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By K. H. Coats

This paper presents the development and solution of a mathematical model for aquifer water movement about bottom-water-drive reservoirs. Pressure gradients in the vertical direction due to router flow are taken into account. A vertical permeability equal to a fraction of the horizontal permeability is also included in the model. The solution is given in the form of a dimensionless pressure-drop quantity tabulated as a function of dimensionless time. This quantity can be used in given equations to compute reservoir pressure from a known water-influx rate, to predict water-influx rate (or cumulative amount) from a reservoir-pressure schedule or to predict gas reservoir pressure and pore-volume performance from a given gas-in-place schedule. The model is applied in example problems to gas-storage reservoirs, and the difference between reservoir performances predicted by the thick sand model of this paper and the horizontal, radial-flow model is shown to be appreciable. INTRODUCTION The calculation of aquifer water movement into or out of oil and gas reservoirs situated on aquifers is important in pressure maintenance studies, material-balance and well-flooding calculations. In gas storage operations, a knowledge of the water movemenr is especially important in predicting pressure and pore-volume behavior. Throughout this paper the term "pore volume" denotes volume occupied by the reservoir fluid, while the term "flow model" refers to the idealized or mathematical representation of water flow in the reservoir-aquifer system. The prediction of water movement requires selection of a flow model for the reservoir-aquifer system. A physically reasonable flow model treated in detail to date is the radial-flow model considered by van Everdingen and Hurst.1 In many cases the reservoir is situated on top of the aquifer with a continuous horizontal interface between reservoir fluid and aquifer water and with a significant depth of aquifer underlying the reservoir. In these cases, bottom-water drive will occur, and a three-dimensional model accounting for the pressure gradient and water flow in the vertical direction should be employed. This paper treats such a model in detail — from the description of the model through formulation of the governing partial differential equation to solution of the equation and preparation of tables giving dimensionless pressure drop as a function of dimensionless time. The model rigorously accounts for the practical case of a vertical permeability equal to some fraction of the horizontal permeability. The pressure-drop values can be used in given equations to predict reservoir pressure from a known water-influx rate or to predict water-influx rate (or cumulative amount) when the reservoir pressure is known. The inclusion of gravity in this analysis is actually trivial since gravity has virtually no efFect on the flow of a homogeneous, slightly compressible fluid in a fixed-boundary system subject to the boundary conditions imposed in this study. Thus, if the acceleration of gravity is set equal to zero in the following equations, the final result is unchanged. The pressure distribution is altered by inclusion of gravity in the analysis, but only by the time-constant hydrostatic head. The equations developed are applied in an example case study to predict the pressure and pore-volume behavior of a gas storage reservoir. The prediction of reservoir performance based on the bottom-water-drive model is shown to differ significantly from that based on van Everdingen and Hurst's horizontal-flow model. DESCRIPTION OF FLOW MODEL The edge-water-drive flow model treated by van Everdingen and Hurst1 is shown in Fig. la. The aquifer thickness b is small in relation to reservoir radius rb. water invades or recedes from the field at the latter's edges, and only horizontal radial flow is considered as shown in Fig. 1b. The bottom-water-drive reservoir-aquifer system treated herein is sketched in Fig. 2a and 2b. Here the aquifer

By R. H. Hopkins, R. W. Kraft

X-ray and metallographic analysis reveal that the preferred cryslallograPhic relationships in direc-tionally solid~fied Pb-Sn eutectic specimens can be stated: interface growth direction, Experiments in which tin single-crystal seeds were used to nucleate the eutectic demonstrate that the normal lamellar structure observed at steady state can be forced to break down initially to a semide-generate structure when the crystallograPhic direction of the tin seed does not lie within the preferred eutectic interface plane. A normal structure eventually develops by preferred grain growth. X-ray topo-graphs and rocking curves substantiate that the perfection of eutectic samples increases as growth proceeds until steady-state conditions prevail. RECENT years have seen substantial progress made in the understanding of eutectic solidification through both intensive theoretical1'' and experimental investigations (see Ref. 7 for a review and extensive bibliography of both aspects). Several important observations concerning the nucleation and growth aspects of binary eutectic solidification have been brought to light. Briefly some of these include the nonrecipro-cal nucleation of one phase upon another,'j9 the tendency for a specific low-index direction of one or both phases of the eutectic to be aligned in the growth direction during unidirectional solidification,'0711 and the production of lamellar microstructures having a preferred interface plane between "11-13 phases. Questions quite naturally arise as to the mechanism by which preferred grain growth evolves during eutectic solidification and what relationships (if any) connect the initial nucleation of one phase upon another with the preferred growth directions and interface planes observed after a few centimeters of growth in many systems. This study was initiated in an attempt to answer these questions. An experiment was devised in which both the nucleation and growth steps in the crystallization of a binary eutectic, Pb-Sn, could be correlated with subsequently developed eutectic morphology and crystallography. This was accomplished by nucleating the eutectic upon a tin single crystal seed and then causing the eutectic to grow from the seed by directional freezing. The morphology of the structures produced in this manner was then monitored metallographically and the orientation relationships and substructural perfection determined by X-ray analysis. The information thus ob- tained was correlated to the growth history of the samples. EXPERIMENTAL DETAILS The eutectic of composition 38.1 wt pct Pb and 61.9 wt pct sn14 was prepared by accurately weighing lead and tin of 99.999+ (from ASARCO and Lytess Metals and Chemicals, respectively), melting in a clean Pyrex beaker under an argon blanket, and casting into the proper crucible for resolidification as described below. Tin seeds were grown by the method of ~halmers," saw-cut, oriented by the Laue method, and soldered to the pull rod of the Czochralski puller. All seeds were given a final electropolishing (to assure the removal of any deformed material from the cutting operation) and acetone degreasing immediately prior to the nucleation experiment in which they were to be used. Eutectic samples were unidirectionally solidified in a horizontal graphite boat1' or by pulling from the melt16 with tin (or graphite) seeds. A flowing argon atmosphere was employed in all experiments and growth rates and temperature gradients, constant for a given run, varied from 2 to 4 cm per hr and 8" to 15°C per cm over the course of all the experi-

