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By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.'" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase 'Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By John Wulff, David A. Stevenson

The solubility of iron and cobalt in liquid lead, the solubility of chromium in liquid tin, and nickel in liquid silver were determined up to 1300°C in an atmosphere of hydrogen. Liquid samples were taken at different temperatures and analyzed. The data obtained were plotted to show the relationship between log mole fraction of solute and the inverse of the absolute temperature. Resulting values for the differential heat of solution (AH) and the excesspartial molar entropy (S)are: for the iron-lead system = _24,200 cal per mole and AT = 5.0 e.u. for the a phase, and AH = 18,300 and S = -0.1 e.u. for the y phase; for the cobalt-lead system AH = 16,500 cal per mole and AS =0.7 e.u.; for the chromium-tin system AH = 15,600 cal per mole and AS = 8.5 e.u.; for the nickel-silver system AH =18,000 cal per mole and AS = 4.0 e.u. RECENT developments in coating, brazing, and heat transfer have focused attention on specific cases of solid-liquid interaction in metal systems, particularly those involving dilute liquid solutions. One fundamental quantity of interest in such systems is the equilibrium phase distribution between solid and liquid phases. In any effort to fully understand such interactions, one must be able to describe the equilibrium state precisely. Furthermore, in order to develop genera! relations for such systems, one must know the equilibrium state in a number of different cases. This investigation was devoted to a study of the equilibrium phase distribution in four binary systems: solid iron-liquid lead; solid cobalt-liquid lead; solid chromium-liquid tin; solid nickel-liquid silver. The iron-lead system was previously studied by Shepard and parkman' and later by Fleischer and Elliott2 with differing results. Both investigations were carried out by sampling the saturated liquid, and analyzing it chemically. The cobalt-lead system was previously reported by Pelzel,3 who noticed no discontinuity near the transformation. A limited investigation of the chromium-tin system was made by Wlodek and wulff4 using a weight loss method. This work was done in conjunction with the development of a process for coating molybdenum with chromium from tin solutions. To more fully under- stand the kinetics of the process, a more accurate determination of a solubility was desirable. No significant data were found in the literature on the nickel-silver system. Data on the latter system were, however, relevant to the investigation of the corrosion kinetics of copper-nickel alloys in liquid silver as carried out by Harrison and wagner,5 EXPERIMENTAL APPARATUS AND PROCEDURE Of the techniques available for the study of such systems the most effective appears to be that of liquid sampling,2,6,7 which is the method used in the present investigation. A schematic diagram of the sampling furnace is given in Fig. 1. Large pieces of solute metal, in excess of saturation solubility, were added to 200 g of the solvent metal, and the entire charge placed in an alundum crucible. Analytical reagent or materials of chemically pure grade were used in all investigations. The crucible was contained in a zircon muffle tube positioned vertically in the uniform hot zone of a Globar resistance furnace. The tube was provided with a number of ports which permitted sampling at temperature and in controlled atmospheres or vacuum; the ports were also useful for evacuation and introduction of gases as well as for thermocouple measurements. A chromel-alumel thermocouple Sheated in a porcelain tube was used for temperature measurements. A purified hydrogen atmosphere was employed in all experiments reported in this paper. The hydrogen was purified by passing it first over hot copper gauze to remove oxygen and then through a molecular sieve immersed in

Jan 1, 1962

By Neil H. Bostick

A specialized electronic data system processes data taken from normal gologic maps and stratigraphic tables to yield predictions of uranium resource location for an area such as much of the United States. Strata underlying specific quadrangle cells of the earth are evaluated for uranium favorability on the basis of selected criteria of lithology, structure, and stratigraphy but not specific past production in the area. Stored data are computer processed to yield volume of likely host rock beneath each cell to a given depth and at a given favorobility level. Results are plotted by machine directly as maps. A specialized and simplified procedure for predicting approximate uranium resources has been devised at Stanford Research Institute (SRI). The prediction is based on general geology beneath specific area cells of the earth in order to provide complete volume coverage; the strata underlying these areas are evaluated for uranium mineral favorability on the basis of a few selected geologic criteria in order to allow rapid data input. In order that the predictions be generally applicable, they are based on geological factors only, not past ore production of a given cell. Since the bulk of U.S. resources are in elastic host rocks, only such strata are considered in this work. This paper describes the structure and some details of the resource system and how it was tested in an area of the western United States.

