test drilling. The portion of the East Orange Water Reserve under consideration is in the flood plain of the Passaic River about 10 miles west of Newark, N. J. The flood plain is about 175 ft above mean sea level and is bordered by low hills rising to elevations of approximately 250 ft. The bedrock underlying the Water Reserve consists of sandstone and shale of the Triassic Brunswick formation and is covered everywhere by deposits of unconsolidated glacial outwash sand and gravel, lacustrine clay, and recent river silt as much as 150 ft thick. Yield of wells in the sandstone and shale averages 100 to 200 gpm. Since production wells constructed in the sand and gravel aquifer in the buried river valley shown on the contour map (Fig. 1) yield 300 to 1400 gpm, it was proposed to locate additional production wells in this buried valley, where the yields per well would be maximum.

Jan 4, 1958

By Owen S. Roberts

During the design phases of a conveyor system, the question arises regarding the type of drive required for each application. The paper shows that the correct drive for any particular application is the one that satisfies the criteria established for that application in the most economical manner consistent with such considerations as site location, availability of spare parts, area environmental conditions, power supplies available, etc. Following discussions of various mechanical arrangements for the drives, motor types and their characteristics are considered along with the control means of modifying these characteristics to satisfy individual requirements. These characteristics are all illustrated graphically. After selecting the motor and its starter, control accessories and interlocking arrangements as applied to material handling systems are discussed.

Jan 1, 1973

By Eckley B. Coxe

I DES~RE to call the attention of the Institute to two deep vertical shafts, which are now being sunk in Schuylkill County, Pennsylvania, about miles north of Pottsville. These shafts are of interest to the mining engineer, not only on account of the novelty of the method of sinking adopted, which promises to produce a revolution in that branch of mining engineering, but also as examples of the manner in which such work should be undertaken. GEOLOGICAL SKETCH OF THE TERRITORY TO BE WORKED BY THE SHAFTS AND REASON FOR SINKING THEM. The Mammoth or E Vein of the anthracite coal-measures in that part of the Schuylkill region near and north of the town of Pottsville lies at a great depth below the surface, and has, in consequence, never been worked in that locality.

By T. A. Rickard

A knowledge of the principles of punctuation is essential to effective and intelligible writing, for the ease and pleasure of the reader, and even his understanding, may depend upon the choice and the placing of punctuation marks. To &apos;punctuate&apos; is to mark with stops or points; the word comes from the medieval Latin punctuare (punctuatus), which in turn is derived from the Latin punctum, a point. The purpose of punctuation is to show the manner in which the writing is to be understood; to indicate the relations between parts of a sentence and between successive sentences. To some extent "it does for the eye what vocal stress does for the ear", but especially it marks logical relations. Some punctuation marks, such as those indicating admiration, exclamation, and interrogation, are rhetorical as well as grammatical, but most of the common ones are logical, or grammatical. My discussion will be confined to grammatical punctuation in ordinary writing. .&apos;The problem of punctuation in text matter", as George Summey * says, "is to employ words, points, and paragraph breaks in such a way as to achieve at the same time clearness; proper distribution of emphasis, and the desired kind of movement." The criticism of the punctuation of a sentence or of a group of sentences is not final until the context, within the paragraph, is read. A paragraph is a sentence or a group of sentences forming an independent unit of the composition; it represents a unit of thought. A multiplicity of paragraphs produces a choppy effect; &apos;on the other hand, paragraphs of. excessive length are tiresome, because the belaboring of one unit of thought wearies the reader. The aim should be to

Jan 1, 1931

By D. O. Ehrenburg

DURING the earlier period of electrical prospecting, the search for orebodies was by far the most important application of this method of geophysical prospecting. In the past few years, however, increasing attention has been paid to the possibilities of this method in the investigation of subsurface structures. Not only have fault zones been located, but attempts have been made to determine the depth to certain strata and thus contouring on some bed which proves to be a good "electrical marker." Many workers have published the results of field tests showing how their particular interpretations have agreed with the actual field conditions, but very few have stated their method of interpretation. Weaver, Hummel and Stefanesco and Schlumberger1 have given a more theoretical discussion of the resistivity methods. Hummel and Stefanesco and Schlumberger have published mathematical solutions for the flow of electricity in a medium involving four layers. In this paper the authors present a solution for the flow of electricity in a medium of any number of horizontal strata. By means of this solution, curves showing the relationship between the apparent resistivity and the electrode spacing can be computed for ideal cases.

