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By L. J. Health

Synthetic rock with predictable porosity and permeability has been Prepared from mixtures of sand, cement and water. Three series of mixes were investigated primarily for the relation between porosity and permeability for certain grain sizes and proportions. Synthetic rock prepared of 65 per cent large grains, 27 per cent small grains and 8 per cent Portland cement, gave measurable results ranging in porosity from 22.5 to 40 per cent and in permeability from 0.1 darcies to 6 darcies. This variation in porosity and permeability was caused by varying the amount of blending water. Drainage-cycle relative permeability characteristics of the synthetic rock were similar to those of natural reservoir rock. INTRODUCTION The fundamental behavior characteristics of fluids flowing through porous media have been described in the literature. Practical application of these flow characteristics to field conditions is too complicated except where assumptions are overly simplified. The use of dimensionally scaled models to simulate oil reservoirs has been described in the literature. 1-3 These and other papers have presented the theoretical and experimental justification for model design. Others have presented elements of model construction and their operation. In most investigations the porous media have consisted of either u ncon soli da ted sand, glass beads, broken glass or plastic-impregnated granular substances—materials in which the flow behavior is not identical to that in natural reservoir rock. The relative permeability curves for unconsoli-dated sands differ from those for consolidated sandstone. The effect of saturation history on relative permeability measurements is discussed by Geffen, et a1.4 Wyga15 has shown quite conclusively that a process of artificial cementation can be used to render un consolidated packs into synthetic sandstones having properties similar to those of natural rock. Many theoretical and experimental studies have been made in attempts to determine the structure and properties of unconsolidated sand, the most notable being by Naar and Wygal.6 Others have theorized and experimented with the fundamental characteristics of reservoir rocks. This study was conducted to determine if some general relationship could be established between the size of sand grains and the porosity and permeability in consolidated binary packs. This paper presents the results obtained by changing some of the factors which affect the porosity and permeability of synthetically prepared sandstone. In addition, drainage relative permeability curves are presented. EXPERIMENTAL PROCEDURE Mixtures of Portland cement with water and aggregate generally are designed to have certain characteristics, but essentially all are planned to be impervious to water or other liquids. Synthetic sandstone simulating oil reservoir rock, however, must be designed to have a given permeability (sometimes several darcies), a porosity which is primarily the effective porosity but quantitatively similar to natural rock, and other characteristics comparable to reservoir rock, such as wettability, pore geometry, tortuosity, etc. Unconsolidated ternary mixtures of spheres gave both a theoretically computed and an experimentally observed minimum porosity of about 25 per cent.7 By using a particle-distribution system, one-size particle packs had reproducible porosities in the reproducible range of 35 to 37 per cent.6 For model reservoir studies of the prototype system, a synthetic rock having a porosity of 25 per cent or less and a permeability of 2 darcies was required. The rock had to be uniform and competent enough to handle. Synthetic sandstone cores were prepared utilizing the technique developed by Wygal.5 Some slight variations in the procedure were incorporated. The sand was sieved through U. S. Standard sieves. A 18-20 sand denotes that the sand passed the Number

Jan 1, 1966

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' 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 Thomas Leonard Watson

Jan 1, 1906

By R. L. Grunes, F. K. Kies, C. D&apos, Antonio

THE several studies concerned with the annealing of thin nickel films have largely been restricted to films of a single thickness.1-4 It is well-known, however, that both physical and mechanical properties depend upon film thickness.5, 6 The strength-thickness relations found in vapor-deposited nickel films in the annealed and as-deposited states, as an example, are at least partially due to the density and arrangement of imperfections within the films.7, 8 For these reasons, the annealing characteristics of thin nickel films as a function of thickness were investigated. Electrical resistance was chosen to monitor annealing behavior since resistance changes are partially dependent upon defect structure. In addition, the equations predicting film resistivity as a function of thickness are already available.9, 10 Further advantages afforded by electrical-resistance measurements are its adaption to continuous readings during annealing and its relative simplicity. Nickel films were vapor-deposited, at average rates of 60Å per sec, on Vycor substrates held at room temperature in vacuums of about 10-5 torr. Afterwards, deposition-thickness measurements were made using a multiple-beam interferometric technique. A more detailed description of deposition procedures and the interferometer appear elsewhere.7, 8 The four-probe method was employed in measuring electrical resistance since this technique measures film resistance without contributions from lead wires and contacts. Resistance measurements were made before, during, and after annealing to temperatures of 700°C under vacuums of approximately 10-4 torr. Measurements were made every 25°C or more often when necessitated by unusual resistance changes. Cooling and heating rates were maintained at approximately 5°C per min. Typical resistivity vs temperature curves are shown in Figs. 1 through 4. It is apparent from these

