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By L. W. Fagg

The purpose of this paper is to present in a convenient form data and examples necessary in making dynamometer card analyses; also to outline a procedure of well weighing. Many articles and papers have been written delving into the mathematical considerations relative to the shape and characteristics of dynamometer cards. However. it is recognized that there are too many unknown factors involved in such calculations to assure a workable degree of accuracy. For this reason the accepted procedure is to take dynamometer cards on wells in question rather than try to calculate the load curve. The polished rod dynamometer is now recognized as a necessary tool for measuring loads, torque, and horsepower. It is also used to determine pump action and trouble-shoot for any seemingly abnormal pumping condition. The apparently infinite variety of a = maximum load (height x scale constant) b = minimum load. Range of load is difference between maximum and minimum load speed—taken with stop watch stroke —measured at polished rod c = beginning of down stroke in direction of arrow. (End of up stroke) d = beginning of up stroke. (End of down stroke). Polished Rod Horsepower = (Area of card) x Scale const. x Stroke x Length x spm (Length of card) 33000x 12 1.35 1.35------x5300x 24 x 12 2.53 --------------------------= 2.06 23000x12 Appraximate Peak Torque: Upstroke = (2390) (12) (1) = 28,700 in. Ib Downstroke = (1 860) (12) (.866) = 19,300 in. Ib Counterbalance should be increased to make up stroke and down stroke peak torque equal. FIG. 1 dynamometer cards that can be obtained is one reason for the general lack of usage of the dynamometer as a control instrument rather than a means for making routine measurements of leads and horsepower. When it is considered that the dynamometer card is a record of the resultant of all forces acting on the polished rod at any particular instant during the pumping stroke. the problem is then one of breaking down this resultant into its various components. As a means of a quick review we shall consider the examples shown in Figs. 1 to 9: and Tables I and II and then proceed to the interpretation of variously shaped cards caused by some abnormal operating condition. In Table 11, when we were considering the factors involved in calculating the peak polished rod load, it can be seen that the factors involved greatly oversimplify the problem. Certain assumptions are made which may or may not he even close to the actual field conditions, such as the specific gravity of the fluid generally considered as one; that the crank has constant angular velocity; that the down-hole friction is zero; and that the fluid lift is from the pump. In the following examples we shall see what a variation in fluid weight and friction can do to the general shape and magnitude of the dynamometer card. (Figs. 10 to 22.) MAKING THE WELL STUDY It is obvious that it would be impractical to consider in detail all of these factors each time a well study is made, inasmuch as each well study job could conceivably be extended into a research project rather than serve the practical requirements of finding the answer to a specific problem. For this reason it is important that some objective be established previous to the time the well study is made. Load at TU = 3070 Ib Crank angle when polished rod is at position TU = ? ? = 30° Maximum counterbalance effect at polished rod = 2760 Ib Torque at TU = (Load at TU — Max. counterbalance effect-lbs) sin 0 x Length of Stroke 2 = (3070-2760) .5 x 24 = 1860 in. 15 2 Torque at TD = (Load at TD — Max. counterbalance effect-lbs) sin ? x Length of Stroke 2 = (530 - 2760) sin 330' x 24 = 13,400 in. Ib 2 Note: sin 0 from c to d on UPSTROKE will be positive value. sin 0 from c to d on DOWNSTROKE will be negative value Torque at c and d is zero because 0 is zero. FIG. 2 —APPROXIMATE METHOD FOR CALCUlATlNG TORQUE

Jan 1, 1950

By C. C. Harris

A critical literature review leads to a descriptive model of tumbling mill operation based upon energy partition concepts and the necessary requirements for particle fracture. As grinding proceeds into the ultra-fine region, conditions which are of little significance during normal operations gradually become controlling. These involve increasing resistance to fracture and an increasing tendency to aggregate as particles become smaller, and a growing fraction of the power input being consumed fruitlessly. The result is that fineness asymptotes to a maximum value as comminution proceeds indefinitely; thus where t is time, p and n are experimentally determined parameters, and Ø is a measure of fineness, which is presumed to be proportional to specific surface area, or proportional to the reciprocal of the size modulus (provided that the distribution modulus remains constant with time), or both. Ø, is the asymptotic value of Ø and is a measure of the grind limit. A method for its graphical determination is given. In a previous paper1 the physical and mathematical principles requisite to a study of the role of energy in comminution were reviewed. The micro-process of comminution — or the comminution event — can be investigated in terms of (a) the magnitude of the force-field localized around the individual particles which gives rise to the stresses generated in the particles, which in turn induces their fracture, and (b) the distribution of fragment sizes, should the event prove fruitful. The entire fragmentation operation can be considered to be the totality of its individual events, and in order to obtain a single independent variable of the process it is necessary to transform and sum the local stresses in terms of energy.1 This energy, however, will account for only a fraction of the energy input to the comminution process, the actual magnitude depending upon the kind of mill and several related factors. From the comminution viewpoint the primary function of a mill is that of stressing as many as possible of the individual particles of the charge to failure, with the maximum economy of energy expenditure. This is difficult indeed to achieve, for stressing a particle does not always break it, while the overwhelming portion of the energy input is involved with various internal mill processes which — almost incidentally — determine the magnitude, frequency, and manner in which the forces are applied to the particles. Essentially, these processes depend upon the mill dimensions, loading and speed, and they may be little affected whether fracture occurs or not. These processes must be delineated if a complete description of the role of energy in comminution is to be given; the energy account sheet1 (Fig. 1) in showing how the energy is partitioned for the requirements of the several functions it performs, provides a framework for the development of a model of the comminution process. Actual numerical values for the variables appearing in Fig. 1 will depend upon the mill, materials, and operating conditions. A possible general relationship between the variables will be suggested in this paper. Before proceeding further, a cautionary note must be issued. It was pointed out in an earlier paper' that while energy input is not changed by increasing the power and decreasing the time in the same proportion, and vice versa, the results of the process in terms of particle fineness may be different. Thus, although energy is chosen as the independent variable of a comminution process, it is not absolutely independent, and care must be exercised to ensure that it is used within its range of valid application. Time has the necessary independence, and it will be used in place of energy where it is appropriate. The residence time in a mill is usually of the order of minutes. Under these conditions the particles are subjected to "... a relatively constant fracture producing environment".2 However, under the more rigorous conditions of greatly extended time, which pertain in ultra-fine grinding, indications are that the fracture producing environment no longer remains constant; this is the major subject of this paper. At this extreme limit the mill is probably taxed to its utmost, and at the same time the bulk material properties are becoming closer to ideal, while the physico chemical effects associated with surfaces, edges and corners are multiplying. (The edge length per unit volume is proportional to the square of the specific