Jan 1, 1971

By Philip Henry

THERE is a difference of opinion among engineers on the subject of depreciation in general, and still more on its application to any given case. The committee which was appointed by the American Society of Civil Engineers to make a report on Valuation of Public Utilities, states "There is no subject connected with valuation about which there are more diverse views than those relating to depreciation;" and in the discussion which took place upon the presentation of the preliminary report of this committee in January, 1914, that part of the report dealing with depreciation called forth more discussion than any other. From this discussion it was evident that the word " depreciation" was not always used in the same sense, so it is quite important that some definition be adopted. As this paper relates to the proper method of treating depreciation by corporations or individuals operating oil properties, both of which must make a return of annual net income to the government in connection with the income tax, it will be in order to adopt the definition of the Internal Revenue Bureau. Under date of Mar. 29, 1910, the Commissioner of Internal Revenue of the Treasury Department stated "Deduction on account of depreciation of property must be based on lifetime of property, its cost, value and use." Again, on Form 1035, "Return of Annual Net Income" for miscellaneous corporations (Section 2, Act of Congress approved Oct. 3, 1913), a deduction from gross income is allowed for "Total amount of depreciation for the year." This item is defined more particularly as follows: "The amount claimed under Item No. 5 (b) for depreciation should be such an amount as measures the loss which the corporation actually sustains during the year in the value of buildings, machinery, and such other property as is subject to depreciation on account of wear and tear, exhaustion, or obsolescence. The amount taken credit for on this account in order to be allowable should be so entered on the books as to constitute a liability against the assets of the corporation. The amount claimed under this item should not cover losses in the value of stocks and bonds. Decrease in the book value of securities owned, so far as such decrease represents a decline in the actual value of such securities, should be deducted under item 5 (a) of the return.

Jan 1, 1915

By Arthur S. Coffinberry, Ralph Hultgren

WE have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, combined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atoms, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electronto-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such information is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By Arthur S. Coffinberry, Ralph Hultgren

We have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, combined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atoms, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such information is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By Arthur S. Coffinberry, Ralph Hultgren

We have studied the gold-aluminum system by X-ray diffraction and by the microscope over the entire range of composition for temperatures between 300° and 500° C. Results obtained are shown in Fig. 1, combined with the work of Heycock and Neville1 at higher temperatures. The diagram differs in important details from that given by Hansen2 in his critical compilation of the literature of binary alloy systems. This work was undertaken both because of the intrinsic value of a knowledge of the phase diagram of this system and because of the need of theoretical metallurgy for precise and accurate data, particularly X-ray diffraction data. Systematic studies of equilibrium diagrams, particularly by Hume-Rothery,3 have shown regularities that yield a certain insight into the nature of alloying forces. It has been shown, for example, that solid solubility depends on the concentration of free electrons in the alloy, on the relative radii of solvent and solute atoms, on the forces of attraction between atoms, and on the relative stability of intermediate phases. The well-known Hume-Rothery rule states that the crystal structures and compositions of many intermediate phases depend on the electron-to-atom ratio. This has been confirmed and extended by wave mechanical calculations.4 A knowledge of the forces between atoms in alloys, even an imperfectly developed empirical one, should be a valuable guide in the preparation of technological alloys of desirable properties. Furthermore, such information is basic in such problems as rate of diffusion, age-hardening, phase transformations, and others. The most valuable data for this purpose are furnished by X-ray diffraction studies. Unfortunately, work has been