Jan 1, 1965

By F. Keller, E. H. Dix, L. A. Willey

The consideration of alloying elements for aluminum has led to a series of investigations of the equilibrium relations between aluminum and those alloying elements. Therefore, the aluminum end of the aluminum-antimony diagram has been studied. The general form of the aluminum-antimony equilibrium diagram has been worked out by Campbell and Mathewsi and by Tammann.2 Canlpbell and mathews described principally the beginning of solidification. They found the curve of beginning of solidification rising gradually from the melting point of pure alunlinum to a maximum at about 67 per cent. aluminum. After a slight lowering of the curve at a little greater antimony concentration the curve again rises to a maximum at 18.4 per cent. aluminum, which corresponds to the compound AISb. The curve then drops to the melting point of pure antimony. Tamrriarln explained the maximum occurring at about 67 per cent. aluminum as the result of the slow formation of the single compound AISb. The space lattice of the compound AISb, according to Owen and Preaton,³ is face-centered cubic, the antimony atoms being intermeshed with an identical aluminum lattice. Very little, if any, work has been done on aluminum alloys containing small amounts of antimony. The Present Investigation It has been the purpose of this investigation to determine the solid solubility of antimony in aluminum and also to investigate the eutectic temperature and concentration. The experimental work has been carried out in a manner similar to that described in a previous paper4 from this laboratory.

Jan 1, 1931

By H. R. Hanley

The characteristics of alloyed anodes and their influence on the products of electrolysis and power consumption have been noted previosly ously in the literature.' This paper presents data in continuation of the subject given in an earlier paper by the authors.2 As noted in the authors1 previous paper, the objectives of this work are the reduction in the cell voltage and the purity of the cathode product resulting from the use of alloyed lead anodes. The fundamental facts developed in the previous paper were: (I) that the presence of a small amount of calcium lowers the anode potential approximately 50 per cent. below that of pure lead; and (2) that thallium when present to the extent of 4 per cent. rendered the anode practically stable, thereby lowering the contamination of the cathode by lead to a very insignificant amount. The specific features determined in this recent work are as follows: 1. The lowest limit of calcium in the lead which will still give maximum lowering of the anode potential. 2. The characteristics of the thallium-calcium-lead anode. 3. The characteristics of the silver-calcium-lead anode. 4. The characteristics of the thallium-silver-calciurn-lead anode. It was determined that 0.1 per cent. calcium in the anode was sufficient to lower the anode potential approximately 50 per cent. Table 1 shows the characteristics of alloyed anodes tested. The anode composed of 0.1 per cent. calcium, 4 per cent. thallium, and 95.9 per cent. * Professor of Metsllurgy, Missouri School of Mines. t Professor of Metallurgy and Ore Dressing, Hea.d of Department, Missouri School of Mines. Assistant Professor of Metallurgy, Missouri School of Mines. 1 Among others, see C. G. Fink and Li Chi Pan: Insoluble .Anodes for the Electrol-ysis of Brine [Trans. Amer. Electrochem. Soc., (1926) 49, 83-1341 and other papers by these authors. U. CJ. Taintori, 8. G. Taylor arid H. P. Ehrlinger: Lead Alloys for Anodes in Electrolytic Production of Zinc of High Purity. Truns. A. I. M. E. (1929) 192-200. 2 H. R. Hanley, C. Y. Clayton, D. F. Walsh: Investigation of Anodes for Production of Electrolytic Zinc. Trans. A. I. M. E. (1930) 275

Jan 1, 1931

By G. Donald Emigh

WESTERN phosphate resources which lie in Ida- ho, Montana, Utah, and Wyoming, have seen great expansion of activity in recent years. Growth has been two-pronged: expansion in fertilizer use, and since 1949, into the elemental phosphorous industry. Elemental phosphorous, produced in the electric furnace, goes largely into chemical making. Phosphate ore was first recognized in the West about 1889. Production started in 1906, and for many years consisted of underground operations by small companies operating sporadically. In 1920 Anaconda Copper Mining Co. opened the underground Conda mine near Soda Springs in southeastern Idaho, and has maintained and increased its operations since then. About 1930 Montana Phosphate Products Co. began underground mining in Montana and has remained a steady producer. In 1945 San Francisco Chemical Co., one of the oldest companies in the western field, initiated strip mining at the Waterloo mine near Montpelier, Idaho, and later at Leefe mine near Sage Junction, Wyo. In1946 J. R. Simplot Co. began open pit mining at Gay mine near Fort Hall, Idaho. In 1950 Victor Chemical Works began underground development work in the area of Maiden Rock, south of Butte, Mont.: and has since mined there. Monsanto Chemical Co. began open pit mining near Soda Springs, Idaho, in 1951.

