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By R. S. Wagner, W. C. Ellis

A new mechanism of crystal growth involving oapor, liquid, crnd solid phases explains many observations of the effect of implurities in crystal growth from the vapor. The role of the impuuitq is to form a liquid Solution with the crystalline tnalerial to be grown from the vapor. Since the solution is n prefevred site for deposition firorti the uapor, the liquid becorrles supersaturated. Crystal growth occurs by precipitatzon from the supersaturated liquid crt tlie solid-liquid zntevfnce. A crystalline defect, such as a screw dislocation, is not essetztial for VLS (vapor -liquid-solid) growth. The concept of the VLS mechanism is discussed in detail with reference to tire controlled growth of silicon crystals using gold, platinum, palladium, nickel, silver, or copper as an implurity agent. RECENTLY a short communication' described a new concept of crystal growth from the vapor, the VLS mechanism. In this paper we present a detailed description of the process and its application to the growth of silicon crystals and we discuss its relevance to existing concepts of .'whisker" crystal growth. Crystal growth from the vapor is usually explained by a theory proposed by Frank2 and developed in detail by Burton, Cabrera, and Frank.3 In this theory a screw dislocation terminating at the growth surface provides a self-perpetuating step. Accommodation of atoms at the step is energetically favorable, and is possible of much lower supersatu-ration than required for two-dimensional nucleation. Crystals of a unique form resulting from aniso-tropic growth from the vapor are "whisker" or filamentary ones. Such crystals have a lengthwise dimension orders of magnitude larger than those of the cross section. For most filamentary crystals both the fast-growth direction and directions of lateral growth have small Miller indices. The special growth form for a whisker crystal implies that the tip surface of the crystal must be a preferred growth site. sears4 proposed that, according to the Frank theory. a whisker contains a screw dislocation emergent at the growing tip. Such an axial defect provides a preferred growth site and accounts for unidirectional growth. The hypothesis was extended by Price. Vermilyea. and Webb," still implying the presence of a dislocation at the whisker tip. They postulated that impurities arriving at the fast-growing tip face become buried while those arriving on the surface of slow-growing lateral faces accumulate and thereby hinder growth. These considerations led to a whisker morphology. There is increasing evidence that most whisker crystals grown from the vapor are dislocation-free. Webb and his coworkers6 searched for an Eshelby twist7 in zinc? cadmium, iron. copper, silver, and palladium whisker crystals. They found unequivocal evidence for an axial screw dislocation in only one element, palladium. However, not every palladium crystal examined contained a dislocation. Observations with the electron microscope have failed to show dislocations in whisker crystals of zinc, silicon.9 and one morphology of AlN.10 Since many whiskers are completely free of dislocations, an axial dislocation does not appear to be required for whisker growth of many substances. A significant advance in understanding whisker growth has been a recognition of the need for impurities. This requirement has been clearly demonstrated for copper,11 iron,13 and silicon9-1 whiskers. For silicon, detailed studies proved conclusively that certain impurities, for example, nickel or gold, are essential. Another pertinent phenomenon which has received little attention is the presence of a liquid layer or droplets on the surface of some crystals growing from the vapor. Crystals in which this has been observed include p-toluidine,14 MoO3,15 ferrites,16 and silicon carbide.'" The liquid layers or globules were considered to be metastable phases, molecular complexes, or intermediate polymers originating from condensation of the vapor phase. The possibility has been suggested that the halide being reduced is condensed at the tip18 or adsorbed on the surface11 of a growing metal whisker, for example copper. The literature on whiskers discloses illustrations of rounded terminations at the tips. These appear. for example, on crystals of A12O3,19,20 sic,21 and BeO.22 For BeO, Edwards and Happel suggested that during growth of the whisker the rounded termination consisted of molten beryllium enclosed in a solid shell of BeO. A recent paper9 on the growth of silicon whiskers contains many observations pertinent to an understanding of the mechanisnl of whisker growth. These observations are summarized as follows. 1) Silicon whiskers are dislocation-free. 2) Certain impurities are essential for whisker growth. Without such impurities the silicon deposit is in the form of a film or consists of discrete polyhedral crystals.

