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By Frank Schrader

INTRODUCTION THE present sketch is submitted by request in the hope that it may serve as a basis for geologic discussion of the mining camps in Mohave County, which is experiencing a marked revival of activities. The region, commonly known as the Mohave district and Kingman district, lies in western Arizona in the southern part of Mohave County, bordering California and Nevada on the west (Fig. 1). Kingman, the principal-town; is situated near the center of the area. on. the Atchison, Topeka & Sante Fe Transcontinental Railway. This region is composed of naked desert ranges of mountains and broad detritus-filled valleys, the southern extension of the characteristic topography of the Great Basin. In altitude it varies from 500 ft. in the southwest to 8,300 ft. on Hualpai Peak southeast of Kingman. The mountains trend north-northwest. They rise about 3,000 ft. above the valleys, are generally rugged and were formed mainly by erosion. They are composed in the main of a, complex of pre-Cambrian granitoid rocks which underlies the area as a whole. Like the valleys, they average about 10 miles in width. Beginning on the east, they are the Grand Wash Cliffs, the Cerbat Range, the Black Mountains or River Range, and the Eldorado Range. The upper or dominantly cliff half of the Grand Wash Cliffs, marking the edge of the Colorado Plateau, is composed of nearly horizontal sedimentary Paleozoic strata of the Grand Canyon section, and the lower half of the underlying pre-Cambrian complex. The Cerbat Mountains situated in the central part of the area, and the Black Mountains situated between Detrital-Sacramento Valley on the east and Mohave Valley, the great trough of the Colorado River, on the west, are locally flanked or overlain by Tertiary volcanics (Fig. 2). The latter consist of five groups of mountains of which the most important is the Black Mesa group on the south. The Eldorado Range, rising from the great trough of the Colorado on the west and containing Searchlight, Eldorado Canyon, and other camps, is topographically and geologically similar to the Black Mountains.

Jan 10, 1916

By J. W. Graham

For many years the author has been cognizant of the difficulty encountered by some in treating with the water influx formulas for unsteady-state fluid flow as pertain to the material balance equation. This has particularly applied in establishing reservoir performance and identifying reservoir pressure, which to the practicing engineer has entailed a trial-and-error procedure, and for others has necessitated resorting to computing devices and reiteration processes. In retrospect this difficulty stems from the fact that reservoir pressure in the material balance formulas, as well as associated with the water influx equations, is an inexplicit term, and the work reported in the past is irrefutable. However, what will be presented in this paper is another approach to the problem, whereby the entire material balance equation will be treated by the Laplace transformation, and reservoir pressure which hereto has been inexplicit, can now be isolated by mathematical procedure to relate that parameter with all the factors contributing to its change. This is the simplification entailed, that treats first with an undersaturated oil reservoir as an integrated effect from the inception of production. The second phase pertains to saturated oil reservoirs that encompass a survey traverse. Although both methods of approach are necessarily different in aspect, the most interesting fact is that the mathematics so deduced are identical. Both the linear and radial water-drive systems are incorporated. for which an illustrated factual example is offered for the latter, treating with a saturated oil reservoir. INTRODUCTIO N What is performed in this work is the simplification of an involved computation by advanced analysis. Although such may be construed as a contradiction when one treats with higher mathematics; nevertheless, when direction is given to such an undertaking the results car. be most revealing. Likewise, it is to be mentioned that the bases for these mathematics have been developed on the expediency of the occasion. This is not to be inferred as a qualification of this work, but rather the demands frequently placed upon the author in his private prac- tice in meeting a time limit. A situation, instead of being fraught with hazards, often has given emphasis to creative thought. What will be entailed in this work is the simplification of the material balance formulas by the Laplace Transformation., Although this reveals entirely new horizons that will be given expression in a forthcoming tract, it suffices in the present instance to limit our attention to this phase of the development that treats both with an undersaturated and saturated oil reservoir. To orient the reader's thoughts as to what is involved in this simplification is the recognition that reservoir pressure, as such, is an inexplicit term in the material balance equation. This is the independent parameter that defines the total history of performance in the author's' unsteady-state water influx formulas, as well as the basis for the physical dependency of fluid behavior within the formation as prescribed in the Schil-thuis' material balance equation. Therefore, to isolate reservoir pressure, which is the most essential factor in any reservoir study, is rather a cumbersome procedure entailing either a trial-and-error calculation for the engineer; or as some prefer, a reiteration process performed on a computing device. However, once such an equation can be transcribed as a Laplace transformation, this inexplicitness so expressed can be alleviated to identify reservoir pressure as an explicit function of all the factors contributing to its change. This is the simplification encompassed, that will treat first with an undersaturated oil reservoir as an integrated effect from the inception of production, and secondly, with a saturated oil reservoir as a survey traverse. Although the two approaches are necessarily different because of the uhvsics involved. it is an interesting commentary that the mathematics are identical, showing the interdependency of the two methods. In order to acquaint the reader with this development, the simplest case will be treated first; namely, an under-saturated oil reservoir subject to a linear water drive. However, what may be construed for this example as an idealistic case is actually a most practical application in certain parts of the world, where the size of the fields are so large that radial water-drive approaches the configuration of a linear drive. Further, to avoid the repetition of much symbolism, frequent references will be made to the work of the author and an associate on Laplace Transformations3,