Jan 11, 1954

By L. A. Updegraff

Before discussing the application of capacitance for the measurement of moisture content in a moving stream of coal it might be well to first give a brief description of the process and then show how it can be applied to the coal industry. A capacitor may be described as a device having two conductors separated by an insulator, the conductors hereafter being designated as a test cell or test plates and the insulator as the dielectric. Capacitance, therefore, is a measure of the ability of a capacitor to store an electrical charge. Two basic factors that affect capacitance are the dimensions of the capacitor and the dielectric constant of the insulator. Capacitor dimensions which affect its capacity are the area A of the conductive surface, and the distance d between plates. Capacitance is inversely proportional to the distance between plates and directly proportional to area A, so if capacitance is indicated as C and the dielectric constant as K the equation for capacitance would be C = AK/d. The dielectric constant can be described as the ratio of the actual capacitance of any given material to that of a vacuum, which is unity. In industrial applications the area of the plates remains constant as also does the distance between them, leaving the dielectric constant as the only variable to affect the capacitance measurement. Figure 1 is a schematic diagram of an r-f excited capacitance bridge in which a test cell is part of the circuit. This bridge consists of four capacitors in two pairs connected across an a-c voltage source. In one side of the circuit the two capacitors are fixed but in the other side they are variable, one being the rebalance capacitor operated by the servo motor and the other the test plates between which the dielectric passes. Capacity of the plates is a function of the dielectric constant of the material between them and is measured at radio frequency. Within the recording instrument is an r-f oscillator and a 60 c ps modulator. The radio frequency signal is generated by the oscillator, modulated by a 60 cps wave, and sent to the bridge. Therefore the signal entering the capacitive bridge is a radio frequency carrier with a 60 cycle envelope, If the bridge is in balance as the signal enters there would be no voltage drop and so no output by the detector. As long as the dielectric constant remains the same the bridge will stay in balance. However, any change in the dielectric constant, which in this case would be a change in moisture content, would affect the bridge. Higher moisture increases the capacity of the test cell which causes less voltage to develop across it causing imbalance of the bridge. This in turn causes a radio frequency signal to appear at the detector. Output from the detector is a 60 cycle ripple which is in proportion to the imbalance of the circuit. A 60 cycle amplifier boosts the detector signal to enough power to drive the servo motor which positions the recording pen and also rotates the variable capacitor, to which it is mechanically connected, to bring the bridge back in balance. An increase in moisture causes the servo motor to rotate in one direction, but a decrease causes imbalance in the opposite direction, and thus rotates the motor in that direction. This brings the bridge back in balance and stops the motor. The bridge shown in Figure 1 has been modified so as to provide a wide range of adjustments. Coarse and fine span adjustments located in the recording instrument are set to govern the amount of pen movement for a given change in capacitance. A measuring head unit contains coarse and fine zero adjustments for

Jan 1, 1961

By Lawrence A. Shepard, Richard H. Krock

A series of ductile, two phase W-Ni-Fe composites, sintered in the presence of a liquid phase, were tested in tension. Identical room temperature stress-strain curves were obtained for specimens containing from 80 to 92 wt pct W (58 to 75 vol pct W particles). The composites exhibited a maximum elongation of 29pct at room temperature, and 10.7 pct at 77 °K. The tungsten particles in the composite elongated by the same amount at these temperatures. Single-phase alloy specimens matching the composition of the composite matrix showed about one half the flow stress of the composites. The test results demonstrated that the mechanical properties of W-Ni-Fe composites are determined by the tungsten particles alone and are independent of matrix volume fraction or mean free path over the composition range studied. A general prediction of the plastic behavior of two-phase alloys or composites from a knowledge of the properties, size, shape, and dispersion of the individual components is not, at present, possible. The excellent theoretical and experimental exposition of the dispersion-strengthening problem applies only to cases where the stronger phase is present as fine particles and in volume fractions of a few percent. Materials in which the stronger phase constitutes a significant fraction of the volume, although of broad engineering interest, have received comparatively little analytical attention. This important group of materials is the concern of the present study. The degree of deformation of each phase during the plastic working of a ductile two-phase alloy has been established by Boas and Honeycombe,1 Clare-brough,2 and Clarebrough and berger.3 These workers empirically correlated the recrystallization temperature of the individual phases with the degree of cold work sustained by each. It was shown that the deformations of both phases are equal and therefore the same as that sustained by the composite whole when the volume fraction of the stronger phase exceeds 35 pct. At yielding, however, deformation begins in the weaker phase. A direct correlation of composite strength, as a function of deformation, with the strength of the individual components cannot be made. In the presence of stronger phase particles, the flow stress of the weaker matrix phase is enhanced by an additional hydrostatic component. The development and potential magnitude of matrix strength promotion upon straining has not even been experimentally established. Quantitative work in this field has been confined to ceramic-metal composites. These materials fracture at strains considerably below 1 pct by cracking of the ceramic particles.4-6 An indication of the potential constrained matrix strength capacity is given by the observation by Nishimatsu and Gur-land4 that the maximum tensile strength of a WC-Co composite is almost double the bulk strength of the cobalt matrix. The relationship between composite strength and geometry is ordinarily expressed in terms of the mean-free matrix path (referred to subsequently as MFP) between the stronger particles.* This factor takes into account both the volume fraction of matrix phase and the average size of the particles. unke17 concluded that composite strength varied directly with the decreasing log MFP, following the Gen-samer8 relationship. However, Gurland and ~radzil~ reported a strength maximum at an MFP of the order of 1 p in WC-Co composites. A ductile two phase metallic composite was chosen for the present investigation of composite mechanical properties with the view of avoiding the difficulties and ambiguities noted above. The W-Ni-Fe heavy alloy of Green, Jones, and pitkin9 contains 80 to 94 wt pct W, and nickel and iron in a weight ratio

