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By H. H. Rachford, D. S. Howard

In the withdrawal of fluids from tilted aquifers it is of value to be able to predict pressure patterns during the course of the pressure decline. As an example of this, in the displacement of fluids from oil reservoirs being produced by water-drive, prediction of the reservoir pressure is an important factor in fixing production rate. The prediction of pressure patterns in the depletion of an inclined aquifer has conventionally been made by solving the well known flow equations for the pressure Patterns in a horizontal aquifer, and correcting these patterm for the pressure difference due to the hydrostatic head associated with the vertical distance between a point in the horizontal aquifer and the corresponding point in the tilted aquifer. Inasmuch as the equation describing flow in tilted strata is different from that for horizontal flow. there was question as to the validity of the simple corrective procedure current1y in use. To examine the magnitude of error made using this procedure, an inclined aquifer was chosen for which the error was expected to he large, and the equation for flow in this tilted stratum was solved numerically. The results of the conventional procedure of correcting the solution of the equation for horizontal flow was compared with the solution of the correct equation by studying the difference between predicted pressures by the two methods. Three forms of the hydrostatic head correction were studied. The results for all three forms of the head correction are similar. The error in the approximate solution is quite dependent on the position of the horizontal aquifer with respect to the inclined one. The error is greatest at the producing end ad increases with amount of fluid withdrawn. The magnitude of the errors is not large if a good choice is made for the position of the horizontal datum. The most satisfactory position for the datum in all cases is near or slightly about the mid-point of the inclined stratum. Use of the best approximate method studied with the best datum tested yielded predicted pressures in error no greater than 7 psi. INTRODUCTION The movement of water by expansion from an aquifer to displace fluids from a contiguous oil reservoir was first recognized over 20 years ago.9 Since that time much work has been done to relate this mechanism to reservoir behavior mathematically. The result of this effort on the part of many workers has led to an understanding of underground fluid movement which has enabled us to follow and predict the behavior of the water-drive reservoir. One reason that good progress has been made in the application of mathematics to the study of pressure patterns and water movements in aquifers has been that the differential equation which describes this process is of a relatively simple form. The equation for the isothermal, horizontal, viscous flow of water through homogeneous sandstone is identical with that for the diffusion of heat through homogeneous solids, and this equation and means of obtaining solutions for it with many types of boundary conditions have been studied extensively. That this work has been highly successful is clearly emphasized by the large number of solutions developed for problems of interest both by methods of formal mathemat-

Jan 1, 1957

By Oscar Johnson

The industry has been canvassed for information on methods of handling grinding steel at milling plants, an important subject overlooked in most descriptive articles on milling plant arrangements. The data collected are offered in this paper as a guide to designers and planners who have loading and storage problems to solve. WITH capacities of milling plants expanding from a few hundred tons per day to many thousand, replenishment of grinding media is an important phase of mill operation. Information on this aspect of milling procedure, solicited from several mining companies, is summarized here. At International Nickel's Copper Cliff concentrator the normally strenuous job of changing rods is considerably simplified by the use of the Garrow rod charging machine, Fig. 1. The overhead crane, Fig. 2, brings a bundle of rods, weighing four to a ton, to the loading platform of the machine, positioned in front of the mill. The rods roll one by one down the slight incline of the platform onto a conveyor which sends them into the mill. A modified version of the Garrow machine, Fig. 3, is used at the Federal mill of St. Joseph Lead Co. An overhead crane places the portable steel structure in position in front of the discharge end of any one of the five 9x12-ft rod mills. It then raises a bundle of about twenty 3-in. rods to the discharge platform of the charging machine. The rods are 11 ft 7 in. long and weigh about 278 lb. By tripping a lever the operator allows one rod at a time to roll onto the inclined rollers. A slight push by the operator sends the rod smoothly into the mill. The Union Miniére du Haut Katanga rod charging machine, Fig. 4, is mounted on a pair of wheels at the forward end with swiveling castors at the back for steering it to position for use or storage. Wheels are equipped with locking brakes to maintain the machine in position while it delivers rods to the mill. The device is made in two parts. The first consists of the base, which carries the supporting wheels, grooved rollers, and drive. The other part serves as the rod deck, which can carry up to six 3-in. x 12-ft rods. A short boom built integral with the base reaches through the mill trunnion and delivers the rods into the mill barrel. Three grooved guide rollers ,are provided to receive the rods from the sloping charging deck. One rod at a time is fed to the rollers and thus delivered into the mill. Two of the rollers are driven by 11/2-hp motor through a V-belt drive. The third roller is driven off the first by a single V belt in a groove below the rod groove and on the same center line. Rods are delivered to the charger by an overhead crane in bundles of three to six as needed. The power is supplied by cables plugged into power outlets, suitably located near the rod mill discharge end. The Oliver Iron Mining Co. uses a rod charger, Fig. 5, suspended from a monorail by cables. It is constructed .of structural steel and has two decks, each capable of carrying five rods of 4-in. maximum diameter. The rods ride in grooved free-turning rollers. Legs extending down from the mill end of the mechanism act as supports when the unit is ex-

Jan 1, 1955

By J. S. Crump, H. L. Stone

Laboratory studies have indicated that displacement of oil from a reservoir by means of a condensing gas drive results in extremely high oil recovery, approaching 100 per cent under the most favorable circumstances. A condensing gas drive is defined as a gas drive in which the gas utilized is appreciably soluble in the oil it is displacing. The laboratory studies consisted of a number of gas drive displacement experiments, all using a horizontal, sand-packed, steel tube as the laboratory reservoir. The experimental results indicate that the more soluble a gas is in the oil to he displaced, the more efficient that gar is as a displacing fluid. Experiments were conducted utilizing both a light, volatile crude and a heavy, asphalt crude as the in-place oil. In both cases, oil recovery was appreciably enhanced by solubility of the displacing gas. It is believed that the use of condensing gas drives would result in increased oil recovery from many reservoirs during either primary or secondary phases of production. INTRODUCTION Since the early days of the oil industry there has been an increasing awareness of the problems of oil recovery. During the last few decades particularly a growing recognition of the problems has led to widespread attempts on the part of the industry to increase oil recovery by improved technology. One method which has been used to increase recovery is the maintenance of reservoir pressure by injection of gas. Part of the beneficial effect resulting from this gas injection was to prevent evolution of the gas dissolved in the reservoir oil, since such evolution would cause the oil to shrink and become more viscous, thereby adversely affecting oil recovery. In most instances, the gas injected was predomillantly methane, and so the possibility of oil recovery by retrograde vaporization existed. Laboratory investigations of displacement of reservoir oils by methane, carried out at high pressure, have indicated that considerable additional recovery of light oils could be effected by vaporization, but only at the cost of a severe volumetric shrinkage of the residual oil which would cause a decrease in relative permeability to oil in the reservoir. Consequently, recovery of oil by physical displacement would be impaired. The study suggested, therefore, that recovery of oil might be enhanced by injecting into the reservoir a gas known to be appreciably soluble in the oil at reservoir conditions. Swelling of the oil due to solution of gas should result and yield a consequent increase in the relative permeability to oil. The work described in the following sections was, therefore, undertaken to investigate the possibility of increased recovery by this mechanism. Research similar to that reported in this paper has been conducted by The Atlantic Refining Co.1,2,3 In these studies, Whorton, et al, and Slobod, et al, used methane-rich gas to displace oil from model reservoirs. Solubility of the gas was achieved by keeping the reservoir pressure greater than the saturation pressure of the original oil, and the degree of this solubility was varied by operating at different reservoir pressures. Thus the Atlantic project was primarily a study of the effect of reservoir pressure upon oil recovery by gas drive. The objective of the work reported in this paper was to study the effect of gas composition upon oil recovery while holding the reservoir pressure constant. DESCRIPTION OF EXPERIMENTS The discussion of the preceding section suggests that

