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By P. K. Strangway, H. U. Ross

Briquets consisting of pure artificial magnetite, pure artificial hematite, and mixtures of the two were reduced by hydrogen in a loss-in-weight furnace at temperatures in the range 500° to 1000° . The rate of reduction of the pure hematite briquets increased continuously with increased temperature. In contrast, the pure nmgnetite briquets exhibited a pronounced rate ninimutn at about 700°C. Metallographic studies of partially reduced briquets rerlealed that, at this temperature, the he.matite samples reduced in a topo-chemical manner while the magnetite ones reduced uniformly throughout, and after partial reduction their cross sections contained a mixture of iron and unreacted wustite grains. No iron shells could be detected on the surfices of any of these uwstite grains. X-ray diffraction investigations indicated that these grains had a rzinimum lattice parameter when they had been formed at the rate rninimum temperature. Also, it was found that an activation energy of 41,000 cal per mole zoas required for reduction when only these wustite grains were present. Thus, it is suggested that the overall reduction rate of the rnagnetile su?nples at temperatures in the range influenced by the rate nzinirnum phenomenon was limited by the rate qf iron ion diffusion in the unreacted wustite grains. THE rate minimum phenomenon, which has often been observed when reducing iron oxides at a temperature of about 700°C, is one of the most interesting, yet unresolved, problems in the field of reduction kinetics. Basic principles of chemical kinetics and 'In some instance, a second rate minimum has been observed at about 900°C. Since most investigators are in agreement that this minimum is directly related to the transformation from a to y iron (which takes place at 911°C) and since it was not encountered during the present reduction tests, it will not be referred to in this vaver. fundamental laws of diffusion all agree that, as the temperature is increased, the rate of reduction should also increase. However, with certain ores, it has been found that their reduction rate actually decreases with an increase in temperature up to some value X where a minimum reduction rate is reached. With further temperature increases beyond X the rate becomes more rapid again. Temperature X is usually referred to as the "rate minimum temperature", while the overall type of behavior constitutes the "rate minimum phenomenon". This phenomenon has been reported by numerous investigators. They have found rate minima during the reduction of both artifiial' and natural374 magnetites and artificia15j6 and natural5" hematites. Rate minima have been observed when reducing high-purity material2 or low-grade ores,3'4 when studying particles in the micronsize range5 or relatively large agglomerates,g10 and during reduction with either hydrogen7 or carbon monoxide.11"2 Previously, this phenomenon has been attributed to many factors; these include sintering and recrystallization of the iron formed during reduction374 changes in microporosity of the ore upon redction,"" formation of dense iron shells around retained wustite grains,11716 and chem-isorption,17 to name only a few. However, most investigators who have reported a rate minimum merely speculated as to what seemed to influence it and they did not examine the fundamental causes. Consequently, the present experimental study was initiated in order to evaluate the basic factors which could be associated with this phenomenon. MATERIALS AND METHODS The experimental techniques, followed during this investigation, are similar to those which have been described previously.18 The chemically pure magnetic powder was prepared by partially reducing Fisher reagent-grade hematite with a gaseous mixture of carbon monoxide and carbon dioxide in a rotating-drum furnace. Three-quarter-inch diam cylindrical briquets which weighed about 12 g were formed from this magnetite powder and pure hematite powder. All of the briquets were sintered while they were slowly raised through the 1200°C hot zone of a vertical tube furnace. An argon stream was continually flushed through this furnace in order to prevent oxidation of the magnetite briquets, while in the case of the pure hematite briquets sintering was carried out in air. The sintered hematite briquets had a density of 5.06 g per cu cm while the density of the sintered magnetite briquets was 4.27 g per cu cm. The sintered briquets were reduced by purified hydrogen in a loss-in-weight furnace at temperatures in the range 500" to 1000°C. In all instances, the critical reducing gas velocity was exceeded and, in order to ensure that the results were reproducible, duplicate briquets of each type were reduced under each set of experimental conditions. A continuous record of the weight loss during reduction was obtained with the aid of a Statham transducer. The present experimental setup was capable of detecting a change in weight as small as 10 mg. Since a weight loss of over 2 g usually occurred during each reduction test, an accuracy of better than 0.5 pct of the total weight loss could be achieved. RESULTS AND DISCUSSION Reducibility Tests. In the first set of experiments, pure hematite and pure magnetite briquets were used.

Jan 1, 1969

By A. R. Gregory, A. L. Podio, K. E. Gray

Dynamic elastic properties of dry and water-saturated Green River shale samples were computed from compressional- and shear-wave velocity measurements. P- and 5-wave velocity measurements were made in three mutually perpendicular directions with respect to the bedding planes. Measurements were also made in several different directions by varying the angle between the bedding planes and the direction of propagation of the wave for angles of 0, 30, 45, 60 and 909 The oriented samples were subjected to both confining pressure and axial loads, in excess of the confining stress, in the direction of propagation. In general, P- and S-wave velocities increased with increasing stress levels, with a corresponding increase in Young's modulus. Water saturation caused the P-wave velocity to increase and the S-wave velocity to decrease. Elastic moduli decreased upon saturation, except for Pois son's ratio, which increased, indicating some degree of weakening of the material. The samples showed a moderate degree of anisotropy; this was to be expected from the laminated nature and shallow occurrence of Green River shale. INTRODUCTION This paper presents some results of an experimental determination of the elastic coefficients of anisotropic materials (in particular, finely layered rocks and minerals such as Green River shale) from measurements of dilatational and shear-ultrasonic-wave velocities. Ultrasonic techniques have been used extensively in nondestructive testing. Several methods have been proposed by Mcskimmin, 1 and some of these have been used successfully to measure ultrasonic velocities in rocks. Hughes and Cross, 2 Wyllie et al., 3 and Birch 4,5 developed pulse first-arrival techniques for the measurement of dilatational and shear velocities. Williams and Lamb 6 used the method of cancellation of a traveling wave, which was later modified by Myers et al.' and perfected by McSkimmin. 8 Although this method is highly accurate, it has not been used as widely as the pulse-transmission methods recently reported by Jamieson and Hoskins 9 King,10 and Mattaboni and Schreiber. 11 It has been common practice to use some form of crystal transducers, either quartz or ceramic, that has been cut or polarized in different directions in order to generate either compressional or shear waves. However, accurate determination of shear wave velocities has been difficult due to problems that arise in obtaining a pure shear wave from cross-polarized crystals, which usually also generate a small amount of compressional energy. As reported by Gregory, 12 this energy can be seen as a long precursor preceding the sharp break of the shear first arrival. The need for generating pure shear waves led to interest in mode-conversion techniques, which are based upon conversion of the mode of vibration through wave reflection or refraction at a discontinuity. Arenberg13 showed that for certain materials and for certain angles of incidence it is possible to generate pure shear modes by reflection at a boundary. Jamieson and Hoskins 9 used a pyrex glass-air interface for generating pure shear waves, and King 10 used this method successfully for measuring shear-wave velocities in rocks. Gregory l4 arrived at a similar result by refraction of a wave at an aluminum-oil interface. A plane compressional wave, traveling in the oil phase, is incident on the aluminum at an angle larger than the critical angle for compressional waves, and thereby generates a purely transverse, plane-polarized wave in the aluminum. During the last few years methods have been developed that allow the simultaneous determination of shear and compressional velocities in solids.

