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By David J. Mack

A SURVEY and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CALCULATION OF YOUNG'S MODULUS FROM THEORETICAL OR EMPIRICAL CONSIDERATIONS Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Southerland (1891), but Fessenden 41,42 made extensive calculations a few years later and arrived at the relationship: [2E = 78. 101 (_L V] where V is the atomic volume. In 1923, Peczalski,43 working from the same stand-point but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: [E=B(m) 2] where B is a constant of value about 8 • 10 7, p is density and m is atomic weight; the atomic volume, of course, being m/p. Portevin44 immediately pointed out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: [E _ KT'Vb] where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson.45 Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff. 50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs.46-48 He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium,

Jan 1, 1945

By Thomas Leonard Watson

Jan 1, 1906

By H. Conrad

The strain hardening associated with the creep of magnesium single crystals at room temperatu.Je was investigated by shear tests in which the direction of stressing was reversed a number of times after creep in a <100> direction. The strain hardening was strongly anisotropic; the largest amount occurring in the direction of flow and the least 180 deg to this. The time law for creep changed from a parabolic type to logarithmic for the first and subsequent reversals of stress. For a given stress the creep strain decreased significantly for the first and second reversals and then only slightly for subsequent reversals. The logarithmic creep constant a changed in a similar manner. A linear relationship was observed between the creep strain for a given reversal and the stress. The slope for the third reversal yielded a strain hardening coefficient 12 to 16 times greater than that observed for unidirectional flow. Al-though no recovery was observed upon resting at room temperature, the hardening resulting from stress reversals could be completely removed by heating to 450" C. PREVIOUS work1.&apos; indicated that the creep rate of magnesium single crystals tested in the temperature range of 78" to 364°K decreased with time. This was attributed to an increase in internal stress resulting from an accumulation of dislocations at internal obstacles. The object of the present investigation was to further evaluate the nature of this hardening by conducting tests in which the direction of stressing is changed after previous creep in shear in a given slip direction. Previous to 1950 three investigations indicated that a Bauschinger effect3 occurred for single crystals as well as polycrystals brass in tension compression,

Jan 1, 1960

By W. C. Maurer

A study of the mechanics of shear failure of rock under pressure has been made. The transition from brittle to ductile failure occurs when the friction along the fracture surfaces exceeds the shear strength of the rock. A machine has been developed for measuring both the shear strength of rock and the friction along rock fracture surfaces. In this shear machine, the fractures are forced along definite planes; as a result, the rock is stronger than in compression tests where the fractures choose the weakest paths through the specimens. Friction is composed of several forces: (1) the forces to slide irregulurities on surfaces over each other; (2) forces to shear some of these irregularities; (3) molecular attractions across the fractures; and (4) forces required to break bonds resulting from melting and welding at the tips of irregularities on the surfaces. Friction along rock fracture surfaces is not proportional to contact pressure as usually assumed; instead, it increases as the contact pressure raised to the 0.4 to 0.8 power. INTRODUCTION It is difficult to produce tensile stresses under the high compressive stresses present in the earth; therefore, in deep drilling and geological faulting, shear failure predominates. This shear failure mechanism is complicated because rock is a heterogeneous material containing pore spaces, microfractures, elastic discontinuities and other imperfections. A study of shear failure of rock under pressure has been made to obtain a better understanding of this complex mechanism. A machine has been developed and used to measure the shear strength of rock and friction along sheared surfaces. This machine has certain advantages over the compression test — shear properties can be measured under low normal stresses and shear stress and normal stress can be varied independently. The first part of this paper is a description of shear failure of rock under pressure. The role of shear strength and friction along fracture surfaces in the shear failure mechanism will be discussed. The second part consists of a description of the shear machine and a discussion of the shear strength and friction data obtained using this machine. It will be shown that shear strength depends upon the size of the stressed zone, and that friction does not increase linearly with contact pressure as usually assumed. Attempts are made to relate some of the new concepts to tectonic failure and to dril ling. SHEAR FAILURE IN ROCK TRIAXIAL TESTS The shear failure mechanism is illustrated by the triaxial test shown in Fig. 1. In this test, a cylindrical rock specimen is subjected to a confining pressure, PC, and an axial pressure, pa. These external pressures produce normal a and shear T stresses on inclined planes within the specimen equal to1 where 0 is the angle between the specimen axis and a normal to the inclined plane. Fig. 2 shows how triaxial specimens deform as the axial pressure is increased. The pressure is