Jan 1, 1969

By J. J. Pye, J. B. Drew

The surface-diffusion coefficients of Ni63 diffusing on low-index planes of nickel single crystals have been measured over the temperature range from 400° to 1000°C using a precision autoradio-gvaphic technique. The activation energy for sur -face diffusion appears to he the same on the {111}, {110), and (100) planes and amounts to -0.60 ev. This is in good agreement with the value (-0.62 ev) reported for (111) planes obtained by mass-transport techniques. In an earlier paper, the authors have reported self surface-diffusion coefficients on silver.' In that work, a deviation of the diffusion coefficients from linearity in the Arrhenius plot was observed at high temperatures. This effect was attributed to a loss of tracer atoms into the bulk by volume diffusion. The purpose of the present work was to extend the technique developed to the nickel surface-diffusion system up to the point where volume diffusion would come into play. The nickel system especially lends itself to this technique due to the high efficiency of the isotope in darkening the film and the large absorption of the weak radiation (0.063 mev /3- particle of the trapped tracer atoms. The diffusion coefficients and ictivation energy for different orientations on nickel can also be compared with a report published by Blakely and Mykura 2 where a mass-transfer technique was used. This paper reports the self surface diffusion of nickel on the low-index planes over a wide temperature range using a precision autoradiographic technique. EXPERIMENTAL PROCEDURE The experiment is similar to that described in the earlier publication consisting of a radioactive needle as a source resting on a flat, smooth, chemically polished surface annealed in a dynamic dry-hydrogen atmosphere. The needle is held snugly on the surface by a holder fabricated from commercially pure nickel. The point source is made by grinding down a small-diameter nickel rod until a tip of approximately 0.1 mm radius is formed. It is then etched and the needle tip plated with the radioactive isotope Ni63. Nickel single crystals were used whose main impurities were spectrographically determined as Co 0.05, Fe 0.007, C 0.005, and S 0.003 pct. The surfaces, oriented to within 1/2 deg of the low-index planes, were carefully mechanically polished and etched in a 50-30-10-10 hot solution of acetic, nitric, sulfuric, and phosphoric acids giving a smooth polished surface. The crystals were then washed in distilled water and alcohol. Annealing temperatures ranged from 400° to 1000°C with a furnace arrangement in which the crystals could be brought up to temperature in times short compared to diffusing times. The temperature was maintained constant to ±10°C. In the temperature range investigated, the ratio of the surface-diffusion coefficient to the volume-diffusion coefficient (Ds/Du) was 105 or more and the mean bulk-penetration values, calculated from literature values of volume-diffusion coefficients,3 were on the order of 10-5 cm. After the diffusion anneal, the sintered needle is removed, and both the radius of the needle point and spot left on the crystal face are measured. The crystal is then placed on photographic film. Diffusion profiles are obtained by scanning the film with a recording microdensitometer which has a slit width of 10µ. DISCUSSION AND RESULTS The experimental conditions are such that the source strength and needle radius are essentially constant and the time is adjusted such that the mean bulk penetration is small. An exactly analogous heat-flow problem has been considered by Carslaw and Jaeger4 and the solution can be written in integral form as:

Jan 1, 1964

By K. N. Weaver

In the early 1950's the cement industry began putting a new emphasis on geology. This article points up some of the industry's raw materials problems that geologists are uniquely qualified to handle. Portland cement can be made from relatively abundant industrial minerals and rocks, and this may explain why cement producers placed little emphasis on geology during the early days of the industry. After World War 11, however, the industry began to recognize the need for geological exploration and some of the larger companies began to build a permanent geological staff. This development has its roots in: 1) The rapid expansion of the industry. After World War II and continuing into the early 1950's the demand for cement far exceeded the production capacity. This placed a great deal of pressure on the producers to enlarge capacity at their plants and to develop new sites. 2) The closing of many cement plants due to inadequate raw materials. Producers feared lack of raw materials due to inadequate exploration and evaluation. 3) An ever increasing pressure for upgrading of the quality of portland cement, necessitated upgrading the quality of raw materials. 4) The increasingly large capital investment needed to build new cement plants required a higher degree of accuracy in reserve calculation. These reasons are more or less self explanatory and will not be elaborated on. They are outlined to illustrate the probable evolution of thought among cement management to justify the development of a geological staff. In the author's personal experience the geologist must continually readjust to changing conditions within the industry. For example, cement production capacity grew so rapidly that today production is only about 70% to 75% of rated capacity (73.8% in 1963). Therefore, whereas the geologist's function during the active expansion of capacity was primarily one of exploration, one of his major functions today is the development of existing reserves. This assumes of course that reserves at existing plants have been proven to be adequate in terms of the company's reserve policy. Through the proper development of raw materials, the geologist can markedly influence quality control, production and long range planning. Examples of several of the operations of Medusa Portland Cement Co. will illustrate how proper attention to geologic detail pays off in the above areas. Because limestone is the major raw material of port-land cement, the examples will be concerned with it. DEVELOPMENT OF GEOLOGIC DETAIL One of the prime objectives of an exploration or development project should be the establishment of the stratigraphy and structure of the deposit. The basic tool for exploration and development is still the core drill, and the geologist must gain a maximum amount of information from a minimum amount of drilling. In order to obtain this objective the following is essential: 1) Adequate detailed geologic logging of cores. The core is first logged and separated into lithologically distinct units. In order to make the lithologic breaks as meaningful as possible, representative pieces of core (not all) are etched in dilute HCI. This removes the "drill polish", brings out the structure of the rock and indicates the proportion of dolomite and argillaceous material because dolomite and argillaceous material etch in relief. In this way the lithologic breaks become clearer and one gains a general idea of the chemical makeup before analysis. This method of logging lessens the probability of including two types of stone, e.g. limestone and dolomite into the same sample for chemical analysis. 2) Representative sampling for chemical analysis. After logging, the lithologic units are sampled for chemical analysis. A representative analysis can be obtained by extracting a 1-in. sample for every foot of core. For example, a lithologic interval of 10 ft to 20 ft would yield ten 1-in. samples taken at 11 ft, 12 ft, 13 ft... and 20 ft. These samples are then crushed, pulverized and split into a sample for chemical analysis. This sampling method represents a significant saving of time over splitting the entire core. 3) Preparing the core as a record. Because of the expense of storage and the difficulty of handling large amounts of core, only representative samples of each lithologic unit are saved for reference. An

Jan 1, 1965

By T. Gleason

Problems involved in applying wet scrubbers to gas cleaning coal dust from thermal dryers are reviewed. Careful consideration of all the elements going into a modem coal preparation plant is required in view of the increasing difficulty of applying suitable gas cleaning equipment. This problem arises not only from the presence of finer coals to be handled, but also from the pressures applied by both the general population and the plant operators to improve the standard of gas cleaning performance. The Peabody scrubber is presented by the author as a machine designed to help improve this cleaning operation. Wet scrubbing of fine coal from thermal dryers poses a number of problems in adapting the gas cleaning equipment to the fine particulate matter. Among them are: 1) Dust in gases leaving the thermal dryer cyclones is often extremely fine with high percentages of total dust loading less than 1p in size. 2) Flue gas entering the scrubber is corrosive since the coal fired in the thermal dryer furnace is in the range of 0.7% by weight sulfur or higher. Therefore, comparatively high cost stainless steel alloys or corrosion resistant linings are required for a satisfactory service life. 3) Requirements for residual coal loadings leaving the gas scrubber are continually being lowered, while modern coal preparation operation is imposing heavier burdens on the collection system through introduction into the thermal dryer system of very fine coal previously not recovered. The advent of flotation systems in increasing numbers is typical of this trend. 4) Installation of a scrubbing system on thermal dryers is made primarily to reduce air pollution and product recovery value is of little or no value. Therefore, the operating costs of gas pressure drop and water requirements must be held to a minimum. We have, then, the basic situation which calls for comparatively high cost stainless steel alloy wet scrubbers, which must be highly effective in removing coal fines particularly in the 0 to 5-p size range. Further, the standards of scrubber performance are continually being raised towards the level where gas discharged from the scrubbers must be essentially free of any coloration due to residual dust. In view of the highly refractive nature of fine coal dust, residual loadings of 0.01 grains per cu ft or less are required to provide a color free discharge gas. In the present specifications under consideration a residual coal loading of 0.05 grains per cu ft would be considered color free, since the discharge gases are saturated in the range of 150°F. The steam plume acts as a masking agent at the point of discharge, and upon dissipation of the 150° saturated vapor stream, the effluent gas stream could be essentially color free. The specification under consideration calls for residual solids loading of 0.05 or less grains per cu ft, given a coal size distribution shown in the basic data in Table I. It is noted that the dust laden coal stream has a size distribution by weight of 33% in the 2 to 5-p size range and 55% in the 0 to 2-p size range. The particle size distribution given in the specifications does not detail the percent by weight less than 1-p in size, and more important, the size distri-