Jan 1, 1969

By Walter H. Ortel, George B. Wallace

INTRODUCTION A greater understanding is required about the factors which control tunneling operations if we are to meet the expected demand for tunnels. Much of the needed information can best be achieved by the proper use of instrumentation and advanced engineering concepts. Tunnel measurements and their analysis may prove to be the key which will give the insight necessary to understand the relationship of rock, tunnel supports, and linings. There are three main areas which can be improved through the use of tunnel instrumentation. First, and of prime importance, is safety for men and the project. When unstable conditions occur, sets become distorted. Even without measurements, it is sometimes possible to tell when trouble is approaching. In effect, the set acts as a load cell. Distortions in the set indicate reinforcements may be required to maintain stability. Additional sets or rock bolts, if they are placed soon enough, may provide this stability. However, when large rock displacements occur in short periods of time, it could be too late. Figure 1 is an example of the difficulties encountered in stopping moving rock. To stop the movement and possible failure, large props were placed above the spring line and the massive concrete gravity buttress was constructed along the legs. Rock bolts from the buttress deep into the rock were also used in an attempt to stabilize the rock mass. However, this work is for a highway tunnel and eventually these props and buttresses must be removed.

Jan 1, 1971

By Francis A. Pocock

The writer is continually asked, if this electricity:is all you claim for it, why do not the mines put it in and use it? The best answer was given by Mr. John Fox Tallis, in his paper read before the South Wales Institute of Engineers in 1888, namely, that the reasons are similar to those which have prevented the more general employment of other systems of haulage. Managers, as a rule, are " not experienced mechanical engineers; neither are they all versed in electrical engineering." It may be said that there are a number of " able and practical electrical engineers who could do the work; but those electrical engineers are not conversant with the practical routine of colliery work and are, therefore, placed at a disadvantage by not knowing the actual requirements of mining engineers, and the many little difficulties to be met and contended with in underground workings; and, until mining engineers have acquired the necessary knowledge and a confidence in electricity, it is only natural that they will continue to follow the beaten path." In the above remarks, Mr. Tallis has hit the nail on the head. In the face of the partial failure, financially, of the haulage-plant which the Union Electric Company of Philadelphia had set to work at Lykens Valley, Pa., an electric haulage-plant was installed near Scranton, Pa. The question was not whether electricity could do the work, but whether any electrical company knew enough about the practical difficulties to attack and overcome them. That point being settled, the remainder was easy. The contract for the Erie Colliery haulage-plant was signed in January, 1889. This colliery is owned by the Hillside Coal and Iron Company, Mr. Samuel Hines, President, and Captain W. A. May, Superintendent. The company has been using arc-lamps in its breakers for three years. It is the only company in the Lackawanna Valley which has had enterprise enough to do so. Consequently, it was acquainted

Jan 1, 1890

By Elmer W., Pehrson

NOT much serious consideration was liven to the military aspects of raw materials before World War 1. Following the outbreak of war in Europe in 1914, however. this situation was promptly changed. Disruption of allied shipping and German submarine warfare soon cut off a substantial part of the material the United Staten was accustomed to receiving from overseas. At the same time, raw material requirements rose rapidly as the tempo of industrial preparedness was stepped up in anticipation of war. By April 1917, when we entered the war, serious shortages threatened and consideralde attention was being given to our "deficcient" raw materials. The term "war mineral," began to appear after we became active combatants. But there is no evidence that "strategics" and "critical." as now used, had entered the lexicon of our raw materials experts during the last war nor were there apparently any officially recog¬nized list or definitions of what con¬stituted war materials. According to G. A. Roush in his book, `'Strategic Mineral Supplies," C. K. Leith, while serving as mineral advisor to the War Industries Board. compiled the first unofficial list of deficient minerals in 1917.

Jan 1, 1944

President MRS. ROBERT HURSH River Road, Silvermine Norwalk, Conn. First Vice -President MRS. WILLIAM C. SCHNEIDER 45 Wayne Ave. White Plains, N. Y. Second Vice-President MRS. ERNEST H. WOLFES 180 Riverside Drive New York, N. Y. Third Vice-President MRS. JOHN C. BURTON 271 Fox Meadow Road Scarsdale, N. Y. Fourth Vice-President MRS. S. A. IONIDES 379 Marion Street Denver, Colo.

Jan 1, 1941

President MRS. HARRISON SOUDER south Paramus Road Ridgewood, N. J. First Vice-president MRS. ROBERT HURSH New York N. Y. Second Vice-president MRS. RICHARD LLEWELLYN LLOYD Great Neck, L. I'. N. Y. Third Vice-president MRS. PERCY E. BARBOUR New York N. Y. Fourth Vice-president MRS. E. P. MATHEWSON Tucson Ariz.

