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By William Braden

IT is obvious that the choice of the method to be employed in the handling of blast-furnace slags and mattes depends upon local facilities and conditions which may indicate as advisable some particular plan. As a result of the variety of such conditions hardly any two smelters use identically the same method, though they be located only a few hundred feet apart. For instance, of the several plants in Leadville, Colorado, each has a more or less distinctive system. The same is true of Salt Lake City and vicinity. In view of this it is evident that the existing diversity of practice cannot be accepted, prima facia, as evidence

Jan 1, 1897

By J. B. DILWORTA

Ix estimating the investment-value of a mining-property or plant, the value of which decreases with operation, it is often necessary to know the sum which must be set aside periodically from earnings either to renew the plant at the end off its life, or to return the capital involved when the earning-power of the investment has ceased. In such cases it is manifestly incorrect simply to divide the total amount to be retired by the number of periods (usually years) during which the investment shall be active, as the sums periodically withdrawn have a certain interest-earning power varying with the length of time they are held and with the opportunities afforded for their investment. But though the interest may be considered to accumulate regularly year by year, yet the rules and tables for compound interest do not apply, owing to the addition of a fixed amount of new money to the total at the beginning of each period. Briefly stated, the problem of sinking-funds is, to find the amount of money which must be periodically set aside at a certain rate of interest, regularly compounded, to yield a certain sum in a given, length of time. In most practical cases the interest is compounded and the fresh amount added at the same time-usually once a year-and on this basis the problem may be solved as follows

Nov 1, 1909

The banquet Wednesday evening was attended by about 700. The list of speakers was unusually brilliant and each one proved to be so interesting that it was nearly midnight before the dancing began. Capt. Robert W. Hunt was toastmaster. Captain Hunt is about to celebrate his eighty-first birthday but is blest with unusual vigor and it was a great pleasure to all his friends to honor him at this time. His selection is toastmaster was a happy one. The guest of the evening, if among so many stars one could be selected from the rest, was Charles M. Schwab, who said nothing but the urgent telegram from his dear old friend, Captain Hunt, could have drawn him away from his seclusion on his Pennsylvania farm to attend the meeting in Chicago. Mr. Schwab's address was, as usual, scintillating with wit and humor; and while lie did not directly or indirectly allude to the steel strike lie did at the end of his talk discuss serious things and gave it as his opinion that any effort to legislate or control the high cost of living would be futile until this country got down to a basis of an honest day's work for an honest day's wage.

Jan 11, 1919

By Lachlan Gilchrist

MEASUREMENTS of resistivity by methods involving the use of two current electrodes and two potential electrodes in general collinear with the current electrodes have been made extensively in geophysical investigations. In the method developed by Wenner and made use of by Gish and Rooney, and later in a modified form by Lee, the distance between the current electrodes is divided into three equal parts by the potential electrodes. In one of the methods developed by Schlumberger prospecting methods and by Koenigsberger, one current electrode is placed at considerable distance from the other and potential measurements are made in the immediate neighborhood of one of the current electrodes. The method is described as the single current electrode method, and the effect of the distant current electrode is considered negligible or a correction is made for the effect in the calculation of the resistivity. Usually the correction that is introduced is based on the calculated effect for measurements made in a homogeneous conducting material. The useful application of these methods in prospecting for minerals, of course, is in regions where nonhomogeneous conditions exist. In many of these conditions it is very doubtful whether the effect of the distant current electrode may be neglected, except for measurements in the immediate neighborhood of the "single" current electrode, and corrections based on homogeneity of the medium will necessarily be inadequate. In order to obtain a degree of symmetry that would preclude the necessity for corrections for the distant electrode and that would simplify interpretation, it appeared desirable to use a central current electrode and a set of distant end current electrodes symmetrically placed about the central electrode as shown in Fig. 1 and to provide by means of auxiliary resistances that the currents passing into the earth at the distant end electrodes should be equal. Circumstances did not permit the operation of this plan in complete detail but a degree of symmetry was obtained by using a central current electrode and two distant collinear end current electrodes and by taking measurements along a line passing through