Jan 1, 1968

By W. S. Cavender

The Round Mountain mining district, Nye County, Ne- vada, was discovered in 1906 on claims owned by Lewis D. Gordon. Initial mining operations uncovered gold veins of spectacular richness, and within a few days of discovery, Gordon sold his controlling interest for some $87,000. From this sale emerged the Round Mountain Mining Co., predecessor of Nevada Porphyry Gold Mines, Inc., the latter destined to become the major property owner in the area. Vein mining in the district continued sporadically into the early 1930s, yielding 9.3 Mg (330,000 oz) of gold plus substantial silver credits from approximately 626 kt (690,000 st) of ore. In addition to the lode deposits, the early miners recognized the placer potential in the alluvial fan material accumulated around the west and north sides of Round Mountain itself. Intermittent placer operations were carried out for a number of years, and in the 1940s and 1950s, Round Mountain Gold Dredging Co. worked the placers under a lease from Nevada Porphyry Gold Mines. The last placer operation terminated in 1959 when it, like some of its predecessors, proved uneconomic. Total placer production for the district is estimated at 3657 km (4 million yd) of gravel containing 59 Mg (210,000 oz) of gold and possibly 2.0 to 2.3 Mg (70,000 to 80,000 oz) of silver. Round Mountain is a small hill situated on the east flank of the Toquima Range in central Nevada. The hill is com- posed of relatively flat-lying Tertiary rhyolitic ash flow tuffs, which overlie Paleozoic metasediments and Cretaceous granites. Throughout the surrounding Round Mountain mining district, most of the known gold ores occur in the tuffs, although the metasediments and granites are also mineralized. Mineralization is structurally controlled, principally by a series of northwest-trending shears and shattered zones. Vein, stockwork, and disseminated ores occur, usually containing simple quartz-pyrite-gold mineral assemblages. The gold itself is electrum, having a silver content of 30% to 40%. In September, 1967, Elwood Dietrich, a prospector and mine promoter, obtained a purchase option on the 4452 ha (1 1,000 acres) of mineral rights held at Round Mountain by Nevada Porphyry Gold Mines. The original option had a buy-out price of $1 million and was established through Dietrich's friendship with officers of Nevada Porphyry. In April, 1968, Dietrich conveyed his option to Ordrich Gold Reserves Co., a partnership created by a group of west coast investors, mostly employees of the airline industry. There- after, Ordrich invested considerable funds in trying to test and develop the property, but soon recognized the need to seek financial and technical support from the mining industry. In December, 1968, Dietrich contacted Wayne Cavender, then Regional Geologist, Southwest, for Copper Range Exploration Company (CRX) in Tucson, Arizona, and made a data presentation. Shortly thereafter, Cavender was appointed Manager of Exploration and Chief Geologist for Copper Range Co. (parent company of CRX), New York City, and he asked C. Phillips Purdy, CRX Regional Geologist, Northwest, to make an initial property examination. Purdy's one-week field study took place in March, 1969, and resulted in a recommendation that CRX pursue its investigation of the property. The presence of low-grade gold mineralization in both the alluvial gravels and in the bedrock was verifiable, but the placer was deemed to have the greater immediate economic mining potential. At that time, gold was in the $1.41/g ($40 per oz) price range. Working from Purdy's information, Cavender decided to attempt acquisition of the property, and the first in a long series of negotiations was initiated with Ordrich. Basically, CRX felt that the placer had a promising potential for several reasons, including (I) past operators had recovered free gold but not the gold contained in the pebble fraction of the gravels; (2) past operations appeared to have been ineffectively designed or managed and not costefficient; and (3) the price of gold appeared to be poised for an upward move. Negotiations with Ordrich were prolonged and difficult, with CRX competing against several ma* mining companies, but finally an agreement was reached, effective June I, 1970. Gold was then back to $35. It is believed that, in