Jan 1, 1931

By C. M. Weld

The southeastern coast of China, from Ning-Po to .Macao, represents an element in the continental mass of Asia which has at practically all times in the remote past exhibited a tendency to rise rather than to subside.&apos; This strip of land, 1,000 or more miles long by perhaps 150 miles wide at its widest part, has in fact stood above sea level since at least early Cambrian times, while the great basins to the north and west were receiving their massive accumulations of Sinian (Cambro-Ordovician), Carboniferous, and later deposits. We find, .therefore, a coastal fringe of metamorphic and igneous rocks bordering the huge expanses of sedimentary rocks which occupy the interior. Hong-Kong is situated toward the southwestern extremity of this fringe. Hong-Kong is an island of approximately 30 sq. miles, on the north shore of which is situated the city of Victoria, with its 325,000 inhabitants. This island was ceded to Great Britain in 1842. In 1560 the peninsula of Kowloon (about 5 sq. miles), being that part of the mainland lying directly across from the city of Victoria, was added to Hong Kong. Thirty-eight years later, in 1898, a stretch of territory, including the mainland behind Kowloon and. numerous adjacent islands, was leased to Great Britain for 99 years. This last addition is known as the "New Territory of Hong-Kong" and comprises 376 sq. miles in area. A map of Hong-Kong, Kowloon, and the "New Territory" is shown in Fig. 1. My studies of this total area of over 400 sq. miles were devoted primarily to an investigation of the mineral resources. Systematic mapping of the immensely complex exposures of rocks was not possible in the time at my disposal. However, observations in, this. direction warrant a few generalizations.

Jan 2, 1914

By Fritz Wald, Martin Weinstein, Herbert E. Bates

ONE of the methods for preparing a fiber-reinforced composite is that of directional solidification of a eutectic melt. Its major drawback lies in the fact that the matrix in this case is a pure constituent (or a terminal solid solution of fixed concentration) and the ratio of fiber to matrix volume is fixed. Only very few, if any, pure metal matrices possess technically useful properties, and the necessity for alloying is the inevitable consequence of this fact. Nevertheless, structures similar to binary eutectic ones can be obtained in higher-order systems by pseudoeutectic reactions of a type where crystallites and a solid-solution matrix are simultaneously precipitated from a liquid.1"3 Trials to solidify such alloys directionally—the matrix consisting of a solid solution of chromium, nickel, and silicon and the reinforcing phase being Cr3C2— will be reported elsewhere.4 This note describes constitutional studies carried out primarily to determine -the position of the pseudoeutectic and further to insure that no undesirable reactions between the reinforcing phase and components of the matrix occur in the solid state at elevated temperatures. In the investigation it was specifically desired to reinforce a matrix which is as close as possible to the 80/20 Nichrome composition with Cr3C2 to insure good oxidation resistance and improve the strength at high temperatures. No konstitutional information on the quaternary C-Cr-Ni-Si svstem in the range of interest was found in the literature. Nevertheless, the two most important ternaries c-cr-Ni5 and have been completely investigated. On C-Cr-Si some investigations have been conducted,7"9 and C-Ni-Si was studied with a few alloys in the course of the present investination 9 Eight alloys were prepared to investigate the changes in the constitution of the ternary C-Cr3Ce-yNi eutectic5 with silicon contents up to 10 wt pct. Five alloys were made with varying chromium and carbon contents around compositions containing -60 to 70 wt pct Ni and 5 to 6 wt pct Si. The latter alloys were designed to locate the y(Ni-Cr-Si-C)-Cr3C2 pseudoeutectic reaction and to determine the maximum chromium content in solid solution compatible with a two-phase equilibrium between y and Cr3C2 only. The alloys were prepared from electrolyte nickel, semiconductor-grade silicon, high-purity chromium (99.999 pct pellets), and semiconductor-grade graphite. They were melted inductively in high-purity alumina crucibles under flowing argon. Twenty-gram charges were prepared and investigated by optical microscopy (including hot-stage investigations), X-ray powder methods, and electronmicroprobe analysis. The alloys were studied in the as-cast condition and also after a homogenization annealing treatment of 48 days at 900°C in evacuated quartz ampoules. The structures of all alloys based on the ternary eutectic plus silicon in the as-cast state consisted generally of an inhomogeneous solid solution and at least two other phases. Annealing of the alloys showed that the solid solution was homogenized but that an incomplete solid-state reaction had taken place in all alloys with silicon contents over 5 wt pct. This reaction is clearly visible in Fig. 1 around the large Cr3C2 crystals (gray areas). Below this concentration, the alloys consisted of a homogeneous matrix and precipitates of Cr3C2 plus graphite, Fig. 2. The Cr3C2 was entirely unreacted here. From these observations and subsequent X-ray and microprobe investigations, it was deduced that the

