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By Chester O. Ensign

Many publications to date have advocated under- seas mining operations, optimistically overlooking the paucity of information on mineral distribution and the ocean environments in which minerals occur. Such articles (smattered with opinion, as is this article) are herein tempered by my more conservative views on the economics of mining under the seas. For purposes of this paper, underseas mining refers only to the deeper surficial deposits of the continental shelf and the deep sea floor, i.e., the deposits of phosphorite and manganese nodules.

Jan 9, 1966

By W. J. Slatosky

As a means of effecting better control of endpoint temperatirres at the Jones & Laughlin basic oxygen furnace plant, a set of mathematical equations has been developed. The eqlutions are the product of a themlochemical anaysis of the process and aye designed to calculate the required scrap, lime, and hot metal additions in terms of a number of independent variables. Results of test heats have warranted adoption of this technique by the Prodrrction Department. BECAUSE of the autogeneous nature of the basic oxygen steel-making process, bath temperature can be controlled without an external fuel supply by charging the furnace with additions that are thermally balanced. The thermal requirements of the charge materials are such that, during the refining process, they throttle the heat generated by the metallurgical reactions in a manner designed to result in a speci-fied temperature at the completion of the heat. In the past, operating personnel at the basic oxygen furnace plant of Jones & Laughlin's Aliquippa Works relied on their experience and technical knowledge of the process to determine the quantities of charge additions needed to result in a finishing temperature in the range 2880"to 2920" F. (The charge consists primarily of 93 tons of scrap and hot metal plus an amount of lime sufficient to maintain a basicity ratio of 2.8 to 3.2). Estimates of these materials are based on a consideration of the effects on finishing temperature of 1) iron silicon content, having a variation of 0.8 to 1.8 pct; 2) iron temperature, ranging from 2250°to 2600°F; and 3)any excessive cooling of the furnace due to a production delay. The end temperature of the preceding heat also serves as a guide in that, if a heat was within the specified temperature range, the succeeding heat could be charged with materials of nearly the same proportions, provided the hot metal used in each of the two charges was of approximately the same temperature and composition. On the other hand, if a heat was outside the specified tapping range, or if the hot metal used in that heat was of different analysis and temperature from that of the iron to be charged, an adjustment in the proportion of additions is in order for the following heat. Due to the complex thermochemical behavior of the process and to the inexact and subjective nature of the described method of determining charge additions, consistently accurate temperature control was not to be expected. Therefore, those heats out- side the specified tapping range necessitated subsequent adjustments by either reblowing the cold heats for a suitable length of time so as to elevate the bath temperature to the desired level, or cooling hot heats with a proper amount of scrap. Because extra time is required to make these adjustments, production is delayed. In an attempt to devise a method for improving temperature control, an analysis of the thermochemistry of the process was undertaken. This, in turn, led to the development of a set of mathematical equations which enable the calculation of the quantities of scrap, lime, and hot metal needed to result in any specified tapping temperature range. The analysis was not intended to be a repetition of work done by others such as McMulkinl or ~hilbrook.' It was meant to be an extension of their work so that charge additions could be calculated not in terms of silicon alone but, rather, as a function of all independent variables. This paper presents the derivation of these relationships, their effectiveness in controlling bath temperatures, and a method of utilizing them on an operational basis. The Heat Balance—The first step undertaken in the analysis of the problem was the enumeration of the pertinent variables. A list is presented in Table I where it is noticed that these quantities have been separated into the following three categories: important variables, variables considered as constants, and variables to be neglected. The breakdown was an arbitrary one designed to facilitate the analysis; otherwise, the mathematical treatment would have been exceedingly cumbersome and complex. Fortunately, experience has shown that these simplifying assumptions do not seriously impair the accuracy of the calculations. These variables along with the limiting assumptions listed in Table n were then used to write a heat balance of the process by applying the equation of continuity, Rate of Rate of Rate of Increase = Income - Outgo PI ] of Heat of Heat of Heat.