Jan 1, 1966

By R. B. Booth, W. F. Linke

The continuous interest of the American Cyanamid Company in producing superior polymeric flocculants and dispersants for the mining industry has resulted in a broad, general study of the physical chemistry of mineral-polymer systems. The aim of this program has been to establish a sound theoretical basis on which practical problems could be analyzed, and which would lead to the development of new and improved flocculating and dispersing agents. This study has required the cooperative effort of physical, analytical, and polymer chemists, as well as engineers familiar with mining problems. This report summarizes the results of some of our investigations over the past two years. Further studies along these and other lines are in progress and will be reported in the near future. MEASURING FLOCCULATION IN THE LABORATORY The foremost problem in studying flocculation in the laboratory has been to establish reproducible methods of comparing and evaluating the effectiveness of various reagents. Previous workers have measured settling -rates 1,8 filtration rates2 , and sediment volumes3 . Direct observations of the floc size, or the clarity of the supernatant liquid, can also be used. AIthough these parameters are all interrelated, they do not always measure the same physical properties of the suspensions, and hence are not equally useful or reliable. Whatever the method of comparison selected. the testing procedure must be carefully defined and standardized. The results must be satisfactorily reproducible, and for practical purposes must accurately reflect the results obtained in mill use. In order to compare the data obtained in these various types of test, the physical nature of the flocculated system must be examined in some detail. In an unflocculated system, only the larger or denser particles (the "sands") settle at a useful rate. The sediment can be observed to build up from the bottom of the cylinder, while the fines remain in suspension for a long period of time. If the system is not disturbed, even the microscopic fines can be seen to classify themselves as they fall over a period of days. When a high molecular weight polymer is added to the system, the colloidal particles are tied together randomly in flocs, and the sands and fines settle together. The line of demarkation between solid and liquid phases moves downward from the top of the cylinder. The settling rate of the flocs depends on their size and on their effective density. For a given mineral sample, the larger the flocs, the faster the settling. Since the large flocs cannot pack as closely as small ones, they produce a sediment with more pore spaces, and hence of larger volume, which is easier to pump and to agitate. Although it is nearly impossible to measure individual floc sizes, it is relatively easy to determine settling rates and sediment volumes. Of these two, the settling rate is simpIer to measure, and hence generally more practical. Reproducible sediment volumes can only be obtained by allowing the solids to pack for a rather long period of time (e.g., hours to days), and although the volumes thus observed are directly related to the degree of flocculation (average floc size), it is often impractical to wait so long for the results.

Jan 1, 1961

By H. Kazemi, G. W. Thomas, M. S. Seth

The double-porosity model of Warren and Root7 for examining pressure drawdown and buildup phenomena in naturally fractured reservoirs has been extended to intetpret interference test results. Both analytical and numerical solutions are presented. The practicality of some of the assumptions in the Warren-Root model was also investigated. The standard procedure for interpreting interference tests in naturally fractured reservoirs beretofore employed an equivalent homogeneous reservoir model. A comparison of our results with the equivalent homogeneous model indicates the latter is inadequate for early time responses. For late time responses, however, the simpler equivalent homogeneous model yields favorable results. Finally, the effects of well spacing and the magnitude of the interporosity flow parameter are briefly cited. INTRODUCTION Interference tests can be used to provide reservoir information not obtainable from conventional pressure drawdown and buildup tests. The technique involves measuring the response in one or more wells arising from a pressure perturbation introduced into another well. It has been. successfully applied to single-layer, homogeneous, unfractured, isotropic and anisotropic formations to arrive at values of well storage capacity and a measure of directional permeability.l The techniques of interference testing usually can be extended to heterogeneous systems, provided the permeability contrast between any existing rock layers is not excessive.9 In such cases, the practical interference effects in an observation well of an interconnecting heterogeneous reservoir can be predicted using an equivalent homogeneous model. The calculated properties are then average values. Russell and Prats2 have demonstrated the utility of this approach for a single-phase, two-layer system. For naturally fractured reservoirs, some different approaches usually are necessary. The major departure from homogeneous or nearly homogeneous reservoir treatment is to characterize the fractured system as an entity having "double-porosity"; namely, we suppose the existence of both primary and secondary porosity, where the former is contained within a systematic array of identical rectangular matrix blocks and the latter is contained within an orthogonal system of continuous, uniform fractures (see Fig. 1). It is sufficient to assume that the permeability of the rock matrix is so small that movement of reservoir fluids to the producing wells is entirely through the fracture network. This assumption has been validated by Barenblatt3 and .employed by others?-7 Warren and Root7 used the double-porosity model to develop an interpretation of pressure drawdown and pressure buildup tests in naturally fractured