Jan 1, 1938

By Harry C. Swanson

TRANSPORTING concrete from mixer to forms has always been a problem. Twenty-five years ago this task was generally accomplished by means of wheelbarrow or concrete buggy. On large dam jobs, as the number of these projects increased, the gantry crane or highline came into use. Today several methods of handling concrete are employed on smaller surface construction jobs, for example, transit-mix trucks or dumpcrete trucks, which have crawler cranes with buckets for placing concrete into forms. In 1944, during early stages of developing Mather mine A shaft, several large underground concrete jobs were necessary. At this time the Cleveland-Cliffs Iron Co. purchased the first pumpcrete machine, introduced by the Chain Belt Co. of Milwaukee. The machine was used to pour approximately 200 cu yd of concrete for a dam, or bulkhead, located 400 ft from the shaft. Concrete was mixed on surface, lowered down the shaft 1000 ft in a 2-cu yd bucket hung under one skip, spouted into the bowl of the pumpcrete machine from the bucket, and pumped directly into the forms.

Jan 4, 1954

Joseph Hartshorne was born in Philadelphia in 1852. He died Aug. 23, 1918. After graduating from Haverford College, he took a special course in chemistry at the Massachusetts Institute of Technology, and later at the University of Pennsylvania. He started with The Pennsy!vania Steel Co. as an apprentice in 1873, working in the laboratory and mills for two years, and then one year as foreman in the Bessemer Department. Next, he was assistant chemist in the second Geological Survey of Pennsylvania. In 1878, he went to Prance to investigate the Pernot open-hearth furnace for the Cambria Iron Co. Upon his return, he assisted in designing and erecting the plant in Johnstown and was foreman of a turn for one year, and superintendent for the next. In 1881, he became superintendent of the Bessemer and rolling-mill departments. In 1884, he went to Pottstown and also made a trip to Europe to investigate the Bessemer basic process. Upon his return he dcsigned and erected the basic Bessemer plant for the Pottstown Iron Co., and was superintendent there until 1893, when the company failed. Since then he has been a consulting metallurgical engineer, and expert in patent cases. The !most important of the latter was that of Krupp versus Midvsle on the armor-plate patent case, in which he was leading cxpert for Midvale. He was a good linguist, having command of French and German, and a fair knowledge of Italian and Spanish. In all, he made eight professional trips to Europe.

Jan 1, 1920

By I. L. Dillamore

A purely geomentrical analysis based on oriented-growth relationships is presented to derive annealing-texture orientations in bcc metals from their- known deformation textures. The analysis takes as its starting point a description of- the bcc deformation texture and follows previous work on fcc metals in considering pvobable nurleation sites for recrystallization and the textural limitations on grains growing into a deformed matrix. The analy-sis accounts for the prominent and the minor coinponents of the annealing textures formed from two the deformation textures and can account for the ob-sem:ed temperature dependence of the annealing texture of bcc metals. THERE have been a number of investigations of annealing textures in bcc metals but few attempts to relate these textures to the deformation textures. This has been largely due to the lack of definition of both annealing and deformation textures, neither of which shows sharply defined orientations. It is, however, necessary to get a better understanding of primary recrystallization textures in bcc metals in view of increasingly exacting demands upon the quality of steel sheet for drawing purposes and as a necessary step towards the control of textures through processing. An analysis is presented here which relates annealing textures to deformation texture, by a purely geometrical method. This takes as its basis the oriented-growth theory of recrystallization and makes some reasonable assumptions regarding the make-up of bcc deformation textures and the limitations on growth relationships in bcc metals. Detailed information on this latter point is not available at the present time, and the present analysis may need to be streamlined or extended when such information is at hand. It is felt, however, that despite these limitations the analysis provides useful results and a valuable aid towards understanding the effect of processing variables. 1) BCC ROLLING TEXTURES Different workers have used a variety of descriptions for the texture developed in bcc metals by rolling. For the present purpose it will be assumed that two different deformation textures can be obtained: 1) a texture containing a major (112)[li0] component and a minor (001)[1i0] component for which increasing deformation causes the (001)[li0] component to increase at the expense of the (112)[li0] component, as suggested by Dillamore and ~oberts' (this is the texture predicted to arise starting from randomly oriented material); 2) a t~xture containing the above components and (111)[110] and (ii1)[112] components. This texture could arise from a material with an initial (110)[001] or (iil)[112] texture. It is well-known that the (ll0)[001] orientation rotates to (ii1)[112]that on roll-