Jan 1, 1969

By Bruce Vandre

Jan 1, 1985

By N. B. Davis

I. Introduction. II. Definition of Plasticity. III. Theories of Plasticity. A. Structure of the clay particles. (1) Fineness of grain. (2) Plate structure. (3) Interlocking particles. (4) Sponge structure of particles. B. Presence of hydrous aluminum silicates. C. Molecular attraction between particles. D. Presence of colloidal gelatinous matter. (1) Review of theory of colloids. (a) Suspension colloids. (b) Emulsion colloids. (2) Experiments. IV. The Formation of Clays. A. Residual clays. B. Transported clays. V. Summary. VI. Conclusion. I. IntRodUction While working with a number of very sticky cracking clays from western Canada the writer became interested in a study of the cause of the excessive plasticity. This led to a review of the rather bulky literature on the subject and the finding that plasticity still remains to be satisfactorily explained. Most of these investigations seem to have been carried on solely from the chemical viewpoint, the geologic aspects having been ignored. In nearly every case, the investigators have worked with the higher-grade clays of low to medium plasticity, such as the kaolins, the excessively plastic ones having generally been neglected, partly because of their limited application, yet the author believes that these are

Jan 1, 1915

By R. E. Gilmore

This paper is a revision of a former paper published in mimeograph form by both the Canadian and American coal classification committees, and is now presented for the purpose of acquainting those interested with the present status of coal classification in Canada. The classification employed for "Customs purposes" is detailed, and the classification schemes from which the customs classification was derived are reviewed and discussed. The activities of the Canadian coal classification committee, namely, the Associate Committee of Coal Classification and Analysis of the National Research Council, is also reviewed. Reserves, Production and Uses of Canadian Coals The total coal resources of North America are estimated to be 69 per cent. of those of the world, and of this portion, the distribution is 52 per cent. for the United States and 17 per cent. for Canada. Accordingly, Canadian coal resources amount to approximately one-third of those of the United States, and one-sixth of those of the world. As for the geographical distribution, the bulk of the known coal deposits are in the extreme eastern and western portions of the country. Employing the usual, more or less loosely defined, designations for the different classes and subclasses of coal, the distribution of the Canadian coal resources, according to provinces, is as follows: Maritime Provinces: Nova Scotia and New Brunswick Bituminous and semibitu- minous coals. Ontario (northern part).............................Lignite. Saskatchewan, (and Manitoba)....................... Lignite. Alberta and British Columbia........................ Lignites, subbituminous, all kinds of bituminous, semibituminous and semianthracite coals. Of the total reserves, roughly 92.5 per cent. is credited to the noncok-ing lower rank subbituninous and lignite groups, the bulk of which are