Jan 1, 1965

By R. C. Ku, A. J. McEvily, T. L. Johnston

The microplastic response of a series ofas-quenched Fe-Ni-C martensites has been measured at 77°K. At strains less than JO'3 the flow stress is governed primarily by the transformation-induced dislocation structure of the martensite. Only at strains in excess of 10-3 is the influence of carbon manifested in the flow stress. At these macroscopic strains, typically 10-2, the solid-solution hardening is proportional to (wt pct C)1/3, and, in an alloy containing 0.39 wt pct C, amounts to 50 pct of the flow stress. THE technological significance of high-strength ferrous martensite has stimulated many investigations of its structure and properties. Although our knowledge of the characteristics of martensite has increased immensely, especially with the advent of high-resolution techniques, an understanding of the basic strengthening mechanism still remains elusive. The purpose of the present paper is to consider certain aspects of micro-plastic behavior of Fe-Ni-C martensite which we feel can help to resolve this important problem. Such alloys are particularly suitable for experimental investigation because their compositions can be adjusted to reduce the M, to a temperature low enough essentially to eliminate the diffusion of carbon in the freshly formed martensite.1 The mechanical properties in this condition are of interest inasmuch as they reflect a state that is free of the important but complicating influence of precipitation processes. In this virgin martensite the carbon is distributed as it was inherited from the parent austenite; i.e., it is present interstitially, and gives rise to tetragonality through strain-induced ordering.' In order to determine the source of strength of such alloys, Winchell and Cohen1 investigated the low-temperature macroscopic stress-strain behavior of a series of virgin martensites of increasing carbon content but of common M, temperature (-35°C). They found that the flow stress increased rapidly with carbon content up to 0.4 wt pct; beyond this point the flow stress increased at a much slower rate. It was concluded that martensite is inherently strong. To account quantitatively for the strength of virgin or as- quenched martensite in terms of the role of carbon, Winchell and cohen3 suggested that the carbon atoms, trapped in their original positions by the diffusionless martensite transformation, interfere with dislocation motion according to a model akin to that of Mott and Nabarro. 4 In this treatment, individual carbon atoms are considered to constitute centers of elastic strain and thereby generate an average stress resisting the motion of dislocations throughout the lattice. The additional stress necessary to move dislocations, over and above that necessary for motion in a carbon-free martensite, is given by where L is an effective length of dislocation capable of motion. L was assumed to be limited to the spacing between the twins that are an essential structural element of Fe-Ni-C martensites. They assumtd the spacing to be invariant and of the order of 100A. However, recent work5 has shown that L is variable and can be in excess of 1000Å, so that the assignment of an appropriate value of L is not straightforward. In contrast to the above conclusion that there is an intrinsically high resistance to plastic flow, it has been suggested by Polakowski6 that freshly quenched martensite is in fact "soft" in the sense that dislocations are initially free to move upon application of stress. The high indentation hardness and macroscopic yield stress of ferrous martensites are then a consequence of rapid strain hardening that depends upon carbon in solution. Consistent with this point of view are the results of Beau lieu and Dubé who measured the rate of recovery of internal friction as a function of aging (tempering) temperature in a freshly quenched steel containing 0.90 wt pct C, 0.37 wt pct Mn, 0.1 wt pct Cr, and 0.07 wt pct Ni. The kinetics were clearly consistent with the idea that many dislocations are unpinned in the as-quenched state and that during aging they become progressively pinned by carbon at a rate controlled by carbon diffusion in the body-centered martensite lattice. In order to provide a basis upon which to distinguish between the "hard" and "soft" interpretations indicated above, we have made studies of the initial stages of plastic deformation in Fe-Ni-C martensites similar to those'used by Winchell and Cohen. It will be shown that the results support the contention that dislocation segments in as-quenched material are indeed

Jan 1, 1967

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner' makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,' is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors'' derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel' terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones'" initiates steady-state

Jan 1, 1967

By S. A. Falconer

Much attention and publicity has been given, during recent years, to grinding, classification, flotation, and thickening. The various technical papers, and symposiums held to discuss these important phases of milling, have contributed to a better under- standing of the fundamental principles and operating variables involved. Another important part of milling- to the flotation operator-is a treatment step to which frequently too little attention is given-" conditioning," or the treatment the ground mineral pulp receives before it enters the flotation machines. Conditioning" is a hackneyed and frequently misused term, commonly employed to describe the pretreatment of surfaces of minerals in ore pulps or mill pr6ducts prior to froth flotation. In general, such pretreatment is for the purpose of changing the flotation characteristics of these mineral surfaces to enable them to respond in some desired predetermined manner when subjected to flotation. Taggartl states that the function of conditioning is "either to insure selective collector coating of one mineral species while another species is not; or to take such steps as will compensate for departure there from."