Jan 1, 1965

By F. D. Rosi, F. C. Perkins, L. L. Seigle

An investigation was made of the mechanism of plastic flow in coarse grained specimens of both sponge and iodide titanium at low (-196°C) and high (500° and 800°C) temperatures. Deformation by slip occurs predominantly on a {1011} plane and in a <1120> direction over this entire temperature range, and secondary slip on {101-1} planes becomes more prevalent with overthisentireincreasing temperature.range, The crystallographic habit of the predominant twin planes becomes more prevalent with type is temperature-dependent, and deformation by twinning increases as the temperature of testing is lowered. Kink bands were not observed at -196OC and rarely at the high temperatures. A LTHOUGH the deform a tional mechanisms in . -titanium at atmospheric temperature have been extensively investigated," there is little information regarding the influence of testing temperature on these mechanisms. The only available data come from the recent work by McHargue and Hammond, who extended single crystals of iodide titanium at a temperature of 815°C. No significant changes in the types of slip and twinning planes were observed, but increased activity on the type I, order 1 pyramidal slip planes and on the type 11, order 2 twinning planes was reported. These planes contribute very little to the deformation process at room temperature.&apos;&apos; &apos; Since there is interest in titanium as a material for use at both low and high temperatures, the present investigation was undertaken to examine the slip and twinning behavior in coarse grained specimens of titanium at -—196", 500°, and 800°C in order to determine the general effect of temperature on the mechanism of plastic deformation. Experimental Material Used and Specimen Preparation—Both sponge and iodide titanium were used in the present investigation; chemical analyses appear in Table I. These materials were arc-melted under argon into 25 g slugs, which were then cold-rolled approximately 90 pct to a sheet thickness of 0.05 in. Since the strain-anneal technique was used for obtaining coarse grains, the cold-rolled sheets were made into tensile specimens which were then annealed to produce a relatively coarse uniform grain structure prior to critical straining. The details of the strain-anneal treatment. size of grains, and the method for preparing the specimen surface for optical microscopy have been described in a previous report.&apos; In order to obtain a wider spread in crystal orientation for the present work, it was necessary to vary the rolling schedule to reduce the degree of preferred orientation in the annealed sheets prior to critical straining. Methods for Tensile Testing—The apparatus for experiments at the temperature of liquid nitrogen (—196°C) consisted of two concentric stainless steel

Jan 1, 1957

It is doubtful if the far-reaching sociological influence and effects of the last few years will be fully appreciated within the present generation, but there are certain lessons and morals already apparent from which we should profit immediately. One of these has been an insistent, though vague, feeling among engineers and men of technical training and experience, that their worth as political and economic factors is not recognized by society. This feeling has found expression first in a tendency on the part of these men to organize for the purpose of securing recognition, or to demand greater activity in their interest on the part of societies already organized. However it may be accomplished, the demand for some means of binding engineers together for purposes of self-interest and public good is in the air and will not be denied. In other words, the time is&apos; propitious for two things: vastly increasing the membership of engineering societies, and serving that membership according to its desires. There are particular reasons why every mining and metallurgical engineer, in the United States at least, should hold membership in the

Jan 6, 1919

By A. G. Willard

Quantification of size, shape and composition has been one of the more difficult areas for those concerned with fine particle processing of coal.&apos; Image analysers fed by optical microscopes and by scanning electron microscopes possessing backscatter detectors and energy dispersive facilities now offer techniques to improve the speed and precision of previous methods. This paper discusses the methodology and procedural difficulties associated with the microanalysis of coal. Photographs show display quality on the image analyser monitor and the equipment mentioned. Data illustrating several of the procedures are included. The major portion of data for design and operation of plant for fine particle processing depends on information regarding size, shape and composition of granular material. The lower limits of particle sizes become more important as lower grade deposits are mined. Because of the trends towards treatment of finer materials, the use of image analysis offers advantages in time, effort and accuracy. As energy becomes more critical, the above applies especially to coal processing. The Zeiss Microvideomat 2, a leading member of the second generation instruments, is now available for image analysis. There is a precision television scanning system with monochrome camera, display, control panel and central processor (see Figure 1).

