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Jan 1, 1943

Jan 1, 1943

By C. E. McManus

MANY mechanical advances have been made on mining equipment during the year 1951. There have been a number of trends established and many modifications made on open-pit equipment to increase the efficiency and availability of all the machines necessary in the moving of overburden and iron ore. Some years ago, the trend toward larger shovels for the loading of off-highway trucks began, but in the last year, it has become general practice to use the 5 to 7 ¼ -yd quarry-type shovels in the loading of haulage units. For years these larger shovels were used in the locomotive haulage pits. As the truck capacities increased from 15 to 20 to 30 tons, the need for larger loading units became apparent. Today in most mines, large shovels are in evidence and a few 8-yd shovels will be delivered this year for loading off-highway trucks. Torque Converter-Shovel The Diesel-driven shovel with its friction bands has been modernized with the torque converter. There have been about ten shovels remodeled to take a torque converter in the drive system. The large high-torque, low-speed Diesel engine was removed and replaced by a high-horsepower, high-speed, automotive-type engine. This engine was connected directly to the torque converter. The torque converter was connected to the shovel through the standard original sprocket and chain. Dual governors controlled engine performance. One governor controlled the high idle of the engine; the other governor, which is connected through a flexible shaft to the output shaft of the converter, controlled the loading of the engine. With this dual governor hook-up, the engine anticipates load conditions and is operating at high idle and full throttle before the shovel load is transmitted back through the converter to the flywheel. It has been found that with this automotive-type engine and converter, the shovel capacity has been increased about 20 pct. Also, the wear on the friction bands, breakage of hoist cables, and other mechanical breakages has been reduced materially. Alloy-Steel in Shovels The shovel equipment manufacturers have been experimenting with low-temperature-strength, high-alloy steels to combat the excessive breakage that occurs in extremely cold weather. High-nickel alloy steel has been used in critical areas that are affected by low temperatures, the most notable being dipper sticks. Most shovels ordered today are equipped with some of this special, alloy steel. More and more manganese alloy is being used for replacement parts such as shovel pads, idlers, drive sprockets, etc. Although the initial cost of these parts is considerably higher than the standard replacement items, the life of these manganese parts is considerably longer and well worth the added expenditure. Dipper-teeth repair is still a problem. Most companies use the small replaceable inserted tooth. It has become common practice among some of the companies to "job out" their dipper-tooth repairs to outside welding companies. This necessitates an additional inventory of teeth, but it does guarantee an adequate supply of replacement teeth at all times. These contractors have set up their shops on a production basis and can do an acceptable job at a high rate of speed. Thermite welding has been used in retipping teeth. To date, the process cannot be called successful but with improvements the time required to repoint the dipper teeth will be decreased considerably. The submerged arc process has been tried in the replacement of these dipper points, but like thermite welding has not proven successful. Here again, if a method can be developed to use submerged arc, the job of teeth repair will be made much easier. New model shovels in 6 ½ and 8 cu yd sizes fea-

Jan 1, 1952

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By P. O. Metz, E. L. Wiehe, J. S. Foster