Jan 1, 1970

By C. E. Sims

THE following presentation is more a summation of observations made and conclusions drawn over a period of three to four years than a report of experiments made with a definite objective. Tests were made, of course, to verify hypotheses, but the large mass of data was collected incidental to other work. Lack of space forbids the presentation of more than a few of those data. On the other hand, it is unfortunate that some of the most illustrative examples are not available. The work is admit¬tedly incomplete but is presented in the hope that it will stimulate further work along a similar line. The answers to many of the questions left unanswered by this paper will be found only after long and painstaking study, such as is scarcely possible in a commercial laboratory where problems of immediate importance consume most of the time. It is also hoped that this study will in some measure throw light on some of the dark spots of steelmaking, and help to clarify some of the annoyingly vague references to "good practice." Only cast steel was studied and the conclusions apply to cast steel, but it is the authors&apos; opinion that the quality of rolled or forged steel is largely dependent on the quality of the ingot, which is a casting. Although this discussion deals almost entirely with inclusions, it is important that the reader understand that only those natural inclusions which owe their origin to the solubility of certain materials in steel and to the chemical reactions of steelmaking are considered. Accidental inclusions, such as entrapped particles of slag, nozzle, runner, or mold are outside its province and are not considered. Such accidental inclusions are always dangerous and should be carefully avoided.

Jan 1, 1932

By F. W. Jessen, C. C. Patton

Adsorbed films were formed on polished stainless steel specimens from dilute benzene solutions of two crude oil distillation residua. Although the two residua were extremely dissimilar in composition, contact angle measurements showed that the two films increased the wettability of the steel specimens to oil by equal amounts. Furthermore, the wettability of the films was essentially unaffected by the desorption techniques used. Paraffin deposits were formed from heptane-wax solutions on the same stainless steel specimens. These deposits definitely adhered to the surface. Presence of an adsorbed crude oil film on the metal surface increased its free surface energy and resulted in increased deposition of paraffin. The addition to the heptane - wax solution of small amounts of the same distillation residua that were used to form the adsorbed films resulted in decreased cohesive strength in the deposits formed, which resulted in decreased deposition. The presence of a crude oil fraction both in the solution and as a preadsorbed film eliminated the adherence of a deposit of any kind. A mechanism of deposition is proposed which explains the results obtained. INTRODUCTION The natural formation of any predominantly organic accumulation in oilwell tubing, surface flow lines or other production and storage facilities is called a paraffin deposit. These deposits restrict the production of crude oil, causing a substantial increase in production costs because of decreased flow capacity, expense for periodic deposit removal and unproductive downtime. The conditions under which such deposits form, their physical characteristics and the nature and severity of the problem created are extremely varied. Over the past several years, much progress has been made in developing and utilizing methods to remove accumulated paraffin deposition. However, like so many other problems, the basic stumbling block appears to be a lack of understanding of the fundamental mechanism involved in the formation of such deposits. Crude petroleum is known to contain considerable quantities of polar, surface active substances which Doddl has shown to be present at the oil-water interface. Denekas, Mattax and Davis2 observed that the wettability of reservoir rocks was drastically altered by exposure to crude oil fractions; and Zisman, et a1.3 showed that the nature of the compounds adsorbed on a surface would determine its wettability characteristics. Cole and Jessen4 and Ehrig5showed that surface wettability can have a profound effect on the magnitude of paraffin deposition, and Parks6 demonstrated chat the presence of certain adsorbed films on a metal surface would reduce the adherence of paraffin to that surface. Zisman7 has since advanced the theory that the conditions for adhesion are the same as for wetting. Therefore, it was felt that there was adequate evidence to support the supposition that adsorption of compounds from a crude oil might play an important part in paraffin deposition. ADSORPTION-WETTABILITY EXPERIMENTS Initial experiments were conducted to determine the effects of adsorption from solution of crude oil residua on the wettability of a polished stainless steel surface. Distillation residua with initial atmospheric boiling points of 700F were used in preference to the whole crudes in order to concentrate on the molecular weight range of interest, and to eliminate the possibility of composition change due to evaporation of the light ends. Also, these high boiling materials would be expected to be adsorbed from the whole oil in preference to similar compounds of lower molecular weight.