Jan 1, 1980

By J. E. Chappelear

We are concerned with the problem of calculating the forces produced by passing waves on a submerged object (in particular a drilling barge) located on the ocean floor. We employ the linearized theory of waves (the Airy1 theory), since solutions are generally more easily obtained in such a theory. It will be indicated how an approximate solution to the problem can be obtained for waves of finite height by use of a linear combination of Airy waves. We shall assume the submerged object has an infinite length, thus neglecting diffraction and making the problem two-dimensional. We find that there is not a considerable difference between our solution and the usual engineering solution. The force, as a function of time, is plotted in Figs. 4 and 5, together with the usual solution for easy comparison. So far, no experiments have been found to compare with the results. As will be shown, the calculations can be extended to waves of finite height (Stokes2-Struik3 waves) in an approximate fashion. This can be done by calculating the force produced by each Fourier component of the wave, separately, and omitting the coupling between the various harmonics produced by Bernoulli&apos;s theorem. The problem and its boundary conditions will be briefly stated. We seek a function, +, the velocity potential, which is harmonic, ?2?=0...........(1) and which satisfies the boundary conditions ??/?n =0 .......(2) (the normal derivative of + is zero) on the ocean floor and the sides of the barge, and s??/?y = ?..........(3) on the ocean surface, where s = g/w2........(4) The physical reasons for these choices and an interpretation of ? are given by Lamb.&apos; As previously stated, we assume also that the problem is two-dimensional. We set up our coordinates such that x = 0 is the center of the barge and y = 0 is the ocean floor. The coordinates are shown in Fig. 1, together with the location of the barge on the bottom. Our solution may be decomposed into a function which is symmetric about x = 0,?e, and one which is antisymmetric, +,, ? = ? + ?o...........(5) Thus directly above the barge we have as boundary conditions that for x = 0, ?o = 0, ...........(6) and ??e/?x = 0........(7) Now, far from the barge, we have that (for x positive and assuming the waves are incident from the left) ?e ? Ae cosh ky cos k (x + a) , . . . (8) and ?e ? Ao cosh ky cos k (x + ß) . . . . (9) where + means ". .. approaches ... for x large." Let us put Ae, Ao, and k equal to one, and remember that, in accordance with the derivation of Eq. 3, a sinusoidal time factor is to be supplied. Then we may rewrite Eq. 8 for ?e, and we find that

Jan 1, 1958

By Paul B. Crawford, Bobby L. Landrum

An electrical model study has been mode to estimate the effect of horizontal fractures in thick reservoirs on pattern conductivity. For the patterns studied, it is shown that fracturing all the wells in the pattern in-creases the conductivity considerably more than frac-turing only single wells. For certain conditions one large fracture is more effective in increasing conductivity than several fractures of half the radius. Particularly in thick reservoirs and with large fractures, the center of the pay is found to be more responsive than other locations. For the seven-spot pattern fracturing the center well is more effective in increasing pattern con-ductivity than fracturing all outer wells with fractures of the same size. INTRODUCTION Although commercial fracturing has been used for some time very little quantitative information is known about the effects of fractures on reservoir behavior. The purpose of this work was to estimate the effect of horizontal fractures in thick reservoirs on the con-ductivity of various flooding and cycling patterns.2 Circular fractures originating at the wellbore and extending symmetrically into the pay were considered. ANALYSIS Electrical models were used in making this study. Horizontal fractures were simulated by copper sheets shaped like the fractures and of a proportional size; the wellbore was simulated by a copper wire. A dilute salt solution served as a conducting medium. A con-ductivity bridge was used to measure the conductivities of the various patterns studied. EFFECT OF HORIZONTAL FRACTURES ON CONDUCTIVITY Fig. 1 shows the effect on square and staggered line drive patterns of horizontal fractures located in the center of the pay. The model is shown schematically in the insert. The upper and lower groups of lines show the effect on conductivity when all wells are fractured, and when only one well is fractured, respectively. In general, pattern conductivities are substantially improved by fracturing all wells. Fig. 2 shows the effect of multiple horizontal frac-tures on the conductivity of a line-drive pattern. At