Jan 1, 1985

By Alan J. Strauss

The Group IV elements germanium, tin, and lead form nine 1:1 compounds with the Group VI elements sulfur, selenium, and tellurium. This paper reviews the properties of the pseudobinary solid solutions formed by these compounds, including the extent of mutual solid solubility, temperature-composition phase diagrams, transport properties, deviations from stoichiometry, optical properties, and energy band structure. Particular emphasis is placed on the Pbl-xSnxTe and Pb1-xSn,Se alloys with rocksalt structure, because of current interest in these malerials for generating and detecting infrared ,radiation. ThE Group IV elements germanium, tin, and lead form nine 1:1 compounds with the Group VI elements sulfur, selenium, and tellurium. Some of the physical and electronic properties of these compounds, including their melting points1-8 and energy gaps,4'9-12 are listed in Table I. Four compounds (SnTe, PbS, PbSe, and PbTe) have the cubic rocksalt (Bl) structure. At room temperature GeTe has a rhombohedra1 structure closely related to the B1 structure, into which it is transformed at about 400°C. Four compounds (GeS, GeSe, SnS, and SnSe) have the orthorhombic B29 structure. In samples which have not been intentionally doped with impurities, the electrical conductivity is due primarily to electrons or holes produced by the ionization of donor or acceptor lattice defects associated with deviations from stoichiometry. Undoped samples of PbS, PbSe, and PbTe may be either n type or p type, depending on whether they contain excess lead or an excess of the Group VI element, respectively, but only p-type samples of the other compounds have been reported. This paper will review the properties of the pseudo-binary solid solutions formed by the nine 1:l compounds. The topics to be considered include the extent of mutual solid solubility, temperature-composition phase diagrams, transport properties, deviations from stoichiometry, optical properties, and band structure. Particular emphasis will be placed on the Pb]-xSnxTe and Pbl-xSnxSe alloys with B1 structure, which are promising materials for generating and detecting infrared radiation in the 8 to 14 µm atmospheric window and beyond. MUTUAL SOLID SOLUBILITY The extent of mutual solid solubility in the pseudo-binary systems has been investigated for fourteen of the eighteen ternary systems (in which the two terminal compounds have a common element) and for nine of the eighteen quaternary systems. In most cases, X-ray diffraction measurements made at room temperature were used to determine the structure and lattice parameter(s) of the phase(s) present in samples of various compositions prepared by freezing from the melt. In many investigations, including the extensive studies of Krebs and co-workers,13'14 the samples were annealed at elevated temperatures before X-ray measurements were made. In some cases, metallographic examination and thermal analysis have also been employed. The results for the ternary and quaternary systems are summarized in Tables II and III, respectively. (The original references should be consulted for the annealing temperatures.) The solubility of one compound in the other is at least 5 mol pct in all cases, and is often much larger. Complete solid solubility has been observed in all systems so far investigated in which the terminal compounds have the same structure, although in the PbS-PbTe system complete solubility is limited to elevated temperatures. Thus complete solid solubility occurs in five systems where both compounds have the B1 structure (SnTe-PbTe, PbS-PbSe, PbS-PbTe at temperatures above 805°C, PbSe-PbTe, and SnTe-PbSe) and in three where both compounds have the B29 structure (GeS-SnS. GeSe-~n~e-, and SnS-SnSe), as well as in two involving GeTe and a compound with B1 structure (GeTe-SnTe and GeTe-PbTe). On the basis of thermal analysis data, complete solid solubility at sufficiently high temperatures has also been reported for the GeSe-GeTe2 and SnS- pbS22 systems. This seems unlikely, however,

Jan 1, 1969

By R. T. O’Brien, J. M. W. Mackenzie

A microelectrophoresis technique has been used to measure the zeta potential of quartz over a range of pH and Ni (11) and Co (Ilj concentrations. Results have been discussed in terms of adsorption of Ni (11) and Co (11) cations and hydroxide precipitates. Possible relationships between the experimental results and the formation of lateritic nickel deposits have been discussed. The adsorption of metallic cations to the surface of silicate minerals is of significance in many industrial and natural processes. In an earlier publication,' the adsorption of Fe (111) to the quartz surface, a phenomenon of importance in flotation, was studied qualitatively using microelectrophoresis techniques. This paper reports the extension of this work to an investigation of the adsorption from aqueous solution of Co (11) and Ni (11) to the quartz surface. The adsorption of these metals was of interest for two reasons; firstly, the importance of such an adsorption process in the formation of nickel deposits by the lateritization of nickeliferous rocks, and secondly, the comparison of electrophoresis data for these metals, whose hydroxides precipitate in the pH range 7-8, with similar data for Fe (111) where the hydroxide first precipitates at pH 2.8. The development of laterites is essentially a near-surface geological process involving vertical and, in part, horizontal redistribution of elements derived from rock-forming minerals. This redistribution of elements leads to the formation of layers within the lateritic profile which are enriched in one or more of these elements and, depending on the nature of the original rocks, continued lateritization may give rise to iron ores, bauxites or nickeliferous laterites. The mechanisms discussed in this paper deal with the last mentioned type of deposit although the considered factors are applicable to laterites in general. Nickeliferous laterites are derived from basic and ultrabasic rocks containing ferro-magnesian silicates. These rocks may be partly or wholly converted to serpentinites. Besides their high Mg, Si and Fe contents, they also contain small amounts of Mn, Al, Cr, Ni, Co, Cu and Zn. The nickel content is usually near to 0.2-0.3%, but for economic use this must be increased during lateritization to over 1% and preferably over 2%. The zone of nickel enrichment is usually at some depth within the lateritic profile. Unpublished work by Mr. O'Brien on nickel-bearing laterites in eastern Australia indicated four visually different types of material which were separated from crushed samples under a stereo-microscope. Although chemical analyses indicated that all four types of fragments contained 2-4% nickel and smaller amounts of cobalt, X-ray diffraction and optical studies revealed only quartz, hematite and chromite as well as, in one of the types, a serpentine mineral. No distinct, nickeliferous minerals were detected. Furthermore, it was possible to extract some 60% of the nickel content of the laterites with cold 0.5N hydrochloric acid. It was therefore postulated that much of the contained nickel was present as amorphous, adsorbed material. In considering this fact, as well as the problem of the actual method of transfer and fixation of elements within the lateritic profile, it was further postulated that the transfer of these elements probably took place partly as solutions and partly as colloids and that the fixation of these was caused by adsorption and flocculation. The existence of nickel in solution in water draining from serpentinites has been confirmed by Smurov.2 Although we have no evidence for the transportation of nickel in the colloidal state, it is well accepted that colloids are important in the formation of laterites. Previous work by Mr. Mackenzie' has already indicated that iron may be adsorbed on quartz under conditions which could be expected in a lateritic profile, but no information was available for nickel or cobalt. Although adsorption possibly also takes place on minerals other than quartz, the latter is significant because silica is an important constituent of the silicate parent rocks. During lateritization, it is released to form free quartz and it is likely that it is initially extremely fine-grained. This would provide abundant opportunities for adsorption and it was de-