Jan 1, 1963

By A. Vifian, I. lwasaki

Several samples of copper-nickel ore from the Duluth Gabbro were studied to relate their mineral-ogical characteristics with their amenability to concentration by flotation. The most common rocks in the samples were norites, gabbros, and troctolites. The texture of the rocks varied from coarse pegma-titic to very fine. The copper contents ranged from 0.2-0.7% and the nickel contents from 0.07-0.15%. The ore minerals were chalcopyrite, cubanite, pyrrhotite, and pentlandite. Most of the ore minerals occurred in interstices between laths of plagioclase, but some were included in the gangue grains. The samples responded readily to xanthate flotation. After a 65 to 100-mesh grind about 95% of the copper and 85% of the nickel were recovered in a bulk sulfide concentrate. Such recoveries remained constant even with grinds as fine as 270 mesh due to the extremely fine inclusions of sulfides in the silicate gangue. A finer grind than 270 mesh was necessary to free the copper-iron sulfides from the nickel-iron sulfides. A combination of time and British gum* was quite effective in producing concentrates analyzing 25-30% copper. The nickel concentrate averaged 1.5% nickel. Most of the nickel lost in the tailing was present as un-liberated sulfides and not as nickel in the olivine structure. The nickel content of the olivine was only about 0.05 or 0.08%. Western world nickel usage in 1967 is expected to be the second highest on record, amounting to 825 million lb. Despite a rise in mine production, however, demand is expected to exceed supply in 1968. ' Hence, exploration, development, and production expansion projects are being accelerated on a world scale. In Minnesota the copper-nickel bearing Duluth Gabbro is receiving much attention. During the past year 11 companies have been granted leases in the region, and the 1967 Minnesota legislature enacted a tax law designed to encourage the development of a copper-nickel industry. Although it is only during the past few years that mining companies have shown an active interest in the Minnesota copper-nickel deposit, copper-nickel minerals have been known to exist in northeastern Minnesota since 1899.3 At the 28th Mining Symposium, Dr. P. K. Sims, from the Geological Survey of Minnesota, gave a review of copper-nickel exploration in northeastern Minnesota,4 in which he emphasized that the potential of the Duluth Gabbro complex is large. Tests on samples from the Kawishiwi River area were reported by the United States Bureau of Mines in 1955.' In 1964, the Mines Experiment Station described tests on samples from the Gunflint Trail: and in 1966 the Minnesota Geological Survey published a geological map of the Gabbro Lake Quadrangle. The Mines Experiment Station published a study of the concentration of a Minnesota copper-nickel ore in 1967.7 The present paper is divided into three parts. The first describes the mineralogy of some rock samples from the Kawishiwi River area of northeastern Minnesota; the second summarizes the results of numerous flotation tests that were made on the samples, and the third explains the loss of nickel in the flotation tailing. MINERALOGY OF KAWlSHlWl ROCKS Recently five samples of mineralized gabbro from the Kawishiwi River area, a few miles east of Ely, were received at the Mines Experiment Station. One of the samples was a 175-lb composite, which was designated Ore 1556. The other four samples were 7-lb grab samples that had been obtained from four different exploration pits. They were designated Ore 1626, Lots 1 through 4. Basic Mineralogy: Many authors have reported that the rocks of the so-called gabbro of the Duluth Intrusion vary widely in composition.8-9 The samples on which our studies were based also contained a wide range of rocks. A gabbro, olivine-gabbro, anorthosite-gabbro, norite, and a troctolite were represented. The essential minerals in the samples were plagio-clase, pyroxene, and olivine, in variable proportions.

Jan 1, 1969

By N. Jaffe, J. E. Dorn

This investigation is concerned with the possibility that the creep resistance of metals might be reduced as a result of recovery at the creep temperature when the applied stress is reduced. For this purpose the effect of stress on the recovery of the creep behavior of pure polycrys talline aluminum was investigated in the cross-slip temperature range where the activation energy for creep is 28.000 cal per mole. Before recovery all specimens were given the same substructure by creeping them under a stress of 7800psi to a strain of 0.218. Recovery was then accomplished by holding the specimens at the creep temperatures of 327" and 337°K under a series of reduced stresses for various periods of time. When the original stress was reapplied the specimens crept more rapidly than when the original stress was first removed, illustrating that recovery did take place. The extent of recovery could be indexed in terms of the UNDER certain conditions of test, the creep rate decreases over the primary stage of creep often by as much as a factor of 10~B. Since the external variables of stress and temperature are held constant, such pronounced and significant changes in the creep rate must be attributed to various substructural modifications that are introduced as a result of creep itself. At the secondary stage of creep, over which the creep rate remains constant and the substructure no longer changes, a balance must be achieved between the rate of increase in creep resistance due to creep straining and the rate of recovery of the substructural modifications. The general validity of these concepts on substructural changes has already been shown,' including the corollary that a more creep-resistant substructure is introduced under a more rapid creep rate arising from a higher applied stress.' In spite of these well-documented facts, very little progress has been additional strain undertaken by the recovered specimen to achieve the same strain rate as the unrecovered specimen. It is significant that the higher recovery stresses gave the most rapid rates of recovery. Over the high range of reduced stresses, where some creq took place during recovery, the activation energy for recovery equaled that for creep, namely 28,000 cal per mole. But for stresses during recovery below 0.80 of the original creep stress, no creep was detected during recovery and an activation energy for recovery of about 72,000 cal per mole was obtained. Whereas the activation energy of 28,000 cal per mole suggests that cross-slip of dislocations is responsible for this recovery, the mechanism for the 72,000 cal per mole process is not known. This activation energy, however, is about twice that for self-difhsion. made in determining, in satisfactory detail, precisely what substructural changes so effectively modify the creep rate.' Up to the present, electron microscopy has failed to uncover, in a satisfactory quantitative manner, the mechanistic processes involved. Since, however, creep, at least at moderate and high temperatures, arises from one or more types of dynamic recovery processes, it should be possible to shed additional light on the total problem by investigating the recovery of creep resistance. The importance of such an investigation becomes apparent when the fact is recognized that there has yet been no direct experimental proof that the rate of softening due to substructural changes as a result of recovery equals the rate of hardening due to creep-induced substructural strengthening over the secondary stages of creep. Furthermore the problem of what happens to the creep-strain induced strengthening when the material recovers either at zero or some reduced operating stress has significant engineering consequences. It was for these reasons that the present investigation on the recovery of creep behavior was initiated. Inasmuch as a substantial background has now developed on the creep of high-purity aluminum, this material was again selected for the current investigation. Furthermore extensive evidence is now