Jan 1, 1937

By C. T. Liu, J. Gurland

The deformation behavior in tension of spheroidized carbon steels was studied at room temperature as a function of carbon content, 0.065 to 1.46 wt Pct, and carbide particle size, 0.88 to 2.77 p. It was found that the Hall-Petch strength-grain size relation is directly applicable to the yield and flow stresses of the two lower-carbon steels , 0.065 and 0.30 pct C. The strength data for the medium- and high-carbon steels, 0.55 to 1.46 pct C, also satisfied the Hall-Petch relation, provided that these data are based upon the particle spacing. Beyond 4 pct strain, the flow stress data of all the steels studied could be represented by the same Hall-Petch relation with dinerent spacings for grain boundary and particle strengthening. The behavior of the higher-carbon steels was consistent with the postulated formation of a dislocation cell network during processing and initial deformation (up to 4 pct strain). The cell size was assumed to be equal to the planar particle spacing. The true stress at the ultimate tensile strength was also found to be a function of the particle spacing. At a given temperature and strain rate, the yield and flow stresses of carbon steels depend on the type and dimensions of the microstructure. Starting with the work of Gensamer et al. in 1942,' experimental studies on pearlitic and spheroidized carbon steels revealed that the strength of steels is a function of two main parameters: the ferrite grain size2'3 and the carbide particle spacing;1'4'5 on this basis, two different strengthening mechanisms have been developed to apply to steels of low and high carbon contents, respectively. In polycrystalline iron and mild steels the grain boundaries are regarded as the major structural barriers to slip. The relation between strength and grain size is generally represented by the Hall-Petch equation which is based on a linear proportionality between strength and the inverse square root of the average grain size.2'3y677 However, Gensamer et al.' and Roberts et related the yield strength of medium -and high-carbon steels to the carbide particle spacing alone, and they found a linear relation between the logarithm of the mean free path in the ferrite and the yield strength in both spheroidized and pearlitic steels. By means of the electron microscope, Turkalo and LOW' extended the study to finer structures; they concluded that the logarithmic relation is not valid for the entire range of microstructures unless grain boundaries are also included in the measurement of the mean free path. For the specific case of spheroidized steels, Ansell and aenel' found that the yield strength data,4'5 when plotted as a function of mean free path, fit the Hall-Petch equation; however, T'ysong found that the same data fit the 0rowanl0 relation if a planar inter-particle spacing is used. Recently Kossowsky and ~rown" studied the strength of prestrained spheroidized steels, 0.48 and 0.95 pct C, and concluded that the strength due to the carbide dispersions varies linearly with the reciprocal of the square root of the mean free path between carbide particles and dislocation networks. Such networks were first observed by Turkalo." The conclusion common to all these studies is that the available slip distance in the ferrite is the most important variable in determining strendh. Previous work on carbon steels is restricted to limited composition and strain ranges. The mechanism which governs the flow properties is not clearly understood, and, in particular, little is known about the composition dependence of the transition between grain boundary strengthening and particle hardening. The purpose of the present work is to investigate the strengthening mechanism in spheroidized steels over a wide range of carbon content, 0.065 to 1.46 wt pct, and plastic strain, yielding to necking. The spheroidized structure was chosen because of its relative simplicity and the relative ease of control and measurement of the structural parameters. The experimental work is limited to tensile testing at room temperature at constant extension rate. The effects of the carbide particles on the fracture behavior of spheroidized steels are discussed elsewhere.13 EXPERIMENTAL PROCEDURE Eight different grades of vacuum-cast carbon steels were supplied in the form of forged and rolled plate by the Applied Research Laboratory of the U.S. Steel Corp. The compositions furnished with these steels are given in Table I; the carbon content ranges from 0.065 to 1.46 wt pct, or from 1.0 to 22.3 vol pct of carbide. The steel plates were cut transversely into rods a little larger than the test specimens, 1 in. gage length, i in. diam. The rods were austenitized in air (enriched with CO by a consumable carbon-rich muffle) at 50° C above theA, orA., temperature for 2 hr and then quenched in oil with vigorous stirring. The as-quenched rods were tempered in two stages in order to obtain the desired distributions and sizes of carbide particles. The rods were first tempered at 460° C for 10 hr and then at 700" C for periods ranging from 4 hr to 3 days, in vacuum. After final machining, all specimens were vacuum-annealed again at 650°C for 1 hr in order to relieve residual stresses. The tension tests were carried out in two steps. The initial part of the load-strain curve, up to about 2 pct strain, was determined on a Riehle testing machine with an extensometer of small strain range, 4 pct strain, in order to obtain the yield and initial flow piopertiesi As soon as the first part of the test was finished, the specimen was placed in an Instron testing machine equipped with a strain gage extensometer with a maximum strain range of 50 pct. The load-strain curve to fracture was

Jan 1, 1969

By A. Gatti, R. L. Fullman

A very fine dispersion of aluminum oxide is produced by internal oxidation of solid-solution alloy of 0.14 pet A1 in Ag. The particle size of the aluminum oxide is approximntely 50 to 100A in radius. The yield strength of the alloy is increased markedly by internal oxidation. A further increase in strength is produced by cold working the internally oxidized alloy. Recrystallization is retarded by the finely dispessed aluminum oxide particles, so that the strength increase resulting from cold work is retained on annealing at temperatures 14 to about 700°C. MANY workers'-3 in the past have studied various aspects of the internal oxidation of aluminum-silver alloys. This paper is an extension of these studies with emphasis placed on the effect of time and temperature of annealing on the strength of these alloys after oxidation and subsequent cold working. Two general conditions are necessary to internally oxidize an alloy. First, oxygen must diffuse through the base material more rapidly than does the addition; otherwise oxidation will take place as a surface layer. Secondly, the affinity of oxygen for the addition must be greater than for the base material. After internal oxidation of certain alloys takes place, a marked increase in hardness accompanied by higher yield stress and improved creep properties is noted, presumably as a result of the highly dispersed oxide within the base material. Meijering and Druyvesteyn1 also noted that the internally oxidized portion of a partly oxidized alloy failed to recrys-tallize under annealing conditions that led to coinplete recrystallization of the unoxidized part. EXPERIMENTAL-METHODS AND PROCEDURES Few alloys can be made to contain a second phase that is extremely stable at high temperatures. Silver plus aluminum in solid solution was chosen for these internal oxidation studies because of the high rate of oxygen diffusion through silver and the very stable nature of aluminum oxide. Two alloys were vacuum cast. The nominal compositions were: Alloy A—1 pct Al, balance Ag; Alloy B—0.1 pct Al, balance Ag. Chemical analysis, which does not distinguish between aluminum and aluminum oxide, showed the conlposition to be: Alloy A—1.6 pct Al, and Alloy B—0.14 pct Al. The ingots were machined for surface cleaning, swaged and drawn to 0.020-in. diam wire. A sample 20 ft long of the 0.020-in. dianl wire of each composition was annealed 24 hr at 800°C in pure dry hydrogen. Each wire was then cut into two equal pieces. Photomicrographs of the 0.14 pct A1 alloy are shown in Fig. 1, the annealed 0.020-in. wire at the left and the oxidized wire to the right. The oxidation treatment for the first set of data was 1000 hr at 800°C in air. After this treatment the 1 pct A1 proved to be brittle. It is assumed that high alunlinum oxide concentration at the grain boundaries was responsible. The 0.14 pct Al wire remained ductile and all further data were derived using this alloy. One-half of this wire, about 5 ft, plus 5 ft of as-homogenized wire, was then drawn cold to 0.005 in. diam. All tensile tests were conducted with an Instron Engineering Corp. tensile-testing machine, Model TT-B. Unless otherwise indicated, the tests were made at room temperature with a strain rate of 0.1 per min. All metallographic samples were etched with an aqueous solution of 2 pct each of CrO3 and H2SO4 . EXPERIMENTAL RESULTS AND DISCUSSION PARTICLE SIZE DETERMINATION A study was made of the particle size of the aluminum oxide produced in the samples of Ag + 0.14 pct Al, oxidized 1000 hr at 800°C. A cross section of the as-oxidized wire was mounted in bakelite, polished, and etched with an aqueous solution of 2 pct each of CrO3 and H2SO4. The specimen was then thoroughly cleaned by stripping successive coatings made by applying 10 pct nitrocellulose in amyl acetate. The final replica of the cross section was made by applying 2 pct nitrocellulose in amyl acetate. The replica was stripped, transferred to a copper screen, shadow cast with chromium at 10 deg and photographs taken using a Phillips Metallix electron microscope at an accelerating potential of 100 kv. A photograph of an etched sample of the as-oxidized material is shown in Fig. 2. We believe the pits in the photograph are places were A12O3 inclusions were sitting in the matrix. By inspection, it appears that the volume fraction ob-