Jan 1, 1949

By George W. King

The yield strength of a dispersion-hardened W-3.8 vol pct Tho,alloy, in both the recovered and recrys-tallized condition, was investigated and cornpared with that ofrecrystallized pure tungsten over the temperature range of 325" to 2400°C. It is deduced that the Orowan mechanism is obeyed in the recrystallized alloy. In the recovered alloy, a further enhancement of the yield strength results from the retained substructure which is stable up to temperatures in excess of 2700°C. Temperature and strain rate cycling tests were also performed, and the apparent activation energy for the deformation process was derived. This activation energy, - 3 ev, for the recovered and also the recrystallized alloy was about the same as that for re crystallized pure tungsten. However, the activation volume of the recovered alloy, -10-2 cu cm, was about an order of magnitude lower than that of the recrystallized alloy or pure tungsten. This fact accounts for an enhancement oj- the temperature dependence of the yield stress of the recovered alloy. A dislocation velocity exponent of about 4 to 13 was deduced frorn the strain rate cycling tests , which is in good agreement with values reported for tungsten single crystals. VARIOUS theories have been developed to explain the enhanced yield strength of a metal containing a dispersed second phase of small hard particles. These theories are thoroughly reviewed by Kelly and Nicholson.' The theoretical models can be separated into two types. The first type assumes direct interactions between moving dislocations and dispersoids. One of the most widely investigated models for this mechanism is the bowing out of dislocations between the dis-persoids and their subsequent pinching off in order to bypass the obstacles. This is the well-known Orowan mechanism.' The second type is an indirect effect of the dispersion because of its ability to stabilize to high temperatures the substructure introduced by cold working. In this instance, the increment in the yield strength is expected to be inversely proportional to the square root of the subgrain diameter. In the present work, a quantitative study was made of the strengthening effect caused by a thoria dispersion in a recrystallized W-3.8 vol pct Thoz alloy over the temperature range 325" to 2400°C. The results are compared with the increment predicted for the Orowan mechanism based on the calculations by ~shb~.~ In addition, the alloy was tested in the recovered state so that any additional strengthening resulting from the substructure produced during fabrication could be measured. The respective contributions can be separated in this manner, provided that the particle size distribution of the dispersion remains the same in both the work-hardened and the recrystallized state. Particle size distribution measurements showed that this condition was met in the present work. I) EXPERIMENTAL PROCEDURES A) Material Production and Fabrication. The alloy investigated is essentially the same as that reported much earlier by ~effries,~ who also found the strength of tungsten to be improved by the thoria dispersion. The procedure for producing the alloy consisted of mechanically blending a thorium nitrate solution in proper concentration with tungsten oxide (WO3) powder, followed by hydrogen reduction to metal powder. After reduction, the dispersed second phase is present as thoria (Thoz). The pure tungsten powder used for comparison was produced in the same manner except that the thoria doping step was omitted. The powders were consolidated by cold pressing and self-resistance sintering in hydrogen. The resulting ingot had a cross section about 0.6 sq in. and a density about 93 pct of theoretical. The ingot was swaged to 0.174-in.-diam rod at temperatures varying from 1650°C initially to -1200°C near final rod sizes. Two intermediate recrystallization anneals were employed during fabrication. Analysis of the swaged rods is reported in Table I. B) Electron Microscopy Techniques. Carbon extraction rrPxcas prepared by a technique reported by ~00' were used to quantitatively evaluate the thoria particle size and distribution. Electron nlicrographs of extraction replicas were taken at 20,000 times but were then enlarged two to three times in printing. The areas photographed were randomly selected. A Zeiss Particle Size Analyzer (Model TGZ3) was used to count and measure the sizes of all particles present on the print. About three thousand particles were counted in determining a distribution curve. Electron transmission microscopy was used to determine the effect of annealing on the substructures of the materials. Thin foils were produced by a two-stage thinning process. The rods were first ground on emery paper to ribbons about 10 mils thick and then a jet of 5 pct KOH was used to electrolytically reduce a portion of the cross section of the ribbon. Final perforation was achieved by immersing the specimen in a 5 pct KOH solution and electrolytically polishing at a current density of about 0.3 amp cm-'. The foils were examined with a Hitachi HU-11A electron microscope. C) Tensile Testing. Tensile testing was performed in an Instron Testing Machine equipped with a radiation-type vacuum furnace which operates at about 1O"S torr at temperatures as high as 2400 °C. The same furnace was used for annealing the tensile specimens.

Jan 1, 1970

By J. B. Clark

In 1933, R. paris1 published a phase diagram for the entire Mg-Ca-Zn system. He reported the existence of a ternary intermetallic phase, Mg5Zn5Ca2, which formed a quasi-binary with the magnesium solid solution. Since then, no extensive work has been reported on the system. Recently however, indications of the existence of a second ternary in-termetallic phase in equilibrium with the magnesium solid solution led to a reinvestigation of the solid phase equilibria involving the magnesium solid solution. The 335°C (635°F) isothermal section was chosen for study. Metallography and powder X-ray diffraction were selected as the best mutually corroborating methods for determining the solid phase constitution. Seventy-six alloys were prepared from singly sublimed (99.95 pct) magnesium, electrolytic (99.95 pct) zinc and USP calcium. The analyses of some of the alloys are shown in Fig. 1. The alloys were melted in a graphite crucible under a chloride flu and chill cast in a split graphite mold. Dif-fusion couples (see Fig. 2) were prepared by casting molten Mg-20 wt pct Zn alloy around a cylinder of Mg-30 wt pct Ca alloy. The alloy samples and the diffusion couples were sealed under argon in Pyrex vials and annealed in a furnace capable of controlling within 1/2°C of 335°C. At the conclusion of the anneal, the alloy samples were quenched in ice water and the diffusion couples were air cooled. Procedures standard for magnesium alloys were used for metallographic examination. Powder X-ray diffraction patterns were taken on a G. E. camera with a 14.32 cm dim using nickel-filtered copper radiation. The redetermined 335°C (635°) section of the Mg-Ca-Zn phase diagram is shown in Fig. 1. TWO ternary intermetallic phases, designated w and