Jan 1, 1963

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

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 Charles Stein

The effects of several different prior treatments an the creep behavior of 99.9995 pct aluminum at 260°C and 1000 psi canstant stress are compared with annealed specimens. Quenching from 538oC, irradiation with 2 mev electrons, and tension-compression room temperature fatigue damage were used to change the substructure of the specimens prior to their creep testing. The quenched and the irradiated specimens showed a larger primary and transient stage contribution to the creep curve than those specimens which were only annealed prim to creep testing. The specimen receiving prior fatigue damage at room temperature showed no first stage or transient creep when tested under identical conditions as the above specimens and had an average creep rate seven orders of magnitude lower than that of either the annealed, the quenched or the irradiated creep specimens. In a previous electron transmission microscopy investigationl of the substructure developed during the creep of pure aluminum at 0.57 Tm, it was noted that a large concentration of vacancy loops and dislocation loops were present in and near the subboundaries while the interior of the subgrains contained few of these defects and had a low dislocation density, see Fig. 1. Yim and Grant2 and Hazlett3 have shown that the presence in nickel of a substructure developed by prior cold work effectively reduces the primary and transient contributions to the creep curve. Hultgren,4 McLean,5 Gervais, Norton, and Grant,6 Chang and Grant,7 and others have shown the same effect with the higher stacking fault energy material, aluminum. However, the specific defect responsible for the change in the creep behavior developed by the prior cold work was not established. Specifically, what effectively interfered with dislocation motion in these materials at elevated temperatures? Was it jogs on dislocations produced by their interaction with other dislocations or with vacancy or dipole loops, see Fig. 1, or did the subgrain walls determine the mean free path for glissile dislocations? This would be a realistic possibility only if subgrain boundaries are effective barriers to dislocation motion. The ability of a subgrain boundary to act effectively against glissile dislocations depends on the number and the arrangement of dislocations in the subboundary,8 which in turn is a function of the creep strain.' This paper compares the creep rate of specimens possessing a large vacancy concentration to that of annealed specimens and with specimens having a stable subboundary wall containing Lomer locks produced by prior fatigue damage. EXPERIMENTAL PROCEDURE Vacancy Loops. Aluminum creep specimens, 99.9995 pct pure, were machined from zone refined rod to a 2-in. gage length and a cross-sectional area of 0.025 in. These specimens were annealed at 538oC, 1000°F, for 10 min and quenched into ice water. They were then reheated to the creep test temperature of 260°C, 500°F, and held at this temperature for 18 min to al-low for vacancy condensation and loop formation. The specimens were subsequently creep tested at 1000 psi constant stress at 260°C. The temperature along the gage length was monitored by three Pt-Pt, 13 pct Rh thermocouples, two embedded in the upper and lower shoulders of the specimen and one attached to the mid-point of the gage length- The temperature gradient was held to ± l°C or less throughout the Creep test. Elongations were measured by two LVDT's 'connected in an averaging 'On-figuration, with quartz extension arms placed against the specimen at the extremes of the 2-in. gage length. i K 3J?--' * *H - >^> - ' ^L r 77 . *y J OJL, J Fig. 1—Transmission electron micrograph of pure aluminum strained 8.2 pct at 260°C and 1000 psi constant stress. Note the presence of numerous loops near the light dislocation tangle