Jan 1, 1963

By F. Forward, H. Veltman, A. Vizsolyi

Activities of oxides in the ternary FeO-MnO-SiO system are calculated from data on the binaries, using the Gibbs -Schuhmann method. These activity data are used, together with thermodynamic relations, to calculate the contents of oxygen, silicon, and manganese in liquid iron, and the composition of the corresponding oxide phases in equilibrium with it. Excellent agreement was found between calculated and experimental metal compositions, indicating that thermodynamic methods, such as those presented, can supply useful data on slag-metal equilibria, and are therefore capable of wider application. When molten steel containing oxygen is treated with a deoxidizer, the product of the reaction is composed of the oxides of the deoxidizing elements together with more or less iron oxide. This assemblage of oxides is presumably very close to equilibrium with the melt since it is formed directly from elements dissolved in it. Therefore, it is likely that metal analyses corresponding to a given oxide phase composition are calculable with considerable precision where sufficient information is available on activities in both phases. The present study was made to test this hypothesis in the case of deoxidation by silicon and manganese. Here experimental data on the relationship among oxygen, silicon, and manganese in the metal phase are available, as are activity data for the MnO-SiO2, FeO-SiO2, and FeO-MnO binary systems. A further objective was to demonstrate in a specific example how gaps in the data may be filled by judicious interpolation, and how the Gibbs-Schuhmann method is applied to obtain activities in ternary systems. The rigorous derivation of the latter, requiring considerable facility in handling partial differential equations, tends to mask the real simplicity of the method, and repel the very engineers and experimenters who would benefit the most from its use. I) GENERAL PROCEDURE Deoxidation of steel with silicon and manganese results in the formation of two phases, metal and oxide. The number of components is four—Fe, Mn, Si, and 0. The phase rule then gives the number of degrees of freedom: If temperature and pressure are fixed, 2 deg of freedom remain. Consequently, it suffices to fix the concentration of two of the components of the system for all the concentrations to be determined and, at least in principle, calculable. The practical problem is then to discover a straightforward method of calculation with a minimum of trial and error solutions. The type of reactions to be dealt with are like the following: Si (in steel) + 2 O(in steel) = SiO2(in oxide phase) The standard free energy of this reaction is readily obtained from the literature, so that the equilibrium constant can be calculated by the expression: Since the metallurgist is concerned with percentages rather than activities, a real solution requires information that will permit activities to be converted to concentrations. This information is fairly adequate for the elements dissolved in molten steel, but is not available for the FeO-MnO-SiO2 oxide system. Therefore, the first step in this study was to find the relation between activity and concentration for the three oxides making up the system. The next step was the calculation of slag and metal compositions that are in equilibrium with one another. As shown by the phase rule, it is sufficient to assume the values of two composition variables in order to calculate the rest. But which two are picked makes a vast difference in how difficult the calculation turns out to be, so that it is necessary to make preliminary trial of several routes to find the easiest one. A convenient method is to begin with the slag, and to pick FeO concentration and that of one of the other oxides. Starting with the relation between oxygen dissolved in the liquid steel and FeO in the slag permits a good first estimate to be made of the oxygen content of the steel in equilibrium with FeO, because the iron content being fairly close to 100 pct, Fe has an activity close to unity. Using this first estimate of oxygen activity, approximate values of the manganese and silicon contents of the melt are readily calculated from the appropriate equilibrium constants. A minor correction for the depar-

Jan 1, 1963

By T&apos Kê, ing-sui

INTRODUCTION ACCORDING to the classical theory of elasticity, the elastic portion of the stress-strain curve is represented by a straight line. Such a representation implies that there is a linear relationship between strain and stress and also that strain is a single-valued function of stress and vice versa. Actually, such a one-to-one correspondence between strain and stress does not exist in real metals. A well-known example is the elastic after-effect on unloading. Another familiar example is damping or internal friction, that is, the dissipation of energy attending vibration. In an extensive review of such phenomena, Zener1,2 has proposed the term "anelasticity" to denote that property of a solid in virtue of which strain is not a unique function of stress in the non-plastic region. The phenomena arising from anelasticity are called anelastic effects. The measurements on inelastic effects are, important in many fields of metals technology. Thus, in precise instruments such as watch springs, difficulties often arise from the slight dimensional changes after fabrication. The internal friction or damping capacity of metals is often an important factor in deciding whether they are appropriate for instruments in which there are accompanying vibrations.' However, for metal scientists, the study of anelastic effects furnishes a powerful tool for understanding many properties of metals in terms of their microstructures or atomic interactions. In order to utilize the anelastic measurements to their fullest extent for acquiring such information, the experimental studies of anelasticity must be interpreted by appropriate mathematical analysis. For a great many problems, however, the necessary information often can be obtained by general qualitative arguments. From the definition of anelasticity, any physical changes occurring in a specimen as a result of the applied stress will cause anelastic effects if such physical changes are accompanied by a delayed change of elastic strain. Under these circumstances, we have the condition that strain lags behind the stress. We may mention the stress-induced transportation phenomena as examples. These include the stress-induced thermal diffusion," the stress-induced diffusion of particles,8-12. and the stress-induced viscous slip along the microelements in metals.12-15 The differential equations describing the microscopic mechanism in these phenomena lead to relations in which stress is linear with respect to strain (and/or their derivatives). Thus if we can - demonstrate that the superposition principle is valid under the circumstances in which the anelastic effects are observed, we would expect in. the macroscopic relation a linear relationship between stress and strain and their derivatives. This report is to describe a number of anelastic effects observed in alpha-iron, and an attempt is made to derive valuable information from a critical study of these