By Walter B. Lenhart

Introduction and Importance of the Industry Sand, as described in this chapter, is a crude product used for ballast on railroads and highways, and as the fine aggregate in concrete, mortar, plaster and in asphalt paving materials. The sand used in glass, as a molding sand, and as a source of silica is described in Chapter 43. Sand and gravel together constitute the mineral raw materials of largest volume produced from the earth. In 1958, as reported by the U.S. Bureau of Mines,21 680,080,000 tons of sand and gravel (including industrial sand) were produced in the United States. The nearest competitor was crushed rock of which 532,818,000 tons were produced. Coal, both bituminous and anthracite accounted for only 431,616,689 tons in the same year. In dollar value, sand and gravel were exceeded only by cement, crushed rock and fuels. Hence it is a major unit of the mineral-producing industry. As an example, one plant in California operates around the clock at an average rate of 1,500 tons per hour, and at peak intervals has shipped over 4,000 tons per hour, all by trucks. Nevertheless, it is controlled by one man through a panel of push buttons that control the crushing, screening, washing, grading, stock piling, and reclaiming of the products. Because sand and gravel are low-valued commodities, but are used in every construction undertaking in every city, village, farm, dam and highway, they are produced in almost every county in the United States and southern Canada, by thousands of individual operators, very few of whom operate in more than one community. Many operations, particularly those established to supply the needs of major dams that are under construction, or of major segments of new highways, are temporary in nature, and the equipment installed is more or less portable. Because of the bulky nature of sand and gravel, there is very little interstate movement, and almost no exports or imports, except a little movement back and forth across the border of the United States and Canada. First, the material needs definition. Definitions Sand and gravel have been defined as continuously graded unconsolidated materials that appear in the earth's surface as a result of the natural disintegration of rocks. Both normally appear together, but in a wide variety of sizes, types and range of size classification. The American Society for Testing Materials has tentatively revised its definition of "sand" as: granular material passing the 3/8-in. sieve and almost entirely passing the No. 4 (4760-micron) sieve and predominantly retained on the No. 200 (74-micron) sieve, and resulting from natural disintegration and abrasion of rock or processing of completely friable sandstone (ASTM Designation C 58-55T). The Society's tentative revision of its definition of "gravel" is: granular material predominantly retained on the No. 4 (4760-micron) sieve and resulting from natural disintegration and abrasion of rock or processing of weakly bound conglomerate (ASTM 125-55T). Sand and gravel deposits contain materials from the finest silt to the largest boulders. Chemical definition of the two materials is nearly impossible. Sand and gravel always are