Jan 1, 1957

By K. P. Gupta

The Cb-rich boundary of the (Cb,Al) a phase field at 1250OC is near 41 pct Al. The Al atoms tend to occupy the C. N. 12 sites in this structure. A homologous (Ta,Al)a phase was identified. No a phase was found in the Mo-Al system at 1200°C. The first binary o-phase with a non-transition element as a major component was found1,2 in the Cb-Al system. The composition of this phase was reported2 as approximately 34 at. pct Al, based on X-ray diffraction patterns taken of alloys in the as-cast condition. Further study of the composition of this o-phase, therefore, appeared desirable. Since Si was previously found3,4 to occupy preferentially the lowest C.N. sites (I and IV) in the a phase, and preliminary resultsa indicated that Al may show similar ordering, one of the aims of the present work was to obtain more complete information on ordering in (Cb, Al) o. Among the binary systems of Al with Ti-, V-, and Cr-group elements, the Ti-Al, Zr-Al, V-Al, and Cr-Al systems are known to comprise no o-phase. In the present work a Ta-Al and a Mo-Al alloy were studied in an effort to find additional o phases with Al as a major component. EXPERIMENTAL PROCEDURES AND RESULTS An alloy with the intended composition of Ta + 40 at. pct Al was prepared by arc melting in He atmosphere. In both the as-cast condition and after annealing for 10 days at 1250°C and quenching in cold water this alloy consisted of two phases, as seen in the X-ray pattern and the microstructure. One of these phases was identified as the o-phase; the observed and calculated d-spacings are shown in Table I. The lattice parameters of this o-phase are a = 9.972 A, c = 5.214 A and c/a =0.5228, as determined from a Debye-Scherrer pattern using Fe K a radiation. The d-spacings for the unknown second phase are given in Table 11. The alloy contained approximately 25 pct of the unknown phase after annealing, as estimated on the basis of microscopic examination. A Mo-Al alloy was prepared by arc melting, with an intended Al-content of 35 at. pct. The alloy button was annealed for 7 days at 1200°C and water quenched. The X-ray pattern of the alloy in both the as-cast and the annealed state showed the reflections of Mo3Al (Cr30 type structure) and an unknown phase different from a. Six Cb-Al alloys were prepared in the composition range 30 to 50 pct Al. All alloys were arc melted in He atmosphere. After annealing for three days at 1175oC in evacuated silica capsules and quenching in water, the alloys with 30 to 40 pct Al contained three phases, namely the o-phase, Cb3Al (Cr3O-type structure) and an unknown phase. The alloys with more than 40 pct Al contained two phases, namely, what appeared metallographically, the o-phase and the same unknown phase. In the alloys containing less that 38 pct Al, the unknown phase was not present after annealing for 4 days at 1250°c,

Jan 1, 1962

By H. R. Brannon, R. J. Robinson, G. W. Kattawar

Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and .98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gulf water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given. INTRODUCTION Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydro-dynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. l-3 One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice5.6 in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker 7 have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire,8 among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii,10 establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other areas as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents (1) a practical approach to computing wave profiles hat depict shapes of waves for use in force calculations, (2) a summary of relations for predicting probabilities of wave crest elevations, (3) correlations of parameters needed to apply these methods in the Gulf of Mexico and (4) examples of application of the techniques. THEORETICAL BACKGROUND The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities. These relations also identify quantities that must be related to storm

By Will Mitchell, Ford F. Miskell, C. L. Sollenberger

THE taconites in general are hard, tough ores, difficult to grind. Liberation of iron mineral constituents usually is accomplished by grinding the ore through at least 100 mesh, and often it has been found necessary to grind substantially through 325 mesh to achieve satisfactory recovery and grade in the concentration process. Because of the fineness of grind required and the enormous tonnages of material contemplated for treatment in the future, costs resulting from grinding media wear and power consumption, together with capital investment required for comminution, approach astronomical figures. Economy in any one of these elements per ton of material ground could very well reflect a considerable saving to the ferrous industry in yearly costs. With this in mind, the Research Laboratories of Allis-Chalmers Manufacturing Co. have launched a program to discover means of effecting this economy. The initial phase of the work as described here deals with a heat treatment of crushed raw ore, followed by thermal shock in cooling, for the preparation of rod mill feed. Several investigators 1-5 have noted an improvement in the grindabilities of ores treated in this manner. One investigator2 subjected low grade iron ores to heat treatment in an electric furnace. Basing his conclusions on screen analyses of crushed products, he observed that treated ore was more easily crushed than the untreated. He reported that observation of the treated and untreated ore through a microscope revealed cracks following the grain boundaries in treated ore, whereas no cracks were present in untreated ore. However, few if any have quantified the improvement in terms of total hp hours saved, reduction of wear of grinding media, or reduction of capital costs of grinding equipment involved. By means of Bond rod mill and ball mill grindabilities6 and by comparative wear tests, the conditions maintained during this investigation have been definitely evaluated. Heat treatment experiments have been made on a batch scale in a muffle furnace, followed by continuous scale experiments in a rotary kiln under various conditions of temperature, atmosphere, retention time, and quenching to determine the combination that would give the greatest improvement in the grindability of a taconite without affecting adversely the magnetic susceptibility of the magnetite. From these data, relative costs have been calculated for grinding both untreated and heat treated ore on a basis of plant capacity of 120 tons per hour. Heat requirements for a rotary kiln, as well as the kiln capacity required for the treatment, have been estimated. For these tests 50 tons of ore were obtained from the Aurora mine of the Erie Mining Co., Hibbing, Minn. The ore was reported' to have been selected from the magnetic portion of the lower chert horizons. An average chemical analysis of this portion is shown in Table I and an approximate mineralogical analysis is shown in Table II. No attempt was made to differentiate between the various silicates because the compositions vary widely on the different horizons and depend on the degree of oxidation. Minnesotite, however, is the predominant silicate. The siderite grains were dispersed throughout the ore but were essentially associated with the rock-forming minerals. In a series of preliminary tests in which batches of -6 mesh ore were heat-treated in a muffle fur-