Jan 1, 1962

By A. Grant Elliot, H. W. Lavendel

qualitative picture has been developed to describe the oxidation behavior of TaSi2-coated tantalum and CbSi2-coated columbium. These systems have a significantly lower inherent oxidation resistance than MoSi2-coated molybdenum does. This stems primarily from the fact that Ta2O5 and Cb2O5 are nearly as stable thermodynamically as SiO2, whereas MoO2 or Moos are not. Further, diffusion of silicon in the Ta- and Cb-Si system is considerably slower than in the Mo-Si system. These ,factors prohibit the mechanism of selective oxidation of- silicon which accounts for the oxidation resistance 01- MoSi2-coated molybdenum. The silicide can be stabilized by adding suitable Modifiers which increase the thermodynamic stability of the silicate formed during oxidation. Modifiers, such as aluminum, can be inroduced into solid solution in the coating. in controlled amounts through proper selection of the source in the pack cementation process of coating fov~rzatiorz. Addition of aluminum to TaSi2, coatings on tantalum was effective in moderately increasing the oxidation resistance. EXTENSIVE experimental work and analysis have established the nature of the oxidation behavior exhibited by MoSi2- and MoSi2 -coated molybdenum-base alloys, and defined the conditions for maximum protection against oxidation of the substrate.'-* The oxidation resistance of MoSi2 in the temperature-pressure range of 1100°C-PO2 > 10-5 atm to 1900°C— PO2 > 10-1 atm is due to the formation at the surface of a continuous film of SiO2 which results from selective oxidation of silicon. Under the prevailing kinetic conditions, this film is stable toward the molybdenum silicide with which it comes in contact. Initially molybdenum oxidizes also, but it forms volatile species. SiO2, however, nucleates and grows as a condensed phase. Once a continuous film of SiO2 has formed, the oxidation rate falls to that observed for the oxidation of pure silicon indicative of diffusion through the oxide film as the rate-controlling mechanism. This oxidation behavior is of course highly dependent upon temperature and oxygen pressure. Bartlett and Gage13 and Bartlett, McCamont, and Gagelb define precisely this dependence in terms of the oxygen partial pressures and silicon diffusivities required to support a stable SiO2 film. At low temperatures (near 500°C—the "pest" region) silicon diffuses too slowly to be selectively oxidized. Hence, molybdenum and silicon oxidize readily in proportion to their stoi- chiometry. At high temperatures and low pressure, SiOz dissociates to form volatile SiO(g), and a protective film cannot be maintained. Application of the MoSiz/Mo system is limited to temperatures below 1900oC, the eutectic between MoSi, and MO5Si3.5 The oxidation behavior of MoSi2-coated molybdenum is essentially the same as that outlined above with the exception that the MoSi2 is not in equilibrium with the molybdenum substrate. At the temperatures under consideration silicon will diffuse rapidly into the molybdenum eventually converting the coating to MosSi3.4 The rate constant for subsequent decomposition of Mo5Si3 into Mo3Si plus silicon, and/or the diffusivity of silicon through Mo3Si then becomes low enough to allow active oxidation of both molybdenum and silicon with subsequent degradation of the specimen. A stable silica film can be formed but at temperatures and/or oxygen partial pressures higher than those required with MoSi2 present as a source of si1icon.l, 4 Because of the similarity between the silicides of molybdenum and those of columbium and tantalum one would expect similar oxidation behavior for coatings in the respective systems. This is not entirely the case, however, as shown by the experimental results reported herein. Regarding tantalum and columbium disilicide coatings on tantalum and columbium substrates, respectively, the oxygen arriving at the surface of the coating partitions itself nearly equally between the metal and the silicon, and a two-phase oxide layer (Me2O5 plus SiO2) is always formed. The diffusion of silicon in the tantalum and columbium silicides is relatively slow, compared to that in the molybdenum silicides, which further enhances this equipartitioning of oxygen. Thickening of the coating during service by inward diffusion of silicon into the substrate is correspondingly slow, and the effective thickness of the coating at the roots of cracks and defects is only slightly changed providing high probability for premature coating failure. Furthermore, the SiO2 glass that is generated is not thermodynamically stable with respect to the coating. The metal silicide tends to reduce the SiO2 liberating either free silicon or SiO. The situation can be improved by suitably modifying the coating such that the stability of the protective glass which is generated during service is increased. Thus, selective oxidation of silicon and the modifying agent will occur, and the silicide coating will not tend to reduce the oxide layer. Modifying agents can be introduced into the coating by the pack cementation process. Using sources containing the modifier at controlled chemical potentials allows control of the coating composition. Partially substituting aluminum for silicon in TaSi2 coatings by forming a Ta(Si,Al)2 solid solution was effective in moderately increasing the oxidation protection.

Jan 1, 1968

By John D. Wiebmer

First, a definition of a small scale miner is in order. The US Bureau of Mines classifies him as one who produces 360 t/d (400 stpd) of ore or less. In Canada, he would be refered to as a "junior company." Mexico identifies the small scale miner as one whose gross income from operations is less than $880,000 per year. A small surface mine in India employs less than 400 people, and a small underground mine employs less than 150. Peru considers a small scale miner one who produces less than 54 000 t/y (60,000 stpy) of ore. Obviously, the term is relative. What may be a small mine in one country is a medium or large mine in another. This lack of agreement is understandable since small scale mining does not often cross national boundaries. Rather, its effects are felt at the regional and local levels within each nation. Its importance doesn't lie with any huge contribution to the GNP or balance of trade. Instead, its value is as a local employer and as a frontrunner in geologic exploration.