Jan 1, 1960

By W. G. Jeffery, James F. McDivitt

THE FRAMEWORK Consider where you, the reader, would place the emphasis m your answer to the following questions on mineral supply. Do you think of the mineral resources of developing countries in terms of the contribution which they can make to world mineral supply or in terms of the contribution they can make to development of the country? Do you look upon developing countries as a source of minerals for world industry or as a potential enormous market for minerals? If you are from a developed country it would be surprising I£ you did not emphasize the first alternative in each case, but it is also possible that simply raising the questions will call for some mental adjustments, because usually we do not think in these terms. If you are among the two-thirds of the world's population which comes from developing countries, you might well emphasize the second alternative. And to a growing extent during the reaming decades of the 20th century this is where emphasis must be placed. Increasing amounts of the world's mineral production come from countries which are in the early stages of development. Mineral consumers of the world look to these regions for continuing supplies of material to help meet their ever-growing needs; the producing countries look to mineral exports as one means of stimulating and financing their economic development-this seems a happy and fortuitous relationship. But due to the complexities of world mineral supply, it is a relationship which is fraught with potential confusion and misunderstanding. That this is so is not surprising when one considers that many of the producing countries are new countries which are urgently trying to find the path along which they can move towards development; that the direction of the path is by no means clear because various theories of economic development, as a planned and deliberate process, are relatively recent in origin and none are well understood; and that the very concept of the less developed countries (LDC's) is a relatively new one. To further complicate the situation there has never been a clear under- standing of the full role which minerals play in economic development, either in the case of those countries which are already classed as developed, or in the case of countries which are in the process of development. Before embarking on an investigation of some aspects of the relationship between minerals and developing countries, it seems wise to establish broad terms of reference, which may not be totally valid but which will at least give an initial direction for a journey with no clearly definable goal. First it can be noted that the world has been divided somewhat arbitrarily into a group of countries that are termed developed or advanced and a group of countries which

Jan 1, 1976

By S. J. Hruska, G. M. Pound

The critical supersaturations for appreciable nucleation rate of cadmium crystals on copper and glass substrates at 186°Kwere measured as a junction of thermal-beam energy over a range of source temperatures between 616" and 839OK. There was no effect of source temperature on critical super saturation. This implies that the adsmbate prior to nucleation is in thermal equilibrium with the substrate. THE deposition of metallic vapors on solid substrates has been found to exhibit a critical behavior in that the rate of formation of deposit increases markedly when the intensity of the vapor source is increased slightly.* Evidence of the ability of sub- where Je is the flux which would arrive if the substrate were equilibrated with bulk condensate at the adsorbate temperature. The following work was undertaken to test this hypothesis. A) Energy Exchange Between Metallic Vapor and Substrates. When a freely translating atom collides with a stationary solid body its energy and momentum undergo changes which determine whether the atom is reflected or adsorbed. An atom is considered to be reflected if it returns to a freely translating state after remaining under the influence of the body for only a time comparable to the period of oscillation of atoms on the surface. An atom which remains for a longer time is said to be in an adsorbed state. The parameter which describes the energy transfer occurring at the interface is the thermal-accommodation coefficient which may be defined in terms of energy as Ei = average energy of impingent atoms, Eeq = average energy of an emergent atom which has equilibrated with the substrate, and Eem = average energy of an emergent atom. If a temperature is assigned to each of these energies, we have at as defined by Knudsen.2 Since this allows no distinction between reflected and evaporated atoms, a more specific definition is introduced for the present purposes, namely 71 = probability that an impingent atom is transferred to an adsorbed state, aj = thermal-accommodation coefficient for reflected atoms, and aTc = thermal-accommodation coefficient for adsorbed atoms. During a time t,, the mean stay time, prior to evaporation the adsorbed atom (adatom) will interact with the substrate and this will have the net effect of transferring the adatom towards a state of