Jan 1, 1952

By I. Fatt, D. N. Saraf

A method is described for measuring two- and three-phase relative permeabilities in sandstones or sand packs using a nuclear magnetic resonance (NMR) technique to determine fluid saturations. Two- and three-phase relative permeabilities have been determined on Boise sandstone using the NMR technique of saturation measurement. Three-phase relative permeability to water was found to depend only on the water saturation, whereas three-phase permeability to oil depended on both the water and oil saturations. Relative permeability to gas in three-phase flow was found to depend only on the total liquid saturation. INTRODUCTION Three-phase relative permeabilities are extremely useful in calculating field performance for reservoirs being produced by simultaneous water and gas drives. Three-phase relative permeability data are also needed for analyzing solution gas-drive reservoirs which are partially depleted and are being produced by water drive. Some thermal recovery processes involve three-phase flow which require three-phase relative permeability data for predicting reservoir behavior. Unfortunately, three-phase relative permeability measurements have rarely been made. Also, because of the scarcity of three-phase data, it has not been possible to date to relate other measured rock characteristics to the relative permeabilities with a great certainty. Leverett and Lewis,l Reid2 and Snell3 have reported three-phase relative permeability data on unconsolidated sands. Leverett and Lewis used ring electrodes spaced along the length of the sand sample to measure the resistivity of the sample which was assumed to be monotonically related to brine saturation. Gas saturation was determined from pressure-volume measurements. Oil saturation was obtained by material balance on the cell containing the sand sample. This method is involved and time consuming. Another difficulty arises from the fact that the resistivity of the sand is a function not only of saturation of brine but also of the distribution and saturation history of the brine in the pore spaces. Reid2 used a gamma ray absorption technique for measuring liquid saturation. This method has the disadvantage that total liquid saturation rather than oil or brine saturation is all that can be measured and still another method is required to determine the saturations of individual components. snel13 used a neutron bombardment method which also required a separate determination of the individual component saturations. Caudle et al.4 measured three-phase relative permeability on consolidated sandstones using vacuum distillation for determining fluid saturations. Distillation after each reading makes this technique very lengthy and time consuming. Corey et a1. 5 and Naar and Wygal 6 measured three-phase relative permeability on sandstones by the capillary-pressure method. Semipermeable diaphragm assemblies were used at each end of the core specimen to keep the water phase in the core. Gravimetric methods were used to determine fluid saturations. Sarem7 recently reported an unsteady-state method for measuring three-phase relative permeability on sandstones. This method is an extension of Welge's method8 for measuring two-phase relative permeability. Although Sarem's method is simple and comparatively fast, the assumptions involved may oversimplify the problem. Sarem's assumption, that in all rocks relative permeability to each fluid will depend only on the saturation of that fluid, seems to be rather unrealistic. Neglecting capillary effects at the end of the core is also a weak assumption. Donaldson and dean9 measured three-phase relative permeability using a method similar to Sarem's.

By A. G. Metcalfe

Observations at temperature are used to investigate the phase changes in alloys containing more than 50 pct Co and above 1000°C. The nonsuppressible transformations in cobalt above 1120°C and in the intermetallic compound Co2Cr3 are studied. The liquidus and solidus surfaces are determined. Insufficient data is obtained to complete the constitution diagram. A REVIEW of some of the earlier work on cobalt' and on the binary systems with chromium2-4 and with molybdenum,5 showed that one likely source of differences might be attributed to the presence of phases at high temperatures which could not be retained by quenching. Consequently, the decision was made that only methods of examination at temperature should be used in this work. The correctness of this decision was confirmed during the course of the work by the investigation of the martensitic nature of the transformation in cobalt- and by the decomposition of the high temperature form of the phase Co2Cr3 on quenching.' The use of high temperature methods, including dilatometry and thermal etching led to the postula-tion of the existence of a high temperature form of cobalt with a probable hexagonal close-packed structure, transforming from cubic cobalt over a range of temperature from 1119° to 1145°C.8 One of the important pieces of evidence for this transformation was that it was observed in alloys with chromium and molybdenum which were nonmagnetic at this temperature so that confusion with magnetostriction effects was impossible. These results were not reported in this earlier paper, so that the data given here supply further evidence for the existence of a second allotropic transformation in cobalt. High temperature observations are necessarily much slower in producing results than the examination of quenched specimens at room temperature by conventional means such as X-ray diffraction or microexamination. The investigation has only covered a limited part of the field, as a result, extending from the liquidus down to about 1050°C and from the cobalt corner up to 50 pct alloying elements. The differences between the various reported diagrams for the constitution of the Co-Mo and Co-Cr systems have already been mentioned. The best available diagram in the first system is due to Sykes and Graff' which is shown in Fig. 1. Fig. 2 shows the latest Co-Cr diagram due to Elsea, Westerman, and Manning.' A comparison reveals that these are incompatible because of the disagreement with regard to the number of allotropes of cobalt. Elsea, Westerman and Manning took their liquidus and solidus curves from Wever and Haschimoto.2 The temperature horizontal in the two-phase field beneath the eutectic was placed 35" to 39°C higher than in earlier work2,4 with a new interpretation of the nature of this transformation. This interpretation also required a peritectic horizontal at about 1470°C, which has been confirmed here for an alloy with 53 pct Cr. No investigation had been made of the ternary system until after this work had been terminated, when a section at 1200°C was published." In this work a ternary compound was found by the X-ray diffraction examination of quenched alloys. This compound contained less than 50 pct Co, and was thus outside the field investigated here. However, some reactions were found dilatometrically which could not be fitted on the diagram and are now believed