Jan 1, 1962

By K. Leutwyler

The key to realistic casing stress analysis in thermal recovery installations is accurate knowledge of the temperatures involved. Much information leading to prediction of heat losses from tubing string to wellbore has been published. This .same information permits calculation of casing temperature under certain conditions. This paper reviews the basis for most of the published work, the line source solution to the diflusivity equation and examines some of its application criteria in the light of unsteady-state conditions. An alternate finite differences method is presented for correlation, and experimental data pertaining to the heat transfer mechanism in the annulus is reported. In the light of the information presented in the paper, it appears that the assumption of a line source for the tubing-wellbore system is valid even for reasonably short periods of heat flow, .such as "steam soak" operations. The empirically modified equation presented earlier matches computer derived results of the finite differences approach lor periods as short as 50 hours. Previously predicted cas ing temperatures and the associated stress levels are thus verified based on these correlative computations and the reported experimental information. Fall out from the computer output resulting in some studies of the influence of insulating cement properties on casing temperature, and experimentally studied effects of nitrogen placed in the annulus at various pressures., are described. INTRODUCTION Generally speaking, predictions of average casing temperatures have been based on an idealized model involving a centralized tubing string at uniform constant temperature radiating energy towards the casing under steady-state conditions.'. ' Heat is transferred away from the casing to the formation by unsteady-state conduction across thermal barriers consisting of cement and the mud sheath. Heat balances written on the casing permit prediction of instantaneous casing temperatures. During early periods of injection, casing temperature varies appreciably as a function of time; however, for long injection times this variation decays as heat flow from the wellbore to the formation stabilizes, and it becomes virtually negligible as conditions surrounding the wellbore become quasi-steady-state (Fig. 1). Carslaw and Jaeger -escribe a solution to the diffusivity equation for a line source (Fig. 2). A constant supply of heat is introduced into the medium from the line placed into the origin of the x-y coordinate system and parallel to the z-axis. Heat spreads outward in the infinite cylindrical solid and the temperature increase on a line going through point (x, y) parallel to the z-axis at a distance r can be predicted by: The following criterion must be considered: the Carslaw and Jaeger equation is obtained on the basis of a large

Jan 1, 1967

By A. H. Larson, L. G. Twidwell

DURING the roasting of zinc sulfide concentrates and by-product recovery from flue dusts, the zinc sul-fate phase may occur in various stages of the processes. In addition to zinc sulfide, other sulfide phases are usually present such as CdS, PbS, CuzS, and FeS. Consequently, the effect of these sulfides on the thermal decomposition of ZnS04 was investigated. Merck high-purity, anhydrous zinc sulfate was used as the starting material. The sulfate was heated under an argon atmosphere, at a rate of 10°C per min. With the first slight indication of decomposition as determined by gas analysis, the sample was removed from the furnace and allowed to cool. X-ray patterns showed no other phase present. It is estimated that less than 0.05 pct of the ZnS04 decomposed. The metal sulfides were also heated under an argon atmosphere to drive off any adsorbed water. The materials were then sized (-200 to +270 mesh), mixed in predetermined mole ratios, and pressed into pellets. The experimental measurement of the reaction rate consisted of purifying the argon carrier gas, continuous flushing of the heated reacting mixture with argon, and collection and analysis of the SOn product gas. The reaction system was heated to 600°C and al-