Jan 1, 1964

By J. L. Huitt, B. B. McGlothlin

The introduction of new fracture propping agents that are brittle but much stronger than sand created the problem of what loading strength is required for a propping agent to be effective in a given formation. It is shown that the load at which the propping agent crushes should exceed the load at which total embedment in the fracture faces is possible. Simple laboratory tests to determine loading strength of the propping agent and embedment in the fracture faces, and use of these data in selecting a propping agent for a given formation, are discussed. INTRODUCTION One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively provide the fracture flow capacity needed for stimulation of a well. Sand, once generally accepted as being synonymous with propping agent in hydraulic fracturing, is now recognized as having limited effectiveness in many formations because of its low resistance to crushing. Sand particles are brittle and have relatively low strength. Because of this property, sand particles are crushed in rocks that offer high resistance to the penetration of fracture faces by the proppant particles when the fracture attempts to close under the action of the overburden load. For rocks that offer a high resistance to penetration, deform able particles are more effective propping agents than sand. However, for this same type of rock, a propping agent that does not deform, yet does not crush, is often more effective. Thus, a rigid propping agent with sufficient strength to prevent crushing is desirable. A method for determining the strength required for a rigid propping agent to function effectively in given formations is discussed. BEHAVIOR OF RIGID PROPPANTS AND FRACTURE FACES RELATED STUDIES An early qualitative description of the reaction of propping sand in fractures was given by Hassebroek et al.' In discussing fracturing in deep wells, the authors mentioned that even though propping sand entered the fractures, a high flow capacity did not result due to crushing or embedding of the propping sand. Dehlinger et al.2 in discussing the reaction of propping sand surmised that, because of the hardness of sand particles, deformation occurred in the fracture faces contacting the propping sand. In later studies,3,4 methods of determining the embedment of propping sand in fracture faces of soft rock and the critical load at which propping sand is crushed by the fracture faces in hard rock were discussed. In working with de-formable proppants, Kern et al. considered proppant particles to be deformed into cylindrical disks by action of the overburden and then pressed slightly into the fracture faces by further action of the overburden. Rixie et al.'0 reported on embedment pressure and presented a method of selecting a propping agent for use in given formations. The propping agents included sand, walnut shells and aluminum pellets. All these studies have contributed materially to a better understanding of propping agent behavior; however, the strength of brittle proppants (sand, glass and ceramics) required to result in embedment rather than crushing has not been discussed. This topic will be covered in the ensuing discussion. PROPPANT PARTICLE CRUSHING—-EMBEDMENT For this discussion, a rigid propping agent is considered to be one that is brittle and fails under tensile stress when loaded to a critical value. In an earlier study4 it was shown that the Hertzian4 loading theory could be applied to a spherical brittle propping agent if the propping agent and fracture faces behaved elastically. At the failure of the proppant, the ratio of the load to the square of the diameter of the particle should be constant for a given material combination, or: Lc/dp2=C ............(1) A partial derivation of this equation from proppant and formation properties is included in the Appendix. Should a rigid particle not be crushed as a load is applied, it embeds in the fracture faces. A study3 of particle embedment in fracture surfaces has been published. The embedment can be described by an equation based on Meyer's metal penetration hardness relationships: d1/dp=B 1/2[L/dp2]m/2..........(2) In Eq. 2, B and m are constants that are characteristic of the rock; the significance of the other terms is shown in Fig. 1. A STANDARD DEFINITION FOR PROPPANT LOADING STRENGTH Eq. 1 is useful in appraising propping agent strength," but it is strictly applicable only when the area of contact between a particle and a fracture face (or loading plate)

Jan 1, 1967

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By L. A. Rapoport, W. J. Leas, C. W. Carpenter

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.' More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" ' ratio.""' These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations:

By F. J. Plecity, W. C. Leslie, F. W. Aul

During isothermal recrystallization, the rate of grain growth in dilute Fe-hlo alloys decreased rapidly with increasing Mo content, up to -0.04 at pct, and less rapidly therea-fter. Rate of growth also decreased sharply with time at constant temperature. The observed rates of boundary migration did not cor,espond to predictions of the Lucke-Detert theory. It is proposed that the growth of recrystallized grains is inhibited by clustering of solute atoms at inzperfections in the unrecrystallized matrix. It is now firmly etablished" that the rate of re-crystallization of cold-worked metals, i.e., the rate of growth of recrystallized grains into the deformed matrix, is greatly inhibited by the presence of alloying elements in solid solution. The effect is greatest with the first very small quantity of alloying elements, and additional increments cause much less pronounced retardation of growth. The early papers on this subject were reviewed in Ref. 6. The mechanism of retardation of growth is not clear; only one theory, due to Lucke and Detert? has been advanced. This assumes an elastic interaction between grain boundaries and solute atoms which tends to increase the concentration of the latter in the grain boundaries. Except at very low solute concentrations or at high temperatures, the mobility of the boundary is assumed to be controlled by the rate of diffusion of the accompanying solute atoms. Abrahamson and Blakeney2 have noted a correlation between "recrystallization temperature of binary alloys of iron and the number of d-shell electrons in the solute atoms. There is need for considerably more experimental data on the effect of solute elements on the rate of migration of grain boundaries into the deformed matrix, to provide the basis for an understanding of the annealing process in metallic solid solutions. Only a start has been made in this direction. To avoid unnecessary complications, alloys in which precipitation does not occur should be used, but to produce the maximum effects it is desirable to select alloys with a large difference between the sizes of the atoms of the solvent and solute. For these reasons, alloys of iron and molybdenum sen for this study. MATERIALS AND PROCEDURES A 30-lb. ingot of iron and four similar ingots of Fe-Mo alloys were vacuum melted in magnesia crucibles and poured into cast-iron molds. The molybdenum contents were planned according to the results of Abrahamson and Blakeney2 sothattwoalloyswould fall in the region of rapid change of recrystallization kinetics with change in composition (0.006 to 0.015 and 0.030 to 0.045 at. pct Mo) and two alloys would fall in the region of gradual change (0.18 to 0.24 and