Jan 1, 1954

By R. D. Satterley

The Sherwood mine is an iron-ore mine owned and operated by the Inland Steel CO. in the Iron River district of the Menominee Range in Michigan. The property consists of an 80-acre tract in the village of Mineral Hills, about a mile north of the city of Iron River. The Ore mined is a reddish brown, nonbessemer hematite and limonite. The ore bodies lie in a large syncline having an east-west strike and are associated with a rock structure that is folded in a complex manner. The two 40-acre tracts run north and south and the shaft is at about the center of the north forty. The shaft is 1286 ft. deep, with the principal operating level at a depth of 1000 ft. from surface. A new level at a depth of 1200 ft. is in process of development. The ore body at the 1000 ft. level is east and west at approximately the line between the north and south forties and at this elevation is from 50 to 250 ft. wide and extends above the level at varying heights of from 50 to 250 feet. The 1000-ft. haulage drift extends south from the shaft, through the east-west ore body to the slates on the south side of the body. The ore body was intercepted in the drifting at about goo ft. from the shaft and was about 200 ft. wide at that point. A crosscut was extended to the east and west property lines along the south boundary of the ore body. This east-west ore body is laid out in areas go ft. wide for stoping with pillars 40 ft. wide. With this plan a stope is approximately 80 by 200 ft. and has a pillar on both sides that is approximately 40 by 200 ft. The ore has a height of from 50 to 250 ft. above the elevation of the level, therefore the height of the stopes varies in accordance with the height of the ore body at each location. From the crosscut, two main raises, each 6 by 7 ft., are put up into each 80 ft. stope area (Fig. 1). One of the main raises serves as a manway and the other as an ore raise, through which the ore is transferred from the stope to the tramming equipment. The original layout as for scraping of the ore from under the stopes into the ore raises. The ore raise is put halfway (east and west) along the 80-ft. stope area and usually is in iron formation. The manway and ore raise are on approximately 15-ft. centers. These main raises are Put up to a height of from 22 to 30 ft. above the level floor, then from the toll of the ore raise a scraper drift (8 X 8 ft.) is driven across the width of the ore body, which is in the neighborhood of 200 ft. From the scraper drift, mill raises are put up at 12½-ft. centers, staggered on opposite sides of the drift, and these are extended 23 ft. above the elevation of the scraper-drift floor. The sublevel connecting the top of these mill raises is called a mill "sub." Other sublevels are developed parallel to the scraper and mill subs at 25-ft. vertical intervals above the mill sub. The mill sub and the other subs above the mill sub are known as sublevels or dog drifts, and are 4 ft. wide and 6 ft. high. These dog drifts

Jan 1, 1946

By M. H. Gaskell, D. M. Kehn, G. T. Pyndus

A correlation of the bubble point pressure for black oil systems is developed using the standard physical-chemical equations of soiutions. The correlation is based on 158 experimentally measured bubble point pressures of 137 independent systems and is expressed in terins of the usually measured field pnrameters— flash separation gm-oil ratio, rank oil gravity, total gas gravity, and reservoir temperature. The data were obtained on systems produced in Canada, Western and Mid-Continent01 United States, and South America. The average error (algebraic) in the representation is 3.8 per cent, and the maximum error encountered is 14.7 per cent. INTRODUCTION In the absence of experimentally measured properties of reservoir fluids, it is often necessary for the field engineer to make estimates regarding the fluid properties based on the usually measured producing parameters. To aid in these estimations, various correlations have appeared in the literature in recent years. Among the pertinent properties of interest is the bubble point pressure. A correlation for this parameter has been reported by Standing'. However, this correlation was based essentially on California produced crudes and this limitation was pointed out with its presentation. The correlation presented in this paper utilized data on crude oil systems from Canada, Wes- tern and Mid-Continental United States, and South America. CORRELATION DEVELOPMENT The basic assumption used in this development is the same as employed by Standing', There is a wide variety of ways to combine these parameters; however, in this instance the combination was made on the basis of Henry's law2. Accordingly, the relationship proposed is Although Eq. 2 defines an individual system, it is of limited value since H' is a function of gas-phase composition and the system temperature. It was observed that for the systems where the bubble point was measured at several temperatures that the ratio of the bubble point pressures and the ratio of the corresponding absolute temperatures (R) were practically identical. Thus, for correlation purposes the bubble point pressure may be taken as a direct function of the absolute temperature. This relation is valid only for those systems that are not near the critical point. Accordingly, this correlation will be inadequate for systems in the region of the critical point. The solubility of the various hydrocarbons found in the gas phase increases with the molecular weight. Thus, the saturation pressure should be inversely related to the gas gravity. Applying these principles to Eq. 2 and rearranging terms gives: The variables 02 the left side of Eq. 3 were designated as the "hubble point pressure factor". The number of mols of tank oil per barrel is a function of the "mclecular weight" of the tank oil. Although the tank oil is a complex mixture, it was assumed for the purposes of this correlation that a unique molecular weight could be assigned to a given oil. This was designated as the "effective molecular weight", and was related to the oil gravity, This empirical relationship was developed simultaneously with the correlation by assuming values of M,. and working to obtain a smooth curve for both the correlation and the effective molecular weight. The relationship between the oil gravity and the effective molecular weight used in this correlation is shown in Fig. 1. The effective molecular weight is somewhat higher than the molecular weight of the C fraction. The difference between these values is largest for the low-gravity systems. It is noted that this effective molecular