Jan 1, 1931

By N. K. Chen, R. Maddin, R. B. Pond

A METHOD has been described by Andrade' for obtaining very rapid grain growth so that single crystals of high melting point metals could be made with comparative ease. The furnace construction was essentially a very thin wire through which was passed an electrical current so that "a high uniform temperature" was maintained. The wire was surrounded by a fused quartz tube from which the air had been evacuated. Andrade applied this method to the growth of single-crystal wires of alpha iron, and Tsien and Chow2 prepared single crystals of molybdenum 0.25 mm diam in this way. In the present report a method is described in which the basic idea of the Andrade furnace is utilized. However, modifications are employed so that large single crystals of molybdenum or of any refractory metals can be grown. Furnace The modified Andrade furnace is shown in Fig. 1, and the detailed drawing of its construction can be seen in Fig. 2. The furnace proper consists of a 2'/2-in. diam fused silica tube, 20 in. long, which is evacuated continuously at the bottom. Two water-cooled copper electrodes hold the specimen by means of collets held in place in the electrodes by set screws. These electrodes serve also to transmit power to the specimen. The lower electrodes can be clamped to the stand, while the upper electrode is fastened in place to the bellows which in turn is further connected to one side of the lever arm, flexibly supported at the top. After the specimen is mo;nted- and the vacuum is secured, the lever arm is adjusted by means of the counter weight so

Jan 1, 1952

By M. J. Mullikin, J. B. Conway

Several different equation forms were studied to determine the extent to which each particular equation type yielded an accurate representation of a given set of first-stage creep data. Specially developed least-squares computer programs were employed to obtain unique solutions for the creep-equation constants. In studies of creep data for lead at 14.5"C, nickel at 70OCC, and arc-cast tungsten at 2400°C consistently good representations were afforded by a third-degvee polynomial in t113. Other effective correlations were obtained with the Andrade, Cottrell-Aytekin, and de Lacombe equations along with a third-degree polynomial in t112. A newly proposed creep equation involving a hyperbolic-sine term in t1'3 was also found to yield very satisfactory results. This appears to be the first use of such a functional relationship in the analysis of transient creep behavior. In general, the deformation behavior of a material subjected to a tensile load is described in a strain-time plot. Experiments have shown that, following the instantaneous elongation which results on loading, the instantaneous slope (i.e., creep rate) of the strain-time curve decreases gradually with time and approaches what appears to be a constant value. Equations, therefore, which are proposed to provide an analytical representation of such first-stage or transient creep behavior must be consistent with these observations. In other words, at time zero, these equations must yield a finite deformation value corresponding to the elongation on loading. Furthermore, the first derivative of these equations must exhibit a fairly high although finite value at time zero, and then values which decrease with time. It is also preferable, in general, that the derivative eventually assume a constant value at high time values. Although many studies of first-stage creep behavior have been made and numerous equation forms have been proposed for expressing this type of deformation behavior, it is still not possible to state with any assurance which functional relationship will be adequate for a given set of measurements. Parabolic relationships have been employed most extensively although logarithmic expressions have been shown to be applicable in some instances. Combined forms1 have been studied in considerable detail and have on occasion been found to be very effective. One such expression is that of iXndradea and involves a modified parabolic expression: where 1 is the instantaneous length, lo is the length immediately following load application, t is the time, and p and k are constants. Another combined form has been proposed by weaver3 as follows: where E is the instantaneous strain, is is the linear creep rate, t is the time, and a and b are constants.