Jan 1, 1962

By Wilson Lundy

THE history of the production of sulfur from salt domes in Louisiana and Texas originated with the operations of the Union Sulphur Co. at Sulphur, La., followed by the Freeport Sulphur Co. at Bryanmound, Tex. Including the present development of Grande Ecaille by the Free-port Sulphur Co., which constitutes the tenth dome to be equipped for the production of sulfur in the Gulf Coast, less than 10 per cent of all the known domes have proved to contain sulfur in commercial quantities. The Grande Ecaille salt dome is in the tidal marsh of the Mississippi River delta in Plaquemines Parish, Louisiana. It is 10 miles southwest of the right descending bank of the river approximately 45 miles below the city of New Orleans and is within 4 miles of the shore line of the Gulf of Mexico.

Jan 1, 1934

By Peter Greenfield, Paul A. Beck

Thirty binary systems of vanadium and chromium group transition elements with second and third long period transition elements were explored in regard to the intermediate phases formed. It was found that the phases predominating in these systems are s, AB type with ordered a-tungsten or C8 structure, close-packed-hexagonal with small unit cell dimensions and, finally, phases isomorphous with 1-manganese. IN recent years, considerable information has become available concerning the intermediate phases in binary systems of the transition elements. Thus, the s phase has been found to occur in most of the binary systems of vanadium, chromium, and molybdenum with the group of elements manganese, iron, cobalt, and nickel.' It was observed that, while the rr phases formed by chromium with manganese, iron, or cobalt possess a considerable temperature range of stability, particularly in the Cr-Co system, the corresponding s phases with molybdenum are limited to a temperature range of less than 400" above about 1200°C. Goldschmidt' reported v phases of tungsten with iron and cobalt, and these are apparently stable only at (and above?) 1400°C." Exploratory work in this laboratory with Fe-W and Co-W alloys of approximately 60 atomic pct W annealed at 1300°C did not produce X-ray patterns suggesting the presence of a phase. It appears then that the phases of iron and cobalt with the chromium group elements decrease in stability as the two components are chosen from long periods further removed from each other. From the available information, it might be concluded that the controlling factor is the increasing difference in atomic radii between the components. In contrast to the a phase, the phases formed by iron and cobalt with chromium group elements' are stable only when the latter have large atomic radii (molybdenum and tungsten); the corresponding phases with chromium do not occur. When the difference in atomic size becomes still larger (r,/r,, approaching the ideal value of 1.225), the u and p phases are replaced by Laves phases (AB,), as in the alloys of iron and cobalt with columbium," tantalum." and titanium."-" However, atomic size certainly cannot be the sole determining factor, since, for instance, in contrast to the very stable (Mo, Co)p phase, no such phase occurs in the Mo-Ni system even though the atomic diameters of cobalt and nickel are nearly the same. Similarly, chromium and cobalt form a a phase in a wide temperature range," but the corresponding s phase in the Cr-Ni system is missing. It has been shown that the composition of the u phase in various binary and ternary systems of transition elements in the first long period may be correlated in a fairly quantitative manner with the number of electron vacancies. The influence of electronic structure is probably present also in binary and ternary phases' and to some extent, apparently, even in Laves phases." " Although the absence of phases in the Cr-Ni and Mo-Ni systems has not as yet been explained on the basis of electronic structure, it appears reasonable to suspect a connection. One of the great difficulties in arriving at well founded rules in regard to the alloying behavior of transition elements lies in the lack of reliable information concerning the details of their electronic structure in the metallic and alloy form. The theoretical penetration of this field appears to be beset by very considerable difficulties, even when the complications due to alloy formation are disregarded. Another great source of uncertainty is the scarcity of phase diagram information even for binary systems of the transition elements so that only a very limited basis is provided for generalizations as to the occurrence of intermediate phases. For instance, very few binary phase diagrams of second and third long period transition element systems have so far been published. The present work was undertaken in order to survey the various types of intermediate phases occurring in 30 binary systems of elements of the group vanadium, columbium, tantalum, chromium, molybdenum, and tungsten with the elements rhenium, ruthenium, rhodium, palladium, and platinum. For most of these binary systems phase diagrams are very incompletely or not at all known, as will be further reviewed.*