Jan 1, 1966

By V. N. Cox, C. H. Grant

Both the underwater method and the rock cratering method contribute useful information in evaluating and comparing new explosive compositions. Results indicate that metallized explosive systems which contain no high explosives can be formulated to offer more energy and to do potentially more work than other slurry explosive systems. Commercial field trials are presently being conducted with a metallized explosive that does not contain any high explosive. Although there have been only a few commercial blasts to date, the results are encouraging. The Dow Chemical Co. has been engaged in explosives research since 1953. The incentive for this research was based on the desire to find additional markets and uses for magnesium metal of which DOW is a heavy producer. The thermodynamic calculations for explosives incorporating light metals indicate energies approximately twice that of nonmetallized explosives currently being used. Early in 1960, additional patent rights were acquired from independent inventors and a development station at Virginia, Minn., was set up to conduct a commercial testing and market evaluation program with this new product. The actual manufacturing of the explosive was to take place in the boreholes. Due to the complexities involved in controlling the manufacture of the explosive in the borehole, performance was sometimes in doubt. Furthermore, experience indicated that the metallized explosive systems could not be evaluated by the standard laboratory methods then being used, and it was necessary for us to look for more suitable research methods. Tests were conducted on several known methods for explosive evaluation. The most promising were the Navy underwater method for energy evaluation and a modified Livingston crater method intended to compare explosive performance in rock. After shooting over 2000 charges of 8 to 60 lb under water and in taconites and granites with many types of explosives, a metallized explosive was developed which is now being manufactured at a pilot plant in Virginia, Minn. and is being evaluated commercially. UNDERWATER METHOD An underwater method of evaluating explosives has a number of advantages. A permanent site can be established and operated indefinitely. A large number of charges may be fired in a short length of time. The medium in which the explosive is shot is exactly the same for successive shots. Data are recorded electronically minimizing human judgment. A disadvantage of the underwater method is the lack of confinement provided by the water medium. Many explosive compositions require a greater degree of confinement to develop good energy release. Although the relative significance of the two components of energy release that are usually measured, the shock energy and the bubble energy, and their relationship to breaking rock are not clearly understood, the underwater method is a valuable research tool for screening explosive compositions and gaining an insight into the manner in which explosives release their energy. Fig. 1 shows schematically the underwater apparatus. The piezoelectric gages are calibrated tourmaline crystals which convert the shock wave to an electrical impulse which is transmitted to an oscilloscope and recorded on Polaroid film. The shock traces are picked up by scopes 1 and 2. Scope 1 is timed to pick up the full trace whereas scope 2 is timed to cover the first increment of the shock trace expanded, and therefore allows full inspection of the propagation and peak pressures. Scope 3 records the bubble trace. When the explosion occurs, a bubble of gaseous detonation products is formed. The outward momentum of the water keeps expanding the bubble even after

Jan 1, 1963

By Young C. Kim

Abstract-The use of computer models to design the ultimate open pit limits during feasibility studies as well as during long-range mine planning is becoming an enforced Practice in all types of mining, e.g., ferrous, non-ferrous, and coal. As a result, the state of the art in computerized ultimate pit limit design methodologies and associated computing and optimizing techniques has advanced considerably in recent years. Unfortunately, very little has been published to date regarding the preferred ultimate pit limit design philosophy, i.e., optimizing m satisfying, or regarding the modeling approaches being used for different types of orebodies. This paper reviews the current state of the art in various modeling approaches and optimizing techniques that are in use for different types of deposits, through available literatures and personal communications.