BASED on their analyses of growth kinetics, ibbs' and Harris et al.' have recently proposed that the rate of subcritical graphitization of steel is controlled by the rate of diffusion of carbon in ferrite. illert has concluded that this is the rate controlling growth mechanism when the growing graphite particles are relatively large. Harris et al.' also propose that the matrix surrounding a growing graphite particle is plastically deformed to make room for the growing particle. If this plastic deformation does occur, then preferred recrystallization may be observed around the larger particles. If diffusion of carbon in ferrite is rate controlling, then a graphite particle growing in a matrix of, say, tempered martensite or pearlite, should be surrounded by a carbide depleted zone. Thus, the simple metallographic experiments reported here are sufficient to determine whether or not diffusion of carbon in ferrite is the dominant mechanism for the growth of graphite in steel. The present investigation considers graphitization in five alloys. The compositions are given in Table I. Graphitization was carried out at three temperatures: 900°K (627"C), 950°K (677"C), and 990°K ('717°C). Samples were reacted in both the martensitic and the pearlitic initial conditions. In the hypoeutectoid steels, Sets 7 and 8, .and in the hypereutectoid Fe-C binary, Set 6, graphitization was very limited after 1000 hr at temperature. In these samples graphite particles observed were less than 10 p in diam. In the hypereutectoid commercial steels, Sets 1 and 3, large graphite particles (100 p) did not appear until after 250 hr at temperature. The limited number of graphite particles observed and the range of sizes obtained prohibited measurement of growth rates in this investigation. However, in all samples showing graphitization, neithe a carbide depleted zone nor recrystallization was observed. illert's model predicts that diffusion of carbon in ferrite should become dominant for graphite particles larger than about 300 p in diam. The largest graphite particle observed in this investigation was approximately 450 p in diam. No evidence of carbide depletion was noted. Fig. 1 shows a typical graphite particle. This nodule is from an initially pearlitic sample from Set 3 after

Jan 1, 1970

By George L. Heath

This paper is devoted chiefly to the coal-fields of the western part of the province of Chili and the eastern part of the province of Shansi; but the outline of this belt will give some idea of the extension of the coal-fields over northeastern China. This part of China is topographically divided into: (1) the mountainous peninsula of eastern Shantung; (2) the coastal plains, extending W. and SW. from the gulf of Pechili; and (3) the mountains and table-lands N. and W. of the coastal plains. The plains extend N. and W. from the gulf to within from 10 to 25 miles of the Great Wall, while their SW. extension covers western Shantung and reaches W. along the Yellow river almost to the southern boundary of Shansi. A line joining the mapped coal-fields, shown in Fig. 1, almost gives the western boundary of the plains; since these areas lie on the border of the plains—except the Tsê Chou field, which is on the table-land, 20 to 25 miles from that border. The coal-fields which have been mapped and investigated by the author are shown in Fig. 1. The one at and around Tongshan is known as the K'ai-p'ing coal-field; the one W. of Peking has been called the Wang-p'ing coal-basin; the one SW. of Pao-ting and N. of Chêng-ting may be called the Lingshan coal-field; and the one at and around Tsê Chou is known as the Tsê Chou coal-field. I. The K'ai-p'ing Coal-Field. As is shown in Fig. 2, most of this field lies in the coastal plains, and is therefore covered by alluvium and loess, which have buried the older rock-beds, and the more gentle and older topographic outlines, to such an extent that most of the re-

Jan 1, 1902

By W. A. Hockings, D. W. Fuerstenau, A. L. Mular

This paper briefly describes a simple air pycno-meter and its use for rapid determination of the composition of mixtures of solid particles. Research on such problems as the pelletizing of solids, the mixing of solid particles, and the comminution of mixtures can be simplified by means of this analytical tool. THEORY OF OPERATION Liquid pycnometers1 are commonly employed to measure volumes. These devices are time consuming and sometimes give inconsistent results. The liquid used in the pycnometer may have an undesired influence on the material to be measured; moreover, complete displacement of air by the liquid is seldom