Jan 1, 1930

Benjamin B. Thayer was elected as representative of the Institute on the John Fritz Medal Board of Award vice Albert Sauveur, whose term expires. Robert M. Raymond was confirmed as member of the, Engineering Foundation Board for two years in accordance with the By-Laws of the United Engineering Society. The following preambles and resolutions were passed: WHEREAS, the Chamber of Commerce of the United States is taking a vote, through the Chambers of Commerce, Boards of Trade and other constituent members of the National Chamber situated throughout the country, on the question whether or not the primary natural resources, comprising timber, the ores and deposits of useful metals, and&apos; the deposits of minerals, which are a source of heat, light and power, should he exempt through remedial Congressional legislation from the restrictive limitations of the Anti-Trust Acts, and WHEREAS, a Committee of the National Chamber, the Chairman of which is a Past President of the American Institute of - Mining Engineers, has recommended favorable action upon this question, and

Jan 2, 1917

By Clarence O. Babcock

Model pillars of limestone, marble, sandstone, and granite, with length-to-diameter (LID) ratios of 3, 2, 1, 0.5, and 0.25 (0.286 for granite), were broken in axial compression to determine to what extent an increase in end constraint increased compressive strength. Radial end constraints of 13 to 23% of the average axial stress in the pillar, produced by solid steel rings bonded with epoxy to the ends of dogbone-shaped specimens, increased compressive strength somewhat above that of cylindrical pillars without ring constraint. However, when the results were compared with those obtained by other investigators for straight specimens of several rock types taken collectively, with LID ratios greater than 0.5, the resulting strengths were not significantly different. Thus, the amount of end constraint produced by the solid steel rings was about the same as that produced by the friction from the steel end plates. In other tests, a radial prestress of 3000 or 5000 psi was applied prior to axial loading by adjustable hardened steel rings to increase the constraint above that obtained for the solid rings. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 3000 psi prestress, was 54.3% for limestone, 40.3% for marble, 44.7% for sandstone, and 23.4% for granite. The average radial constraint stress, expressed as a percentage of the average axial pillar stress at failure for the 5000 psi prestress, was 74.2% for limestone, 51.2% for marble, 61.6% for sandstone, and 29.7% for granite. These constraints increased the compressive strength significantly above the strength of straight specimens and solid-ring constrained specimens. These results suggest that large horizontal stresses in orebodies mined by the room-and-pillar method should increase the strength of the pillars and allow an increase in ore recovery by a reduction of pillar size when major structural defects are absent. One important objective of the U.S. Bureau of Mines (USBM) mining research program is the rational design of mining systems. In the design of room-and-pillar mining operations, pillar strength is a fundamental variable. It is customary to estimate this strength from uniaxial compression tests of rock samples and to correct this value for the length-to-diameter (LID) ratio of the in-situ pillar. This method of estimating pillar strength corrects for pillar shape but does not consider the effect of a large horizontal in-situ stress field that sometimes exists in underground formations. The purpose of the work covered in this report was to determine to what extent the compressive strengths of model pillars of relatively brittle rock loaded in axial compression were affected by lateral end constraint. In previous work, Obert l used solid steel rings bonded to the ends of dogbone-shaped specimens to study the creep behavior of three quasi-plastic rocks -salt, trona, and potash ore - during a test period of 1000 hr. These rings provided radial constraint during the loading cycle of 20 to 50% of the axial stress for specimens with LID ratios of 2, 0.5, and 0.25. He concluded that (1) "for a quasi-plastic material the end constraint strongly affects the specimen strength, and (2) as D/L increases (length-to-diameter decreases), the specimens lose their brittle characteristics and tend to flow rather than fracture." He also concluded that model pillars constrained by rings were better for use in predicting the strength of mine pillars than either cylindrical or prismatic specimens. This conclusion appears to be valid where mine pillars, roof, and floor are a single structural element. In the present study, 460 specimens of four relatively brittle rocks — limestone, marble, sandstone, and granite - were tested to failure. The study consisted of two parts: (1) the effect on the compressive strength of end constraint produced during the axial loading cycle by solid steel rings bonded with epoxy to the ends of the specimens, and (2) the effect on the compressive strength of increased end constraint produced in part by a prestress applied prior to axial loading and in part by lateral expansion of the specimen during the loading cycle. The first part of this study was reported in some detail earlier.2 EXPERIMENTAL PROCEDURE AND EQUIPMENT Model rock pillars of the sizes and shapes shown in Fig. 1 were broken in axial compression when the ends were constrained as shown in Fig. 2. he straight specimens were broken without ring constraint. The specimens of dogbone shape were broken with (1) solid

Jan 1, 1970

By Price E. R.