Jan 1, 1967

By E. P. Dahlberg, R. E. Reed-Hill

On the assumption that stress or strain relaxation occurs as the result of a thermally activated process, equations are derived relating to tensile experiments that give the strain as a function of the time under the condition of constant stress, and the stress as a function of the time for constant strain. It is demonstrated that if the strain-rate equation i = previously proPosed by Kuhlmann., is used as a starting point, then the relaxation of strain at constant stress may be expressed by the equation c = (-RT/(Y) 1tz tanh (t + is the strain capable of being relaxed at any given instant. Similarly, it is shown that the relaxation of stress at constant strain may be given by a = (-RT/B) In tanh (t + t0)/27, where a is the instantaneois value of the relaxable stress. The fact that these relationships reduce to well-known empirical equations at both large and small values of the stress Or strain is also shozcn. The present theory is shown to agree well with experimental data obtained from tensile elastic aftereffect experiments on a zirconium specimen prestrained at 77 k as to make it strongly anelastic. It is also demonstrated that elastic aftereffect data obtained using torsional specimens ?,Lay agree reasonably well with the equation derived for the case of tension. RELAXATION experiments are often employed as a means of studying metallic deformation mechanisms.' The simplest and most commonly employed techniques involve stress relaxation at constant strain and strain relaxation at constant stress. In general, however, investigations of this nature have been seriously handicapped in the past by a lack of suitable equations giving the time dependence of the relaxing variable over an interval that extends from small strains up into the region where internal-friction experiments become strain-amplitude dependent. This paper presents a derivation of such a set of equations for the case where the time-dependent part of the strain is anelastic or recoverable and the specimens are loaded in simple tension. The relaxation of strain under the condition of constant stress will be considered first. Let us assume that strain relaxation occurs as the result of a reversible thermally activated process that occurs at a number of relaxation centers lying in an elastic matrix. Then, following Kuhlmann,2 we may express the rate of strain relaxation as follows: where C is the strain rate, AFx the free energy of activation of the process controlling strain relaxation, a, the effective or average resolved stress at the relaxation centers, u an activation volume, R the universal gas constant, T the absolute temperature, > a factor with dimensions of a volume that accounts for the strain contribution of a successful operation of a unit process, N the number of relaxation centers per unit volume, and v the Debye frequency. The first term on the right of Eq. [I] represents a strain rate in the direction favored by the stress, while the second term represents the rate in the opposite direction. It is implied in Eq. [I.] that both F and v are symmetrical with respect to the two basic directions of operation of a relaxation process. Eq. [I] may also be written where and S and Q are the activation entropy and activation energy, respectively, of the relaxation process. In the following, A will be considered a constant. This is compatible with a set of experimental conditions where the relaxation rate is controlled by a single basic reversible process in which it may be assumed that the temperature dependence of the product ?Nv is negligible in comparison with the temperature variation of the exponential term. It is also implied that v, 7, and N do not depend strongly on a, . In deriving a relationship for the strain as a function of the time from her equation, equivalent to Eq. [2], Kuhlmann2 chose to consider only the limiting cases where the time was either very small or very large. It will now be shown that it is possible to integrate Eq. [2] to obtain a single equation valid over a wide range of strains if the concept of relaxable strain is introduced. The use of this quantity, which is the difference between the instantaneous value of the strain and the value of the strain at complete relaxation, represents the primary point of departure of the present theory from that of earlier workers. Let us express the effective stress at the relaxation centers in terms of strain. For this purpose we may use the following equation derived by zener3 for the case of strain relaxation at slip bands: where M? and M are the relaxed and unrelaxed moduli respectively, go the applied constant tensile stress, and m an average orientation factor that takes account of the fact that a,, the effective stress at the relaxation center, may not be a tensile stress (i.e., a

Jan 1, 1967

By R. Stefanko

The use of strain gauges and compression pads for an underground bolt installation in a central Pennsylvania coal mine revealed that satisfactory anchorage could not be maintained in the shale stratum that constituted the immediate roof. Comprehensive laboratory tests resulted in a new shell designed with an increased area of contact and smaller surface serrations. Retightening of the bolt was also found to be beneficial for maintenance of high load values. Roof bolting in coal mines has progressed very rapidly in the last decade, and today this method of support is in general use. There are many theories concerning the functions of roof bolts, but the importance of beam building is indisputable. Proper tension in the bolts minimizes shearing along bedding planes and creates a thick, competent beam from individually weak layers. Bolting must be accomplished immediately upon exposure of the roof, and bolt tension must be maintained if roof failure is to be prevented. Seams are being mined today with roof bolt support where conventional timbering was not effective.' The widespread use of continuous mining equipment was made possible by roof bolts which permit long supported spans free of obstructions. Since adequate anchorage is the key to successful bolting, better methods for determining the efficiency of anchorage are continually being sought. Attempts have been made to measure bolt loads, thus assessing anchorage efficiency by employing sensing devices between the bolt head and roof. 3-s None of the techniques appears to be very accurate, and all have at least one serious deficiency. The greatest efforts are being directed toward the standardization of the pull test.6" Nevertheless, the author believes that the pull test is only one criterion for establishing the efficiency of anchorage and not necessarily the most important one. The conventional pull test involves the short-term application of forces, whereas the success of roof bolt installations is dependent upon the ability of anchorage to sustain relatively long-term forces. Therefore, it would appear that the time-dependent function of the anchor is the single most important parameter for the success of roof bolting in many types of rocks. UNDERGROUND TESTS Strain gauges and compression pads were employed to measure bolt loads in a central Pennsylvania coal mine.8 Bolting had been employed only sporadically in the shale top since dubious benefits were obtained with this type of support. Table I shows some typical results from this investigation. Anchorage losses were extremely variable among the bolts, but all showed a considerable degree of bleed-off. The tests indicated that anchorage efficiency was extremely low in this type of shale. The results confirmed that bolting under these conditions was practically worthless, and thus a waste of material and labor. Probably even more important, bolting constituted a hazard when reliance was placed upon it for support. Certainly the complete lack of confidence in roof bolting, which was apparent in the mine personnel, was justifiable since the bolts did not accomplish their purpose. PRELIMINARY LABORATORY BOLT TESTS The extreme losses in bolt tension that were detected in underground installations prompted a comprehensive study to assess the causes. However, preliminary studies were first made to determine the combined stresses in a roof bolt and to prove conclusively that the observed bleed-off phenomena were due to anchorage: slippage and not to some other physical manifestation. In all of the ensuing tests