Jan 1, 1970

By J. F. Smith, J. R. Ogren, N. J. Magnani

The uapor pressrcres of magnesium over binary alloys of magnesium with twelve of the yare-earth eletnetzts have been measured by the Knudsen effuion method in the temperature range 675° to 910°K. These vapor-pressure measurments were combined with data concerning the tevtrlitzul magnesium solubility and the vapor pressure of pure magnesinm to evaluale the standuvd free energies of pluase jormation. These free-etzergy values indicate that the CsCl structures of the heacy rave earths tend to be somewhat less stable than those of the light rare earths. This dif-]eying- behaviov covrelates with differences which have been obsevz~ed in other alloy systetns wherein a phuse appeurs, disappeavs, or changes crystal stvucture as the atomic number of the rare-earth com-ponent is changed. This behauior also appears to correlate with the struclurul rariations within the rare-earth elements themselves, and it is speculated that cariations in the spatial extent of the 4f orbitals are responsihle. STUDIES of the phase relationships and crystal structures in the binary systems between rare-earth metals (lanthanons) and magnesium are extensive but far from complete. However, the currently available information1-10 does produce a rather interesting pattern. This is illustrated in Table I. If one excludes europium and ytterbium from consideration because of their generally atypical behavior, it can be seen from the table that the phase relationships in the magnesium-rich regions show a distinctly different pattern for the lighter lanthanons as compared to the heavier lanthanons. For the lighter lanthanons, LnMg2 phases occur from lanthanum to gadolinium with the cubic MgCu2 structure, LnMg3 phases occur from lanthanum to terbium with the BiLi3 structure, and magnesium-rich phases occur from lanthanum to gadolinium with stoi-chiometries between Ln5Mg42 and LnMg12. In contrast, for the heavier lanthanons, those LnMg2 structures which have been examined have the hexagonal MgZn2 structure, LnMg3 phases have not been observed beyond terbium, and the magnesium-rich phases occur with the a manganese structure near a stoichiometry of Ln5MgZ4. The heavy lanthanon-magnesium systems thus appear to be analogous to the Y-Mg system""2 wherein YMg has the CsCl structure, YMg2 has the MgZn2 structure, and the region Y4Mgz5-Y5Mg24 has the a manganese structure, and no other intermediate phases are observed. Similarity in alloying behavior between yttrium and the heavy lanthanons occurs commonly, and on this basis it seems likely that LnMg2 phases will be found with the MgZn2 structure in the binary systems of dysprosium, thulium, and lutetium with magnesium when the appropriate investigations are made. In the case of the magnesium-rich phases of the lighter lanthanons, only the Ce-Mg phase relationships have been investigated thoroughly and in detail, and until similar investigations are made for the other systems there will remain questions as to which magnesium-rich stoichiometries represent equilibrium phases and what systematic variations occur in the sequence from lanthanum to gadolinium. Thus the data in Table I show that only the LnMg phases occur with the same crystallographic structure throughout the sequence from lanthanum to lutetium. It was speculated that the relative stability of these LnMg phases might vary from one lanthanon to the next in such a way as to presage the differences which occur among the more magnesium-rich lanthanon-magnesium phases. On this basis the present investigation of the thermodynamics of phase formation was Gndertaken for the LnMg phases. PROCEDURE AND RESULTS A generalized phase diagram for the lanthanon-rich portion of a lanthanon-magnesium alloy system is shown in Fig. 1 where ß represents a high-temperature bcc

Jan 1, 1968

By C. Laird, C. E. Feltner

An investigation into the effect of a material's slip character on its high strain fatigue properties has been carried out using copper and Cu-7.5 wt pct A1 as representative wavy and planar slip mode materials, respectively. In copper, the constant term and exponent in the Coffin-Manson equation, ?EpNf1/2 = const, are unaffected by the temperature of testing or the history of the metal. On the other hand, in Cu-7.5 wl pcl Al, while the exponent is invariant, the constant is increased with respect to copper and increased further with decrease in temperature. The life in Cu-7.5 wt pct A1 is double that of copper at room temperature and about four times at 78°K. Fractoflaphic studies indicate that these diffevences in life are associated with the early stages of cracking. In copper, severe surface rumpling provides crack nuclei at pain boundaries independent of' testing temperature or the history of the metal. In Cu-7.5 wt pct Al, the planar slip mode of deformation prevents grain boundary folding; crack nucleation is therefore mainly transgranular and the increase in life with respect to copper is associated with a prolonged linking-up stage of such transgranulay cracks. At the lower temperature the increased difficulty of cross slip inhibits multiplication of trans-granular cracks and retards the linking-up process, giving a further enhaancement in life. It is expected that such behavior will be found general in materials of wavy and planar slip mode, respectively. STAGE II crack propagation in high strain fatigue takes place by a repetitive process of crack tip blunting in the tension part of a fatigue cycle followed by resharpening of the crack in the compression part.1-3 This mechanism has come to be called the "plastic relaxation process".3 At very high strains (lives to failure less than 103 cycles), most of the life of a specimen is spent in crack propagation by the plastic relaxation process.4,5 Since the differences in the cyclic strain hardening behavior of metals and alloys are comparatively small in this strain range,6,7 the amount of blunting at a crack tip depends primarily on the applied strain amplitude. The rate of crack propagation in this life range is therefore nearly constant with respect to material and temperature of testing. In the longer life portion of the high strain fatigue range (l03 to 103 cycles to failure), a considerable fraction of the lives is spent in crack initiation and Stage I growth. Grain boundaries have frequently4,5,8 been found to be the sites for this growth which is also associated with a surface folding process.4'5 Such folding behavior may also be general in any material having a grain structure and capable of plastic deformation. It has therefore been suggested475 that the universality of the Coff in-Manson law,9'10 constant,* where ?Ep is the plastic strain range and Nf the number of cycles to failure, is reflected in the approximate invariance of both the crack initiation and propagation behavior. It happens that, in most investigations of the phenomena associated with failure,4,5,8 materials with a wavy slip mode have been used as vehicles for the studies, or else "normally" planar slip mode materials have been tested under conditions giving rise to wavy glide deformation, e.g., stainless steels cycled at high temperature.'' The purpose of the present investigation was to determine whether or not different cracking phenomena would occur when the slip mode of a material is planar and if the associated life to failure would be different than that of a wavy slip