Jan 1, 1970

By R. L. McCarron, G. R. Belton

The diffusivities of oxygen and sulfur in liquid iron have heen determined hy a capillary technique in which the surface concentrations of the solutes were established by means of appropriate H2/H2 and H2S/H, gas mixtures. Total diffusate and concentration profile results are shown to be in good accord, yielding for- 1560 and Supporting results at 1660°C are also presented. The conditions necessary to avoid gas transport control in this type of experiment are discussed. IN spite of their importance in understanding the kinetics and mechanisms of refining reactions, the dif-fusivities of oxygen and sulfur in liquid iron are not well established. Accordingly, as a first step in studies of rates of solute absorption from the gas phase into liquid iron, new measurements of these diffusivities have been made and are presented in this paper. The only published results for the diffusion of sulfur in pure liquid iron are those of Kawai.' He used a diffusion couple technique in which two cylindrical specimens, one containing sulfur and the other with negligible sulfur concentration, were joined together and held in a refractory capillary. After an experiment, the sample was quenched and the concentration distribution of the solute determined. Kawai recognized that significant changes in solute distribution occurred during melting and freezing and he attempted to correct the concentration profiles for these effects to give a sulfur diffusivity of 4.6 x 10-6 sq cm per sec at 1560°C. The method of correction, however, was not rigorous and the uncertainty in this result cannot be easily assessed. Koslov et a1.2 have reported the diffusivity of oxygen in iron as 7.8 x 10"3 sq cm per sec at 1660°C. This value appears to be unreasonably high but, unfortunately, details of their experiments are not available. Shurygin and Kryuk have used the rotating disc method for a study of oxygen diffusion in liquid iron. In their experiments a silica disc was rotated in liquid iron containing oxygen, and the rate of formation of liquid iron silicate was determined by measuring the decrease in weight of the disc. On the assumption that the rate of dissolution was controlled by the diffusion of oxygen in the iron, the diffusion coefficient was computed to be 5.2 x sq cm per sec at 1550°C. However, the Levich equation, which was used to interpret the rate data, was originally de- rived for the case of mass transfer between a solid disc and a single-phase liquid. The hydrodynamic and diffusion boundary layers in the iron stirred by a disc, via coupling of the silicate melt, may be appreciably different from those predicted by Levich's equations. Recently, Novokhatskiy and Ershov, using an identical experimental method to that of Shurygin and Kryuk, obtained a diffusivity for oxygen in liquid iron of 1.22 x 104 sq cm per sec at 1550°C: no reasons were offered for the disagreement. Schwerdtfeger5 has also recently studied the diffusivity of oxygen in liquid iron. He reacted shallow melts of liquid iron, 0.5 to 1.0 cm deep and contained in high-purity alumina crucibles, with appropriate H20-HZ-He mixtures. The total sample was analyzed, without sectioning, to obtain the average concentration of diffusate. A value at 1610°C of D = 12(3) x 10-5 sq cm per sec was obtained from the results of twenty experiments.= Oxygen profile measurements, which were carried out in three additional experiments using long capillaries and the semiinfinite boundary conditions, indicated a diffusivity about half that computed from the shallow bath experiments. Possible sources of error in Schwerdtfeger's study will be discussed later in this paper. EXPERIMENTAL TECHNIQUE The essential arrangement of the diffusion cell is shown in Fig. 1. The liquid iron was contained in an alumina capillary, 3 to 4 mm diam and 3 to 9 cm long, which was supported by a hollow alumina pedestal and this whole assembly was held within a movable alumina reaction tube. This tube, which was about 7 mm in bore