Jan 1, 1962

By J. E. Cannaday, R. J. Austin, R. K. Saxer

PREVIOUS investigators have determined activation energies and have postulated various controlling mechanisms for creep.'-' Recently Barrett et 01.I5 have suggested, as the result of their work with cadmium, that the apparent activation energies for creep (AHc) above 0.5 T, could be correlated by means of activation energies for self-diffusion (AHSD) and modulus of elasticity functions: AHC = AHSD - (5RT/E) dE/dT. The wide disparity of apparent activation energies previously obtained with nickel compared to those reported for other fcc metals and the desire to test the postulate of Barrett el al. prompted this study. The as-received 17.5-mil nickel wire used during this work assayed 99.87 pct pure, Table I. X-ray analysis indicated that the wire was in a stress-re- lieved state and metallographic examination revealed an equiaxed grain size of approximately 0.01 mm. Specimens degreased in acetone and cut to 1-1/2 in. lengths were tested in a cam-mechanized constant-stress creep machine. A vacuum of at least lo-5 mm Hg was maintained during all tests. Stresses were applied when thermal equilibrium was established. When a measurable (at least 0.5 pct) secondary creep was observed, the temperature was pulsed to a higher temperature. Pulsing time varied from 30 sec at 480°C to 2 min at 1300'C and above. Slopes of creep curves were determined after the initial acceleration in the strain rate had subsided and steady-state creep was achieved. To confirm the results obtained, additional tests were performed incorporating a temperature pulsing method suggested by sherby. In this method the load was removed during temperature pulsing and reapplied after thermal expansion had occurred. No appreciable differences in results were obtained. Tests were performed over a wide range of temperature (470" to 1310°C) and stresses (250 to 17,000 psi). The expression was used to calculate activation energies. In this expression T1 and T2 are the initial and final temperatures, and el and i2 are the creep rates at T, and T2. The variation of the apparent activation energies with the mean test temperature calculated by means of Eq. [I] are shown in Fig. 1. The mean test temperature (Tmean) was calculated from the relationship

Jan 1, 1967

By Byron Johnston

IN 1926 I had occasion to make numerous measure-ments with a Pitot tube. The differential gage was mounted in a box, and since the work entailed setting upon girders, staging, and flues of various shapes and slopes, much time was generally expended in getting the box blocked into the level position. This inconvenience was so considerable that I devised the gage stand shown in the accompanying illustration. The gage is bolted to the board seat, the bolt per-mitting unlimited adjustment in the plane of the paper. The seat, carrying the gage, revolves on trunnions, per-mitting unlimited adjustment in a second plane, per-pendicular to the first. Consequently, the stand may be stood up, hung by one corner, leaned against some-thing or simply laid down, and the gage levelled from any position. On uneven surfaces, where the stand naturally rests on only three of its legs, it may be swung in the manner peculiar to the tripod, bringing the center of gravity within the triangle formed by the legs, thereby providing a firm set-up. Rubber stoppers under compression were found to give sufficient friction to hold the seat in the desired position.