Jan 1, 1963

By J. van Lookeren

In the case of a reservoir where the oil underlies a large gas cap and overlies bottom water, production can be inzproved considerably if wells are perforated below the water-oil contact rather than opposite the oil-bearing section. The theoretical arguments for this improvement, which in some cases may be tenfold, are supported by experimental evidence. INTRODUCTION Reservoirs frequently consist of one sand body containing an oil layer underlying a thick, gas-bearing section and overlying bottom water (Fig. 1). Wells in such reservoirs are customarily opened up opposite the oil-bearing interval or, rather, opposite the lower part of this interval (Fig. 2). More often than not, it is inefficient or prohibited to blow off large quantities of gas with the oil. This im-psses a severe limitation on the drawdown, which results in low oil-production rates. Because of the small difference in specific gravity between oil and water, the latter will easily cone upwards, so that the production of water together with the oil is not prevented by this completion method. In such a situation wells should be opened deeper, in the originally water-bearing zone. The gas can be shut off by not perforating over the upper part of the interval (Fig. 3) or by a tubing hung close to the bottom of the interval (Fig. 4). Initially much water will be produced, but when steady-state conditions have been established (as depicted in Figs. 3 and 4) larger drawdowns are permissible than in a conventionally completed well, and correspondingly higher oil-production rates will result. Water cuts are only slightly higher because of the small effect of gravity on the water-oil flow distribution. CALCULATIONS The ratio of improvement has been estimated by means of approximate calculations. The completion depicted in Fig. 4 is the most convenient basis for these calculations. By postulating that vertical flow gradients can be disregarded, the Appendix shows that the well-known Dupuit formula can be obtained except for some complication due to the presence of two fluids rather than one. The Appendix makes the reasonable assumption that, for suitable boundary conditions, the oil layer occupies a constant fraction of the total fluid height throughout the reservoir. The oil- and water-production rates can thus be related to the liquid levels in the borehole as follows:

Jan 1, 1966

By Howard R. Pratt, Jimmie L. Bratton

The Air Force Weapons Laboratory (AFWL) has been carrying out a series of experiments whose principal purpose is to measure the dynamic response of rock media to large pressure pulses. Coupled with the field experiments have been theoretical calculations simulating this response. These two approaches allow an appraisal of the current ability to measure in-situ rock response under extreme conditions and also give a fair estimate of the current state-of-the-art in the area of computer calculation of the response of "real" geologic media to a large load. The area chosen for the test series is composed of a sequence of sedimentary units (shale, sandstone, and limestone) located in the Estancia Valley 45 miles east of Albuquerque, N.M. (Fig. 1). The units, which dip gently off the uplifted Manzano Mountains to the west, are essentially horizontal at the test site. An extensive geologic and geophysical investigation of the area was carried out in the form of surface mapping and seismic exploration. Numerous holes were cored and material properties were determined from tests of the cores. In-situ geophysical measure¬ments were also carried out. The experiment consisted of loading a 60X40 ft test area with a 4000-psi transient exponentially decaying pressure pulse. The pulse was initiated at one end and traveled the 60-ft length of the test bed. The test area was instrumented with acceleration, velocity, and strain measuring devices placed in drill holes to depths of 30 ft. Theoretical computer calculations of the response of the layered geologic media have been carried out on the AFWL CDC 6600 using one and

Jan 1, 1972

By G. S. Brooks

DURING the past few years, the Mineral Point Zinc Co. has had under consideration the improvement of various types of gas-filtering apparatus used in the removal of dust from crushing and milling plants, in the manufacture of oxide, and on blast-furnace fume and sintering furnaces. The original equipment of the various plants of the company was, of course, along lines of the standard stationary bag house. These houses required large surfaces, hand shaking, and varied only in the manner of the collection of solids and in the distribution of the gas. Early in 1908, the first trial of a mechanical bag house was made at Nassau Plant at Depue, Ill. The duty of this installation was on dust-laden gas from a fine-crushing mill. The Printz and Rau bag machine was finally adopted and put into operation. This ingenious machine embodied what were then to us two novel features in bag-house practice: 1. An intermittent crinkling and snapping of the filtering fabric to free the meshes of solids. i 2. A reversal of gas flow for a short period by a temporary connection w th the suction trunk. This equipment worked fairly well except in cold weather, when we ran into condensation troubles. Had we at that time understood more fully some of the limitations of fabric filtering work, these might well have been remedied. We were impressed by this experience, however, with the efficiency of sudden tension on the fabric under suction. After a study had been made of some of the Western blast-furnace houses using the reversal-of-flow feature, experiments were started early in 1914 with a view to developing an automatic equipment along the best lines of our past experience. The objects sought were: 1. Keeping labor out of the houses for hygienic reasons. 2. Reduction of labor costs. 3. Reduction in -size of hag houses. 4. Accessibility. 5. Ability to handle relatively hot gases where required.