Jan 2, 1979

By Walter Renton Ingalls

IN SEVERAL papers and addresses during the past two years, I have dwelled upon some of the economic consequences of the war. The fundamental thought that I have sought to convey is that the world became immensely poorer by the war, not only in material wealth and population, but also in the psychology and morale of the people. I do not see how there can be any intelligent dissent from that statement. All the ideas of post-war prosperity were manifestly fallacious, manifestly fallacious from the outset. If there had been any truth in them it would have followed logically that a great war, with all its destruction of wealth, health and life would be a good thing. Therefore, let us have a great war every ten years or so. Such an idea would be both monstrous and absurd. Assuming then the acceptance of my premise, I have tried to show that the losses by the war could be made good in a short time, i.e., in a relatively short time, only by doing things a great deal better than formerly, and that the accomplishment of such a result called for greater transparency in industry, for industrial cooperation, for thinking in terms of industries as a whole, and for the greater exercise of engineering functions. All of this introduced, of course, the position and psychology of labor. I say frankly that I do not look for labor to contribute any constructive thought to the upbuilding. I neither expect it nor hope for it. This is a pity, for it could do so much for its own economic advancement if it would. However, it never has done so, but rather has benefited only from the exercise of the talents of the few, and the main hope now is to bring it into a passive state, dispelling the resistive fallacies that developed during the war. Let us briefly examine the nature of these.

Jan 1, 1921

By R. A. Wattenbarger, H. J. Ramey

A systematic study has been made of the application of the real gas pseudo-pressure m(p) to short-time gas well testing. The m(p) function can be used in real gas flow problems to account for the variation of viscosity and z-factor with pressure. A mathematical model was solved numerically to generate solutions of various real gas flow problems. The effects of turbulence, formation damage and wellbore storage were included in the model. The analysis of simulated well tests showed that the interpretation methods normally used for liquid flow are generally accurate when the m(p) is used. For practical rates without turbulence, the solutions are not rate-sensifive, and the flow capacity.. kh and skin effect can be determined accurately from either a buildup or a drawdown test. However, the kh calculated from a drawdown test can be significantly low when turbulence is present. A case was simulated in which this error wa.s 36 percent. Turbulence does not affect the determination of kh from buildup tests. The proper determination of kh from p and pa buildup and drawdown plots is developed by analyzing their relationship to the m(p) method. A simple equation is given that can be used for long-range gas well performance forecasting. This expression is compared with a method pre-sended by Russell et al." Introduction The formation flow capacity and wellbore damage condition can be determined for liquid-producing tests by means of buildup and drawdown tests. These tests make use of short-time pressure transient data rather than stabilized flow tests that are often used for gas well testing. Tracy' presented a method of gas well testing that was based on ideal gas equations and utilized p2 buildup plots. This method was shown to be good for low pressure wells. MatthewsZ suggested plotting p and using an average slope and average gas properties. This method was more successful on high pressure wells. Al-Hussainy, Ramey and Crawfordh howed that variation in gas properties could be simplified by using the real gas pseu do-pressure m(p). Some cases showed that the use of the m(p) function Original manuscript received in Society of Petroleum Engineers office Aug. 8. 1967. Revised manuscript received June 11, 1968. Paper (SPE 1835) was presented at SPE 42nd Annual Fall Meeting held in Houston Tex., Oct. 1-4. 1967, and at SPE 4th Annual Eastern Regional ~eetin$ held in Pittsburgh. Pa., Nov. 2-3. 1967. 0 Copyright 1968 American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. 'References given at end of paper. provided an accurate method of interpreting buildup and drawdown tests. Because the work of Al-Hussainy et al. included only a few actual cases, there was a need to explore the use of the m(p) method for a greater variety of flow conditions. The occurrence of turbulent flow around the wellbore often is an important factor in gas well testing. Swift and Kiel,' and Carter et a1.' treated turbulence in gas well testing, but did not consider the variation of viscosity and z-factor with pressure. This paper presents the results of an investigation of the application of the m(p) method to buildup and drawdown testing. Vhe investigation included the effects of turbulence, formation damage and wellbore storage. Gas Flow Equations To formulate the mathematical model, many of the assumptions usually used in well testing theory are applied. The system has radial geometry with a closed outer boundary and is composed of a horizontal porous formation that has uniform and isotropic rock properties and uniform thickness. Allowance is made, however, for a radial region of reduced permeability near the wellbore. This region represents formation damage. The geometry of the system is shown in Fig. 1. Darcy's law does not always apply to gas flow. A more general expression is needed for non-Darcy, or "turbulent" REGION OF DAMAGED PERMEABILITY SEALED BOUNDARIES ClRCULAR WELL BORE Fig. 1—Radial flow model. AUGUST, BT7

Jan 1, 1969

By J. S. Marsh

AN incomplete statistical analysis performed wearily on the morning after Thursday, Feb. 12, indicates that the unavoidable items of conversation among steelmen were the current shortage of sleeping time and the "Normandie." No analysis is needed, however, to be certain that many thousands of valuable words were uttered, both in and out of technical sessions, concerning matters of deep interest to members of the Iron and Steel Division. The opening session consisted mostly of papers that have appeared, or will appear shortly, in Metals Technology. One, however, that was not finished in time to be printed in any form, but that aroused great interest, was by E. L. Ramsey and L. G. Graper (Wisconsin Steel Works). Its subject was the production of high-sulphur steel by treatment with sulphur dioxide derived from anhydrous sodium sulphite or bisulphite added to the ladle or to the mold. The sulphide distribution in the finished steel is such that increased machinability and longer tool life result. Both items are of obvious importance in these days of mighty production.