The coal industry was beset with work stoppages and strikes throughout the year, and there was some loss in markets to oil and gas. These conditions, along with the mild decline in industrial activity, the steel strike, and the reduction in exports, contributed to an unfavorable year for the industry. All coal mines are working three days a week at the time of writing, and in estimating production for the year, it will be assumed that the mines will continue to work on that basis through December. Total production of bituminous coal in 1949 is estimated at 420 million tons, which is 179,518,229 tons under the production in 1948. Anthracite production is expected to reach 39,400,000 tons as compared with 57,139,948 tolls in 1948, a loss of 17,739,948 tons. Coal stocks, as of January 1, 1949, were 69,373,000 tons but at the end of the year will have dropped to approximately 22 million tons. Regardless of the difficulties during the current year, the industry has made substantial

Jan 1, 1950

By B. M. Larsen

Jan 1, 1965

By L. L. Handy

Solvent floods using slugs of solvent have been found to show continuity in behavior from the vapor pressure of the solvent to the critical pressure for the two-component driving gas-solvent system. In the pressure region between the solvent vapor pressure and the critical pressure for the gas-solvent system, the gar and solvent are only partially miscible. Although complete miscibility cannot be obtained at these pressures, complete oil recovery is possible in principle. In two-phase solvent floods the solvent is propagated tllrough the reservoir, primarily, in the vapor phase. The carrier gas requirements constitute a significant factor in the economics of the process. A qualitative theory is proposed for estimating the amount of dry gas required to move the solvent through the reservoir. The theory shows that for two-phase solvent floods the total gas needed is a minimum at the vapor pressure of the solvent and at the critical pressure for the gas-solvent system, and is a maximum at some intermediate pressure. The predictions of the theory are supported by experimental studies using methane, butane and decane or methane, propane and decane in a natural sandstone core. INTRODUCTION Previously, solvent slug processes have been found effective for oil recovery in two pressure ranges. First, conventional miscible displacements are possible at pressures greater than the critical pressure for the gas-solvent system. Second, Jenks, et al,&apos; have shown that, at pressures slightly in excess of the vapor pressure of the solvent, a solvent slug can be propagated through a reservoir by a gas essentially insoluble in the liquid solvent. The solvent bank displaces the oil ahead of it. Both of these processes, at least ideally, are capable of recovering all of the oil in the swept regions. Slug processes for which the gas and solvent are partially miscible have not been considered; that is, those systems for which the solvent and driving gas form two equilibrium phases in which the vapor phase contains a significant amount of solvent and the liquid phase an appreciable amount of the driving gas. Welge and Johnson&apos; have shown that the gas needed to movc a solvent slug through the reservoir increases with increasing pressure above the vapor pressure of the solvent. It will be shown that solvent slug processes can, theoretically, recover all of the oil at any pressure greater than the vapor pressure of the solvent. But the amount of gas required to move the solvent through the reservoir depends very much on the pressure and temperature. In the present study a maximum in the gas requirements was both predicted theoretically and observed experimentally. This result has not been reported previously, and would not have been predicted from the Welge and Johnson model. The gas requirements are a minimum at the pressures corresponding to the vapor pressure of the solvent and again at the critical pressure for the gas-solvent system, and are a maximum at some intermediate pressure. AN APPROXIMATE THEORY FOR TWO-PHASE SOLVENT FLOODING The differences and similarities between conventional solvent floods and two-phase solvent floods are best understood by referring to concepts developed for miscible displacement in which miscibility is generated in the reservoir. In Fig. 1(A), a ternary diagram is shown for a hypothetical gas-solvent-oil system. To be rigorous the three components should each consist of a single molecular species. The pressure for Fig. 1(A) is greater than the critical pressure for the binary gas-solvent system at the specified temperature. Diagrams of this type are the ones most frequently referred to in discussions of enriched-gas drive and miscible displacement. A limiting tie line is shown tangent to the two-phase envelope and intersecting the gas-solvent line at Point A. To obtain generated miscibility with this type system, others have shown that, for an oil of Composition D, a mixture of gas and solvent must be injected which is richer in solvent than that composition indicated by A. An oil repeatedly contacted with a gas phase richer than A changes toward a composition which would be at equilibrium with the injected mixture, that is, a composition lying on a tie line which passes through the injected-gas composition. Since no such tie line exists, the oil is enriched to the point at which it becomes directly miscible with the injected mixture. At pressures lower than the critical pressure for the gas-solvent system, other types of phase diagrams are observed. The ones of interest in this paper are for pressures greater than the vapor pressure of the solvent, but less than the critical pressure of the gas-solvent system. Such a ternary diagram is shown on Fig. 1(B). In this case, two-phase behavior is observed not only for gas-oil mixtures, but also for certain compositions in the gas-solvent system. If a gas of Composition A (a dew-point vapor) is injected, once again the original oil is enriched by successive