Jan 11, 1917

By I. C. Edwards, G. E. Agar

INTRODUCTION Many research efforts over the past years have been devoted to the study of energy consumption in comminution and the characteristics of the broken material. The old "laws" have been superseded by more general methods of analysis1,2,3 but these methods have not received much attention outside the laboratory. The work to be described here was done in order to obtain scale-up information on wet rod milling of sylvinite. EXPERIMENTAL A 30 x 51 in. Denver rod mill with a scoop feeder was used for these tests. Ore was fed from a variable speed screw conveyor into the feed box along with saturated brine. The mill was filled to approximately 45% of its volume with 2400 lbs of a mixed rod charge. The minimum possible feed rate was 2.5 tph and the practical maximum for this mill was 8 tph. Individual tests were run by setting the solid feed rate, then adjusting the brine flow rate to give the desired pulp density. After steady state, as evidenced by constant discharge pulp density, had been reached, samples of the discharge were taken at 15-minute intervals. These samples were filtered, washed with alcohol, dried, then screened on Tyler screens using a Ro-tap shaker. The sylvinite feed was regular plant feed that had been scalped at 20 mesh and was tapped from the coarse ore bins. It had been previously passed through a roll crusher set at 3 inches and after scalping was essentially minus 1 in. plus 20 mesh. RESULTS The screen analysis of samples from each series of tests was plotted on double logarithmic scale paper to determine the reliability of the series. In some cases, a faulty sample or screening procedure dictated that the results of one test be discarded. The criterion is a simple one — if the slope of one plot was noticeably different from the others in the series, it was discarded. The only cases that caused difficulty were those in which the brine was not thoroughly displaced from the solids. When this occurred agglomerates were easily identified on the screens and the whole of the sample was retained on 3 or 4 screens. There were no border line cases. The number N given in Table 1 is the number of size analyses that were pooled to form the data shown in Fig. 1. While examining the reliability of the sizing and sampling by plotting the data, it became apparent that there was no significant difference between grinds made at 50 and 60% solids. For the analysis given here, these tests were regarded

Jan 1, 1967

By Louise Reber

THE town of Jerome is located in Yavapai County in north central Arizona. It has a population of over 6000 people and the two important mines of the district, the United Verde and the United Verde Extension, lie almost within its limits. Perched high on the southwest side of the Verde Valley, at elevations of 4800 and 5500 ft.. (1463 and 1676 m.), both mines have long tunnels from their lower levels through which ore is hauled to their respective smelters. The two smelter towns of Clarkdale and Verde, out in. the center of the valley and about 2000 ft. (609 m.) below, form part of the wide panorama that meets the eye at Jerome. This panorama and the topographic and surface features and the geologic formations are shown in a separate pamphlet. In the vicinity of Jerome, the great southern escarpment of the Arizona plateau forms the northeast side of the Verde valley. The general level of this escarpment, or "the rim" as it is called, is about 4000 ft. above the Verde River. A corresponding elevation is reached only by the, highest parts of the Black Hills, which bound the valley to the southwest. The two lava-capped mesas, known as Mingus and Woodschute Mountains, form the culmination of the Black Hills. That part of the old Black Hills mining district which lies between their crests -and the Verde River is now known as the Jerome or Verde copper district. However, if the smelters are not included, a strip about 7 mi. long and 3 mi. wide (11 by 5 km.) embraces practically all the properties belonging to the Jerome district. This strip lies parallel to and along the side of the Verde valley from about First View, 2 mi. northwest of Jerome, to the neighborhood of Allen Spring, near the south end of Mingus. Mountain. The rank of the district in copper production, as well as features of peculiar geologic interest in connection with the ore occurrences, entitle the district to much more consideration than it has received in the literature of copper mining. Arizona stands preeminent as a copper-producing state. In 1918, it produced four-tenths of the total amount produced in the United States, and nearly equaled the, combined production of its three chief competitors, Montana, Michigan, and Utah. The production of the Jerome district places it in the sixth place among the copper