Jan 1, 1967

By N. A. Gjostein

The formal descnption of the decay of an isolated scratch can be written in terms of an appropriate Fourier integral. With the application of certain approximations, this description leads to the second-moment analysis developed by King and Mullins. It is shown that the second-moment analysis does not adequately describe the behavior of a decaying, isolated scratch, and that it is difficult to obtain internally consistent values of the surface self-diffusion coefficient, D,,from this analysis. This inconsistency arises from contributions of higher-order moments to the decay process. Two new analytical methods, based on the Fourier integval representation of a scratch profile, have been developed for determining values of D, from the decay kinetics of isolated scratches. In the profile-matching method, a given initial profile is resolved into its Fourier components, the components are allowed to decay exponentially over an annealing time interval, At, and finally they are synthesized to form a decayed profile. The predicted profile is adjusted to fit the experimental profile by varying only the parameter, D,At; the contribution from volume diffusion is directly taken into account and the integrals involved in the Fourier analysis are evaluated by numerical integration on an electronic computer. In the kinetic method, the widths, W, of a series of predicted profiles are determined for various volume-diffusion contributions, and the results are plotted in the form W vs DSAt. For a fixed ratio of surface to volume diffusivities, R, these plots are linear; the slope of the lines increases as R decreases. A simi-lar analysis can be performed on the depths of the predicted profiles. In this case, plots of (l/df3 vs D,At are found to be nonlinear. The proper value of Ds is found by superimposing the data for the experimental widths and depths on Plots of this kind and adjusting Ds until a fit is obtained with the line having the appropriate value oj R. An analysis of the slopes of these plots for R —= (surface diffusion only) reveals that they do not give the correct value, 2276, for width tf second-moment standard profile. This finding allows one to modify the second-moment analysis in such a way as to obtain internally consistent values of Ds. ThERE are several processes, involving a flow of matter along a surface, due to gradients in curvature of the surface, that may be used to determine the surface self-diffusion coefficient, Ds. These processes are commonly known as 1) thermal grooving, 2) single and 3) multiple scratch decay, 4) blunting of field-emitter tips, and 5) sintering. In this series of papers, the first three of these processes are examined in detail in an attempt to subject the phenomenological theories governing these processes to a critical test and, furthermore, to make a critical comparison of the values of D, obtained from these techniques. Although the thermal grooving technique has been established'' as a reliable method for determining D, , this has not been the case for the process of scratch flattening. Mullins and coworkers374 have proposed phenomenological laws governing the growth of the width and the decay of the amplitude of an isolated scratch, but only in one study5 has the width-growth law been supported by experimental evidence. In paper I of this series detailed experimental evidence is presented that points up the deficiencies of the second-moment analysis; the origins of these deficiencies are also discussed. Following this development, some new analytical procedures, based on representing the scratch profile by Fourier integrals, are presented as a means of obtaining reliable values of D, from the kinetics of the scratch-flattening process. Further applications of the Fourier integral approach are reported in papers 11' and 111,~ where the method has been useful in interpreting the anisotropy of flattening rates of isolated scratches (paper 11) and in describing the multiple scratch decay process (paper 111). THEORY OF SCRATCH DECAY Following ~ullins" approach we consider an arbitrarily shaped scratch profile, Fig. 6, at some time, t. The profile is designated by a function z(x,t) which can be expressed in terms of a Fourier integral as follows:

Jan 1, 1967

By AIME AIME

THREE of the addresses presented at this interesting and important session are printed in full else- where in this issue. The fourth, Mr. Hewett's paper, on "Cycles In Metal Production" has been issued as Technical Publication 183, and an abstract of it was published on page 162 of last month's issue. The general discussion that followed these four important papers is given in full below. S. A. TAYLOR: I would like to ask Mr. Veasey whether the control of oil in pools includes royalties, and, if so, in case of a new pool how are you going to control, or rather how are you going to describe the limits of that pool?

Jan 1, 1929

By M. G. Benz, J. F. Elliott

A new type of solution calorimeter has been constructed to measure heats of mixing, enthalpy increments, and heats of fusion, formation, and reaction at temperatures above 1000°C. With it, measurements hove been made of the partial molar heats of mixing joy tin in the Cu-Sn system from 0 to 13 at. pet Sn at 1127°C and fir nickel in the Cu-Ni system from 0 to 9 at, pet Ni at 1200°C. The integral molar heat of mixing for the Cu-Sn system is strongly negative with a calculated minimum value corresponding to the composition Cu3Sn. The integrnl molar heat of mixing for the Czi-Ni system is slightly positive at these temperatures. These integral molar values have been measured with a probable error less than 30 cal per g-atom at an atom fraction of nickel or tin equal to 0.1. The estimated probable error for the Cu-Sn system is approximately 450 cal for a measured heat of solution of approximately 9000 cal. For the Cu-Ni system it is approximately 700 cal for a measured heat of' solution of approximately 60 cal. A new type of heat of solution calorimeter was designed and constructed to provide a more accurate experimental method for determining heat effects at high temperatures, (T > 1000°C). With it, partial molar heats of mixing, enthalpy increments, heats of fusion, and heats of formation and reaction for metal systems can be measured directly. Previously it has been necessary to rely upon the use of the dropping calorimeter or the van't Hoff equation applied to equilibrium data for this information. For the most part equilibrium data are scarce and difficult to obtain in many cases, and it has been necessary to rely upon the "method of mixtures" for the desired enthalpy measurements. An earlier study1 provides a prototype for this work. The "method of mixtures" as outlined by K. K. kelley,2 "consists of dropping the substance under investigation from a furnace, with controlled and measured temperature, into a calorimeter operating at or near room temperature.'' In this manner the change in the total heat content (enthalpy) of the substance between the temperature of the furnace and that of the calorimeter is determined. In order to determine high-temperature heats of mixing, enthalpy increments, and heats of fusion, formation, and reaction, it is necessary to take the difference between two such measurements, one before and one after the occurrence of the enthalpy change being studied. The desired enthalpy change is then the small difference between two large numbers. Small errors in the large numbers are included as large errors in this small difference. It is this difficulty that must be avoided for accurate measurement of the desired functions. The procedure with the new solution calorimeter consists of dropping the substance under investigation from a furnace, with controlled and measured temperature, into a solution calorimeter operating in the temperature range of 1000o to 1200°C. Measurements in the range of 1200" to 1600°C are planned for the future. By selection of the composition and