Jan 1, 1942

By R. J. Evans

THE Combined Metals Reduction Co.'s plant is at Bauer, Utah. It was built primarily to treat ore from the Combined Metals mine at Pioche, Nevada. Shortly after its completion, the company acquired the old Honerine mine, and ores from this mine, as well as custom ores from widely scattered districts, are now being treated at the Bauer plant. PIOCHE ORE The Pioche ore, which comprises about 50 per cent. of the mill feed, occurs as a replacement of an impure thin-bedded limestone. The lime beddings are separated by thin layers of micaceous shale containing appreciable quantities of sericite and graphite. The ore is an exceptionally fine-grained, dense mixture of minerals and gangue, assaying approximately 0.03 oz. gold, 7.2 oz. silver, 7 per cent. lead, 15 per cent. zinc, 16 per cent. iron, 29 per cent. insoluble and 1.5 per cent. lime. Of the total lead 7 per cent. is in the form of sulfate and carbonate. Approximately 10 per cent. of the ore consists of chert nodules impregnated with barren pyrite; the nodules average 0.8 mm. in size, and are extremely hard, compared with the other constituents of the ore. Microscopic examination of Pioche ore ground to 80 per cent. minus 150 mesh shows pyrite, sphalerite and galena still attached. EARLY ATTEMPTS AT ORE DRESSING Metallurgists, both professional and those working for private companies, have been more or less familiar with the Pioche ore since 1913; in fact, a total of 35 commercial and plant laboratories experimented with the ore between 1913 and 1921. The work during this period was decidedly negative, it being seemingly impossible to effect a satisfactory separation of the valuable minerals into marketable products. In 1913, it was recognized that fine grinding-that is, about minus 200 mesh-was required to liberate the minerals from one another, and from the gangue, but such fine grinding was not considered practicable at this time.

Jan 1, 1928

By Joseph Hyde Pratt, Douglas B. Sterrett, CHAPEL HILL

I. DESCRIPTION. MONAZITE is one of the minerals which, for a long time, was considered rather rare in its occurrence, but, upon a commercial demand arising for it, prospectors and engineers soon located large deposits of it in the Carolinas and Brazil, and the supply has always been able to meet the demand. During 1908 further sources of supply of monazite have been discovered and developed in Idaho. North and South Carolina, however, are the only States that have thus far put any monazite on the market. Monazite is essentially an anhydrous phosphate of the rare-earth metals, cerium, lanthanum, and didymium (Ce, La, Di)PO;. There is nearly always present a varying but small percentage of thoria, ThO2, and silicic acid, SiO, which are very probably united in the form of a thorium silicate, ThSiO4 Some monazites contain but a fraction of a per cent. of thoria, while others have been recorded that showed the presence of from 18 to 32 per cent. ; but the majority contain from 3 to 9 per cent. of this oxide. It is the presence of the thorium oxide that gives the monazite its commercial value. The analysis occasionally shows also the presence of other constituents, as the yttrium and erbium oxides, zirconia, alumina, magnesia, lime, iron oxides, manganese oxide, and titanium oxide. Monazite is light-yellow, honey-yellow, reddish-, brownish-, or greenish-yellow in color, with a resinous to vitreous luster, and is translucent to subtransparent. It is brittle, with a conchoidal to uneven fracture, and is from 5 to 5.5 in hardness, and from 4.64 to 5.3 in specific gravity. It crystallizes in the monoclinic system, and some crystals have been observed that were 6 in. in length. The more perfect crystals are, however,

Jun 1, 1909

By A. C. Stevenson

THE hoisting equipment selected for use at the Hecla mine in 1907 was one of the first Ilgner type Ward-Leonard controlled hoists put into ser- vice. Development of the Hecla below the 2000-ft. level, which is the ultimate depth of the old equipment, and the additional service required by the "Star," necessitated additional hoisting capacity. It will be our endeavor to give j70u a brief summary of the engineering which determined the selection of the new equipment. The engineer in making his decision as to size, speed, etc., must .make a duty study approximating as closely &s possible the actual opePating conditions which will eventually result. Primarily, it is necessary to know what work must be done. The amount of material which must be hoisted under the maximum condition, as well as its distribution from the various levels of the mine was carefully studied by the mining engineering department, as the ore reserves, their relative-position and the probable method of working them had to be considered. The final figures reached, taking into consideration four different operating conditions, were, in tons per day, as follows:

Jan 1, 1930

By C. BARING HORIVOOD

(Chattanooga Meeting, October, 1908.) THIS paper is intended, in the light of recent investigations, to call attention to some of the essential features of good practice in sampling and mine-valuation. Mine-sampling may be divided broadly into two classes : (1) development-sampling and computation of ore-reserves; and, (2) stope-sampling and estimation of stope-values. DEVELOPMENT-SAMPLING. It is with development-sampling only that this paper deals-the term development being taken to mean the opening-up of a mine by cross-cuts, drives, connections, etc., preparatory to actual extraction of the ore for milling. In development-sampling the work of the sampler and the consequent estimation of the probable value of the mine or portions of the mine, as the case may be, cannot be verified until a later period, when the ground thus sampled has been exploited; hence, extreme care and accuracy are essential. Moreover, the development-sampler has to foresee and allow for contingencies which may arise when stoping is started. It follows that the sampling, in development-work, demands familiarity with the conditions likely to be encountered later in actual mining. In stopes, on the other hand, sampling is clone under actual working-conditions, and the sampler's valuations are immediately checked by the gold-output, or in some cases by a second sampling of the broken ore. A stope-sampler therefore need not be an experienced miner, though he should possess sound technical training and work accurately. Should he be somewhat inexperienced, be soon has his errors discovered for him, and learns to avoid them. Taking these facts into account, it is obvious that a mining company employing two or more samplers should

Jan 1, 1909

By Knapp. Arthur

THE ORDINARY well log is subjected to a great deal of criticism, much of which is well founded. Sometimes, though, the difficulty in interpreting the log is due to the fact that the geologist or engineer using the logs does not know the limitations of the drilling method used. The rotary drill, especially, has inherent limitations that make it difficult, to secure .definite information at all times. The identification of well-defined key beds is about all that can be expected from the rotary log. The formation in a drilled hole, as reported by the driller; has a direct relation to the speed with which the drill makes the hole or to the reaction of the various strata on the bit, called the "feel of the bit." When this is not thoroughly understood by the geologist or engineer endeavoring to interpret the log, the result is an erroneous correlation with other wells or a discarding of the log as worthless. GENERAL TERMS Hard and Soft.-Hard and soft are relative terms. In the case of well logs, they are very misleading as they are used in connection with both resistance to abrasion and resistance to percussion. In technical rock classification, hardness is relative resistance to abrasion. The term brittleness is used in connection with resistance to blows. These terms are misleading to the geologist or engineer who is not familiar with both the cable-tool, or standard tool, method of drilling and the rotary method. In the case of the standard tools, the driller's report of the hardness of the formation is in terms of its resistance to blows. For instance, a cable-tool driller might be able to make from 30 to 50 ft. a tour in a brittle limestone, which he would call soft and at the same time he might call a relatively soft (from a purely mineralogical standpoint) gypsum hard, because it is somewhat elastic and is not readily broken by blows. The rotary driller would reverse the terms. The limestone is hard in that it resists the abrasive action of the bit, while the gypsum might be soft in that it is readily cut by the rotary bit. It is rare that wells drilled by the

Jan 2, 1920

By AIME AIME

TWO days of solid discussion, with barely time out for meals, characterized the Tulsa meeting of the Petroleum Division. It was preeminently an earnest gathering devoted to technical matters. Sessions were held in the Crystal room of the Mayo Hotel with luncheon served each day in the back of the same room so that talk of methods, while slightly less formal, extended right through the lunch hour. Thursday evening the Committee did provide a little relaxation in an informal dinner at the Tulsa Club where, after a brief musical program and an amusing skit by the local Herman the Great, brief addresses in non-technical vein were made by President Farish and Vice-president Rice of the Humble Company, Henry L. Doherty of Cities Service, Secretary. Bain of the Institute, and others. The presence of leading executives of a number of the oil companies at the dinner and the sessions, and the cordial approval they expressed of the work of the Division were especially gratifying. The total registration was 215 with 100 at the dinner and 70-to 80 lunching together each day.

Jan 1, 1930

By R. J. Evans

The Combined Metals Reduction Co.'s plant is at Bauer, Utah. It was built primarily to treat ore from the Combined Metals mine at Pioche, Nevada. Shortly after its completion, the company acquired the old Honerine mine, and ores from this mine, as well as custom ores from widely scattered districts, are now being treated at the Bauer plant. Pioche Ore The Pioche ore, which comprises about 50 per cent. of the mill feed, occurs as a replacement of an impure thin-bedded limestone. The lime beddings are separated by thin layers of micaceous shale containing appreciable quantities of sericitc and graphite. The ore is an exeeptionally fine-grained, dense mixture of minerals and gangue, assaying approximately 0.03 oz. gold, 7.2 oz. silver, 7 per cent. lead, 15 per cent. zinc, 16 per cent. iron, 29 per cent. insoluble and 1.5 per cent,. lime. Of the total lead 7 per cent. is in the form of sulfate and carbonate. Approximately 10 per cent,. of the ore consists of chert nodules impregnated with barren pyrite; the nodules average 0.8 mm. in size, and ire extrcmely hard, compared with the other constituents of the ore. Microscopic examination of Pioche ore ground to 80 per cent . minus 150 nicsh shows pyrite, sphalerite and galena still attached. Early Attempts at Ore Dressing Metallurgists, both professional and those working for private companies, have been more or less familiar with the Pioche ore sinee. 1913; in fact, a total of 35 commercial and plant laboratories expenmented with the ore between 1913 and 1921. The work during this period was decidedly negative, it being seemingly impossible to effeet a satisfactory separation of the valuable minerals into marketable products. In 1913, it was recognized that fine grinding-—that is, about minus. : 200 mesh—-was required to liberate the minerals from one another, and from the gangue, but such fine grinding was not considertd practicable at this time.