Jan 8, 1920

By Charles R. Simcoe

The stress-strain curves in the microyield region for various Fe-C solid solutions shown by Davies and Ku are typical examples of parabolic curves defined by the expression a = kEn 111 These data, when replotted on log-log coordinates, as shown in Fig. 9, exhibit three essentially parallel straight lines. It is apparent that carbon increases the flow stresses, but does not affect the exponent n. In other words, the only factor in Eq. [1] affected by in in carbon content is the constant k. As Eq. [1] is written k is the stress at a strain of 1.0. This is unsatisfactory for examining data in the microyield region. Therefore, the equation can be altered to the form: to permit the use of the authors' microyield stress at a strain of 10-6 as k. Extrapolating the curves in Fig. 9 to a strain of 10-6 gives stress values of 2000, 3200, and 5400 psi for 0.008, 0.014, and 0.02 pct C, respectively. These values do not agree exactly with the authors' measured values, but this will not affect the following discussion. The effect of carbon content on the slopes of the stress-strain curves shown in Fig. 2 of the paper by Davies and Ku can be analyzed by differentiating Eq. [2] with respect to strain. Thus: where n is always less than 1.0. Since n is essen- tially constant as a function of carbon content for the data under discussion, the slopes of the stress-strain curves depend only on k and E. If the slopes are examined at various selected Plastic strains. i.e., 10-6, 10-5, and so forth, it follows from Eq. [3] that the dif-ferent slopes for the different carbon contents depend only on the different values of ke=10-6. Thus, the larger ke=10-6, the steeper the linear stress-strain curve will rise with increasing plastic strain. This

Jan 1, 1969

Jan 1, 1883

By Maurice Rey, H. Beavers

THROUGH circumstances connected with the war, the senior author lost his records, therefore it has been impossible to include numerical data in this paper. The arsenical quicksilver ore investigated had been roasted, with poor metallurgical results. The vapor-tension temperature curves of mercury and arsenious trioxide are similar, and the arsenical compound hampers the coalescence of mercury drops in the condenser and is the cause of large stack losses. The ore was a gray limestone carrying small amounts of carbon and mineralized with cinnabar and two arsenic minerals, realgar (As2S2) and arsenopyrite (FeAsS). The proportion of realgar often exceeded that of cinnabar; the proportion of arsenopyrite was smaller. The grade of the ore varied between 0.8 and 4 per cent Hg. The problem was to make a high-grade mercury concentrate, as free from arsenic as possible. The water used throughout the testing was hard, having a pH of about 8. FLOTATION OF REALGAR Realgar showed a very strong tendency to float. It formed a film at the surface of the pulp and floated in abundance with only pine oil. Therefore an attempt was made to float the realgar before the cinnabar, but this was not very successful; the percentage of mercury in the realgar concentrate could never be brought below 2 or 3 per cent. Cinnabar slimed easily and floated with pine oil, so that some of it always accompanied the realgar. There was also the question of the cinnabar-arsenopyrite separation. On further investigation it was found that realgar can be floated not only with pine oil but even better with a combination of hydrocarbons and pine oil. Washing the ore with ether revealed that it contained hydrocarbons, which helped to float the realgar. In this connection it belongs to the same class as carbon, sulphur and talc. It can be floated also with a xanthate, when activated by a heavy-metal salt. The conditions favoring the two types of flotation are opposed, as activation by a copper salt facilitates xanthate flotation (in fact, is even necessary to it), whereas it hinders pine oil and petroleum flotation. One type of flotation can be termed nonpolar and the other polar, a distinction that has been stressed in a previous paper.1 DEPRESSION OF REALGAR AND FLOTATION OF CINNABAR 'Many chemicals were tested in an attempt to float the cinnabar and depress the realgar. Finally starch rendered soluble with caustic soda was tried, also several grades of commercial soluble starch, and dextrin was found to be the best and the most convenient reagent. Several of these starch preparations have a strong flocculating effect on the pulp, which is a distinct disadvantage. Dextrin, with its low flocculating power, is excellent. It is noteworthy that starch preparations are also depressants for carbon and talc, so that the fact apparently has a general