Jan 1, 1960

By K. E. Brown, A. R. Hagedorn

A 1,500-ft experimental well was used to study the pressure gradients occurring during continuous, vertical, two-phase flow through 1-in., 1 1/4-in. and 1 1/3-in. nominal size tubing. The test well was equipped with two gas-lijt valves and four Mathak electronic pressure transmitters as well as with instruments to measure the liquid production rate, air injection rate, temperatures and surface pressures. Tests were conducted for widely varying liquid flow, rates, gas-liquid ratios and liquid viscosities. From these data, an accucrate pressure-depth traverse was construcred for each test in each of the three tubing sizes. From the results of these tests, correlations have beer] developed which allow the accurate prediction of flowing pressure gradients for a wide variety of tubing sizes, flow conditions, and liquid properties. Also. the correlations and equations which are developed satisfy the necessary condition that they reduce to the relationships approprate to single-phase flow when the flow rate of either the gas or the liqutid phase becomes zero. All the correlations involve only dimensionless groups. which is a condition usually Sought for in similarity analysis but not always achieved. The correlations developed in this study have been used to calculate pressure gradients for pipes of larger diameter than those upon which the correlations are based. Comparisons of these calcuclaed gradients with experimetally determined gradients for the same flow conditions obtained from the literature indicate that extrapolation to these larger pipe sizes is possible with a degree of accuracy sufficient for engineering calculations. The extent of this extrapolation can only he determined with additional data from larger pipe diameters. INTRODUCTION The accurate prediction of the pressure drop expected to occur during the multiphase flow of fluids in the flow string of a well is a wideiy recognized problem in the petroleum industry. The problem has been brought even more into prominence with the advent of tubingless or slim-hole completions which use small-diameter tubing. Many of the correlations which give reasonably accurale results in the lager tubing sizes are greatly in error when applied to small-diameter conduits. Small-diameter conduits are defined as 1 1/2-in. nominal size tubing or smaller. The study of the pressure gradients which occur during multiphase flow of fluids in pipes is exceedingly complex because of the large number of variables involved. Further difficulties relate to the possibility of numerous flow regimes of widely varying geometry and mechanism and the instabilities of the fluid interfaces involved. Consequently, a solution to the problem by the approach normally used in classical fluid dynamics based on the formulation and solution of the Navier-Stokes equation has not been forthcoming. This is primarily the result of the nonlincarities involved and the difficulty of adequately describing the boundary conditions. As a result of the foregoing, most investigators have chosen semi-empirical or purely empirical approaches in an efford to obtain a practical solution to the problem. Much of the previous work in this area was done in short-tube models in the laboratory. A number of problems arise, however, when attempts are made to extrapolate these laboratory results to oilfield conditions where a much longer tube is encountered. In those few studies where data taken in long tubes were utilized, the data covered only a limited range of the variables, and as a result inaccuracies are introduced when the correlations are extended outside the range of the original data. Also, as a consequence of the limited amount of data available for these studies, the effects of several important variables were overlooked. The problem of predicting the pressure drop which occurs in multiphase flow differs from that of single-phase flow in that another source of pressure loss is introduced, namely, those pressure losses arising from slippage between the phases. This slippage is a result of the difference between the integrated average linear velocities of the two phases, which in turn is due to the physical properties of the fluids involved. In contrast to single-phase flow. the pressure losses in multiphase flow do not always increase with a decrease in the size of the conduit or an increase in production rate. This is attributed to the presence of the gas phase which tends to slip by the liquid phase without actually contributing to its lift. Many investigators have attempted to correlate both the slippage losses and the friction losses by means of a single energy-loss factor analogous to the one used in the single-phase flow problem. In an approach of this type, hourever, many of the important variables, such as

Jan 1, 1966

By Louis A. Panek

The purpose of this paper is to present a method of designing safe and economical arch structures that are to be constructed of concrete or directly of original earth materials. The experimental data used to illustrate the design method are taken from Bucky and Fen tress,1,2 and the application of the ideas presented by them is extended by obtaining an additional set of curves from which arch structures may be designed. This design method is based upon the following principles of similitude: A scalar model made of the same material as that of the full sized structure will behave similarly to its prototype if the density of the model is increased in the same proportion as its linear scale is decreased. Let R represent the scale or model ratio, namely, the ratio of a prototype linear dimension to the corresponding model linear dimension. The effect of increased density may be obtained by rotating the model in a centrifuge at a speed such that the centrifugal held exerts on the model an accelerative force R times the accelerative force of gravity. Under these conditions; (I) model unit stresses are equal to corresponding prototype unit stresses, (2) the ratio of the prototype deformation at a given point to the model deformation at a similar point is equal to the scale ratio, R, and (3) the model and the prototype will behave similarly within and beyond the elastic limits of strain. According to the above relations, such models can be used to solve the following problems: I. The dimensions of the most economical safe arch structure for a given load. 2. The miaximum safe roof span underground for given geologic conditions. The procedure is described briefly as follows. Tests are made by rotating in a centrifuge a number of models that repiesent a variety of prototype loads and dimensions. From the experimental data, curves are plotted to show the relations between these loads and dimensions. The curves are used to solve directly the problems stated above. Structural design is based upon the working (safe) stress of the material of construction, which is established by applying a factor of safety to the experimentally determined ultimate strength of the material. In conformity with this principle, each model is gradually loaded until failure occurs. A safety factor is then applied to the results. If a safety factor of 4 is used, a given model at failure represents a safe prototype, the linear dimensions of which are equal to one-fourth the model ratio at failure times the corresponding model dimensions. The safe model ratio is computed from the following formula: Safe R =(1/4)4p2n2r/g=p2n2r/g [I] in which: n = centrifuge revolutions per second at model failure; r = radius of rotation of the model in feet; g = 32.2 ft/sec2.