Jan 3, 1928

By Arthur Phillips, C. H. Mathewson

During the past year considerable work dealing with the mechanical properties and microstructure following the anneal under uniform condi-tions of certain types of commercial rolled brass has been done in this laboratory. Since these experiments were conducted with the active cooperation of the Bridgeport Brass Co., involving free use of its product, and have thus furnished information which is characteristic of some of its special mixtures, full publication of the numerical relationships and comparative results encountered does not seem justifiable. Some of the more general features of this work are, however, available and it is our present purpose to use the material in question, along with some results of special tests, in discussing the characteristics of recrystallization as related to the degree of hardening by strain and the ordinary annealing variables. We desire to make acknowledgment of the many courtesies extended by Mr. Charles Ferry, Metallurgist of the Bridgeport Brass Co., and the value of his cooperation, which has greatly stimulated the study of brass in this laboratory. A clear and systematic presentation of the principal relations between temperature and time of anneal, the changing physical properties and microstructure and the degree of previous reduction by cold-rolling, was first made, in the case of rolled brass and copper, by the French engineer, C. Grard,' in 1909, although much fragmentary information of this general character had appeared earlier and the main facts involved were undoubtedly known to many brass specialists through their own private research. From this work, it appears that in the cartridge mixture (67 per cent. copper, 33 per cent. zinc) the properties imparted by cold-working within the limits, 13 to 75 per cent, reduction of area by rolling Original Area — Final Area 0.13 to 0.75), are not affected by anneal- Original Area " ing for a 50-min. period at any temperature below 200°C. At or in the

Jan 1, 1916

By D. L. McElroy

It is too broad a statement to say that the mine car is the most important unit in a haulage system, but almost every mining man will admit that it is one of the most important. The mine car is to the mine haulage system what the railroad car is to the railroads; the main purpose in each instance is to move the greatest number of ton-miles of material at the least cost. The data presented in this paper are taken from a study of mine haulage conducted by the School of Mines of West Virginia University at 42 mines in 8 coal fields of Wrest Virginia. The study was made possible by a graduate fellowship of the School of Mines and the cooperation of the mining companies of the state. Three important factors in the use of mine cars in West Virginia are: (I) the number of mine cars in use per loader; (2) the capacity of mine cars; (3) the distribution of mine cars. ("Loaders" in this paper refers to all men loading coal, whether manually or mechanically.) During the World War many mine managers were annoyed by the reduction of efficiency and production caused by railroad-car shortages. Today relatively little complaint is heard about a shortage of mine cars, yet possibly 50 to 75 per cent. of the mines in West Virginia are suffering from this cause of reduced production and increased costs. The railroads have solved their car shortage by placing in service more cars of larger capacity and better design. Many coal mines in West Virginia should solve a part of their cost problems by the same simple procedure. Such a procedure requires an initial outlay of capital, but there is little doubt that this will be repaid, with a good return on the investment. Determining Number of Cars Needed There can be no mathematical rule to determine the number of cars which should be in use per loader in a coal mine, because numerous factors such as concentration of mining, system of haulage, car capacity, speed of haulage, distance of working places from tipple, and so forth, affect materially the number of cars in use. These factors in turn are more or less determined by height of bed, character of roof and coal,

Jan 1, 1931

By Alexander Sattman, Anton Homatsch

Jan 1, 1894

By R. Bakish, W. D. Robertson

IN the course of a study of stress corrosion cracking of AuCu,, it was necessary to develop new electropolishing and metallographic etching methods. The techniques are generally useful for Cu-Au alloys, including the AuCu composition in which transformation markings are well delineated. For electropolishing, the only satisfactory electrolyte and procedure that has been found1 has the composition given in Table I. The solution must be vigorously stirred while polishing and the temperature maintained in the range of 55" to 62°C. The electrolyte is very unstable and can be used only for 10 to 15 min after which its color changes and a dark-brown precipitate forms. The polishing time is between 1 and 4 min depending on the initial surface preparation. The use of a hood is recommended to avoid the danger of cyanide gas which may form at one of the electrodes even though the solution is alkaline. The optimum current and voltage conditions for vertical anode and platinum cathode are on the plateau shown in Fig. 1, in which voltage is measured across the cell terminals. At voltages below the plateau, etching of grain boundaries occurs and under some conditions, which have not been clearly defined, octahedral etch figures are observed. For general purpose grain-size determination in polycrystalline alloys, a 3 pct solution of iodine in methyl alcohol is used with excellent results. However, when it is necessary to reveal small orientation differences or concentration gradients in an alloy, the iodine etch is not satisfactory. For this purpose, a highly satisfactory etching procedure was developed during this investigation. It involves the use of the vapor given off by freshly prepared aqua regia. The solution employed is 3HC1 to lHNO, which decomposes in accordance with the reaction HNO, + 3HC1 = NOCl + 2H,O + Cl,. The polished specimen surface is held about 1 to 2 cm above an aqua regia solution for 2 to 10 sec depending on the intensity of the contrast required and the surface is not subsequently washed. The results obtained with a coarse grained cast structure are shown in Fig. 2. Subgrain boundaries in a single crystal and concentration gradients within the boundaries are developed by the same treatment with the results shown in Fig. 3. Obviously, any conclusions regarding structure-dependent properties will be modified by the pronounced heterogeneity, which is not clearly evident when more conventional methods are used. Interesting structural details are also revealed by treatment for 4 hr at 850°C in unpurified tank argon. Fig. 4 shows a pattern characteristic of orientation-dependent oxidation.