Jan 1, 1948

By T. L. Joseph

A study is made of the amount of solution loss necessary to maintain the reducing power of the gas stream in the blast furnace. Curves are presented to show the effect of solution loss, moisture in the blast, and carbon dioxide from the flux on the nitrogen in the THE blast furnace process is based upon the counter flow of gases and solids. As CO, N, and H, flow upward from the combustion zones, oxygen is acquired from the descending charge. In the reduction of iron ore, a portion of CO is converted to CO, and similarly a portion of H, is converted to water vapor. The inert N,, from the air used in combustion, passes through the furnace with little change. Its concentration is, however, decreased by reactions such as direct reduction and solution loss which increase the volume of CO in the gas stream; Similarly the evolution of C02 from the limestone also dilutes the nitrogen. he purpose of this paper is to illustrate an idealized and simplified method of studying furnace processes by following changes in the gas phase between the tuyeres and the stock line. A more specific objective is to evaluate the effect of solution loss upon the CO/CO, ratio in that region of the furnace in which FeO is reduced to metallic iron. This last stage of reduction requires relatively high CO/CO, ratios to exceed the equilibrium requirements. Solution loss or the reaction of COZ with C to produce CO has a pronounced effect upon the ratio of the carbon gases and is necessary to maintain the reducing power of the gas stream if the consumption of coke is low. It will be explained later that indirect reduction followed by solution loss is stoichiometri-cally equivalent to direct reduction. Calculations will be made to show how the composition of the gas in the region of the mantle varies with coke consumption and with different amounts of solution loss. Such calculations show the condi- tions under which gasification of C with oxygen in the charge is needed to maintain the reducing power of the gas. Equilibrium conditions for FeO and the carbon gases will be used to establish a minimum CO/CO, ratio below which reduction will not proceed. The manner in which carbon is gasified in the furnace, at the tuyeres with oxygen in the air or above the tuyeres with oxygen from the charge, will be a basic feature of all calculations. It is hoped that greater interest in the use of top gas as a means of following furnace reactions will be aroused by the calculations and generalized curves which are presented. Bosh Gas Equations Subject to some alteration by the amount of moisture in the blast and by direct reduction, the gas leaving the combustion zones of a blast furnace has a definite composition. Because a relatively small amount of oxygen is acquired from the charge in the bosh and in the crucible, the products of combustion undergo little change until they enter the shaft. Bosh gas is, therefore, essentially the products of combustion of carbon in a deep fuel bed with air. The relative weights and volumes of reacting materials are expressed by the equation: 2~ + 0? + 3.76N, = 2C0 $ 3.76NZ [I] Air Bosh Gas -air = 79% N? = 3.76) 21% 02 Starting with a known mass of C consumed largely by air, Eq 1, but partly by water vapor, Eq 2, the volume and C + H2O = CO $ H? [21 composition of the bosh gas can be calculated and subsequent changes followed as reactions take place at various elevations in the furnace. As shown in

Jan 1, 1952

By H. C. George

The Wisconsin Zinc District, or the Upper Mississippi Lead and Zinc District as it is often called, lies in the southwestern corner of Wisconsin, in Grant, Iowa and Lafayette Counties, and it includes adjoining parts of Illinois and Iowa. The district is about 70 miles long, north and south, and about 40 miles wide, east and west. It lies wholly within what is geologically known as the non-glaciated area of the Upper Mississippi Valley. HISTORY OF THE DISTRICT The district was first opened up as a lead producer in 1822. From this time until 1860, about 205,000 tons of cog lead (galena) and washed lead (galena) was produced from shallow crevices and openings. From 1860 to 1900, about 74,500 tons was produced, and since that time, from 5000 to 7000 tons has been produced annually. Since 1900, most of the lead concentrate produced has been as a byproduct of the zinc mines. The first zinc ores were mined about 1862. These were the carbonate ores, locally known as "drybone." Very little zinc blende was mined in the district, previous to 1875. The zinc blende ores mined from 1875 to 1900 were mostly of the high-grade, hand-cobbed, sheet-ore class, which usually contained from 45 to 60 per cent. metallic zinc Such mines as the "Sallie Waters," "Quinlin," 'Lead Mine," "Benton Blende," and "Ida Blende," located near Benton, Wis., were mines which produced ores of this type, during this period. The mines located at Highland, the "Coker Mine" located at Livingston, Wis., and the "Opencut Mine" located at Shullsburg, Wis., were mines that were heavy zinc carbonate producers, previous to 1900. The production of zinc ores in the district from 1862 to 1890 was about 283,500 tons, mostly zinc carbonate, with a probable average metallic zinc content of 30 per cent. From 1890 to 1903, the production