Jan 1, 1957

By B. Zondek, W. T. Cardwell, J. W. Sheldon

The fundamental equations that are used to describe two-phase fluid flow in porous media are Darcy's law for each phase and an equation of continuity for each component. The special case of one-dimensional, incompressible, two-phase flow has received much attention in the petroleum engineering literature.1-10 The basic paper on the subject is that of Buckley and Leverett.2 Buckley and Leverett showed that one could eliminate the pressure and obtain a single partial differential equation for the saturation. They solved this equation for the case when gravity and capillary forces are negligible. A frequently encountered property of the solution of the basic partial differential equation is that, as time progresses, the saturation becomes a multiple-valued function of the distance coordinate, x. Buckley and Leverett interpreted the formation of multiple values as an indication that the saturation-distance curve had be-come discontinuous. They developed a method of determining the position of the discontinuity from a material balance. We solve the Buckley-Leverett partial differential equation using the method of characteristics and the concept of shocks. Our treatment is analogous to treatments used in the theory of supersonic compressible flow." Although the numerical results obtained are the same as those obtained by previous methods, we believe that this approach is more logical and has broader applicability. It can, for example, be generalized to treat the case when the fluids are compressible. It is not clear how one would go about doing this using the method of Buckley and Leverett. To illustrate the power of the method of characteristics with shocks, we solve a problem in gravity segregation which has not been treated previously in the literature. A special case of the general method developed here was used by Welge, to solve a particular fluid displacement problem. We consider two-phase incompressible flow along the vertical direction x in a porous medium. We assume that there is no flow transverse to .x. We measure positive in the upward direction. The fundamental equations are obtained from Darcy's law and the mass conservation law. Since the two phases are incompressible, mass conservation is equivalent to volume conservation.

By Henry Phelps Howland

During the last decade no topic has created more interest or received more thought among blast-furnace men than coke. One reason for this is, undoubtedly, the remarkable increase in the use of byproduct coke. Formerly our coke was made at a distance from the furnaces and by a distinct organization. There was little cooperation or development possible under these conditions. Today the situation is greatly changed. Much of our coke is made by the organization operating the furnaces and the coke oven is operated with the primary object of obtaining the best results in the blast furnace. The effect of changing the method of coke manufacture, even in some minor detail, is often felt almost immediately at the blast furnace. There naturally results one of the most valuable assets of the byproduct coke oven, i.e., the possibility of increased blast-furnace efficiency due to close observance and correct operation of the ovens. The results are evident, but often it is difficult correctly to account for them. In attacking the solution of a problem of as much importance as why one coke is better than another, there are facts which should be kept clearly in mind. The author hopes, in this paper, to bring out some points relative to the use of carbon in the blast furnace which will be of value in solving this question. GeÜner's Ideal Working Years ago GrÜner made a statement regarding the use of carbon in the blast furnace, which has been very generally accepted by metallurgical and blast-furnace men. I quote this theory as given by Prof. Richards on p. 248 of Metallurgical Calculations: "From the standpoint of the generation of the maximum quantity of heat in the furnace, GrÜner was right in formulating his dietum of the ideal working of a blast furnace, vie.: All the carbon burnt in the furnaee should be first oxidized at the tuyères to CO and all reduction of oxides above the tuyères should be caused by CO, which thus beeomes Co2."