Jan 1, 1956

By Gustaf Ising

For relative gravity measurements, the author in 1918 described an instrument1 of which the essential part consists of a highly astatized, standing pendulum turning about a horizontal elastic axis. This type of instrument has been used recently in practical field work, therefore a description of its principle and technical development is given herein. Part I, describing the principle, is a direct translation of the original Swedish paper.1 Part II gives an account of the practical elaboration of the instrument, together with some description of measure-ments performed.

Jan 1, 1937

By T. A. Read, M. S. Wechsler, D. S. Lieberman

A theoretical analysis of the austenite-martensite transformation is presented which predicts the habit plane, orientation relationships, and macroscopic distortions from a knowledge only of the crystal structures of the initial and final phases. THIS paper presents a new theory of the formation of martensite. This theory makes possible the calculation of the austenite planes on which the martensite plates form, the orientation relationship between the austenite and martensite crystal axes, and the macroscopic distortions which are observed. The only input data needed are the crystal structures and lattice parameters of the austenite and martensite. Considerable effort has been devoted over the past thirty years to the development of an understanding of the crystallographic features of martensite reactions. Much of this work has been done on steels and iron-nickel alloys, for which a great deal of data has been accumulated concerning the shape and orientation of the martensite plates, the relative orientations of the austenite and martensite crystal axes, and the observable distortions which result from transformation. These observations are reviewed in refs. 1, 2, and 3. The first major step toward an understanding of these phenomena was made in 1924 by Bain,' who showed that the a body-centered cubic structure can be produced from the 7 face-centered cubic structure by a contraction of about 17 pct in the direction of one of the austenite cube axes and an expansion of 12 pct in all directions perpendicular to it. Since that time, most of the efforts at further interpretation have been made by investigators who have worked from the phenomenological data, incorporating some of the information from the lattice properties, and have sought an analysis into likely deformations which would produce the observed results."- "11 but the three most recent papers on the subject have already been reviewed in some detail." Machlin and Cohenl0 measured the components of the distortion matrix and verified that the habit plane is a plane of zero distortion and rotation for the (259) case. They showed that the measured distortion matrix, when applied to the parent lattice, does not yield the product lattice and hence some inhomogeneous distortion must occur. Frank,u working from the lattice properties and taking some clues from the observations, considered the correspondence of close-packed rows and planes in the austenite and martensite. He predicted substantially the observed lattice relationship and habit plane for certain steels which have a (225) habit. Geisler12 suggested that there is a natural tendency for the habit plane to be a (111) and postulated certain slip processes to account for the fact that the experimentally observed habit plane is irrational and deviates from the assumed one. The present work differs from previous treatments of martensite formation in that it permits calculation of all the major manifestations of the process. Habit plane indices, orientation relationships, and observable distortions are all calculated from a knowledge of the crystal structures of the initial and final phases alone. The calculations contain no adjustable parameters. The agreement found between calculated results and the observations reported in the literature constitutes powerful evidence in favor of the mechanism of martensite formation proposed. The theory is applicable to systems other than steel (as is discussed later in this paper) which exhibit a diffusionless phase change but because of the wide-spread interest in the austenite-martensite transformation, particular attention will be given to the iron-base alloys. For other systems which undergo a similar face-centered cubic to face-centered tetragonal transformation, the mathematical treatment is identical with that presented here. Hence the theory successfully describes the transformation in the indium-thallium alloy.'" Homogeneous Transformation to Martensite The distortion which any homogeneously transforming volume of austenite undergoes in order to become martensite is shown in Fig. 1, as was first suggested by Bain.' (This distortion will hereafter be referred to as the "Bain distortion.") This specification of a contraction along one cube axis ;ombined with an expansion in all directions perpendicular to this axis describes what is properly called the "pure" distortion associated with this transformation. The distinction between a "pure" and an "impure" distortion plays an important part in the discussion which follows. A "pure" distortion is characterized by the existence of at least one set of orthogonal axes fixed in the body which are not rotated by the distortion. (These are called the "principal axes" of the distortion.) No such set of axes exists in the case of an "impure" distortion. On the other hand, an impure distortion can always be represented as the result of a pure distortion combined with the rotation of the specimen as a rigid body. For a given impure distortion the corresponding pure distortion