Jan 1, 1958

THE award from the fund established by Mrs. John-son, in memory of her husband, J. E. Johnson, Jr., to be given to some promising engineer, not over 40 years of age, because of meritorious research, inven-tion or contribution to the professional literature of iron and steel along the lines of blast-furnace process, has been given, for, 1928, to P. H: Royster. Mr. Royster was born at Raleigh, N. C., in 1888. and graduated from the University of North Carolina, in 1907, taking his A.M. degree at, the same school in 1908. He then went to Harvard where he continued research work in physics. After engaging for a while in commercial research in the turbine department of the General Elec-tric Co. and with Cutting and Washington he joined the staff of the Bureau of. Mines in 1916 and was assigned to work on the physical chemistry of the blast-furnace process. He worked with A. L. Feild on slag viscosity and they jointly presented-to the Institute the. papers on "Temperature and Viscosity Relations in the Ter-nary System CaO-A12O3-SiO2" (TRANS. LVIII, 658) and "Slag Viscosity Tables for Blast-furnace Work" (TRANS. LVIII, 650). He also presented a paper on "Production of Ferromanganese in the Blast &apos;Furnace" .(TRANS. LXII, 18), and jointly with T. L. Joseph contributed a paper on "Effect of Coke Combustibility on Stock Descent in Blast Furnaces" (TRANS. LXX, 236), and another on "Pyrometry in Blast-furnace Work" which was included in the special pyrometry volume published in 1920. The titles of these works perhaps sufficiently indicate the part Mr. Royster has played in the notable research work on the blast-furnace process carried on by the Bureau of Mines, and for which the committee recommended him to the Board of Directors to receive the Johnson award.

Jan 2, 1928

Meeting, Aug. 20, 1913, B te, Montana, at 12.45 p.m.-On, the written request of 27 members of oft Institute residing in Montana, the Montana Local Section was established, and the following Committee was appointed by the President of the Institute to complete the organization : E. P. Mathewson, Chair pan; Frank M. Smith, Vice-Chairman; D. C. Bard, Secre-tary, Montana State School of Mines, Butte, Mont., Oscar Rohn, James L. Bruce. The President reported the appointment of a Committee on Mining Law, the names of whose officers and members are given on page xxxv of this Bulletin, and these appointments were approved. It was voted: That the Committee on dining Law be requested to establish a Sub-Committee on Censorship, a majority of whom shall be lawyers; and, further, that no paper on mining law be recommended for publication to the Committee on Papers and Publications, unless it is previously approved by the Sub-Committee on Censorship of the Committee on Mining Law. The President reported progress in the matter of co-operation between the Institute and the United States Bureau of Mines, through Committees of the Institute. The President reviewed the history of plans for a union or affiliation with the Mining and Metallurgical Society of America, and the following minute was then adopted : " The Board of Directors of the American Institute of Mining Engineers has carefully considered for several months the question of union or affiliation with the Mining and Metallurgical Society of America ; and, while at an earlier time and under other circumstances, such. a union might have been accomplished, yet under present circumstances the Directors of the Institute deem such union inexpedient. "While thanking the Mining and Metallurgical Society of America for its consideration of the matter, we believe that further discussion of the subject will serve no useful end, and we conclude it best that the Society and the Institute continue their useful functions and friendly relations side by side, as heretofore."