Jan 1, 1949

By G. W. P. Rengstorff

In an effort to find an oxidation-resistant alloy of molybdenum, binary and ternary alloys containing aluminum, chromium, cobalt, iron, nickel, silicon, titanium, tungsten, vanadium, and zirconium were screened. Fourteen other alloying additions were also tested. Many of the alloys were more oxidation-resistant than molybdenum, but none were entirely satisfactory. MOLYBDENUM oxidizes extremely rapidly above 1450°F in air. At 1800°F, a loss of metal at the rate of 0.1 in. in 4 hr is typical. The high speed of this oxidation may be judged by comparison with the oxidation rate of 0.1 in. per year (0.00005 in. in 4 hr), sometimes taken as the maximum permissible oxidation rate at 1800°F for a satisfactory Fe-Cr-Ni alloy. Great strides have been made in the development of coatings and cladding to protect molybdenum from oxidizing atmospheres. These developments in surface protection will undoubtedly make it possible to take advantage of the excellent hot strength of molybdellum and its alloys in many new applications. Still, even the best coating can protect molybdenum only as long as the surface layer is unbroken. Research was undertaken to determine whether an alloy of molybdenum could be found which would resist oxidation. Such an alloy would not deteriorate suddenly when the protective surface layer was destroyed in a small area. In seeking an alloy of molybdenum to resist oxidation, the physical properties of molybdenum could not be sacrificed entirely. The development of an alloy with the desired resistance to oxidation was not achieved. The information obtained on the effect of a large number of elements on the oxidation of molybdenum is, however, of value in the development of coatings. Indeed, many of the alloys tested for oxidation resistance were already known to have poor mechanical properties but were tested to aid in the development of coatings. Oxidation of Molybdenum The rapid oxidation of molybdenum is usually attributed to the volatility of Moo,,. Gulbransen and Wysong have shown that molybdenum oxidizes very slowly up to 850°F, the temperature at which the oxide film begins to evaporate. Melting as well as evaporation of molybdenum oxides promotes the oxidation of molybdenum. MoO melts at 1465°F. MOO, the oxide which is believed to form at the metal-oxide interface, combines with MoO, to form a eutectic having a melting point of 1432°F.' The liquid oxide, even if nonvolatile, could cause poor resistance to oxidation by allowing easy transport of molybdenum and oxygen ions through the oxide. Actually, a sudden increase in the rate of oxidation of molybdenum at 1460°F has been observed to coincide with the appearance of a liquid phase. The formation of a volatile oxide is not unique with molybdenum. The problem is also encountered with vanadium, tungsten, and some of the Pt-Pd group of metals. Vanadium not only forms the volatile V2O3 but, like molybdenum, forms a liquid oxide coating. Few attempts have been made, however, to prevent the rapid oxidation of these metals by alloying. Oxidation of Molybdenum Alloys At the beginning of this work, very little was known of the oxidation resistance of molybdenum alloys. It was known that molybdenum disilicide (with 37 pct Si) has extremely good oxidation resistance,' but this compound is so brittle that it has few uses. It is an effective protective coating for molybdenum when allowance can be made for its brittleness. Chromium was known to retard the oxidation of molybdenum,' but at least 50 pct Cr was necessary to have an appreciable effect. Other, unpublished, reports show that a few other alloys have been given preliminary tests, but the results have not been promising." Choice of Alloys to be Investigated An alloying element might be expected to protect molybdenum in either of two ways: Its oxide might combine with molybdenum oxide to form a stable, nonvolatile complex oxide (a molybdate); or the oxide of the alloying element might form in preference to molybdenum oxide, developing an impervious layer which would prevent the formation of a volatile molybdenum oxide. The knowledge available about the formation of molybdates was meager. Therefore, the initial study was made on alloys of molybdenum with elements having especially stable oxides. On this basis, binary and ternary alloys containing the following six elements were investigated: aluminum, chromium, titanium, zirconium, silicon, and vanadium. Nickel was also added as an alloying element. Although it does not form a more stable oxide than molybdenum, it does impart some oxidation resistance to copper and iron. Its inclusion in the study was fortunate because its alloys proved to be the most promising of those first tested. Apparently nickel formed a stable molybdate. Because nickel was effective in reducing the oxidation rate of molybdenum, the elements iron, cobalt, and tungsten were added to the list. The ten alloying elements mentioned form ten binary and 45 ternary alloying systems with molybdenum. A series of alloys was tested in each of these systems. In addition, at least one test was made on the effect of each of the following alloying elements:

Jan 1, 1957

By P. G. Shewmon, H. E. Collins

A study has been made to determine the sites at which sulfur adsorption occurs on copper surfaces. measurements were made of the relative torques, Ys, at the intersection of twin boundaries with surfaces near the three low-index orientations, i.e., (100), @lo), and 011), over a range of H2S/H2 ratios. HZS concerztvations j'ro~n 3 to 1500pp)n between 830" and 1050°C were used. It is concluded that sulfur adsorption occurved preferentially though not exclusively at edge sites near the (100) and (110) surfaces in the HzS range — 700 Ppm giving rise to negative torques near these orientations. Beyond this HzS range, adsorption occurred at all sites. Near the (111) surface, 7/y little with HzS concentration up to approxiwzately 75pptn. Above this range, the results indicate adsorption is occurring OH both terrace and edge sites. SCIENTIFIC interest in surfaces and their interactions with a gaseous environment dates back to the beginning of the 19th century. The scientific luminaries of that period—Faraday, Maxwell, Rayleigh, Dewar, and Gibbs—were already concerned about such processes. However, it has only been within the past several decades that adsorption on metal surfaces has been actively studied. This increased interest in adsorption has been brought about by the advent of new and improved experimental techniques and apparatus, e.g., ultrahigh vacuum, and field-emission and ion microscopes. However, most of the work done using these techniques has been carried out at low temperatures. When adsorption studies have been made at either low or high temperatures, they usually gave no indication of the particular surface orientations or type of sites on which adsorption was occurring. In the last few years, there have been a series of studies in which the surface tension, y,, and/or its derivative with respect to orientation, 7, have been studied as a function of orientation and atmosphere.'-7 Nearly all of the work on the relative torque,* ~/y, silver annealed in hydrogen and air.6 Recently Winterbottom and Gjostein" have used a modified and more accurate Mykurian method to determine the y plot of gold in hydrogen The only work in which T/~, has been measured over a range of chemical potentials for a given solute, p2, is that of Robertson and shewmon7 on the Cu-0 system. They measured T/Y, vs Po, (10"" to 10- l3 atm) at 1000°C in various mixtures of Hz0 and HZ. From this work they estimated the value of p2 at which one half of the surface sites are occupied with oxygen, pg, as being in the range 10- l6 to 10- l5 atm of oxygen. They also found that increasing Pa increased the magnitude of ~/y, near the (111) and (100) orientations. This indicates that oxygen is not adsorbed preferentially at step edges, but uniformly over all surface sites. In addition, they did one experiment on sulfur adsorption on copper surfaces, which indicated that sulfur adsorption decreases ~/y, near the (100) orientation, while not affecting ~/y, near the (111). This could be interpreted as indicating that sulfur adsorbs preferentially at step edges near the (100). In this paper the primary objective of the work has been to carry out a study of sulfur adsorption on copper surfaces over a range of temperatures and p,. In conjunction with this work, thermal grooving at grain boundaries has been examined as a method of determining the effect of sulfur adsorption on y,. METHODS Ideally, one would like to have information on the quantity of solute adsorbed on a surface and the types of sites at which it is absorbed as a function of p2. The total quantity adsorbed or the surface excess is given by the thermodynamic equation Thus data on the variation of y, with pz indicates the value of p2 at which adsorption becomes appreciable and the quantity adsorbed. The type of adsorption site is more difficult to deduce but information on this can be obtained from the variation of rz with 8, the angular deviation of the surface orientation. This is obtained from the thermodynamic equationlg Data on t and ys as functions of p2 have been obtained by the following methods. 1) Twin Boundary Grooving—By determining the effect of adsorption on the torque, 7, where T is the variation of surface energy, y,, with orientation, it is possible to obtain some indication as to the preferred sites of adsorption. Experimentally, the torque value measured is the relative torque, 7/ys The twin boundary grooving technique suggested by Mykura'' was used in this study to determine near the three low-index orientations— (loo), (110), and (111). Mykura's equation relates 7 /yS to measurements of the di-