Jan 1, 1954

By R. J. Blackwell, J. R. Rayne, W. M. Terry

This paper presents results of an experimental investigation of factors that control the efficiency with which oil is displaced from porous media by a miscible fluid. The study was made to elucidate the relevant processes both on microscopic level (within individual or between neighboring pore spaces) and on macroscopic level (within a large sand body). Mixing of miscible fluids on the microscopic level was studied in sand-packed tubes. It was found that molecular diffusion is the dominant dispersion mechanism for reservoir conditions of rate, length and pore sizes. Macroscopic channeling was studied for various mobility ratios in reservoir mode1s scaled to relate viscous, gravitational, and diffusional forces. The formation of channels was due to viscous firzgering, gravity segregation and variations in permeability. With adverse mobility ratios, it was found for reservoirs of realistic widths that diffusion will not be effective in preventing the formation and growth of fingers, even in homogeneous sands. At sufficiently low rates channeling was eliminated by gravity segregation in tilted reservoirs. The dependence of recovery on mobility ratio, length-to-width ratio, flow rate and angle of dip is presented. INTRODUCTION Oil recovery by solvent flooding is finding increasing application in the field. While the process promises high recoveries from the region swept by solvent, under adverse conditions only a small fraction of the reservoir volume may be swept at the time solvent breaks through to the producing well. Further, the high cost of the solvent encourages its use only as a bank whose size must be kept at a minimum. Thus, two important questions arise: (1) what fraction of the reservoir can be swept, practically, by solvent? and (2) what is the minimum size solvent bank that can be used to carry out the displacement? The answers to these questions require knowledge of both macroscopic channeling processes and microscopic mixing processes. The studies described here were carried out to gain this knowledge. Microscopic mechanisms which cause mixing will be discussed first, because an understanding of these mechanisms is necessary for proper interpretation of the experimental work on channeling described later. INVESTIGATION OF MICROSCOPIC DISPLACEMENT PHENOMENA FOR MISCIBLE FLUIDS The questions to be resolved concerning microscopic displacement behavior are: (1) how much mixing occurs between oil and solvent in the direction of flow? and (2) does the solvent completely flush the oil from the pore spaces in the region invaded by solvent? The classic work of Sir Geoffrey Taylor' and its extension by Aris2 have shown that it is possible from theory to describe the amount of mixing in single straight capillaries when solvent displaces a fluid of equal viscosity and equal density. Aris showed that the lengths of the mixing zones, 81, corresponding to the 10 per cent and 90 per cent concentration levels of the solvent can be calculated from the formula, 81 = 3.62 \/Kt, .........(1) where 8l is the length of the mixing zone, cm; t is the time, sec; and K is the effective dispersion coefficient, cm2/sec, given by K/D = 1 + (1/48) (au/D)2......(2) where a is the radius of the capillary, cm; D is the molecular diffusivity, cm2/sec; u is the average velocity