Jan 1, 1970

By D. H. Yardley

GEOCHEMICAL investigation of trace elements in surface materials was begun near Ely, Minn., in 1953 along the basal contact of Duluth gabbro with Giants Range granite (Fig. 1). This article presents data on the distribution of copper and nickel in till and in stream sediments in the area and proposes an explanation for the types of distribution found. The Duluth gabbro, one of the world's largest basic intrusives, intrudes rocks which range in age from Keewatin to middle Keweenawan. Within the test area the gabbro is in contact with granite except for short sections where it is in contact with remnants of iron formation. Sulfide mineralization occurs within the gabbro, near and parallel to the basal contact for a distance of several miles. Schwartz and Davidson' have described the geologic setting of the mineralization. The sulfides, believed to be syngenetic, include chalcopyrite, cubanite, pentlandite, pyrrhotite, and minor amounts of bornite. They occur disseminated in the silicates and as small interstitial masses. The ratio of copper to nickel is about 3.8:1, based on 66 chemical analyses of rock samples from various outcrops (Ref. 1, p. 702, and Ref. 2). Test Procedures: With specified exceptions, all nickel and copper tests were made by the chromo-graph method,:' which measures the intensity of a colored spot formed by a reaction between the metal being determined and special reagent paper. The intensity is then compared to the intensity of spots prepared from samples of known metal content. Details of the test procedure are outlined in another article (Ref. 4, pp. 77,78). All soil samples tested in this investigation to date have been weighed on an analytical balance. However, a volumetric scoop designed to provide about 0.1 g of soil adds to the speed and ease of testing and has been found to give satisfactory results (Ref. 5, p. 531, and Ref. 19). The size of the samples used for the tests was 0.1 g. Whenever such small samples are used there is some question as to whether they are representative of the several grams in the field sample. Many repeat tests of the samples used in this investigation demonstrated that results can be reproduced within the limits of accuracy of the method without formal mixing beyond that inherent in screening the soil fractions. Furthermore, the 0.1 g is probably as representative of the field sample as the field sample is of its area of influence. Hawkes and Lakin (Ref. 6, p. 291), who considered the general problem, compared ground and quartered bulk samples of 500 g with 5-g grab samples. They concluded that "there is no significant loss in accuracy of data by substituting grab samples for bulk samples." The term soil implies somewhat different things to the geologist, engineer, and soil scientist.' For convenience the term as used in this article refers to unconsolidated material (the mantle) overlying bed rock. Sampling Procedure: Samples were taken at 100-ft intervals along north-south traverse lines across the gabbro-granite contact. The soil (till) samples were taken at an average depth of 1 ft, which was below the high-humus surface layer and into clean till. Samples taken at 1-ft intervals down to ledge showed as high a metal content at 1 ft below the air-surface as at greater depths and in two instances were slightly higher. The till at 1-ft depth did not appear to differ from material at greater depths. Total depth to bedrock has been tested at only a few points and where measured varied from 1 to 10 ft. Aerial Distribution Contours and Profiles: Plotting of copper, nickel, and cobalt content in contour form (Fig. 2) shows that anomalous amounts of these metal ions occur in till over and closely adjacent to mineralized areas of the gabbro. Contouring nickel content alone, or the copper content, outlines the same target area. Contours of the copper content provide a more distinct anomaly than nickel because of the higher copper concentration. The traverses are rather widely spread for interpolation; however, drilling has confirmed the target area essentially as shown.

Jan 1, 1959

By A. Lubinski, J. L. Logan, W. S. Althouse

A4ost gas twells and flowing oil wells are completed and treated through a string of tubing and a packer. Changes in temperature and in pressure inside or outside the tubing will: (I) if free motion of the tubing inside the packer is permitted, increase or decrease the length of the rubing; or (2) if free motion is prevented, induce forces in the tubing and on the packer. If pressure inside the tubing is greater than outside, the tubing may buckle helically even in the presence of a packer-to-tubing tension. The tubing will always buckle, and much more severely, if free motion is permitted. The buckling may be prevented by pulling the tubing in sufficient tension. The prediction of these forces and tubing movement has here to fore been based upon calculations that did not inciude helical buckling. This paper preseitts means with which these length or force changes can be calculated while taking into account the effect of helical buckling. To avoid damaging formations, failure of remedial operations, or damage to the tubing or packer, application is made to practical problems involving calculations of the required length of seals, amount of sluckoff or tension, and prevention of permanent corkscrewing. INTRODUCTION Leakage of a packer may result in costly failures of such operations as squeeze cementing, hydraulic fracturing, etc. To avoid such failures, the authors are often asked questions pertaining to the length of necessary seals, the amount of necessary slackoff, etc. Published work' does not take into account helical buckling of tubing. Investigation of helical buckling was prompted by the fact that allowance must be made for this phenomenon in order to provide relevant answers. In the past, theoretical work on helical buckling was confined to conditions for which such buckling does not The mathematical treatment of behavior in a buckled condition, given in the Appendix, is novel. Assumptions upon which this investigation is based are listed and discussed in a special section. The following are a few of the many kinds of problems which may be solved with this paper. 1. Consider a packer in which tubing may move. Such movement will occur after pressures and temperature are changed. The paper provides means for: (a) calculating the amount of such movement and, therefore. the required length of seals; and (b) calculating the necessary amount of initial slackoff, for which there is no danger of unsealing the packer, if the length of seals is given. Such calculations, as well as those which follow, tully take into account the fact that part of the movement ib due to elastic helical buckling of the lower part of the string. This buckling may occur even in tubing under tension. Insufficient initial slackoff for a given length of seals, or insufficient length of seals for a given slackoff, may result in costly failures. A field case of such a failure will be given further in this paper. 2. In the case in which tubing cannot move in the packer, changes of pressure and temperature result in tubing-to-packer forces and forces in the tubing above the packer, both of which may be calculated. This knowledge is important because, if these forces are too large, the) could damage the packer or the tubing. 3. For wells in which wireline tools are to be run through the tubing, the paper provides means to keep the tubing from buckling, thereby permitting free passage of tools. 4. In deep wells, mainly in the presence of large casing, tubing may become "corkscrewed", i.e., take a permanent helical set. A field case is described further in the text. Using this paper, one may calculate in advance conditions under which permanent corkscrewing would occur, and then take preventive steps. HELICAL BUCKLING Consider a string of tubing, freely suspended in the absence of any fluid inside casing, as shown in Fig. I(a). Now consider an upward force F applied at the lower end of this tubing. This force compresses the string; and if the compression is large enough (which is always the case in actual problems), the lower portion of the string will buckle into a helix, as shown in Fig. 1 (b). The lower end of the tubing is subjected to a compression F. This compression decreases with the distance from the bottom and becomes nil (neither compression nor ten-