Jan 10, 1978

By D. T. MacRoberts

This paper embodies the results of theoretical studies concerning gas reservoirs, especially the effect of drilling programs of various intensities upon pressure depletion and ultimate recoveries. The primary objective has been to determine the net quantity of recoverable gas that could be obtained as a result of each additional well, in comparison with the gas . that might be secured from a single well ideally placed with respect to both acreage and geological structure. No method is yet known whereby the relative merits of intensive and sparse drilling can be compared experimentally; a reservoir must either be drilled closely or developed with wide spacing, but both programs cannot be conducted simultaneously. Hence, the analytical method seems to be the only approach to the problem. While the present state of our theoretical knowledge does not offer a precise solution to the problem of gas flow in sand bodies, it takes such appropriate cognizance of the limitations of the methods used as to restrict any answer obtained to the realm of engineering accuracy. In solving the problem for the average gas field, it was found that practically the same answers resulted as to pressure distribution, regardless of the size of the drainage radius, even though the latter was assumed to vary from a few feet as a minimum to that of the entire reservoir as a maximum. Such limits represent extreme possibilities; therefore, the practical conditions that are associated with normal development programs, in which wells are placed in the center of tracts varying in size from 40 to 640 acres, will of necessity result in less extreme variations than those indicated in the tables accompanying this paper. Stated more concisely, the amount of gas unrecovered at abandonment (of the particular field used for illustrative purposes) will lie somewhere between 4.6 and 6 per cent of the total original content, no matter how intensively the field is drilled. Gas reservoirs may be divided into two general types, those in which the energy is intrinsic, and those of which the energy is extrinsic. † The first type contains energy in the form of a compressed gas, which expands

Jan 1, 1938

By Richard L. Stowe, Donnie L. Ainsworth

The static, rapid, and shock-loading response of rock is of interest to many in the field of rock mechanics. For example, the effects of loading rates on strength and stress-strain characteristics of rock are quite important in defining input loading for use in the design of underground protective installations. Response data on rock subjected to shock loading over a wide range of pressures are also vital in the field of underground nuclear testing. In addition, material response is needed in design of shock-absorbing liners. A number of investigators have reported that ultimate compressive strength of rock increases with increased rates of loading.1-6 Wuerker3 stated that modulus of elasticity, obtained from sonic determinations, increased in some rocks by a factor as high as 4.5. It appears that only a limited amount of work has been done on comparing static modulus and modulus obtained from impact testing.6 Phillips4 showed that with increased rates of loading the deformation decreased. More recent work by Atchley and Furr5 showed that when moderate-strength concrete is stressed with increased loading rates, the axial strain at failure increased. One would expect this to occur if we think in terms of purely elastic materials. For example, if E is constant and maximum strength [amax], increases, the axial strain would also increase. However, in rock testing thus far we have worked almost exclusively with nonhomogeneous and inelastic rocks. From this fact alone the increase in axial strain with increased load application is noteworthy.

Jan 1, 1972

By L. H. DeWald

During the examination of various commercial brands of copper wire bars, which had exhibited different degrees of adaptability for being drawn into fine gages of wire by the present-day high speed machine, it was found that each brand had a more or less characteristic crystal macrostructure. The extremes of these macrostructures are similar FIG. 1.-EFFECT OF METAL TEMPERATURE IN CASTING ON CRYSTAL MACROSTRUCTURE OF BAR. Reading from left to right, metal temperatures were 1166" C., 1149" C., 1132" C.. 1121" C., 1093" C. to the maximum variation shown in the photomacrographs reproduced in Fig. 1. As the various brands did not differ materially in chemical composition, it was concluded that the differences in structure were the result of variations in casting technique.

Jan 1, 1931

I HAVE striven to demonstrate to you as well as possible the method of bringing the metals of your ores to their ultimate perfection. But one cannot always do with gold that is found in the ores what is done with the other metals, for gold is not always accompanied by fine silver nor is it