Jan 1, 1964

JAmes E. Howard, Watertown, Mass.:—In connection with this paper, it is the desire of the Watertown laboratory to receive suggestions as to the lines of work and the particular direction along which the examination of the ingot-metal should proceed, and any suggestions so offered will be noted with care, and the tests conducted so as to embrace such features as it is thought desirable to have investigated. To me the question of structural continuity seems of para-

Jan 1, 1909

By A. H. Daane, J. F. Haefling

BECAUSE of the wide use of platinum in industry and research, the physical properties of this metal, including its vapor pressure, have been studied in some detail.' The other members of the palladium-platinum group of metals have not been studied as extensively, and only qualitative information is available on the vapor pressure of palladium. Data given in literature by Vines1 and Brewer2 on the vapor pressure of palladium are based on the qualitative observations by Holborn and Austin3 and Crookes4 on the rate of volatilization of palladium filaments in various atmospheres. The general observation that palladium is the most volatile metal of the palladium-platinum metal group was corroborated by Bell, Love and Normand who studied the separation of isotopes of the platinum-group metals by a mass spectrometric method. We have measured the vapor pressure of palladium using the Knudsen effusion technique. In this work, the effusion vessel was suspended from a quartz-fiber microbalance into an induction furnace, and the amount of vapor effusing from the vessel was determined by direct weighing of the vessel during the measured heating times. This technique has been described in a report from this laboratory." The vapor pressure of palladium was calculated from these measurements using the equation P...... = 17.14 -W- (77m)'u [1] a t where ? is the weight loss in grams of vapor of molecular weight m from a vessel having an orifice of a sq cm, during t sec. The derivation of this equation from kinetic theory has been described in a previous report from this laboratory: as well as in texts discussing the kinetic theory of gases.%" Test Vessel—In the search for a suitable material for the effusion vessel, it was found that tantalum reacted with palladium metal to form intermetallic compounds, and graphite was readily dissolved in palladium metal to form what appeared to be a liquid phase at a temperature several hundred degrees below the melting point of palladium. On cooling, the graphite gathered into spherical balls in the palladium, with crystals extending radially from the center of these balls, some of which were a millimeter or more in diameter. However, palladium metal vapor did not attack the graphite vessel, so graphite could be used where it did not contact condensed palladium. Tungsten did not appear to react with palladium vapor or molten palladium at its melting point, but it was not convenient to use a tungsten-vapor pressure vessel because of the difficulty of fabricating this metal. Since the vapor-pressure range to be studied (10 2 to 10 ' mm) did not appear to extend above the melting point of palladium, a combination of tungsten and graphite served to provide a very satisfactory effusion vessel. The lower half of the graphite vessel was lined with some strips of tungsten foil and the sample of palladium consisting of a coil of sheet was placed in the tungsten liner; in this way, no contamination of the palladium by carbon occurred. Procedure After outgassing at 1500C, the tungsten-lined graphite effusion vessel was loaded with 300 mg of

Jan 1, 1959

POSITIONS VACANT (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Superintendent for iron mine operated on the sub-level and caving system. Small output, moderate salary. Location, Southern State. No. 45. Chemist to sample and analyze iron ore. Experience in other branches not essential. Location, Southern State. No. 46. ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introducd by members.) Experienced mine superintendent desires position. Several years' experience in practical management of mining and development work. Has also practiced ass consulting engineer and is thoroughly experienced in the examination and development of mining properties. Mexican experience. Will go anywhere for reliable concern. Salary moderate. References. No. 254. Member, mechanical superintendent, wants position. Has had 12 years' experience as master mechanic of smelting plants in United States and Mexico. Also superintendent of shops doing marine, mining, and general contracting work. . Experienced in manufacture of mining tools and equipment. Up to the minute in copper, lead, and zinc smelting. Has learned a learned a great deal, can forget much, and has the inclination and ability to learn more. Best of references. No. 255.