Jan 1, 1968

By A. J. Ardell, O. D. Sherby

The elevated-temperature steady-state creep behavior of polycrystalline a Zr was studied in vacuo under constant tensile stress. The experiments were conducted from 660° to 845°C over the stress range 870 to 5400 psi. The steady-state creep rate, is, of a Zr was found to be related to the applied stress, a, and temperature, T, by the equation where C is a constant. Two interpretations of the data are considered, each requiring different values of the parameters ß, Q, and . It is shown that this formula can be derived using Gilman's phenomeno logical equation relating dislocation velocity to the shear stress for the case where dislocation mobility is limited by the nucleation of kink motion. From the fundamental dependence of strain rate on dislocation velocity and the density of mobile dislocations, the factor exp(ßo) can be related to the stress dependence of the dislocation density, and Q to the energy of kink formation. The two interpretations considered are as follows: Case I—the parameters are adjusted so that the equation above describes the data over the entire range of stress and temperature, implying that creep is controlled exclusively by dislocation glide; Case IIthe parameters are adjusted to allow for the possibility that creep is diffusion-controlled at high stresses but glide-controlled at low stresses. For both cases the values of the parameters are within the spread permitted by the data. Factors favorable to the observation of the unusual stress -dependence of i, for a Zr are discussed and it is shown that the anomalously rapid rates of self-diffusion and the low modulus on the principal glide system are primarily responsible for the anomalous creep behavior. Metal-lograflhic observations are presented and discussed with reference to the overall creep behavior. PREVIOUS investigations of the creep behavior of a Zr have been conducted from room temperature to about 500C The results of these investigations are primarily of engineering significance because of the variety of conditions under which they were carried out, and the low testing temperatures employed. Little information is available concerning the fundamental nature of the elevated-temperature creep behavior of a Zr. This investigation of the creep behavior of a Zr above half the melting temperature (the melting temperature, T,, of a Zr is estimated to be about 1860"K was initiated because there are two significant anomalies of the physical properties of a Zr: a) the rate of self-diffusion in polycrystalline a Zr is anomalously rapid: b) both Young's modulus for polycrystalline a Zr and the shear modylus as-sociated with the prismatic slip system { 1010)( 1120) (the principal slip system in a Zr 7) have anomalously large temperature variations The importance of these quantities to the understanding of creep behavior has been demonstrated, and it was hoped that this investigation would provide a critical test of the predictions based upon the analysis of creep data for other pure metals. However, as the investigation progressed it became increasingly clear that the unusual creep behavior of a Zr could not be analyzed in a conventional manner. 1) EXPERIMENTAL EQUIPMENT AND PROCEDURES Two grades of zirconium, designated A and B, were used in this investigation. The analyses, as supplied by the vendors, are presented in Table I. Material A, with a nominal purity of 99.84 pct, was supplied by the Wah Chang Corp. in the form of cold-rolled sheet from which specimens were machined without further fabrication. Material B, with a nominal purity of 99.95 pct, was purchased from the Nuclear Materials and Equipment Corp. in the form of iodide crystal bar.