Jan 1, 1942

By E. J. Ripling, M. W. Toaz

Tensile tests were conducted on pure magnesium and on four commercial alloys over a variety of temperatures and strain rates. The high positive slope of the ductility vs testing temperature curves that is found over a short range of testing temperatures for these materaturerials was shown to result from the fact that the microstructure was not stable at these testing temperatures. Pure magnesium did not display a transition temperature, although its sub-room temperature ductility was low. This poor ductility resulted from a grain boundary weakness. The aluminum-bearing commercial magnesium alloys had a higher ductility than the pure magnesium. ness.Thealuminum-bearingcommercialThese alloys did exhibit a transition temperature and grain boundaries that were stronger than the grain material. Both pure magnesium and the commercial alloys began initiating cracks at strains equal to one half of their fracture strain. MAGNESIUM base alloys&apos; enormous potential as structural materials lies in their high strength to weight ratios. At present, the high strength magnesium base alloys such as AZ-80, which will be discussed later, have about as high a tensile strength to specific gravity ratio as the highest strength wrought aluminum alloy, 75s-T6, and, of course, a much higher strength to weight ratio than structural steel. Further, since the magnesium base alloys develop their high strength to weight ratios with moderate strengths and extremely light weights, the ratio of load carrying capacity to the weight of many structures is relatively higher for the magnesium base alloys than their strength to weight ratios would indicate. This results because judicious increases in section size, such as increasing the depth of bending members or adding reinforcing ribs, can frequently increase the weight of a structure linearly while the strength and stiffness increase as the second or third power of the added weight. Strength and rigidity must be designed into lightweight structures by those techniques which establish multiaxial stress states. Consequently, strong, lightweight structures frequently also possess a greater propensity toward brittle failures. In order to insure against these catastrophic failures, an extra premium must be placed on ductility and toughness in light alloys. Current knowledge of the ductility and toughness behaviors—notched behaviors—of magnesium base alloys is limited.* Most of the magnesium base alloys * The state of present knowledge regarding the effect of testing temperature on mechanical properties has recently been summar-ized by Pritchard.&apos; crystallize in the hexagonal system, so that they are expected to exhibit a tough and ductile to brittle transition temperature. Actually, a transition temperature behavior has been reported for commercially pure magnesium in the literature, but the characteristics of this transition temperatureh uggest that it may not be a transition in the usual meaning, but simply the onset of some thermal softening, a performance much like that which face-centered-cubic lead might exhibit slightly below room temperature. If transition temperatures do exist, such important questions as the manner in which they are affected by internal variables such as chemical composition and grain size, or the effect of external variables such as rate of straining or notch severity have never been investigated. The investigation reported upon herein was undertaken in order to define some of the mechanical behaviors of the magnesium base alloys better, to gain a better understanding of the influence of some of the above listed variables, and particularly to understand their effect on ductility and toughness better. Material and Procedure Material-—Pure magnesium and four commercial alloys were used in this investigation. The alloys were selected so that chemically they made up a series with approximately the same minor alloying

Jan 1, 1957

By R. L. Sandefur

Professor Kim&apos;s excellent review article1 on ultimate pit planning contains a statement of the apparently widely held but incorrect belief that "kriging provides information on the confidence limits around the estimate which no other extension technique is capable of supplying." If a geostatistical approach is valid, there are several good reasons for using kriging but uniquely provided confidence limits is not among them. If kriging is possible, then confidence limits can be calculated for any other linear estimate.

Jan 6, 1979

By V. F. Swanson

At the AIME meeting in Tampa in Oct. 1966, an empirically developed equation was presented which allowed the calculation of free settling velocity for any sized particle: 1 [ ] This equation requires the use of two parameters a and p which are coefficients derived from boundary layer theory.2 It was possible to develop values of a and p for several minerals by back calculation of published data. The original equation had one major flaw. When the fluid density exceeds the density of the solids, the solution to the equation becomes imaginary. A flaw was indicated also by the fact that galena and sylvite both having cubic cleavage, did not have similar values for a and b. Galena gave calculated values of a = 1.082 and g = 3.11, while sylvite gave values of a = 1.870 and p = 2.56. These flaws prompted further study of the equation, resulting in the following empirical modification: [ ] It is obvious a real solution of the equation is possible for all values of ps and p. When PL > PS, V is negative, indicating that the particles will rise against the attraction of gravity. The validity of the modification is borne out by the fact that when values of a and p were back calculated for galena and sylvite using the modified equation, both minerals gave values of a = 1.038 and p = 3.01. With the modification shown in Eq. 2, Newton&apos;s friction factor becomes [ ]

Jan 1, 1976

By E. O. Wagner, V. F. Parry

This paper summarizes investigations during 1949 on three pilot plants for drying low-rank fine cool by entrainment in hot gases. Detailed operating results on processing seven coals having moisture ranging from 24 to 62 pct, formulas and data for calculating performance of large units, and general conclusions on the problem of drying fine coal are presented.