Jan 1, 1917

By R. C. Craze

This paper discusses the characteristics of the velocity logs now available to the petroleum industry, and some of their advantages and limitations. The velocity log was designed as an aid to the geophysicist to determine velocity layering in the earth and to provide fast, accurate and economical vertical travel time data. After a number of logs had been made, studies were carried out on their use ia correlating strata in adjacent wells. It was found that adjacent strata usually show sufficient velocity contrast to make it possible to correlate these from well to well, even in areas where electric or radioactive logs fail.' In addition, velocity logs have been useful in the determination of porosity and thickness of reservoir rock.' These uses for velocity logs require an understanding of the characteristics of the log in response to the changes in velocity and in borehole conditions encountered normally in logging. GENERAL DISCUSSION OF INSTRUMENTATION The measurement made in velocity logging is more accurately described as a measurement of time rather than velocity. Ideally the log is obtained by measuring the length of time required for compressional sound waves to travel through a fixed distance in the formation. In practice, the time measurement may be made accurately but the distance through which the waves have traveled may vary slightly. Changes in borehole diameter are responsible largely for the difficulty in maintaining a fixed distance, especially if the diameter variations are so abrupt and frequent that the borehole instrument cannot follow contours of the hole. Several service companies have velocity logging equipment available or under development which have different transmitters, receivers, and measuring systems. While these differences are important, there are actually only two systems in use at the present time (Fig. I)."' The first system initiates a pulse at a trans-mitter and detects it at a single receiver. The transmitter and receiver are separated by a fixed distance, called the spacing. The time measured is that between the initiation of the pulse and the first arrival of acoustical energy at the receiver. The second system uses two receivers and a transmitter. The receivers are separated by a fixed distance and the time between arrivals of energy at the two receivers is measured. Here, the spacing is the distance between receivers. The two systems have much in common for it is possible to record both logs simultaneously. Usually the transmitter is an electro-mechanical transducer which produces discrete

By J. B. Warriner

Stripping is the name given to the process of removing clay, rock, or other cover from deposits of coal or ore. In this paper it is intended to cover the methods used in carrying on this operation in the anthracite coal regions of Pennsylvania. In doing this, attention will be chiefly devoted to those methods wherein practice in different sections of the region differs, or is susceptible to change or improvement, though it is intended to give as complete data as possible concerning all stages of the operation. The data from which this paper has been prepared have been collected and submitted by a committee† representing the larger users of stripping methods, of which committee the writer has acted as chairman. Data and assistance have also been obtained from various mining men, engineers, contractors and manufacturers of stripping equipment, to all of whom our appreciation is due. Early History and Statistics The earliest mining operation on a commercial scale in the anthracite region was a stripping operation. This was the famous Quarry mine at Summit Hill, where this method was used only because no other method of mining a deposit of the nature found there seemed feasible to the early operators. A description of this stripping from a report published in 1821 is as follows: "The coal mine at present worked by the company lies on the top of a mountain, and appears to extend over some hundred acres of land covered by about 12 ft,. of loose black dirt resembling moist gunpowder, which can be removed by cattle with scrapers, and thrown into the valley below so as never to impede the work. The thickness of the coal is not known, but a shaft has been sunk in it 35 ft. without penetrating through. More than an acre of mine has been uncovered and presents a huge rock of coal, which is easily quarried without blasting."

Jan 1, 1918

By G. Meyrick, H. W. Paxton

Observations on the tensile deformation of single crystals of austenitic stainless steels as a function of composition, orientation, and temperature are described and compared with relevant data for other alloys. Crystals free from second phases show sharp yield points followed by Lüders' extensions of up to 20 pct. The critical resolved shear stress is strongly temperature-dependent increasing fourfold between 423O and 77°K. A temperature-independent low rate of hardening follows the Luders' extension and is frequently associated with overshoot. Unlike pure metals where Proficse cross slip usually occurs at the end of linear hardening, this stage is terminated either by cross slip or by slip on the conjugate system, the particular node apparently depending upon initial orientation and composition. The presence of 6 ferrite or martensite has a profound effect upon the magnitude of the yield stress and the shape of the stress-strain curve. In experiments on transgranular-stress corrosion cracking of austenitic stainless steels in boiling magnesium chloride, several workers1'2 have shown that increasing amounts of nickel tend to reduce the probability of specimen failure. Reed and paxton3 have observed in single crystals that the macroscopic crack plane changes as the nickel content is increased. For 18 pct Cr-8 pct Ni, the crack plane is sensibly perpendicular to the applied tensile stress; for 20 pct Cr-20 pct Ni the crack plane is (100). The average crack-propagation speed is much lower in the 20 pct Ni crystals. Furthermore, the possible importance of stack-ing-fault energy in nucleation and growth of cracks has been suggested by a number of workers. While the general effect of variations in stack ing-fault energy appears to be quite well-correlated with observed variations in cracking characteristics, each of the theories assigns rather different detailed reasons for these effects. Because the stack ing-fault energy of austenitic steels is believed to be increased with increasing nickel content, and because some theories of trans-granular cracking postulate a mechanical stage in the crack propagation (rather than relying entirely on electrochemical solution), it appeared to be of some interest to investigate the mechanical properties of a series of different compositions of aus-tenite single crystals. These experiments were considered of intrinsic value in view of the relative scarcity of such data on fcc alloys. This paper gives the results of some experiments carried out with this aim in mind, and suggests various 'other experiments which may be helpful in future studies. The experiments are also of interest in view of the recent interest in obtaining higher-strength steels by control of the imperfection content of austenite; although the compositions are not directly comparable, the results are still probably valuable. Comparisons with experiments on other fcc alloy crystals are made where possible to see how well the general pattern of behavior is understood. EXPERIMENTAL PROCEDURE The alloys used in this investigation were vacuum-melted heats of nominally 20 pet Cr-20 pet Ni-60 pet Fe, 20pctCr-16 pct Ni-64 pct Fe, and 20 pctCr-12 pet Ni-68 pet Fe.* Analyses of the material are