By C. Feng, I. R. Kramer

A study was conducted to determine the influence of the surface on the yield point of fcc metals and high-purity iron. For the high-purity fcc metals, the yield Point produced by restraining a specimen may be eliminated by removing a sufficient amount of the layer. A yield point similar to that in fcc metals was found when iron specimens were pre-strained after a prior deformation. This yield point is not due to an aging effect but is associated with the surface layer. The yield points in age-hardenable aluminum alloy and those connected with "work softening" are not affected by a surface-removal treatment and are, therefore, caused by bulk-type dislocation reactions. The yield point which appears in previously strained fcc metals has been the subject of numerous studies. Several theories have been advanced to explain this "unloading-reloading" yield point. Cottrell and stokes,' from their study on the effect of temperature on plastic properties of high-purity aluminum, considered that it was the result of an avalanche "breakdown" of Lomer-Cottrell sessile dislocations. Haasen and Kelly2 extended this concept of dislocation-dislocation interaction to account for the yield point when unloading and reloading was carried out at the same temperature. On the other hand, strain aging was found to be responsible for the yield point in A1-Mg alloy by Westwood and Broom,3 and in aluminum alloys containing various amounts of alloying elements by Smallman, Williamson, and Ardley.4 In these cases, the yield point is considered to be associated with the locking of dislocations by impurity atoms. Birn-baum and filer5,6 and Takamura and muira7 reported that, when a high-purity copper specimen was prestrained, then held at a lower stress, and finally reloaded at the prestrain temperature, a larger yield point was observed. Such an increase was attributed to the locking of dislocations by point defects. In addition, Bolling8 suggested that both mechanisms, i.e., dislocation-dislocation interaction and strain aging, are responsible for the yield phenomenon, at least in a brass. Thus, there appears to be experimental evidence for both the strain aging and dislocation-dislocation interaction theories to explain the yield point in the fcc metals and alloys. In a previous article,9 one of the authors observed that, if sufficient amounts of metal were electrolti-cally removed after deformation of a high-purity aluminum single crystal, the yield point did not appear upon reloading. Continued pursuit in this area revealed that the effect of the surface on the yield-point phenomenon is not limited to one metal but affects a variety of metals of different lattice structures. Nor is the effect limited to the yield points produced by simple unloading-reloading at constant temperature; the surface exerts an important role on the yield point even when the temperature is changed at some stage during the test. It is the intent of the present article to give additional information regarding the effect of the surface on the yield-point phenomenon and to show the association between the yield point in both fcc and bcc metals and the existence of a heavy concentration of dislocation in the region near the surface of a deformed specimen.10 EXPERIMENTAL Materials. The single crystals used in this study had a nominal cross section of 0.125 by 0.125 in. and a 3-in. gage length and were prepared by a modified Bridgman technique. The initial purity for the metals was 99.997, 99.999, and 99.999 pct for aluminum, copper, and gold, respectively. Bar stock of these same materials was used in the preparation of the polycrystalline specimens of aluminum and copper. The iron specimens were machined from rods of "ferrovac", reported to have a purity of 99.98 pct. In addition, a precipitation-hardening aluminum alloy, containing 1.5 pct Cu, 2.5 pct Mg, and 5.5 pct Zn, was used. The polycrystalline specimens of iron, copper, and the aluminum alloy had a diameter of 0.17 in. and a gage length of 2 in. while the high-purity aluminum specimen had a nominal rec-