By F. R. Zacher

Unmined blocks in the Sewickley seam, surrounded by worked out areas, have been found to transmit overburden oads through the interval strata to the Pittsburgh seam workings 90 ft below. Operating experiences under these conditions are described in this paper. IT has always been understood, in northern West Virginia where both the Pittsburgh and Sewickley seams are mined, that pillaring or splitting in the lower Pittsburgh seam could break the interval strata and make mining in the overlying Sewickley difficult or impossible. In some instances, however, mining methods practiced in the overlying Sewickley have reversed the problem, resulting in a shifting of the intermediate layer and destroying valuable acreages of the Pittsburgh seam below. The Pittsburgh seam in this area is, on the average, 102 in. thick. About 18 in. of low-quality head coal are left for roof protection as it is mined. Immediately over the coal are two draw slates, two rider seams, and a good hard black shale, locally called black rock, which serves as a permanent roof where draw slates and riders are taken down on certain main haulroads. In most areas mined in this seam in the past the bottom has been satisfactory but soft. However, in areas now being mined by the Christopher Coal Co. in Monongalia County the bottom is very hard and unyielding. The Sewickley seam, lying 85 ft above the Pittsburgh, will average nearly 70 in. in thickness and is overlain by massive shales and sandstones. Much of the seam is mined only down to the "sheep skin," a hard band about 4 in. above the bottom, which is composed of relatively hard shale. Fig. 1 shows a typical cross-section through the Pittsburgh and Sewickley seams in the area being discussed. The thin Redstone seam is not deep-mined but is stripped in some locations where it outcrops. Most of the Sewickley seam in the Morgantown areas has been mined out from 10 to 30 years. There are at present only two large mines and five or six others of small production operating in that seam. Mining systems in the past were generally of the room and pillar type with some full pillar extraction. This seam in the Scott's Run area was operated by as many as thirty or forty different companies at one time, during an era beset with strikes, market failures, and depressions. Most of the barrier pillars along the many main haulroads were abandoned, and blocks of Sewickley coal that would be fully recovered with today's machinery were left unmined when conditions became anything less than favorable. Consequently the mined-out Sewickley is spotted throughout with solid blocks varying in size from 100x100 ft to 200x400 ft and larger. It is these unmined Sewickley blocks surrounded by worked-out portions that have caused transmissions of roof stresses to underlying Pittsburgh mining areas, see Fig. 2, resulting in untold difficulty. As the Christopher Coal Co. operates both the Pittsburgh and Sewickley seams, accurate maps of workings in both seams are readily available and are regularly consulted. The first Pittsburgh squeeze attributed to overlying Sewickley blocks occurred in the Arkwright mine, where a shuttle car crew was developing a section consisting of seven panel headings. These entries were being driven in solid coal 3400 ft from the nearest worked-out Pittsburgh area. As mining advanced it was noticed that certain ribs began to slough and certain areas to show signs

Jan 1, 1953

By J. D. Forrester, Erich Sarapuu, T. C. Cheasley

Electrocarbonization of coal will produce cheap fuel for electric power plants. The complete electrification of industry and domestic power consumption of gas generated as fuel in situ is a worthwhile goal for the coal industry. Production of synthetic oils, gasoline, and coal chemicals from coal gas will create additional new markets for the coal industry. RANKING high in the nation's wealth of natural resources, readily available liquid and gaseous hydrocarbons are nevertheless falling steadily in supply, while industrial requirements for hydrocarbon compounds are greater today than during the peak period of World War 11. Theoretically, several processes will increase the future supply of liquid and gaseous fuels, but the practical application of these methods depends on two controlling factors: 1—that enough carbon-bearing material be available to warrant industrial exploitation, and 2—that the given process be physically, chemically, and economically applicable. With regard to the first factor, the Western Hemisphere is fortunately well supplied, see Table I. Table I not only shows the extensive occurrence of many fuel sources, but also the wide discrepancy among quantities of fuel substances in various materials. Great quantities of potentially available fuel have not been recovered. Many coal seams and other hydrocarbon-bearing deposits are so situated that production is uneconomical by present-day mining or oilwell pumping methods, and even in many exploitable deposits where the most efficient production methods are used a large proportion of material is never recovered. Industrial production of hydrocarbon liquids and gases must be better balanced, and processes must be developed which will convert coals, oil sand, and oil shales into fabricated commodities. Among the techniques employed by scientists and engineers to secure fuel masses not economically available at present are several processes of underground gasification. These are all concerned with converting raw materials into gaseous products by thermal treatment of source substances while they are still in the ground and therefore require that a subsurface heat (fire) zone be induced to affect pervasively the buried raw fuel deposit. This is possible only where sufficiently high temperature exists and where the fuel material is satisfactorily opened or channelized. Also, to compete successfully with common mining or oilfield practices, a given method must be controllable and must not involve greater operational expense than regular methods. Preferably, it should be less expensive. Since the close of World War 11, England has continued field studies of underground gasification methods. Experiments have also been conducted in Sweden, Estonia, France, Belgium, Italy, and Germany. The U. S. Government has sponsored field studies at Gorgas, Ala., and because gasification in situ is vitally important to establishment of the nation's fuel resources, the mining engineering department at the Missouri School of Mines has been actively interested in developing the process of underground electrocarbonization. Research was conceived by Erich Sarapuu, and preliminary experiments in treating bituminous coal were begun at the school in September 1947. The work consisted of laboratory experimentation until June 1948, at which time, through a cooperative agreement with the Sinclair Coal Co. of Missouri, pilot plant studies were instituted at the Tiger mine of the Hume-Sinclair Coal Co. near Hume, Mo., to test the encouraging laboratory findings. This comprehensive field program was pursued continuously until the beginning of 1952."'" The broad term underground electrocarbonization describes a unique gasification process that releases by electricity the desired economic constituents from a raw carbon-bearing material, converting the substance of such deposits into deliverable form and greatly reducing the cost-of-mining factor. Underground electrocarbonization is not subject to the major limitations of many other underground gasifi-

Jan 1, 1955

By F. R. Zacher

Unmined blocks in the Sewickley seam, surrounded by worked out areas, have been found to transmit overburden oads through the interval strata to the Pittsburgh seam workings 90 ft below. Operating experiences under these conditions are described in this paper. IT has always been understood, in northern West Virginia where both the Pittsburgh and Sewickley seams are mined, that pillaring or splitting in the lower Pittsburgh seam could break the interval strata and make mining in the overlying Sewickley difficult or impossible. In some instances, however, mining methods practiced in the overlying Sewickley have reversed the problem, resulting in a shifting of the intermediate layer and destroying valuable acreages of the Pittsburgh seam below. The Pittsburgh seam in this area is, on the average, 102 in. thick. About 18 in. of low-quality head coal are left for roof protection as it is mined. Immediately over the coal are two draw slates, two rider seams, and a good hard black shale, locally called black rock, which serves as a permanent roof where draw slates and riders are taken down on certain main haulroads. In most areas mined in this seam in the past the bottom has been satisfactory but soft. However, in areas now being mined by the Christopher Coal Co. in Monongalia County the bottom is very hard and unyielding. The Sewickley seam, lying 85 ft above the Pittsburgh, will average nearly 70 in. in thickness and is overlain by massive shales and sandstones. Much of the seam is mined only down to the "sheep skin," a hard band about 4 in. above the bottom, which is composed of relatively hard shale. Fig. 1 shows a typical cross-section through the Pittsburgh and Sewickley seams in the area being discussed. The thin Redstone seam is not deep-mined but is stripped in some locations where it outcrops. Most of the Sewickley seam in the Morgantown areas has been mined out from 10 to 30 years. There are at present only two large mines and five or six others of small production operating in that seam. Mining systems in the past were generally of the room and pillar type with some full pillar extraction. This seam in the Scott's Run area was operated by as many as thirty or forty different companies at one time, during an era beset with strikes, market failures, and depressions. Most of the barrier pillars along the many main haulroads were abandoned, and blocks of Sewickley coal that would be fully recovered with today's machinery were left unmined when conditions became anything less than favorable. Consequently the mined-out Sewickley is spotted throughout with solid blocks varying in size from 100x100 ft to 200x400 ft and larger. It is these unmined Sewickley blocks surrounded by worked-out portions that have caused transmissions of roof stresses to underlying Pittsburgh mining areas, see Fig. 2, resulting in untold difficulty. As the Christopher Coal Co. operates both the Pittsburgh and Sewickley seams, accurate maps of workings in both seams are readily available and are regularly consulted. The first Pittsburgh squeeze attributed to overlying Sewickley blocks occurred in the Arkwright mine, where a shuttle car crew was developing a section consisting of seven panel headings. These entries were being driven in solid coal 3400 ft from the nearest worked-out Pittsburgh area. As mining advanced it was noticed that certain ribs began to slough and certain areas to show signs