Jan 1, 1918

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,' based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry' has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962

PERSONAL (Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Oct. 10 to Nov. 10, 1914: Jintaro Kojima, Ashio, Japan. E. R. Hinckley, Seoul, Korea. J. Homer Stover, Trenton, N. J. S. A. Taylor, Pittsburgh, Pa. Kirby Thomas, New York, N. Y. Lawrence Addicks, Douglas, Ariz. Keijiro Nishio, Tokyo, Japan. Noel Cunningham, Bethlehem, Pa. Alexander K. Hamilton, Chicago, Ill. E. C. Vigeon, London, England. Harold N. Lawrie, Portland, Ore. S. E. Fairchild, Jr., Philadelphia, Pa. C. Spence Thomas, Cardiff, Wales. W. C. Schmidt, Jr., New York, N. Y. Henry Tackmann, New York, N. Y. Kenneth C. Browne, New York, N. Y. Dr. David T. Day has resigned his position with the U. S. Geological Survey and opened an office at 1331 F Street, N. W., Washington, D. C., for practice as a consulting engineer.

Jan 12, 1914

By Bailey, Lewis Newton

Bailey, Lewis Newton, Master Engineer, Senior Oracle, 4th Regiment, U. S. Engineers, Headquarters Company, died of pneumonia, at Camp Merritt, N. J., on April 30, 1918. Baird, Louis, Lieut., Royal Field Artillery, British Army, died on the battlefield in 1915. Ballamy, John H., Capt., 103d Engineers, killed in action near Fismes, Aug. 9, 1918. Burt, Andrew, died in active service, 1916. Cobeldick, William Morley, Royal Engineers, died from gas poisoning on October 7, 1915. Dougall, Ralph, 4th University Co., Princess Patricia Regiment, killed in action early in the war. Evans, Alfred Winter, Lieut.-Col., New Zealand Rifle Brigade, D. S. 0., D. C. M. killed in action on October 12, 1917. Gorman, Thomas C., Lieut., Canadian Engineers, killed in France, Mar. 18, 1918. Hague, William, 1st Lieut., Engineer Officers' Reserve Corps, died in active service, Jan. 1,, 1918. Hall, William T., Capt., Royal Flying Corps, killed in action, May 19, 1917.

Jan 11, 1918

POSITIONS VACANT (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Wanted for a mill on the Ivory Coast of Africa an experienced amalgamator and millman. Salary, $160 to $200 per month. No. 18. ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Chemist-metallurgist of broad technical training, university graduate, with experience in chemical and metallurgical research work, desires position, preferably in the East. Has successful past that stands investigation. No. 73. Member, mining and metallurgical engineer; thorough technical training, Ph.D., Columbia University, aged 39, married, with-an-extensive experience in smelting, mining, and economic geological work in U. S., Mexico, and South America, desires position as assistant to the Manager or Superintendent, or as a director of experimental and research work, with a reliable mining or metallurgical company. The West, Mexico, or South America preferred. No. 98.

Jan 6, 1914

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Nov. 10 to Dec. 10, 1915: F. Lynwood Garrison, Philadelphia, Pa. E. Fleming l'engle, Costa Rico, C. A. William J. Lakeland, Burma, India. Fred Maccoy, El Oro, Mexico. Dwight E. Woodbridge, Duluth, Minn. 0. N. Scott, Toronto, Ont., Canada. Chester A. Fulton, Yonkers, N. Y. K. P. Swenson, Tokyo, Japan. Willet G. Miller, Toronto, Canada. - H. L. Mead, New York, N. Y. L. G. Huntley, Pittsburgh, Pa. E. DeGolyer, Norman, Okla. L. E. Howard, Lockport, N. Y. J. S. Lane, New York, N. Y. H. W. DuBois, Philadelphia, Pa. T. V. Nonactre, Argentina. Howard R. Stewart, London, England. N. H. Darton, of the U. S. Geological Survey, has returned to Washington after a long season of field work in New Mexico investigating the prospects of finding potash deposits in the Red beds.

Jan 1, 1916

By Vassiliki G. Stavropoulou

Although plane-strain is the preferred method of analysing many rock mecahnics problems, little is known about the behaviour of rock under this loading condition. A simple and inexpensive apparatus has been built for laboratory testing of rocks in plane-strain conditions. A thorough .investigation of the specimen geometry and the friction end effects showed that the results can be considered as reliable. The behaviour of a brittle sandstone in the simplest plane-strain condition [(03 = 0)] is significantly different than that of the uniaxial compression [(02 = U3 = 0)]. The plane-strain values of the Young's Modulus and the Poisson's Ratio are decreased in comparison to the corresponding uniaxial values. Dilatancy is also reduced in plane-strain, whereas the pre-failure brittleness of the rock increases. The most dramatic effect of the plane-strain condition is that on the strength of the sandstone, which increases by 49 per cent in comparison to its uniaxial compression value.