Jan 1, 1950

By AIME AIME

THE Engineering Education Committee of the Institute convened at the Engineering Societies Building on Feb. 18, .1929, with. E. A. Holbrook, dean of the Schools of Mines and Engineering, University of Pittsburgh, in the chair. STATISTICAL&apos; STUDY OF STUDENTS IN MINING The first paper, a statistical study of the students enrolled in courses leading to a mining degree in 40 institutions, was presented by H. D. Keiser,, assistant editor of the Engineering and Mining Journal; who gave a brief outline of an article he was about to publish in ?that journal?. The complete article appears in the issue for March 30; 1929: To avoid repetition the results are summarized as follows: A request was sent to 42 institutions which give courses in mining&apos; for the number of students enrolled as freshmen; sophomores; juniors, seniors and special students in mining for the years 1925-26, 1926-27, 1927-28, 1928-29. Two of these colleges replied that there were no students in mining. Students&apos; enrolled in courses in metallurgy, geology and engineering, other than mining, were excluded from the statistics:. The statistics received were arranged in, four groups, according to the completeness of the information. One complete group of 25 institutions &apos;shows as follows:

Jan 1, 1929

By F. F. Skiba, P. J. Root

A mathematical model has been used to investigate crossflow effects in a stratified reservoir during an idealized displacement process. A process in which one incompressible fluid displaces completely another incompressible fluid of the same density and viscosity was considered. The reservoir was assumed to be composed of homogeneous layers which are discrete but interconnected. Approximate five-spot flow geometry was simulated by arranging two pie-shaped cylindrical (two-dimensional) wedges in series. Some of the common production methods rely, for their effectiveness, on the fact that the formation consists of isolated strata. This is particularly true of selective plugging and single-zone production-injection methods. The effectiveness of these techniques for several cases in which adjacent strata are in communication has been evaluated. The usual production-injection schemes for fluid injection processes involve using the same completion interval in both the production and the injection wells. The efficiency of this, as well as alternative productioz-injection procedures has been examined for some cases involving communicating strata. INTRODUCTION The performance of many fluid injection projects is marred by early breakthrough and by production of a high percentage of the displacing phase after breakthrough. This channeling effect, if it occurs in reservoirs which have large permeability variations, is often explained on the basis of a model composed of discrete, isolated strata. Corrective or preventive measures based on this same model are also common. The behavior of stratified models has been the subject of considerable study. An excellent review of the early literature was given by Seba.1 Studies of the depletion performance have since been made for continuous, unrestricted communication between strata2-4 and for production from one permeable bed in continuous but restricted communication with an adjacent permeable bed.5,6 Model studies of displacement processes in stratified systems with crossflow also have been reprted.7-12 Finally, methods which account for crossflow have been developed for computing displacement behavior in stratified systems.13,14 Most methods for controlling or preventing channeling involve some change in the interval open to production and/or injection. Although many variations of the selective completion problem have been studied in regard to the depletion of a reservoir, little attention has been given to the behavior of a displacement process under similar conditions. Sebal used a resistance network model to study the performance of a process in which one incompressible fluid displaces an identical fluid from a linear, stratified reservoir. He investigated the possibility of improving the vertical coverage by limiting the completion interval of the production well. This investigation deals with techniques in which selective completion of the production and/or the injection wells is used in an attempt to control channeling. At one extreme, selective plugging and single-zone isolation (assuming perfect execution) should be successful if the reservoir is actually made up of independent strata. At the other extreme, they can hardly be expected to be successful if the channeling is caused by a mechanism in which stratification effects are negligible even though there are extreme variations in the formation permeability and/or the injectivity profile of the wells is not uniform. By contrast, it is difficult to anticipate the effect that the amount of communication between the beds of a stratified system will have on the efficiency of selective completion techniques. The objective of this study is the quantitative determination of the effect of communication on the behavior of some particular stratified systems which will at least lead to qualitative conclusions.

Jan 1, 1966