Jan 1, 1967

By Jack R. Elenbaas, Donald L. Katz

A radial turbulent flow formula has been developed which permits the computation of the pressure drop for radial flow in gas wells whether the flow is laminar, turbulent, or partially laminar and partially turbulent. Using the formula a complete back-pressure curve has been calculated and analyzed by a comparison with existing back-pressure curves. A procedure is presented for computing the permeability of the porous media when the porosity, sphericity and average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided new methods for computing flow under turbulent conditions. The present study was initiated as an investigation of pressure -drop computations for flow through porous sands in gas wells and as an analysis of present-day back-pressure tests. Although laminar flow exists in the producing formation of gas wells under normal flow rates, turbulent flow does take place adjacent to the well bore. As the flow rate is increased, turbulent flow exists further and further into the producing formation and under open-flow conditions in relatively deep wells a considerable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wells without resorting to extrapolation of curves drawn from data obtained in back-pressure tests or calculations made in the completely laminar region, it was necessary to have some means of calculating pressure drop for flow through porous sands under turbulent conditions.4.6 As a result, a radial turbulent flow formula was derived from the equations recently presented by Brownell and Katz.1 A rigorous solution of this equation involves a trial and error graphical integration. By making the assumptions of average viscosity, temperature and compressibility factor of the flowing gas, it was possible to graphically integrate the relation for the general case of radial flow of gases through the porous sand of gas wells. A chart has been prepared relating the value of the integral to the radius of the well bore and to the Reynolds number of the flowing gas. The chart actually performs the graphical integration and the solution of the formula is then reduced to a simple trial and error calculation. A typical back-pressure curve is calculated to show the transition from laminar to turbulent flow. This paper will briefly describe the pro-cedurcs for computing flow through porous media, including a method for predicting sand permeability from porosity and grain size and shape. Flow through Porous Media Brownell and Katzl recently reported a correlation for computing flow of fluids through porous media by the use of an enlarged Reynolds number and friction factor in which the porosity of the bed is included as an additional prime variable. The enlargcd Reynolds number com-

Jan 1, 1948

By Donald L. Katz, Jack R. Elenbaas

A radial turbulent flow formula has been developed which permits the computation of the pressure drop for radial flow in gas wells whether the flow is laminar, turbulent, or partially laminar and partially turbulent. Using the formula a complete back-pressure curve has been calculated and analyzed by a comparison with existing back-pressure curves. A procedure is presented for computing the permeability of the porous media when the porosity, sphericity and average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided new methods for computing flow under turbulent conditions. The present study was initiated as an investigation of pressure -drop computations for flow through porous sands in gas wells and as an analysis of present-day back-pressure tests. Although laminar flow exists in the producing formation of gas wells under normal flow rates, turbulent flow does take place adjacent to the well bore. As the flow rate is increased, turbulent flow exists further and further into the producing formation and under open-flow conditions in relatively deep wells a considerable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wells without resorting to extrapolation of curves drawn from data obtained in back-pressure tests or calculations made in the completely laminar region, it was necessary to have some means of calculating pressure drop for flow through porous sands under turbulent conditions.4.6 As a result, a radial turbulent flow formula was derived from the equations recently presented by Brownell and Katz.1 A rigorous solution of this equation involves a trial and error graphical integration. By making the assumptions of average viscosity, temperature and compressibility factor of the flowing gas, it was possible to graphically integrate the relation for the general case of radial flow of gases through the porous sand of gas wells. A chart has been prepared relating the value of the integral to the radius of the well bore and to the Reynolds number of the flowing gas. The chart actually performs the graphical integration and the solution of the formula is then reduced to a simple trial and error calculation. A typical back-pressure curve is calculated to show the transition from laminar to turbulent flow. This paper will briefly describe the pro-cedurcs for computing flow through porous media, including a method for predicting sand permeability from porosity and grain size and shape. Flow through Porous Media Brownell and Katzl recently reported a correlation for computing flow of fluids through porous media by the use of an enlarged Reynolds number and friction factor in which the porosity of the bed is included as an additional prime variable. The enlargcd Reynolds number com-

Jan 1, 1948

By R. G. O’Meara, M. M. Fine

ONE of the principal activities of the Bureau of Mines connected with the recent war was to help to increase the supply of strategic and critical minerals. Fluorite was one of the most critical of the nonmetallic minerals because of the increased demand for it as a flux in basic open-hearth and electric steel furnaces and as a raw material for the production of artificial cryolite used in the aluminum industry. Wartime developments in the technology of hydrofluoric acid, such as the use of the anhydrous acid as a catalyst in production of high-octane gasoline and the use of organic fluorides as carriers for insecticides, also increased the demand for acid-grade fluorite.[t] In 1943 the consumption of acid-grade fluorite was advancing at a more rapid rate than production, and was only slightly less than production during the latter half of the year.1 The outlook for the postwar market for fluorite is encouraging. Steel production is expected to remain high until the domestic demand for commodities not manufactured during the war is satisfied. The uses for hydrofluoric acid are expected to increase under the impetus of war-initiated research. In consideration of these and other factors some authorities predict a postwar demand for fluorite equal to about 60 to 75 per cent of the wartime production.1,2 Others believe that the postwar fluorite industry will be permanently expanded over its prewar status.3 ACKNOWLEDGMENT This paper is one of many reporting on various aspects of the Bureau of Mines program directed toward the more effective utilization of our mineral resources. The program has been under the general supervision of R. S. Dean, Assistant Director, since July 1942. The scope of the paper falls in the province of the Metallurgical Branch, whose activities embrace the separation of difficultly beneficiated ores, the production of pure metals from domestic deposits, the exploitation of marginal ore reserves, the recovery of secondary metals, and the improvement of present industrial metallurgical practice. The investigation was initiated at the request of Mr. J. H. Steinmesch, vice-president and general manager, Minerva Oil Co., Eldorado, Ill. His hearty cooperation and helpful suggestions, and those of Mr. O. E. Anderson, mill superintendent,