By J. W. Spretnak, J. N. Cordea

The gain boundary relaxation in high-purity aluminum, nickel, copper, and silver was studied by means of a low-frequency torsion pendulum. Both internal friction and creep at constant stress tests were conducted. A lognormal distribution in relaxation times was found to account for the relatively wide experimental internal friction peaks and the gradual relaxation behavior during the creep tests. This distribution was separated further into a lognormal distribution of relaxation time constants and a normal distribution in activation energies. A spread of up to ±6 kcal per mole in the activation energies accounted for the major part of the distribution. A "double-peak" internal friction phenomenon was observed in silver. The activation energies in kcal per mole derived from the grain boundary relaxation phenomena are 34.5 for aluminum, 73.5 for nickel, 31.5 for copper, and 41.5 for silver. It was found that the rain boundary relaxation strength in these metals increases with the reported stacking-fault energy. GRAIN boundary relaxation phenomena have been observed in a large number of polycrystalline metals and alloys. Numerous investigations have been conducted to study the structure of the grain boundary through this relaxation process. One of the first investigators was Ke1-4 who observed that the activation energy for grain boundary relaxation in aluminum, a brass, and a iron was about the same as that for volume diffusion. He concluded that the grain boundary behaved as if it were a thin liquid layer with neighboring grains sliding over one another. Leak5 conducted experiments on iron of a higher purity and observed that the grain boundary activation energy is comparable with that of grain boundary diffusion. He suggested that, in metals where this relationship holds, the damping may be caused by a reversible migration of grain boundaries into adjoining grains. Nowick6 has presented an interesting view of inter-facial relaxation with his "sphere of relaxation" model. A relaxed interface is represented as one where the shear stress is greater than the normal value along the edges and zero in the interior of the interface. The region of the stress relaxation is pictured as a sphere surrounding the interface. From his calculations Nowick concluded that the slip along an interface is directly proportional to its length. Therefore, the time of relaxation, T, depends on the size of the relaxation interface. This means that in the Arrhenius relationship, t = TO exp[H/RT], valid for atom movements, the relaxation time T is predicted to be proportional to the grain diameter through the pre-exponential term, TO. Since the internal friction can be given as Q-1 = ?j wt/(1 + w2r2), where ?J is the relaxation strength and w is the angular frequency, an increase in grain size at a constant frequency will shift the peak to a higher temperature. A great deal of work has been done to determine the exact relationship between the internal friction and grain size.1,5,7,8 In metals, the grain boundary peaks are found to be lower and broader than predicted theoretically.&apos; The above model can explain this by a distribution in the size of the interface areas, represented by a distribution in the parameter tO, and an overlap of spheres of relaxation, represented by a distribution in activation energies. Both these phenomena result in an over-all distribution in the relaxation time, which could affect the internal friction peak height, breadth, and also position. This relationship between the experimental data and theoretical calculations appears very promising in the study of interfacial relaxation mechanisms. THEORY A lognormal distribution in t can sometimes be used to adequately describe the spectrum of relaxation times governing an anelastic relaxation. wiechert9 originally suggested such a distribution to explain the elastic after-effect in solids. This choice is particularly applicable to grain boundary relaxation when considering Saltykov&apos;s work.&apos;&apos; He found a lognormal distribution in the grain sizes within a metal. Recently Nowick and Berry11 have introduced a log-normal distribution in T into the theoretical internal friction equations. The form of the distribution function is where z = In(r/rm), and Tm is the mean value of t. The parameter ß is a measure of the distribution and is the half-width of the distribution when is l/e of its maximum, IC/(O). Nowick and Berry have described the methods to obtain the parameters Tm, ß, and ?,J from experimental internal friction and creep test data. In the idealized case, where only one relaxation event occurs with one relaxation time, only ?J and T are necessary to completely describe the event, and 0 = 0. For the broader internal friction curves 6 is some positive number greater than zero. The larger the 6, the greater is the half-width of the distribution in In t.