Jan 1, 1953

By John B. Myers

Vermiculite is the commercial name used to describe a micaceous mineral that expands appreciably when heated. This process, called exfoliation, results in a light weight material. The light weight material is also called vermiculite, or more exactly, expanded vermiculite. Practically all uses of vermiculite are for the expanded material. Composition and Properties Vermiculite, in its natural state, has the characteristic micaceous habit and a perfect basal cleavage and readily splits into thin laminae, which are soft, pliable, and inelastic. The monoclinic crystal faces are often marked by triangular lines at 60° and 120°. The hardness varies from 1.5 to 2 or more, depending on the composition. The specific gravity varies from 2.2 to 2.7; specific heat 0.2; fusion temperature 2,000° to 2,500°F; luster pearly to greasy; color amber, bronze, brown, dark green, and black. Feel is like talc and sometimes soapy when wet. When heated quickly at elevated temperatures, vermiculite exfoliates by expanding at right angles to the cleavage into long wormlike pieces (the name vermiculite is from the Latin vermiculari, to breed worms). This important characteristic of expansion is believed to be a mechanical separation of the layers when the contained water is converted to steam. The increase in bulk volume of commercially prepared material is 8 to 12 times, but individual flakes may expand as much as 30 times. There is no expansion parallel to the cleavage. Vermiculite may also be expanded by several chemical processes such as soaking in hydrogen peroxide, weak acids and other electrolytes. The color changes during expansion. Heat-treated material changes to a light golden bronze or cream color depending on composition. The conditions of heating affect color. Heating in an oxidizing atmosphere produces reddish colors and heating in a reducing atmosphere produces dull gray colors. The iron is generally not oxidized during chemical expansion. Vermiculite is hydrated magnesium-aluminum silicate. Although there has been much research on the chemical and structural composition, there is not yet complete agreement on the exact formula and composition. This is to be expected since vermiculite is not a mineral of fixed composition and different workers have examined different varieties. It has been proposed that vermiculite is not a single species but a family of related minerals. This has also resulted in many names for the particular vermiculite found in a certain deposit. All of this difficulty arises from the very nature of its crystal chemistry. Unlike most minerals, certain crystal structure properties and the chemical composition can be changed by the ordinary forces of nature or in the laboratory. This would suggest that vermiculite be thought of more as a variable mineral rather than a group of related species. It was stated on page 261 of this volume in the chapter on Clay Minerals by H. H. Murray of the Georgia Clay Co., that vermiculite is an equidimensional, expandable clay mineral. Gruner (ref. 14, Chap. 12) showed that the structure consists of a layer made up of two silica tetrahedral sheets with a central magnesium, iron octahedral sheet separated by two layers of water molecules and adsorbed magnesium and calcium ions. Mathieson and Walker,2a in a recent publication, agree that vermiculite must be regarded as a true clay mineral. The characteristic properties of the mineral, such as high cation ex-

Jan 1, 1960

By Brian J. Gorval, Robert L. Kemeny

INTRODUCTION Financing, or providing adequate capital at low cost for developing and bringing a natural resource property into production, is a fundamental requirement for profitable operation. Under the present economic environment the cost of financing any project is gaining more importance than ever. The fundamental keys for success in mining are "the Four M's": Mineral, Market, Management and Money. In recent years, with capital and operating costs skyrocketing, increased emphasis on obtaining adequate and low cost capital funds for bringing in a prospect is essential. For a small mining company there are limited sources for raising funds. In most cases these companies have neither a substantial asset base, nor any cash flow, and they are deemed as risky investments. The issue of shares of capital stock of such a company is probably the most common method of raising funds via the public purse. Alternatively, debt could be used and a source of such capital might be private investors or financial institutions. The company which intends to raise funds from the investing public by way of the sale of equity, subsequently lists those shares for trading on a stock exchange. Going and staying public commits a company to a multitude of complex laws, rules and reporting requirements. The governing bodies are the watch dogs for the public. The largest of such an organization of this kind in the world is the Securities and Exchange Commission (SEC) in the United States. In Canada, the Securities Laws come from within provincial jurisdiction. Most provinces have their own Securities Act, and Securities Commission. It is the Commission which administers the Act, and hence controls the distribution and trading of securities within the province. Extra provincial registration is required for trading and distribution in more than one province. In British Columbia, prior to a public offering, the approval of the Superintendent of Brokers (SOB) and of the VSE must be obtained. THE VANCOUVER AND TORONTO STOCK EXCHANGES There are five stock exchanges in Canada which supply a trading forum in which mining companies may operate. The stock exchanges are located in Montreal, Toronto, Winnipeg, Calgary, and Vancouver. Of the five stock exchanges, the Vancouver Stock Exchange (VSE) and the Toronto Stock Exchange (TSE) are the most heavily used for resource-based issues and are the focus of this paper. The objective of this section is to provide a brief background on the VSE and TSE. The Vancouver Stock Exchange The VSE is Canada's predominant stock exchange for financing resource-based, junior issues. Since 1907, the VSE has acted as a source of funds for mining, exploration and energy companies throughout Canada and the world. Currently, there are over 1400 companies listed on the VSE. During 1983, over 3.1 billion shares traded at a value exceeding CDN$3.96 million. The VSE has developed a reputation as one of the few exchanges where a speculative resource venture may obtain a listing and subsequent financing in a relatively short time, generally five to ten months. The SOB, the Investment Dealer's Association of Canada (IDA), and the VSE all regulate trading at the Exchange. Any irregularities in a company's stock dealings are investigated and trading may be halted by the VSE until a satisfactory explanation has been received from the suspended company. Companies can be suspended from trading or delisted for various reasons. One reason is misrepresentation of facts in documentation submitted to the SOB, VSE, or to the public, through news releases.