Jan 1, 1941

By Robert Pack

INTRODUCTION SOONER or later in the development of any natural resource it becomes highly desirable to know the quantity of this resource in the country as a whole, as well as of the part that is being developed, for the general course and. conduct of the development work must be governed to some extent by the total supply available. An accurate estimate of the quantity of any natural resource is difficult to make; yet if one is diligent enough one can obtain a pretty accurate idea of the quantity of marketable timber, the acreage of tillable land, or the horsepower that may be developed from the streams, for these are things that may be measured. But any attempt to estimate the quantity of some mineral in the ground appears to enter the realm of imagination and it seems that the estimate can be nothing more than a blind guess. It may appear to be especially futile to attempt to determine the quantity of oil and gas that is available in the ground, for these minerals are so vagrant that even if the quantity now available should be known quite exactly, the quantity that will eventually be obtained may be much less, for certain losses in the extraction of both oil and gas are unavoidable, and just what these losses will be cannot be predicted. Though necessarily inaccurate, estimates of such mineral reserves are, however, of distinct value, for they summarize the existing knowledge of the deposits of the mineral and thus enable those who are interested in some industry that depends in one way or another on this mineral to formulate a rational commercial policy. Some time ago, when the price of gasoline suddenly rose in a rather spectacular manner, the writer was one of the U. S. Geological Survey geologists called upon to help to estimate the quantity of oil that could be obtained in the United States, for the fear had become widespread that perhaps the rate of increase in the price of gasoline was a measure of the rate of depletion of the supply of petroleum. It thus became his

Jan 8, 1917

By G. Gabra

The kinetics of acidified thiourea leaching of pyrite concentrate was investigated at temperature ranging form 20 °C to a 60 °C. The effect of various parameters on the dissolution rates are discussed. The gold extraction was found to be zero and first orders with respect to Fe (111) and thiourea concentration, respectively. The order of the reaction with respect to sulfuric acid was found to be zero. The activation energy was determined from the Arrhenius plot as 2,039 kcal mole -1 (for a freshly prepared acidic solution containing Fe (111) as the oxidant and at 800 rpm stirring speed. This relatively low activation energy value suggests that the gold extraction is controlled by a-physical phenomenon. Under optimum conditions, more than 90% of gold has been dissolved in about 30 min. and 95% in 60 min. Attempt to recover gold from thiourea solution using active carbon is also discussed.