Jan 1, 1967

Jan 1, 1953

By Caudle B. H., Cooper H. E. Jr., O. K. Kimbler

The results of studies of areal sweepout behavior in nine-spot injection patterns are presented in this paper. The ratio of the production rates of the two types of producing wells in a nine-spot pattern is considered in its effect on breakthrough. A model study was used to develop a method to predict the production histories of both side and corner wells and to develop the production history of the pattern or the field. INTRODUCTION The importance of areal sweepout behavior in injection operations has been recognized for a number of years. We now know that the fraction of a reservoir which will be reached by an injected fluid is a function of the geometric arrangement of the production and injection wells and of the mobility ratio of the fluids. Of these two, the mobility ratio (which is a measure of the relative ease with which the oil and the injected fluid can move through the reservoir) appears to have the greatest effect on recovery. The effect of mobility ratio on production history has been reported for most of the dispersed injection patterns (i. e., five-spot, staggered and straight-line drives).4-6 ere has been very little published on the nine-spot injection pattern. This may be because the two types of producing wells in the nine-spot pattern can—and sometimes should —be produced at different rates. This adds a second variable (the fist being mobility ratio) to be covered in a study of the nine-spot flooding network. Muskat1 has reported the sweep pattern efficiency at breakthrough for a mobility ratio of one at various ratios of producing rates for the two types of wells. For these conditions he found maximum oil production at breakthrough to occur when the corner well (the producing well farthest from the injection well) is produced 10.7 times as fast as the side well. Other investigatorsa2,3 have studied a few of the many possible operating conditions possible with this injection pattern. This paper presents the results of studies which are strictly applicable to a nine-spot injection pattern surrounded by other nine-spots in a homogeneous reservoir and which has no flowable gas present (no oil bank is formed). Although the full ranges of the variables mentioned above have not been covered, the results reported here should allow reasonable estimates of field operations to be made. EXPERIMENTAL The well spacing geometry of the nine-spot pattern is shown in Fig. 1. Here we see that each injection well is surrounded by eight production wells arranged in a square. Four of these producing wells are located at the corners of the square; the other four are in the midpoints of the four sides. These two types of producing wells are called "comer wells" and "side wells" respectively. It is the ratio of the producing rates of these two types of wells that affects the breakthrough recovery, as calculated by Muskat.&apos; This ratio is defined as the total producing rate of a corner well divided by the total producing rate of a side well. The model used in this study represented one-eighth of a nine-spot pattern, as shown in Fig. 1. It contained the equivalent of one-fourth of a side well, one-eighth of a comer well, and one-eighth of an injection well. Because of these proportions, the actual producing rate ratios in the model were one-half of the ratios of producing rates as

Jan 1, 1965