Jan 1, 1985

By Charles Jones

Discussion of the paper of CHARLES COLCOCK JONES, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 105, September, 1915, pp. 1887 to 1898. D. A. LYON, Salt Lake City, Utah.-For some years I have been interested in the iron-ore deposits of the Pacific Coast, and I feel very much indebted to Mr. Jones for the information he has given us on this subject. I think that we are also very much indebted to him for having presented this paper, as he has given us reliable data in shape of facts and figures, which is just what we need in considering whether or not it would be commercially feasible to attempt to establish an iron and steel industry on the Pacific Coast. Personally, due to lack of market, I do not think it is a commercially feasible proposition at the present time. Mr. Jones states that pig iron can be produced on this coast as cheaply as it can be produced in Pittsburgh. Even. so, what can be done, with it after it is produced? To begin with, iron produced on the. Pacific Coast has to compete with iron produced in China. Last year I had occasion to investigate the subject of the market for iron and, steel on the Pacific slope, and found that it was possible for the producers of Chinese iron to sell it for much less than the price for which iron can be produced in the West, and also for less than eastern pig iron is now sold for, even when shipped through the Panama Canal. I was informed that the agents for Chinese iron had instructions to sell it for $1 or $2 less per ton than that asked for other irons on the market. Of course, I realize that the competition of Chinese iron may not be important, but even if it is not, and even though pig iron ,can be produced at the cost given by Mr. Jones in his paper, I do not see any immediate chance of its being so produced, due to lack of market. C. C. JONES, Los Angeles, Cal.-Mr. Lyon is right. It is a fact that Chinese pig is being sold in San Francisco on some large contracts at $18.50 a ton, while $19 is the usual price. We ought to produce iron. on this coast at $14. Personally I do not think Chinese iron is ever going to be an important factor. It is a bugbear out here now. You are not going to have much Chinese pig iron in .this country. Our little friend Japan is going to absorb everything it can. The price of Chinese pig iron at $18 is about as low as it will ever get. If we can show you that we can produce this iron here at the same price as at Pittsburgh, I. think you will have a good opportunity to compete with anything China or India can ever do. Costs there are very low now. They are going to come up by leaps and bounds in the next few years. The labor cost over there may be very low now, but I. have seen some men from there quite recently

Jan 12, 1915

By V. J. Driscoll

A method is given for checking pore volume reserve estimates and transient water inflzix factors utilizing early well performance. Principal applications are based on the observation that there is a convenient transient time-range in terms of well spacing in which observed pressure drop will give a good indication of fluid-in-place. Primary quantity determined is a porosity-feet value applicable in the vicinity of an observation well. Checks on porosity or net pay thickness and permeability values also are obtained. These are particularly valuable in improving quality of interpretive factors entering into pore-volume reserve determinations for larger fields. In smaller fields, direct determination of total field reserves and approximate location of boundaries may be made in some cases. Well interference and production data plus a build-up curve on the observation well are needed. The build-up curve may be taken at any time. Field applications are given. The method can be applied with the completion of the second well on a new discovery or to older reservoirs by major changes in withdrawal rates from a local area. Appropriate test length permits results to be obtained with equal accuracy on widely spaced wells. Criteria for optimizing test conditions are given. Provision is made for various boundary and well effects including incomplete observation well build-up. INTRODUCTION Due to low quality data, initial pore volume reserve and water influx estimates may often vary by a factor of two or more from results obtained at a later date. Unfortunately, by conventional methods, more reliable answers from performance usually are not available until after most significant economic decisions have been made. Furthermore, in older reservoirs, uncertainties may still exist as to original oil-in-place, recovery factors and residual oil saturations due to incomplete or inaccurate performance data. This paper outlines situations and appropriate arrangements of basic transient theory whereby well interference data can be utilized to improve the quality of estimates under certain conditions. In addition to production data on offset producers, key information required is a measured pressure drop at an observation well, corrected for any incomplete build-up due to previous production, plus a formation capacity value derived from a conventional pressure build-up plot on the observation well. The method, as outlined, is strictly applicable only to a horizontal single-layered system of uniform rock characteristics containing a homogeneous fluid of low and constant compressibility. However, under the set of test conditions devised, requirements can usually be relaxed so that it should be applicable to most low permeability gas, water and undersaturated oil reservoirs. This is an area where more reliable information is certainly needed. BASIC CONSIDERATIONS A, B, C and F as subscripts or in the text refer to producing Well A, observation Well B, a more remote producing Well C and field boundary F. Combinations such as AB refer to distances and dimensionless times in terms of distances between these points, while single letters refer to distances and dimensionless times in terms of the well-bore or field radius. Equations covering definitions of quantities and complex situations are given in the Appendix. Key equations in practical units are given in Table 2. Transient Pressure Behavior Fig. 1 illustrates pressure drop at Point B with time due to initiation of a constant rate of withdrawal from Point A. This is shown as since a quantitative under-

By Nicasio del Castillo

INTRODUCTION The tax structure of foreign mining investment into the United States has a significant impact on the financing and the profitability of the operation. For these reasons, it is critical for the foreign investor to develop and implement a well planned tax strategy that will enable its venture to: (1) reduce its U.S. income tax liability (2) lower U.S. withholding taxes when funds are transferred from the United States, and (3) decrease or defer home country taxation on its U.S. earnings ALTERNATIVE FORMS OF INVESTMENT A threshold business and tax consideration is the form in which the investment is to be made. The most common alternatives include: forming or acquiring a U.S. mining corporation, directly establishing a branch mining operation, or entering into a joint venture or partnership with a U.S. mining company. U.S. Corporations The most common structure through which foreign mining companies engage in business in the United States is to form a U.S. mining corporation. Forming a U.S. Corporation. If the investor decides to establish a new U.S. corporation the organization is relatively simple. No distinctions are made in the United States between "public" and "private" forms of incorporation. Minimum share capital is not usually required and share capital may consist of shares with no par value. Since corporate law is the responsibility of the individual states, the foreign investor must choose a state in which to incorporate. If appreciated mining property is transferred to a corporation solely in exchange for stock or securities in that corporation, and the transferors have control of the corporation (defined as at least 80 percent of all voting shares and at least 80 percent of all other shares) immediately after the exchange, no gain or loss will be recognized. However, if the transferors receive cash or other mining properties in addition to stock, any resulting gain may, in certain situations, be taxed to the extent of the cash and the fair market value of other property received. Acquiring an Existing U.S. Corporation. Acquiring an existing U.S. mining corporation is not as straight-forward as forming a corporation. This alternative may be accomplished through either a stock or an asset acquisition. Generally, with a stock acquisition the purchaser inherits all of the business and tax attributes of the former mining corporation. If the investor is able to acquire mining assets, however, the purchaser will usually be able to avoid any unknown or hidden liabilities that could be attached to an existing corporation. Another principal advantage in acquiring assets is that the purchase price may be directly allocated to the acquired mines or other mineral-related assets with the result that the assets' depreciable base may be increased. Assuming the domestic seller and the foreign purchaser can agree, it is generally advisable to allocate the purchase price in the sales agreement to specific individual assets. From the foreign investor's standpoint, it is preferable to allocate the purchase price to depreciable assets such as buildings and equipment versus an allocation to mineral land holdings or intangibles such as goodwill, which are generally not depreciable. It is not uncommon, however, for a seller mining company being acquired to insist for tax reasons that the investor purchase shares rather than assets. If the foreign