Jan 1, 1984

By B. D. Lichter

The lattice parameters of zirconium and zirconium-oxygen solid solutions (hcp) were determined from measurements of back-reflection X-ray photograms obtained at 29°C using a symmetrical focussing camera. The following linear equations between parameters (c,a) in angstrom units (10-8 cm) and atom ratio (m) of oxygen to zirconium were obtained: c = 5.14764 + 0.2077m a =3.23168 + 0.1099m. The linear equations given are valid over the range 0 to 5 at. Pct 0. The accuracy of individual parameter measurements approaches the limiting accuracy determined by the spectral broadening of the incident characteristic radiation, and exceeds the accuracy of previously reported values. THE present work was undertaken in order to determine the lattice parameters of zirconium-oxygen solid solutions with an accuracy that allows quantitative determination of oxygen in zirconium. The results indicate that this is possible if very careful measurements are made, since the parameter change is only a few hundredths of a percent per at. pct 0.1, 2 In the present investigation the desired accuracy was achieved with large-grained samples using a back-reflection focussing camera and maintaining good temperature control during exposure. In addition a digital computer was used for calculation of the parameters by means of an analytical extrapolation.37 Suitable diffraction photograms were obtained from large-grained samples by using a modification of the technique described by Graf and Monteil.5 This consists of simultaneous rotation and oscillation of the specimen about two mutually perpendicular axes during exposure. Whereas, normally the upper limit of grain size is about 50 µ for useable diffraction photograms, this technique allows extending the upper limit of grain-size to exposure of a single crystal. EXPERIMENTAL Preparation of Alloys for X-ray Diffraction—Zir-conium, designated as hafnium-free, Westinghouse "Grade 1," was swaged from l/2-in.-diam crystal bar to 3/8-in.-diam rods. Substantially all of the hydrogen was removed from the zirconium by annealing at 1200°C in a high dynamic vacuum. The rods were then swaged to 0.2 in. diam without intermediate annealing, and 2 in. lengths were cut for alloying with oxygen. Samples for chemical analysis were taken from portions of the rods between each 2 in. length. Chemical analysis of the dehydroge-nated zirconium is given in Table I. Commercial tank oxygen (99.5 pct 0) was condensed in a liquid nitrogen-cooled trap, and part of the condensate was slowly reevaporated into 5-liter storage flasks. Nitrogen remained as a reactive impurity, and the calculated maximum increase in nitrogen content after a 5 at. pct 0 addition to zirconium was 50 ppm by weight. However, chemical analyses of several of the prepared alloys indicated that the maximum increase in nitrogen content was 10 ppm. The storage flasks, a Sieverts-type gas burette and manometer, and associated traps, pumps, and pressure gauges were connected through a glass high-vacuum manifold to comprise the gas addition system. A fused silica tube, connected to the mani-

Jan 1, 1961

By Marsh S. Watson, Robert A. Howard

An electrolytic model study has been made of the relative productivity of perforated casing. The results show that the relative productivity is roughly one-half to two-thirds of that predicted from point-sink calculations. This discrepancy can he satisfactorily explained on the basis of casing interference. The relative productivity was found to he insensitive to spatial arrangement of the perforations. INTRODUCTION The relative productivity of wells with perforated casing has been treated mathematically by Muskat.' In his treatment the perforations are represented by small spheres, thus enabling him to approximate the flow by that to point sinks. By neglecting interference between the flow into the various spheres representing the perforations, one may deduce the approximate formula Qu 1/rp - 1/rw • (1) I + b/2n _________ 2n In re/rw Where Q is the flow rate into spherical sinks located in the median plane of the sand laver Qo is the open hole flow rate (uncased hole of radius rw) b is the thickness of sand layer under consideration (always one foot in this paper) n is the number of spherical sinks in the sand layer rp is the radius of a spherical sink rw is the well radius re is the drainage radius of the well. Fig. 1 is a comparison of values calculated from equation (1) with Mus-kat's values. It will be observed that the approximate values are in error by less than 21/2 per cent. The disturbing effect of the casing on the flow line; is not explicitly taken into account by Muskat, but he reasons that interference between the flow pat- terns from the various point sinks will result in a negligible flow in the region within the well radius, and that no appreciable error will result from not explicitly excluding flow from this region. This line of reasoning is open to question, however, as the flow impedance, in the immediate vicinity of the well, of a hemispherical cavity in contact with an opening in the casing is twice that of a spherical sink in a continuous sand layer. There will be a difference, moveover, between the flow into a hemispherical cavity and that into a circular hole in the casing. .This latter difference can best be appreciated by comparing the flow from a semi-infinite medium into a hemispherical cavity at the edge of the medium with the flow out of a circular opening of the same radius as the hemisphere and which is also on the edge of the medium. In this case2 ------= —2, showing that the difference in flow rates into differently shaped cavities is quite appreciable. It was the purpose of the investigation reported here to determine to what extent flow into circular perforations in casing departs from the values calculated by Muskat. For this purpose an electrolytic model was used.

Jan 1, 1950

Jan 1, 1968