Jan 1, 1968

By C. E. Gregor

Current modern trends in mining show that hoisting shafts are being expected to fulfill an important ventilation function. However, where rigid guides and supporting structures are mandatory, ventilating power costs will be high, unless the transverse structures (shaft sets) are streamlined. In the complex configurations of hoisting shaft furniture patterns, either for original design purposes, or for the adjustment of an existing shaft, a useful degree of aerodynamic optimization, by reduction of overall resistance, can only be effectively evaluated by model studies in a special purpose wind tunnel, as described herein. The author has shown that, in one particular case, an annual power cost saving of more than $50,000 was indicated, mainly by the selection of buntons and dividers of improved aerodynamic profile. Mining companies are now realizing the advantages that can accrue through proper attention to the aerodynamic aspects of mine shaft design. With progressive demands of civilization for an ever greater supply of coal and metals, and with greater depths of working, higher rates of extraction, advanced degrees of mechanization, and improved standards of environmental health and work comfort, shaft design is becoming an extremely important aspect of mining operations. In addition, because the cost of sinking, equipping, maintaining, and operating a mine shaft is continually increasing, there is a greater incentive to use a shaft for the maximum duty, consistent with economy. The current natural tendency is therefore to sink multi-purpose shafts, to install as much equipment as is safely and effectively possible to operate; and then, over and above all these functions, to use the shaft to its maximum possible ventilating capacity, as a major, or auxiliary, airway. Clearly, this latter additional function can only be employed at a significant cost, since the most economic operating airways are smooth-lined and devoid of internal rigid furniture. It is true that hoisting functions can be carried out in such shafts if rope guides are used, but only under restricted conditions. Where a manway must be provided, fixed guides and supporting structures are mandatory, and ventilation costs become accentuated. It is generally recognized that the prime element of cost in ventilating a mine can be represented by the power required to drive the fan unit. It is also known that the largest component of total mine resistance is that of the downcast shaft, where this shaft is equipped with rigid guides for hoisting purposes. The pressure loss varies directly as the resistance of the shaft, in accordance with a modification of the Atkinson equation p = RQ2/3600. Furthermore, the air horsepower drawn is given by the equation AHP = (p x 0/33000. Therefore, the power required to drive the fan unit varies as the resistance of the shaft and the cube of the air quantity. Clearly, if Q is a specified minimum, then the only way to minimize the pressure loss (and the power costs) is to reduce the shaft resistance R. (See Table I for a list of symbols.) The resistance to airflow of a shaft equipped with rigid guides and supporting structural sets consists of two components which, for the sake of analytical simplicity, can be regarded as additive. 1) Frictional resistance, represented by the viscous frictional forces within the boundary layer, as air flows along the surfaces of the walls and the periphery of the vertical elements (guides, pipes, cables, ropes, etc.) of the furniture. The friction loss can be readily calculated by the Atkinson equation, after selection of a suitable value for the friction factor K from the McElroy compilation.' KxLxO xQ2 5.2 xA3 Friction loss can be minimized by lining the shaft walls (particularly if of circular or elliptical cross-section) with a smooth continuous lining of monolithic concrete.

Jan 1, 1968

By W. C. Knopf, I. M. LeBaron

In the Carlsbad area potash is dry-mined and wet-concentrated. Wet concentration involves recircu-lation of saturated brines, with resultant difficulties of brine disposal and inherent losses in recovery through solution of the KCl. A dry beneficiation process for potash minerals would offer many advantages over present methods. International Minerals & Chemical Corp. has been working on development of a dry process for some time. This article is a progress report. Potash ores available in this country are largely mixtures of halite and sylvite contaminated with slimes and often with many sulfate and magnesium minerals. Electrostatic concentration of KCl when the contaminating minerals are in low percentage has been accomplished. Continuous production of better than 60 pct K2O concentrate from high potassium sulfate ores has not been demonstrated at the present time. Laboratory Procedure: Laboratory work on electrostatic beneficiation of potash minerals has been carried out using both pure crystals and mined ore. Electrostatic separation of the two main components of potash ore, sylvite (KCl) and halite (NaCl), is accomplished by first heat-treating the ore to allow for electric charging of the particles. Preferential exchange of' electrical charges between different mineral particles through surface contact is the principal mechanism involved. After proper conditioning of the particle surfaces, the oppositely charged minerals are dropped vertically into a horizontal electric field having a field gradient from about 5000 to 15,000 v per in. The particles are free-falling in the field. A suitable power supply is used to produce the proper total voltage for the electric field. Total required voltage is, of course, a function of electrode spacing. A typical electrode arrangement with power supply is shown in Fig. 1. In general, the total voltage on any system is 75,000 to 90,000 v. Power consumption is negligible, as leakage at insulators and corona discharge are the main losses in the system. Optimum preheat temperatures for pure material components generally are not the same as for mined minerals. Fig. 2 shows clearly that maximum recovery on a 50 pct pure KCl, 50 pct pure NaCl mixture occurs at a preheat temperature of about 600°F. In this test the preheat mixture was allowed to cool to about 225°F before dropping through the electric field. The optimum temperature for sep- aration is practically never the optimum temperature of preheat. Optimum separation for mined Carlsbad potash ores occurs when a preheat temperature closer to 900°F is used, as shown by Fig. 3, which plots percent sylvite (KCl) in the concentrate and tails as a function of preheat temperatures. Here again the ore was allowed to cool to about 225°F before separation. It should be noted that efficiency of separation increases continuously with increasing preheat temperatures until incipient fusion of the ore takes place at about 950°F. The increase in optimum preheat temperature for Carlsbad ores over the pure minerals can be traced to the effect of the clay slimes intimately associated with the mined potash. If the slimes associated with the ore are removed by washing with alcohol or other non-aqueous material, the necessity of preheating to the high temperature is removed. This temperature range has been proved critical within these limits during continuous pilot plant operation. Concentrate and tailings grade and optimum recovery also are functions of the temperature of the potash mineral particles during separation in the electric field. Fig. 4 presents data indicating that feed to the rougher pass should range between 150°F and 275°F for best results. It has been found by subsequent pilot plant work that these temperatures can be maintained in actual operation.

Jan 1, 1959