Jan 1, 1964

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By Sherwin Kelly

The prime objective of geophysical exploration is to promote the economical and rapid dis-covery of mineral or oil deposits of commercial value. To a few this concept as applied in min-ing may signify the direct discovery of ore-bodies, but to the geophysical engineer this latter Idea is one of the most insidious and detrimental misapprehensions which he has to combat. The destruction of this annoying obstacle to the progress of geophysical exploration reveals the kernel of truth behind it, that the exploration geophysicist has for the better part of two decades been concerned primarily with the discovery of mineral formations favorable to the occur-rence of commercial ore. There is a very real distinction here, since geophysical methods are capable of discovering certain mineral formations such as sulphide bodies or quartz veins, but are totally incompetent to predict whether or not they constitute ore; that is. whether or not they contain minerals of economic value in the amounts requisite to repay extraction. The art of geophysical exploration is now, however, rapidly outgrowing these early limita-tions. The rate of this growth will in large measure depend on the recognition by the mining industry of the fact that geophysics can play a role far wider and more important than it usual-ly does now, in guiding the future exploration and development of mineral deposits. It is my own firm conviction that as time marches on we will see the methods of applied geophysics turned more and more to the delineation of both minor and major structural features. The outlining of such features having a bearing on the probable loci of mineral deposition will be of inestimable value in guiding the development of a mining district. It is in this field that there will In-evitably occur a meeting and overlapping of the activities of the exploration geophysicists and

Jan 1, 1940

By Carl Henrich

Aspen, the flourishing mountain- and mining-town of Pitkin county, Colorado, is located in the valley of the Roaring Fork, 11 miles above Glenwood springs, where that stream empties its waters into Grand river, a tributary of the Colorado. The Roaring Fork heads on the western slope of the Sawatch range near Grizzly peak, and runs in a general northwesterly direction to its junction with the Grand river. Of its numerous tributaries, Castle creek joins it just below the town of Aspen, the town being built on an extensive flat hounded on the northeast by the Roaring Fork and on the west by Castle creek. The latter heads at the junction of the Sawatch and the Elk mountains and flows northward between the two chains, until it empties into Roaring Fork. Opposite the town of Aspen, Hunter creek, coming westward from the western slope of Mount Massive, joins the Roaring Fork. About a mile north of Aspen, the bed of Hunter creek is at least 300 feet higher than that of the Roaring Fork at Aspen. Hunter creek forms thus, at its mouth, one of the best water-powers in Colorado. A portion of it is now utilized for electric lighting in Aspen, while in the near future, the whole of this magnificent natural power will be applied, through electric transmission, for hoisting, pumping and ventilating at different mines of the district. The mountain opposite the town of Aspen, on the east side of Hunter creek (which near its mouth flows southerly), is called Smuggler mountain, from the famous mine at the foot of it. On the other, or western, side of Hunter's creek (see map, Fig. I), a higher mountain rises, on the slope of which the regular dip of the Triassie or Upper Carboniferous red sandstone strata, alternating with white layers of the same rock, can be clearly seen from town. This mountain is called Red mountain, from the prevailing color of its rocky

Jan 1, 1889