Jan 1, 1928

By H. I. Aaronson, H. A. Domian, G. M. Pound

Zener's two-parameter theory of the y a reaction in Fe-X alloys is extended to encornpass austenite-stabilizing as well as fewite-stabilizing elements, and is then cottzbitzed with statistical thermodynamic theories of Fe-C alloys to permit development of a ther-modynamic description of the proeutectoid fewite reaction in Fe-C-X alloys. Equilibrium tielines are calculated for tile a + y rep'on from experimental data and frort extrapolations of the y/y +a equilibrium surface. Sectzovs of the y/y + 0 surface are calculaled for the tzetastable sstuation LYL u-kich alloyrtg eleitzents do not partition betzseen azrstenite andfer-rite. The finding that the metastable y/a + y curves Lie close to their equilibriuwz counterparts when X = Si, .Vo, Co, Al, and Cu but well below them when X = A/ln or Ari pr-elides a thermodunamic explanation for the expcri1?7e?ztally obserted absence of partition during the proeutec toid ferrite reartlon in the fortner alloys and for the occurrence of partition at hzgher ternperatures in the latter alloys. Cotarison ofno- patitzoa free-energy changes and y/y i a curr,es in Fe-C-X alloys with the equilibrium 11al1es of these quantities in Fe-C alloys furnishes additional qualitative insight into the irqluence of allojling elements upon the kinetics of the proeutectoicl ferrite reaction. THE introduction of a substitutional alloying element, X, appreciably complicates calculation of the thermodynamics of the formation of proeutectoid ferrite from austenite. As noted in the preceding paper,' the positional entropy of the interstitial species is the principal component of the free energy of an interstitial solid solution with which theory has so far been able to deal. One would expect, however, that other components of the free energy of this type of solid solution may be significantly altered by the addition of a substitutional alloying element. Even if the assumptions are made, by analogy to the case of Fe-C alloys,' that changes in the positional entropy of carbon represent a significant part of the thermodynamic effects of an alloying element, and that the remaining effects can be taken into account by fitting the equations developed on this basis to experimental data on Fe-C-X phase diagrams or on the activities of carbon in alloyed austenite and ferrite, the experimental information available on either of these quantities is not yet sufficiently accurate or extensive, respectively, to make such an approach useful. An attempt made by Zener on the former basis to explain the effects of alloying elements on the thermodynamics of Fe-C alloys in terms of a temperature-independent "free-energy change" (actually enthalpy hane') required to transfer 1 mole of an alloying element from austenite to ferrite, in which the "free-energy change" was determined by fitting the theoretical relationships developed to Fe-C-X phase diagrams, thus proved inadequate in part because of deficiencies in the available ternary-phase-diagram data.= Other difficulties of a more fundamental nature, however, also indicated the desirability of a different approach to the problem.3y4y6 zener6 subsequently proposed that the free-energy change associated with y — a transformation in pure iron can be decomposed into magnetic and nonmagnetic components. Alloying elements were assumed to affect those components separately. One parameter was used to describe the quantitative effect exerted on each component. These parameters were evaluated from Ms (martensite-start) temperature data and from other experimental information usually either readily available or measurable with acceptable accuracy. Zener applied this treatment only to the calculation of Fe-X phase diagrams in which X is a ferrite-stabilizing element. In the present study, this treatment is extended to include austenite-stabilizing elements, and then combined with treatments previously considered for Fe-C alloys1 to permit calculation of the thermodynamic quantities of interest in the austenite - proeutectoid ferrite transformation in Fe-C-X alloys, where a number of representative, and commonly used alloying elements are chosen for X, including Si, Mn, Co, Mo, Al, Cr, and Cu. The results are used to explain important features of the partition of alloying elements between austenite and proeutectoid ferrite, as reported in a companion paper7 on the basis of electron-probe analysis, and to provide some additional understanding of the influence of alloying elements upon the kinetics of nucleation and growth of proeutectoid ferrite. Portions of this treatment6 have been clarified in the course of a review by Kaufman and Cohen.3 The consolidated summary of these developments with which this section is begun provides a basis for further clarification of the treatment, from which extension to include austenite- as well as ferrite-stabilizing elements is a natural consequence. The division of the free-energy change associated with the 7 - a transformation in pure iron, into two independent components is formally stated as:

Jan 1, 1967

By C. A. Gibbons

AFTER nine years of extremely de- pressed business, marked mostly A with red ink on the balance sheets of most coal companies and with an increasing internal competitive struggle for diminishing markets, somewhat of a change appeared during 1939. Shipments increased and prices generally firmed, giving the coal industry increasing optimism and encouragement for the future. Specifically, it now appears that bituminous coal production for 1939 will approximate 378,000,000 tons, and anthracite production will approximate 47,500,000 tons, bituminous production being around 14 per cent ahead of 1938 and anthracite production 12 per cent better. The curve on p. 31, showing both bituminous and anthracite production, furnished by the bituminous coal division of the Department of the Interior, shows graphically most of the 1939 monthly production and clearly illustrates the increased production.

Jan 1, 1940