Jan 1, 1982

By S. A. Braley

DRAINAGE of acid mine water into surface streams of coal mining areas is one of the most serious problems of stream pollution, since there is no known method that completely prevents its forming and no economically feasible treatment after it has formed. The mine acid problem differs from other pollution hazards because acid production does not end with cessation of mining but actually becomes more evident when pumping is stopped. The acid problem in the Pennsylvania, Ohio, West Virginia, and Kentucky bituminous coal areas of the U. S. began with the first operation in 1761, and the volume of acid discharge today is largely the cumulative result of years of mining. Provided they lie above the drainage area, the oldest mines, now long abandoned, are almost without exception producing acid in the same manner as those now operating or recently abandoned. It is well to consider some of the many procedures that have been used to determine the composition

Jan 1, 1957

By Walter R. Hibbard

Whether we have occasion to think of it or not, an adequate and economic supply of energy fuels is vital to each of us. It is interesting to look ahead at the way in which fuels from supplementary sources will begin to enter into the energy mix to help meet the long-term national energy needs. From 1947 to 1965, the average annual rate of growth of energy consumption was 2.7%, with total energy demand in 1965 being equivalent to 54 quadrillion Btu's. During this short period of 18 years, the cumulative output of coal in the U.S. was 9.6 billion tons; natural gas, 193.5 trillion cu ft; and crude oil, 45.9 billion bbl. During the next decade and a half the nation's energy requirements are expected to grow at an average rate of 3.3% yearly, with consumption of energy expected to reach an annual rate of about 88 quadrillion Btu's by 1980, or 63% over the 1965 level.

Jan 12, 1967

By G. Pizzi, G. M. Ciucci, G. L. Chierici

The use of the material balance equation to estimate the volume of hydrocarbons originally present in a reservoir, whose producing mechanism is partly due to water drive, has been discussed in the literature by several authors. There is no general agreement upon the possibility of obtaining reliable results by this method. Gas reservoirs in contact with an active aquifer are considered in this paper. Theoretical considerations based on the cybernetic principle of uncertainty (which states that the internal structure of a system cannot be uniquely determined from its observed external behavior) lead to the conclusion that the volume of gas originally present in a reservoir of this type cannot be uniquely determined from its past history. The range of values which encompasses the actual value of the reserves varies from case to case and must be determined by either numerical or analogical methods. Results obtained for six gas fields are reported. All these fields were produced with small fluctuations in their production rates, as is common practice for gas reservoirs; no gas storage fields were considered. Results obtained show that reserves values in a range of 1 to 2, associated with appropriate aquifers, allow the matching of the reservoir past history with mean-square deviations less than the experimental errors involved in pressure and produclion measurements. Similar results have been found in several other partial water drive gas reservoirs. From these results it is concluded that gas reserves cannot be uniquely determined from the past performance of partial water drive reservoirs, at least in cases where the reservoir has been submitted to small fluctuations in the production rates, and pressure data of normal accuracy are available. INTRODUCTION A number of authors have analyzed the problem of estimating the reserves originally present in a partial water drive reservoir from its past pressure-production performance. Literature which deals with this subject can be grouped, according to their conclusions, as follows. 1. A reliable value for the reserves can be obtained even if reservoir data (pressure and cumulative production) are affected by errors within the normal range.'-' 2. A reliable value for the reserves can be obtained only if reservoir data are very accurate'- or if past production performance has been subjected to abrupt variations in the production rate."' 3. No unique value for the reserves can be obtained from reservoir past production performance. This conclusion has been based upon theoretical considerations" and verified in several field cases. The purpose of this paper, which deals only with partial water drive gas reservoirs, is to test the above conclusions against actual field cases. Some theoretical considerations on this problem are also presented. THEORETICAL CONSIDERATIONS As the behavior of a gas reservoir communicating with an aquifer depends on both the aquifer and the reservoir characteristics, the physical system to be studied is the combined gas reservoir plus aquifer. The information which is available for studying the performance of such a system is the well production rates and bottom-hole pressures, all given as functions of time. The external behavior of the reservoir-aquifer system is therefore described by 2n input variables (Gp, Wp,) and n output variables (p,), n being the number of wells in the reservoir. In reservoir engineering it is common practice to consider the reservoir as a whole, disregarding the internal distribution of pressures and of producing wells. This practice is equivalent to substituting the above multi-variable system with a single-variable system, where the average reservoir pressure is the only output variable and the cumulative production G,(t) and W,(t) are the input variables. The internal structure of such a system, defined by initial gas reserves G, aquifer shape and dimensions, boundary conditions and petrophysical parameters distribution throughout the aquifer, is unknown. Therefore, from a cybernetic point of view the system is a "black-box It has been demonstrated" that for a blackbox the indetermination principle holds. Accordingly, the number of different internal structures (or set of parameters) which can account for the observed external behavior is infinite. As a consequence, the initial reserves cannot be uniquely determined from the reservoir past performance. When W,(t) is known, the determination of G from