Jan 1, 1946

By W. A. Backofen, D. L. Holt

Push-pull fatigue tests have been carried out at 4.2°K, 77oK, and room temperature on two poly crystalline materials of widely different stacking-fault energy (?): pure copper (? - 70 ergs per sq cm) and the Cu-8 wt pct A1 alloy (? - 2.8 ergs per sq cm). Constant stress-amplilude was imposed and measurement was made of the plastic-strain amplitude (ep) at saturation. Lives extended from 104 to 106 cycles. Designating lives at the various temperatures by NRT, N77, and N4.2. the ratios N77/NNT and N4.2/N77 ranged from 3.5 to 18 under the condition of common Ep . Metallo-graphic examination revealed different crack morphology in Cu-8 Al fatigued at room temperature, and at 77" and 4.2oK. At room temperature, cracks lay in or near grain and lain boundavies; at 77o and 4.2oK. cvacks were transcrystalline. Tests on single crystals of Cu-8 A1 showed that such a change in the cracking mode in polycrystallitle material accounted for a factor of- about 3.25 in N77/NRT . The longer life at lower tewperatztre (conslant cp) has heels attributed to two deuelopinents: a reduced production of the dislocation tangles and subgrain boundaries which serve as paths of rapid cracking, and suppression of oxygen chetni-sorption at the crack tip It was concluded that in both materials the luller accounted for an extension of the life at 4.2oK beyond that at room temperature by a factor of 15. XV ECENT experiments on the fatigue of Cu-A1 alloys in the so-called high-cycle range (greater than lo4 cycles) have emphasized the importance of stacking-fault energy (y) as a quantity affecting crack propagation rate and fatigue life.1,2 It was found in comparisons at essentially fixed plastic-strain amplitude that crack growth rate decreased by a factor of about 5 over the composition range from copper (? - 70 ergs per sq cm) to Cu-8 wt pct Al (? - 2.8 ergs per sq cm). The argument was made that, when stacking-fault energy is high, cross slip and climb are favored, so that dislocation tangles and/or subgrain boundaries form more readily under cyclic loading. Since the boundaries and tangles act as paths of rapid crack propagation ,3, 4 life is shortened as a result. However, when stacking-fault energy is reduced (as by alloying), cross slip and climb become more difficult, with the result that substructure formation is retarded and growth rate is also reduced. A purpose of the present work was to investigate the substructure effect in relation to temperature. As temperature is lowered, ? is varied only slightly (if at all), but decreased thermal activation can interfere with cross slip and climb. Thus substructure formation could be curtailed and life increased. Fatigue life in the high-cycle range is also known to be strongly influenced by environment. Working with copper, Wadsworth and Hutchings observed that life in a vacuum of 10-8 mm Hg exceeded life in air by a factor of 20.5 They isolated oxygen as the agent that furthered cracking. While the details are still unclear, a requirement in any mechanism of oxygen-accelerated cracking is that there be chemisorption at the crack tip. That could prevent welding on the compression half cycle,= interfere with reversal of slip,1, 6 or aid in breaking metal-metal bonds at the crack tip.5'7 In the work being reported here, temperature was lowered by immersion in liquid nitrogen and helium, which also served to reduce both the oxygen concentration and chemisorption rate. A possible effect upon life, i.e., a lengthening, had to be recognized. Several researchers have determined fatigue lives at low temperatures presenting their results in the form of stress amplitude (S) vs cycles in life (N) curves.8-11 Such curves reflect, primarily, the fact that metal is strengthened by lowering temperature; effects of substructure and changing environment tend to be masked. The difficulty can be overcome by comparisons based on identical plastic-strain amplitudes, and in the present work the dependence of life on both plastic strain and stress amplitude was established. EXPERIMENTAL Materials. The principal materials were polycrystal-line copper (? - 70 ergs per sq cm)" and the Cu-8 wt pct Al alloy (? - 2.8 ergs per sq cm),I3 the latter being near the limit of solubility of aluminum in copper and having, therefore, the lowest stacking-fault energy in the CU-Al system. Specimens were machined from 0.118-in.-diam cold-swaged rods of high-purity (99.999 pct) copper and the Cu-8 Al alloy, the latter produced initially in a graphite boat by induction vacuum melting a mixture of 99.999 pct Cu and 99.99 pct Al. The machined specimens were annealed to produce mean grain diameters of about 0.070 mm in copper and 0.190 mm in the alloy. Specimen dimensions are given in Fig. 1. Values of the tensile yield stress, ultimate strength, uniform strain (determined by the Considgre construction), and reduction of area, for both materials at 4.2oK, 77oK, and room temperature, are listed in Table I. The tensile apparatus in which these results were obtained has already been described.14 Apparatus. Specimens were fatigued in push-pull with a machine that is illustrated schematically in Fig. 2. The specimen is first soldered into the top grip (1) with Woods metal, and the grip is then screwed into the inner tube (2) which is connected to the drive rod of the Goodmans vibration genera-

Jan 1, 1968

By E. W. Johnson, M. L. Hill

Cold working of iron-carbon alloys was found to increase greatly the hydrogen solubility and to decrease the diffusivity at temperatures up to 400° C. These effects are increasing functions of both the carbon content and the degree of deformation. The hydrogen behavior is consistent with the idea that cotd working creates "traps", which are concluded to be microcracks in which the hydrogen is chemisorbed. Hydrogen embrittlement is explained by the Petch theory of metal crack surface energy loss due to hydrogen adsorption. HYDROGEN embrittlement of steel has been studied for many years and has been the subject of an extensive literature, but the mechanism of the effect has not been completely understood. The embrittlement is unusual in that the ductility loss is not accompanied by an increase of the yield strength, being primarily a decrease of the fracture strength alone. The loss of fracture strength is usually most severe in the temperature range between 0°and 100°C. Here the solubility of hydrogen in the iron lattice at ordinary H2 pressures is extremely low while the diffusivity is still quite high. From the relationships between the ductility and the hydrogen content, test temperature and strain rate, it is apparent that the hydrogen atoms causing the ductility loss difbse to and concentrate in small regions of the metal which are especially susceptible to the initiation and propagation of fracture. This hydrogen segregation apparently occurs after plastic straining has begun. Below 0°C the ductility loss persists only at low strain rates in confirmation of the view that the embrittlement is diffusion .controlled. The tendency of the embrittlement to disappear above 100°C can be explained by the increasing lattice solubility of hydrogen with rising temperature. A common view of hydrogen embrittlement of steel is that the hydrogen initially dissolved in the metal lattice diffuses to structural discontinuities and there precipitates as H2 gas at very high pressures which assist the external stress in causing premature failure.1,2 The idea of a high H2 pressure in equilibrium with ordinary amounts of hydrogen in steel at room temperature is due to observations of hydrogen behavior in fully annealed material, for which the Sieverts' law constant relating solute concentration to H2 pressure is extremely small. Hydrogen-embrittled steel, however, is always plastically deformed to some extent, and therefore it is important that hydrogen embrittlement be explained primarily in terms of hydrogen behavior in plastically deformed material. Such an explanation is attempted in this paper. Previous studies of hydrogen in cold-worked steel have shown that both the solubility and the diffusion rate are significantly chaned when the steel is cold worked. Darken and Smith discovered that the amount of hydrogen absorbed from acid by cold-rolled steel at 35°C is many times greater than that absorbed by hot-rolled steel. They found also that the hydrogen permeability of the steel is unaffected by cold working. Keeler and Davis4 confirmed the high apparent solubility of hydrogen in cold-worked iron-carbon alloys at temperatures up to and even beyond the recrystallization temperature. They also found that this solubility increase accompanying cold work is a sensitive function of the carbon content, being absent when no carbon is present. The present experimental study was undertaken primarily to obtain an improved understanding of the behavior of hydrogen in cold-worked steel. Data were obtained on the effects of temperature, H, pressure, carbon content, and degree of cold work on the hydrogen solubility and diffusivity in iron-carbon alloys. These data have been helpful in elucidating the nature of the cold-worked steel structure as well as in providing information on the mechanism of hydrogen embrittlement of steel. EXPERIMENTAL Cylindrical specimens for hydrogen absorption and diffusion rate measurements were prepared from three iron-carbon binary alloys and a commercial SAE 1010 steel. The iron-carbon alloys were prepared by vacuum melting electrolytic iron with graphite in a magnesia crucible. The alloys were cast in vacuum as 2 1/2-in. sq ingots weighing about 20 lb each. The ingots were hot rolled (above 1900°F) to 5/8-in.-diam round bars and then cooled in air to room temperature. The resulting metallographic structure consisted of islands of fine pearlite surrounded by free ferrite. Chemical analyses of the materials are given in Table I. The 5/8-in. diam bars were turned to diameters such that cold reduction to the desired final specimen diameters would result in either 30 or 60 pct reduction in area (RA). The machined bars were then cold worked by swaging at room temperature