By A. G. Weber, H. J. Welge

A published calculation method for predicting incompressible, multidimensional fluid displacement has been adapted to the problems of water and gas coning in oil wells. Since depth and radial distance from the wellbore are the two key dimensions affecting the shape of a gas or water cone, coning calculations are well suited to the use of two-dimensional methods. The alternating direction implicit procedure (ADIP) was used for relaxation calculations of two-phase potentials in a two-dimensional grid. From the potentials and the capillary pressure relationship, saturation and pressure distributions were calculated which trace cone growth with time. Predictions have been made for well producing histories both before and after core breakthrough. To check validity of the method, two-dimensional calculations have matched the coning behavior and produced water-oil ratio history of a laboratory sand-packed model. They have also matched the coning behavior of several producing wells, for which the calculations were compared with produced water or gas cuts and logs showing water or gas cone movements. INTRODUCTION The application of two-phase, two-dimensional calculations using ADIP to various reservoir flow problems has been described in the literature.1-3 When adapted for computer solution, this method has proved to be a powerful tool for simulating well and reservoir behavior. This paper discusses the method as applied to well coning calculations. Single-well and coning calculations comprise an especially difficult class of two-dimensional problems which require special techniques for computer calculation and determination of reservoir characteristics. Refs. 4 through 8 describe previous approaches to the coning problem. Several examples of water and gas coning calculations, including studies on both laboratory models and producing wells, are presented here. The two-dimensional method accounts realistically for the most critical parameters affecting coning behavior, including production rate, formation stratification, horizontal and vertical permeabilities, depth of well penetration, gravity and capillary forces. The method considers the different densities and viscosities of the two phases and the relative permeability and capillary pressure characteristics of the rock and fluids. In addition to tracing cone growth in the vicinity of the wellbore, the method calculates the overall movement of the fluid interface throughout the well's drainage volume. Incompressible fluid flow is assumed to occur between the producing interval and the well's limit of drainage. Calculations can be made for the producing history both before and after cone breakthrough. A typical two-dimensional grid or array of blocks used to solve a coning problem contains about 400 blocks. The well's cylindrical drainage volume can be represented by about 20 radial subdivisions and the formation thickness by 20 vertical subdivisions. The grid spacing is normally smaller near the withdrawal interval to define the cone shape accurately. For this work we used an IBM 7074 digital computer having a core memory of 10,000 ten-digit words. A typical study, covering 5 to 10 years of well producing history, required from three to six hours of computing time. MATHEMATICAL SIMULATION OF CONING BEHAVIOR BASIC METHOD In coning calculations, the reservoir volume drained by the producing well is represented by a two-dimensional system of blocks as shown in Fig. 1 for water coning studies. The horizontal dimensions of the blocks increase with radial distance from the well axis in geometric progression, i.e., the block size is small near the wellbore and large near the well's drainage radius (re). Vertically, the blocks are bounded by horizontal planes located at different depths through the

Jan 1, 1965

By R. H. Wightman, C. D. Chandler, P. B. Nalle

SURFACE quarrying at the Crestmore Div. of Riverside Cement Co. in California was started in 1909. In the early 1920's it was considered that these deposits were nearly exhausted for the equipment available at that time, and in 1927 the company began a block caving system. This mine continued operating until February 1954. In 1941 trucks and crawler-mounted shovels had reached a stage of development that permitted reopening the quarries in conjunction with the underground mine. In 1948 surface reserves and the well developed limestone of the caving system neared depletion. To go deeper with the caving system was unattractive because of the economics, changes in physical structure of the rock at depth, and the perched water table

Jan 4, 1957

By Lawrence Addicks

Some three years ago the smelter connected with the Chrome, N. J., refinery of the United States Metals Refining Co. found itself embarrassed by constantly increasing piles of unsmelted blast-furnace flue dust. The charge was fine and 10 to 15 per cent. of it was blown over into the flue. Sulphur was at that time too scarce to make the sintering of the finer part of the charge attractive, and raw-ore smelting in a reverberatory with a partly oxidized charge was not to be thought of. A great many schemes were considered, including leaching, blowing into the converters, and briquetting, the problem finally narrowing down to blast roasting and nodulizing. It was found by experiment that blast roasting would not yield a satisfactory sinter without the addition of coke dust or sulphide fines to augment the fuel value of the flue dust, and on this account, together with the low first cost of a kiln, the latter was decided upon. A couple of tons of flue dust were tried out in the experimental kiln in the laboratory at Yorktown, Va., of J. H. Payne, who acted as consulting engineer in this connection. This kiln was approximately 2 ft. in diameter and 20 ft. long and was fired with fuel oil. A run of several hours yielded excellent nodules. The ki1n showed no tendency to build in and form "nose rings" and gave a fuel consumption of 50 gal, of oil per ton of flue dust. There was no indication of any stack loss. The roasting was strongly oxidizing. A study of what full-size kilns were doing on cement clinker and on nodulizing pyrites cinder indicated that a 60 by 6 ft. kiln would certainly not consume over half of the oil per ton of flue dust shown on the test and as fuel oil at that time was selling around 2 1/2 c. per gallon it was decided to let it go at that. A 60 by 6 ft. kiln was decided on, as that size is standard in cement practice, although fast being replaced by much larger ones with their greater fuel economy, and as it fitted in the building space available. A 6-in. brick lining brought the net diameter down to 5 ft. The inclination

Jan 1, 1915