By Benjamin LeRoy Miller, Joseph T. Singewald

For a number of years Russia, India and Brazil have outranked all other countries as producers of manganese ores. During the 5 years immediately preceding the European war, the average annual production of Russia was 844,000, of India 694,000 and of Brazil 200,000 long tons. Since the outbreak of the war there has been a considerable falling off in the Russian and Indian production, particularly in the former, whereas the production of Brazilian ores has been greatly increased, amounting in 1914 to over 250,000 tons and in 1915 to nearly 350,000, with conditions favorable for a still larger production in 1916. Manganese is one of the few industrially important metals that are not produced in the United States in quantity commensurate with our needs, so that we have been compelled to import annually about 300,000 tons, having a value of over $2,000,000, and these ores have been obtained from the three countries mentioned above. Their rank as contributors to our imports of manganese ores was India, Russia, Brazil; and in 1913, Brazil contributed only one-fifth. During the past 2 years Brazil has furnished rapidly increasing quantities to this country, and, with the falling off of imports from India and Russia, has become our principal foreign source. In 1914, Brazil furnished two-fifths of the imports and more than India or Russia, and in 1915 over nine-tenths. The manganese ores of Brazil are consequently of more than usual interest to us at this time. The Manganese-Ore Distbicts of Brazil , The manganese mining industry of Brazil dates from the year 1894, and since that year the total production has been over 3,000,000 tons. With the exception of a small quantity produced in the State of Bahia from deposits west of the City of Bahia, this output has come from the

Jan 1, 1917

By R. E. Reed-Hill

The lattice reorientations in (1011) and (1013) twins of pure magnesium have been investigated using polarized light. Both forms (Ire subject 20 almost complete second-order twinning on the (1012) plane of the first-order twin. The observed deviations of composition planes by 6 and 3 deg, respectively, from coherent twinning planes are caused by second-order twinning. The experimental data indicate that (1011) and (1013) are reciprocal twins with a twinning shear 0.136. In a previous paper1 it was shown that the primary fracture mechanism in single crystals of magnesium strained in tension parallel to the basal plane is parting or fracture inside twins. In the temperature interval 25oto286oC, the observed twinning form, dominant in fracture, was a very small twin which formed in bands. Because these twins were very small and appeared in extensively deformed regions they did not lend themselves to X-ray analysis. Lacking Cou-ling and Pearsall&apos;s2 recently reported polarized light technique for magnesium, the twinning plane indices (K1) were originally determined by two surface composition plane measurements. This plane fell in a major zone (axis < 1120>) at an angle of 55.75 deg to the parent crystal basal plane. Because its habit deviated by 6 deg from{l0ll), 61.9 deg, the experimental data per se were not consistent with simple (1011) twinning and, for expedience, the twin was designated with habit plane indices (30341, 54.5 deg, representing the lowest set of indices corresponding to measured angles. Couling, Pashak, and sturkey3 have also found bands of reoriented lattice with a similar habit in polycrystalline specimens of magnesium and certain dilute magnesium alloys. These bands are significant because their formation in large numbers during plastic flow permit specific magnesium alloys to undergo very extensive deformation by cold rolling. Using polarized light2 they showed that the basal plane in the reoriented material was nearly parallel to the band habit and, as a result, proposed a mechanism for band formation involving a double twinning process in which (1011) twins form and then retwin according to (1012). Because of the obvious similarity between the twin bands observed in single crystals and in polycrystalline specimens, it was decided to investigate if the two phenomena were not identical and, if possible, to verify the retwinning hypothesis. The present paper is a report of this investigation and shows that the twins with the (3034) habit correspond closely to retwinned (l011) twins. Evi- dence is also given for an analogous retwinning process in (1013) twins. EXPERIMENTAL PROCEDURE Rectangular single-crystal specimen deformed in tension (stress axis in the basal plane parallel to [1010], as previously described,4 were polished electrolytically by Jacquet&apos;s method5 and etched in acetic picral.2 All twins studied in this investigation belong to a major zone, whose axis, [1210], was perpendicular to both stress axis and two sides of each specimen [(1210) surfaces]. These latter contain the plane of shear of the twins and measurements of the basal plane trace of twins on these surfaces determines the lattice orientations of the twins. The position of the basal plane in each case was determined with a polarizing microscope using a modification of the technique of Couling and Pearsall.2 For each twin the four positions of maximum extinction were measured, the data averaged, and then the pair of extinctions corresponding to the basal plane was determined by rotating the microscope stage and observing the position at which the color changed from orange to blue with a gypsum red, first-order plate inserted between the crossed Nicol prisms. EXPERIMENTAL RESULTS (1013) Twins—In general, especially in speci-mens deformed at 150°C, (1073) twins appear in greater numbers and larger sizes than (1011) twins, and the lattice reorientation inside these twins is therefore easier to study and measure. Fig. 1 shows an area of an unetched and unpolished (1210) crystal surface containing a number of (1073) twins sloping upward to the right at about 29 deg with the basal plane of the original crystal (horizontal direction). Slip line segments may be seen in both the parent crystal (running horizontally) and in the twins (sloping downward to the right at approximately -22 deg with the horizontal). As may be seen in Fig. 2, the slip lines in the twin are not at the proper angle (64 deg from basal plane of the

Jan 1, 1961