Jan 1, 1960

By C. R. Knopp

Gas-oil relative permeability ratio is an important relationship in oil reservoir predictive calculations. A correlation has been developed from 107 gas-flood k/k tests on Venezuelan core samples. The correlating parameter is based on restored-state water saturation tests and' is applicable to both consolidated and poorly consolidated sandstone reservoirs. Data of the correlation show that there are no distinguishah1e differences between the mass-data groupings for the two c1assifications A procedure is recommended for running .sufficient relative. permeability analyses to compute a geometric mean of the sample group. The geometric mean is more representative of the total core, and probably the entire reservoir. For example, while only one in four of the k,,/k,., test curves agreed closely with the resultant correlation of this report, the geometric mean curves of the 16 suites (three samples or more). showed good agreetment ill three cases out of four. INTRODUCTION The gas-oil relative permeability ratio is an important, fundamental relationship in most oil reservoir predictive calculations. Predictive calculations are made to estimate future reservoir production characteristics and ultimate oil recovery. The k1,/k2, relationship is specifically needed to relate the surface gas-oil ratio to the reservoir oil and gas saturation, and to calculate the relative movement of these phases within the reservoir whenever some of the more complex driving mechanisms are present. Laboratory k1/k2, tests are not generally run as a routine analysis. Consequently, k1/k2 data often are not available when needed because the cost of laboratory work could not be justified or the need for such data had not been properly anticipated. When laboratory k1/k2, data are available, they are often very difficult to interpret. For example, wide divergence is sometimes shown in a family of k1,/k1, tests representative of the producing horizon in a single well. With these considerations in mind, a study was made to determine if a relationship might exist between the k1,/k2, curve and some other simple laboratory test criteria. The most probable k1/k2, curve correlation for Venezuela described in this paper is the result of the investigation. The presented correlation defines the most probable gas-flood k,,/k,, curve through the medium of air-water capillary displacement and centrifuge water saturation tests. The laboratory procedures of these tests are. relatively simple, and inexpensive; test data should be. widely available- from routine analysis. DATA AVAILABLE, LABORATORY METHODS The report correlation utilized 107 gas-Hood k1/k2, tests run on sandstone cores of Venezuelan reservoirs. Table 1 is a general tabulation of data pertinent to the tests, while Table 2 summarizes the data. Thetests include 96 from Western Venezuela and 11 from Eastern Venezuela. Eighty-two- of the 107 test samples were sandstones that varied from poorly consolidated to-unconsolidated; 25 were consolidated. The average sample porosity was 26.7 per cent and the average permeability was 1,121 md; these values typify the better sandstone reservoirs of' Venezuela. The Welge gas-flood technique,' based on fundamental Buckley-Leverett frontal displacement theory, was introduced in about 1952 and is widely accepted in the industry. The laboratory procedure is relatively simple, rapid, and can be performed on small core samples. While there have been some minor variations in sample preparation and laboratory procedure in the tests used for the correlation, these tests can be generally summarized as follows. The core sample was first sol vent-extracted and dried. Connate-water saturation was restored by the oil-flushing or evaporation-blow down methods. At the beginning of gas flood the hydrocarbon pore volume was completeiy saturated with the test oil phase. Unsteady-state gas-oil displacement then began with the injection of nitrogen or helium. while the displaced oil and gas phases were incrementally metered at the out-flow face. From the test data, the k,,/k,, curve was calculated by the Welge method.' The individual oil and gas relative permeabilities were also calculated." CORRELATING PROCEDURES In attempting to establish a basis of correlation, we found that broad mid-range sections of 105 of the 107 k,,/k,, test curves could be closely duplicated by a straight line. Only two curves did not show a degree of linearity in this region. Correlation-curve definition parameters were subsequently developed from this observation of consistent mid-range linearity. Possible correlating variables were limited to the physical properties measured on core samples that (1) were widely available as common test data and (2) could be easily and cheaply obtained through future laboratory work. The more obvious possibilities were porosity, permeability and

Jan 1, 1966

By Harold B. Goldman, Don Reining

The sand and gravel industry is the largest nonfuel mineral industry in the nation. In 1981, the production of sand and gravel totaled 755 million tons valued at $2.3 billion. California, which leads the nation with more than 110 million tons, together with Alaska, Texas, Michigan, and Ohio, account for 36% of the total production in the nation (Table 1). In commercial usage, sand applies to rock or mineral fragments ranging in size from particles retained on a No. 200 sieve (0.074 mm openings) to those passing a No. 4 sieve (4.76 mm openings). Gravel consists of rock or mineral fragments larger than 4.76 mm, ranging up to 88.9 mm (3 ½ -in.) maximum size. The construction industry consumes 97% of the sand and gravel produced; the remainder is sand used for specialized products such as glass (see the chapter on "Silica and Silicon"). Utilization The building industry uses sand and gravel chiefly as aggregate in portland cement concrete, mortar, and plaster; the paving industry uses sand and gravel in both asphaltic mixtures and portland cement concrete. Aggregate is commonly designated as the inert fragmental material which is bound into a conglomerate mass by a cementing material such as portland cement, asphalt, or gypsum plaster. Portland Cement Concrete Aggregates Portland cement concrete consists of sand and gravel surrounded and held together by hardened portland cement paste. Concrete mixes commonly contain 15-20% water, 7-14% cement, and 66-78% aggregate. Sand and gravel used as concrete aggregate have to meet many requirements (Goldman, 1956). Premature deterioration of concrete has been traced in many instances to the use of unsuitable aggregates. Asphaltic Aggregate Asphaltic mixtures used predominantly for paving consist of combinations of sand, gravel, and mineral filler (material finer than 0.003 in.), uniformly coated and mixed with asphalt produced in the refining of petroleum. Except for the addition of mineral filler, sand and gravel used as asphaltic aggregate must meet the same general physical requirements as materials used for portland cement concrete aggregate. General Requirements of Aggregates Construction aggregate has many requirements that are difficult to meet if only unprocessed material from natural deposits is used. Suitable material is composed of clean, uncoated, properly shaped particles which are sound and durable. Soundness and durability are terms used to denote the ability of aggre- [ ]

Jan 1, 1983