Jan 1, 1965

By C. S. Matthews, P. Hazebroek, H. Rainbow

It ha been suggested that lormation fractures created by well stimulation treatments will adversely affect sweep-out efficrency in injection operations. Fluid-flow model studies involving vertical fractures of various lengths and fluid systems of various mobility ratios have been carried out to study this subject. In addition, limited data have been obtained on one model containing a horizontal fracture. It was found that relatively long and highly conductive fractures (not generally obtained fracturing operations) were required to affect the sweep-out efficiency substantially. In a given case in the field an approximate distinction can be made between the presence of long conductive fractures and shorter or less conductive ones. This is done with pressure build-up analyses along with data on the relationship of fracture length and conductivity to well productivity. This type analysis shows that usually the fractures induced are either short or of limited conductivity and therefore do not damage sweep-out efficiency. INTRODUCTION Improved well productivity and in-jectivity can frequently be exploited in injection operations. Higher total throughput can yield improved economics. On occasion, the achievement of an increased productivity or injectivity in specific wells can bring about a more uniform sweep of the reservoir. Higher rates can be exploited particularly in water floods of "depleted" reservoirs where a rapid "fill-up" is desired and where low pressures contribute to low well productivity. The creation of fractures local to the wellbore is an excellent means for achieving these objectives. Even though fracturing has been employed in some floods with success,1"3 there still seems to be some reluctance to employ this tool for fear of undue damage to the flood pattern and ultimate recovery. We therefore need to examine the influence which fractures of varying length may have on flood performance and then determine the length of fractures which obtain in the field with conventional fracture treatments. A substantial influence of fractures on the recovery obtained at breakthrough of the injected fluid has been presented by Crawford and Collins for equal fluid mobilities for the line-drive pattern.4,5 In addition, the influence which a fracture has on the production performance after breakthrough and on the ultimate recovery warrants consideration in reaching a conclusion concerning the use of induced fractures in flooding operations. This report presents this type of data for the five-spot injection pattern for several fluid mobilities. In arriving at some conclusion concerning the fracture lengths obtained in field operations we must examine the performance characteristic most affected by the fracture. This is the change in the flow system as reflected in the change in productivity and pressure build-up behavior. A study of these changes is also presented in this report. RESERVOIR ANALOGS The X-ray shadowgraph technique, employing miscible displacement in porous models, has been used in the study of the influence of fractures on pattern sweep-out efficiency. The X-ray shadowgraph procedure is described in detail in an earlier report8. Fractures were represented by leaving the proper portion of the model surface exposed to either injection or production. This assumes the fracture resistance to be negligible compared to that of the formation. Actually the flow resistance in propped fractures obtained in the field is sometimes not negligible so that the results with this model indicate the maximum influence of the fracture. Two types of models were necessary to represent vertical fractures in a five-spot flood. These pattern elements are illustrated in Fig. 1. In studying the influence of the horizontal fracture, only one well spacing length to thickness ratio of 50 was used. The pool unit of a Carter Electric Analyzer was used in studying the influence of fractures on productivity and build-up behavior. The square drainage system of a well was represented by a network of 576 elements of equal volume and resistance. One-fourth of this drainage area was studied as a model unit using a network of 144 condensers and resistors. Vertical fractures were represented by a shunt directed from the well perpendicular to the drainage boundary. Horizontal fractures were represented by a circular shunt. Resistance of a shunt was varied in representing different conductivities for the fractures. FRACTURE DIRECTION AND LENGTH The direction at which a vertical fracture extends into the formation and its length and conductivity influence the sweep behavior. The two

By C. C. Harris

The characteristics of some common size distribution equations are critically discussed. A generalized form of several well-known size distribution equations is obtained from a differential equation describing statistical distributions. The equation contains three parameters and can describe the major features of size distributions in the fine and the coarse size regions. A graphical method for its implementation is provided. The application of this and other equations to sets of data are compared both for the quality of fit and from a comminution kinetics viewpoint. If a narrow size range of a brittle material is broken sufficiently to obliterate the feed sizes, but not so severely that excessive secondary breakage occurs, a plot of cumulative fraction by weight undersize (Y) vs. sieve size (X) on a log log grid (sometimes called the Gates-Gaudin-Schuhmann plot)1-3 gives a straight line of slope ~ 1 over much of its range. On closer inspection, deviations in the extreme coarse range covering perhaps 10 to 30% of the total sample may be apparent (frequently, a change in slope from ~ 1 to a value different from unity) together with over-all slight irregular departures from a smooth line. One model of breakage postulates that the same fracture pattern persists throughout all size ranges.4 The fracture pattern is characterized by the slope of the line on a log log grid. Accordingly, a distribution of sizes broken in the manner specified earlier is expected to produce a size distribution having the same slope as that of a broken narrow size range. Additionally, the slight irregularities mentioned above should even out in the summation process, giving a smooth straight line of slope ~1 on a log log plot. This idealized state of affairs does not, however, describe the distribution of a multi-event process such as that for a tumbling mill product. On the average, these curves (plotted again log log) tend to have a slope in the fine region different from and usually less than unity,5 while the coarse size region curves with increasing slope for cases of mild reduction, and with decreasing slope when moderate or severe size reduction has occurred. In addition, there are usually slight irregular deviations from a smooth curve. Most curves display two distinct regions — fine and coarse — and a few curves show one or more intermediate regions. Feed size studies6,7 show an effect which theory is required to explain. For the same material, mill loading and other operating conditions, and the same time of grinding, plotting the dimensionless ratios Y vs. X/(feed size) does not reduce the size distribution data to the same curve. Y vs. X does not correlate the coarse region, but it can provide a crude correlation of the fine region which improves as size diminishes and as grinding time increases. The size distribution in the coarse region is somewhat more dependent on the feed size than is the distribution in the fine region wherein the degree of dependence diminishes as time proceeds; the distribution of sizes in the fine region are determined largely by the nature of the material and the comminution conditions. A comprehensive model of comminution must recognize that several different patterns or modes of breakage can occur in a mill; 5,8,9 that there can be some selection in that some size ranges are broken more than others; and that, while some particles may be the product of a single fracture event, or may even remain unbroken, others result from multiple rebreak-age. Thus, breakage in a tumbling mill is more complex than the Schuhmann4 model admits in that several different types of comminution micro-events* occur rather than just one type, and these events, though different in size scale, are of the same overall pattern as that which is visualized by the model. The concept of an average comminution micro-event has, therefore, a mathematical rather than a physical connotation, at least for tumbling milling. Equations with which to describe particle size distributions have been sought for over half a century.10-13 No equation presently in general use was first derived from an analysis of the statistical mechanics of breakage; whatever theoretical basis the existing