Jan 10, 1913

By L. D. Jaffe, J. H. Hollomon

THE effect of tempering temperature and time upon the properties of quenched steel is clearly a subject of great practical importance, as well as of considerable theoretical interest. It would be very desirable to be able to predict the properties of a quenched steel when given any selected tempering cycle, with a minimum of experimental work upon that heat or even type of steel. Two problems are involved: one consists of relating the structure obtained to the physical properties, and will not be discussed here; the other, with which this paper deals, involves the relations of time, temperature and composition with the structure obtained on tempering. Indentation hardness is perhaps the most convenient quantitative measure of the tempered structure, or of what might be called the "degree of tempering." Undoubtedly, it is not an exact measure, and in some cases (as when temper-brittleness occurs) pieces of the same quenched and tempered steel may have widely differing properties at the same hardness. However, hardness has the advantage of being simple to determine and is certainly the most widely used indication of the degree of tempering. Moreover, for fully quenched steels that are not temper-brittle and do not contain retained austenite when quenched, it appears that, in general, if the hardness of the steel is the same, the tensile and impact properties will also be identical, whether a high or a low tempering temperature is used. The tempering charts available in the metallurgical literature usually give the hardness as a function of tempering temperature for only one tempering time. However, in practice, tempering times frequently vary, and a method of converting tempering curves for one time to tempering curves for some other time would be very valuable. It is also advantageous, in determining the tempering treatment necessary for a given part, not to have to temper samples at several temperatures for the time used for the commercial tempering operation. A more satisfactory procedure would be to employ times of the order of 10 to 30 min., rather than 5 or 10 hr., and if possible to use only one temperature. Furthermore, it is frequently desirable, for reasons such as temper-brittleness,* to obtain a given hardness with short times at relatively high temperatures, and it would be convenient to be able to compute without tests the time required to produce this hardness. Remarkably few quantitative studies of the hardness of quenched steel tempered over wide ranges of temperature and time

Jan 1, 1945

By James T. Gow, Oscar E. Harder, Anton de S. Brasunas

This paper deals with the results obtained and the techniques employed in determining: 1. Liquidus and solidus temperatures of the HH and HT type heat-resistant alloys. 2. The relation of true temperatures (thermocouple) to apparent temperatures (optical pyrometer) for the molten HH and HT type alloys. This work was the outgrowth of needing to know something definite about these temperatures in order to study the effect of pouring temperatures, shake-out times, and heat-treatments on the properties of some heat-resistant alloys. The information developed is thought to be of interest to industry for guidance in foundry practices and the industrial heat applications of the alloys. This paper is based upon work that has been done for the Alloy Casting Institute at Battellc Memorial Institute. Liquidus and Solidus Temperatures of HH and HT Type Alloys Experimenta1 Procedures Temperature-time curves were obtained during the cooling and solidification of several HH and HT type alloys. The metal was melted in an Ajax high-frequency, induction furnace and poured into a core-sand mold for cooling. The temperature measurements were obtained by means of a platinum, platinum-rhodium thermocouple contained within a fused silica sheath, which was extended through the side wall of the dry core-sand mold to a point at about the center of the mold cavity, which was 3 in. in diameter by 5 in. deep. The cold junction of the thermocouple was kept in an ice bottle, and the temperature was recorded automatically on a direct-reading potentiometer recorder. Through a switching arrangement, the temperature recorded was checked occasionally with a portable Leeds and North-rup potentiometer indicator. Less than a 5°F. variation in the two instruments was always found. This is within the limit of accuracy of readings. The thermocouple used was checked for accuracy against a standard couple, both before use on this work and after completion of the work, by the instrument laboratory. Temperature-time Cooling Curves Fig. I is an enlarged reproduction of a part of one of the cooling curves over the temperature range of 2600&apos; to 2200°F. for an alloy of the HT type with 0.45 per cent carbon, 16 per cent chromium, and 36 per cent nickel. This is a typically shaped cooling curve as obtained for the alloys. It will be noted that two temperatures "re shown on Fig. I for the liquidus temperature. It is thought likely that the higher temperature, A, at the point at

Jan 1, 1945