Jan 1, 1985

By F. E. Streigert, J. H. Mallery, A. H. Geisler

The existing data on precipitation in Cu-Be alloys have been reconciled with some new data to present a more complete and rational analysis of the atomic rearrangements involved in the process. Two different coherent precipitates were proposed. Each is responsible for a type of diffuse X-ray diffraction effect. THE nature of the atomic rearrangement involved in the precipitation of the compound y-Cu-Be from supersaturated solid solutions of the copper-base alloys has been the subject of two extensive investigations.'-" he precipitate in this alloy system has a rather simple structure; at equilibrium it has a body-centered cubic unit cell with copper atoms on the corner sites and beryllium atoms on the center site. While a simple mechanism would be expected to obtain for the precipitation process, those which have been proposed do not adequately explain all of the reported data. The purpose of the present report is to rationalize some of the previous observations and to contribute new data on the subject obtained by the usual techniques of structure analyses. The Cu-Be system of alloys represents one of the most extensively investigated precipitation systems, so a detailed review of the pertinent literature on structure is in order. Striations: Since one of the important features of the mechanism—the habit plane—is determined by microscopic examination, microstructural features that have been observed should be considered at this time in order to assess their role in the precipitation process in Cu-Be alloys. One of the most prominent features appears as regularly oriented markings or stripings (ripples or striations) across the crystals on a suitably polished and etched sample of the aged alloy. These have been observed and interpreted by many workers. Masing and Dah14 observed striations in both the a and /3 phases of a 2.5 pct Be alloy, and attributed them to the beginning of the precipitation of very fine y crystals along favored planes of the a matrix and to the local decomposition of the £ crystals into a plus y. These markings were apparent in both the a and /3 phases of the micrographs given by Smith5 for a 2.75 pct Be alloy, while Moore" detected them in the a matrix phase using polarized light. Desch7 attributed the markings to fine precipitate particles lined up on a family of matrix planes like Masing and Dahl had done, and he identified the planes as those of the (111) family, the slip planes of the matrix. The striations were presumably the structure which Northcott- eferred to as "martensitic." He found that this structure was present in samples that had been aged under widely different conditions with hardness values ranging from 160 to 400 VHN. Later Guinier and Jacquet' also found striations in both the a matrix and secondary /3 phase. Their analyses showed that the striations were along (110) planes of the matrix phase, apparently in contradiction of the results of Desch. They found that the striations were developed during aging on the surface of a specimen that had been polished prior to aging.' On this basis they concluded that the striations represented mechanical deformation by slip along (110) planes of the matrix resulting from precipitation stresses.'" Similar but fainter striations were observed in the same manner on an A1-Cu alloy sample, in which the change in volume was much less than for Cu-Be alloys and

Jan 1, 1953

By P. S. Rudman

Crystal-structure occurrences in binary phase diagrams of fifth- and sixth-period elements, zirconium through palladium and hafniun through platinum, are surveyed with the conclusion that average .group number GN is the dominant correlative. This is interpreted in terms of curves of enthalpy differences between competitiue structures that are continuous func -tions of GN. It is further reasoned that the absolute formation energies may also be continuous functions of GN and if so can be simply obtained from the regatives of the heats of sublimation of the elements. It is shown that from such a heat of formation-GN plot the heats of mixing of alloy systems can be quantitatively predicted. For example, for sixth-period alloys very large exothermic heats of mixing are predicted for systems that span GN = 6 (i.e., Hf-Pt, Ta-Os, ...). Thermodynamic data with which to test these predictions do not appear to be available. If in the latter transition (A subgroup) elements we eliminate from consideration the fourth period where magnetic terms contribute to crystal-structure stability, as shown in Table I, there is a very regular sequence of structures. Using the group number (GN) assignments of Table I, which differ from the usual assignments of 8 to the elements listed as 8 through 10, it is perhaps trivial to say that the phase occurrence is a unique function of GN. However, the interesting aspect of alloys from among these elements is that the alloy structures also appear to correlate with GN. The GN for an alloy is given as GN = SixiGNi, where xi and GNi = atomic fraction and GN of component i, respectively. It is difficult to credit anyone in particular with having discovered this correlation, so many people have implicitly or explicitly employed it in the last 10 years. However, Bloom and Grant' in their correlation of s-phase occurrence with total number of d + s electrons were certainly one of the first to appreciate the correlation and Hume -Rothery2 appears to be responsible for the use of average GN as defined above. Only in the last few years have the phase diagrams of enough alloy systems been determined for this correlation to be surveyed with any degree of completeness. We shall here, in an abbreviated format, summarize the available phase-diagram literature and discuss some consequences of the GN correlation. BINARY DIAGRAM SURVEY In Figs. 1 to 3 the phase occurrences are summarized. In Fig. 4 the occurrence limits for the more common structures are summarized. That the GN of an alloy falls within the occurrence limits of a particular structure is a necessary but not a sufficient condition for the appearance of that structure. The preceding figures certainly illustrate that GN is a dominant correlative for structures of these elements. Many of the diagrams have complications, with ordering and other phase changes occurring in intermediate phases, that cannot be clearly accommodated in such a schematic survey and have hence been left out. Such omissions cannot, however, negate the GN correlations discussed here. Relative atomic size is also an important crystal-structure determinant and since atomic size varies quite regularly with GN for these elements it is possible that the apparent GN correlation is basically a size correlation. In Fig. 5 relative size occurrence limits are given for intermediate phases and extended terminal solutions. The relative volume, ?v/(v) - 2(vA - vB)/(vA + uB), has been taken as the measure

Jan 1, 1968