Jan 1, 1969

By R. Hadfield

Last year this institute was good enough to accept some remarks by the writer regarding sound steel, entitle Plant for Hadfield Method of Producing Sound Steel Ingots…

Jan 1, 1915

[Paragraph No. PREFACE ON ASSAYING I BALANCES AND WEIGHTS 2 Balances required for Assaying 13 How assay Weights are made 3 Assay Weights based on the Centner 18]

Jan 1, 1949

Here, published for the first time, is the group of Anaconda officials (New York office) concerned with the planning and operations of the company's copper properties in Chile.

Jan 1, 1952

By W. J. O'CONNOR

THE production of lead in the United States for the period from 1720 to 1912 was 10,432,668 tons valued at $924,600,000. The average price during this period was 4.4c. a pound, although lead sold at times below 3 cents. We know that in the early days of lead smelting in Montana lead was deliberately lost in the slag and only enough reduced as bullion to collect the silver. This bullion was freighted by ox team to Corinne, Utah, the terminus of the railroad at that time, and shipped to Swansea or Omaha, Neb., for refining. The slag from some of the above mentioned operations contained as much as 15 per cent lead and has since been resmelted. Since 1921 the production of lead has increased each year and the price and tonnage have been as follows :

Jan 1, 1926

By V. H. Gottschalk

SEVERAL years ago a group in the metallurgical division of the U. S. Bureau of Mines began a study of the application of new developments in physics to metallurgical problems'. Among these developments were the extensions of what may be termed by analogy the "sound spectrum." Electromagnetic waves, from X-rays to radio waves, have been quite thoroughly explored for metallurgical use, but the sound spectrum, extending from low-frequency vibrations involved in certain types of metal failure by fatigue through the range of audible sound to inaudible vibrations having frequencies of many kilocycles, has had only meager consideration from metallurgists. Because of the general interest in the process recently demonstrated by St. Clair3 for flocculating smoke by means of sound waves, this article is written to point out possible applications of sound and supersonic (ultrasonic) waves in the metallurgical industry.

Jan 1, 1937

A tough Conservation Act has been in force in Pennsylvania since January, 1964. Known as the Bituminous Coal Open Pit Mining Conservation Act, it is now under study by other coal producing states, and seems likely to serve as the blueprint for similar legislation elsewhere. It provides for the conservation and improvement of areas of land affected by open pit mining to decrease soil erosion, prevent pollution of rivers and streams, prevent combustion of unmined coal and generally improve the use and enjoyment of such lands. The cost of backfilling may go to as much as 40[c] or more per recovered ton and is cutting deeply into already reduced profit margins brought on by rising labor and equipment costs, static coal prices and less accessible coal. As a result, operators will be forced to seek greater efficiency.

Jan 7, 1965

By George W. Pawel

OWING largely to its value as a toughener and strengthener of steel for both industrial and military purposes, nickel is playing, an important role in the current war. It is fine of the metals in which the Allies enjoy a definite edge over the Axis nations and this time there is no place to which the Germans may send another submarine "Deutsehland" and expect to pick up a cargo of nickel to replenish their exhausted supplies. Total world nickel production thanks almost entirely to the expanded operation of the International Nickel Co. of Canada at Sudbury must now be at the rate of around 175,000 tons a year scarcely more than 5 per cent of which is accounted for by Germany, Italy and Japan. This represents more than four times the world output at the end of the first World War.

Jan 1, 1943

By Carle R. Hayward

ATHOUGH there are signs of improvement in the lead industry, conditions are still far from what we have been accustomed to call normal. There has been little to stim¬ulate research and those responsible for the finances of the companies have been inclined to discourage expenditures except where need was urgent or the prospect for immediate returns bright. In spite of this fact, improvements have been developed here and there which will be available as business conditions become adjusted. No publicity is allowed at present. The rising price of silver has had a tendency to increase the production of lead from argentiferous ores but the greatest interest continues to be in the secondary field. Practically all lead plants situated near large centers of population are treating scrap materials, particularly battery plates, the quantity of which is increasing with the improvement in automobile sales.

Jan 1, 1936

By AIME AIME

JOHN LIVERMORE CHRISTIE belongs to that group of metallurgists who entered the industrial field during World War I and have been responsible for many of the important metallurgical developments since that time. He was born in Montclair, N. J., on Jan. 31, 1894. After graduating from Montclair High School he attended Sheffield Scientific School, Yale University, received his Ph.B. degree in chemistry in 1915 and that same year was employed by the Bridgeport Brass Co. in its laboratory. Among his first duties was the return to Sheffield Scientific School for two years of graduate work in metallography under C. H. Mathewson; receiving his M.S. degree in 1917. Thus we see him becoming one of that group of eminent physical metallurgists who, with Dr. Mathewson's teaching as a foundation, have done outstanding work in metallurgy.

Jan 1, 1945