Jan 10, 1915

By D. B. RUSHhIORE

I. INTRODUCTION. OF primary importance in mine-installations is the hoist, which has a very direct bearing on the successful operation of a mine. Conditions vary greatly with different mines, and especially in different localities. Such factors as depth, incline, the number of levels, permissible or desirable speeds, conditions of ore, etc., are always more or less special in each case. Veins of ore are never exactly duplicated, and the nature of the ground through which shafts are sunk may considerably modify permissible values. As mining-laws are made by the different States, they necessarily vary somewhat, and, even when not fully observed, they introduce factors which qualify the conditions of hoisting men and ore. The amount of timbering required is often of importance as relating to hoisting-conditions. Methods of loading ore affect the time required, as also does the question of the use of cars or skips. Safety-precautions must be very carefully considered, and the number of men in each mine, the number of compartments, and often the method of removing water from the mine, must. have careful consideration. While a general discussion of the subject. of hoisting is possible, most cases are entirely special, and can be considered only in connection with the peculiar conditions pertaining to that particular installation. The cost of installation of the hoisting-plant may be an appreciable amount, while the cost of raising the ore may be but a small part of the total operating-charge. In many cases, however, the output of the mine is limited by the capacity of the hoist, and the latter thus becomes of the first importance. * Presented also, by mutual agreement, at the meeting of the American Institute of Electrical Engineers, New York, N. Y., Mar. 11, 1910.

May 1, 1910

By H. J. Struth

AN unusual engineering achievement in the Gulf Coast last year was the drilling of a wildcat well in the swamps of Louisiana, using direct current. More unusual was the fact that it was necessary to house a diesel engine and generator on a barge in order to supply power. The remoteness of the well made it necessary to transport living quarters and drilling equipment to the location by means of barges, and involved the digging of a canal from a lake to the location, approximated one mile. The drilling equipment used on this well consisted of two generating units, each having one 210-hp. six-cylinder @$-in. bore type VDMA, 600 r.p.m. diesel engine, direct connected to a type CD-169, 125-kw., 250-volt direct current generator, which in turn is direct connected to a type CD-105, 15-kw. 250-volt exciter. One of these motors operates the draw works, one the mud pump, and one a duplicate spare. The generating equipment on the barge was approximately 250 ft. from the derrick, the control wires being brought from the derrick to the generator barge enclosed in a standard fire hose. This is an original idea for confining the con- 11.01 wires in one cable; obtaining minimum space and ample protection. Both control and power lines were suspended on poles. This well was at Lake Grande Ecaille Dome, which was located by seismograph in 1928. Fig. 1 shows the derrick, power barge and living quarters where direct G. E. current was used with rotary drilling equipment.

Jan 1, 1932

By HOWARD RICHARDS

THE dollar was, selected as the unit of currency by the Congress of the United States of America on Apr. 2, 1792. This "Dollar" currency is so much more convenient than the older British currency that the Canadian Government, among others, has adopted it with corresponding success. Just as the dollar is the unit of United States currency, so the meter is the international unit for measuring length. The various weights and measures used in - the United States have since Apr. 5,. 1893, been based on the metric standards. These fundamental standards are kept by the International Bureau of Weights and Measures, which is supported by the United States, Great Britain and the, other leading countries. of the world. Copies are held-in Washington and other capitals. (2) As the dollar is divided into 100 cents, so the meter, which is 10 per cent. longer than the yard, is divided into 100 centimeters or cm. And as the cent is divided into 10 mills, so the centimeter is divided into 10 millimeters or mm. In measuring clothing and other articles which do not require great accuracy, the centimeter is most con¬venient, so that such work is done in terms of centi¬meters.. Instead of speaking of a 15;2-in. collar, a 40-centimeter or 40-cm. collar is referred to. Where accuracy is needed, as in mechanical drawing, machineshop work, etc., millimeters are employed. Thus 8 mm., is the convenient equivalent for 5/16 inch.

Jan 1, 1921

By Glenn R. Zellars, J. P. Morris

The carrier gas method was used to measure the vapor pressure of copper over liquid copper and Fe-Cu alloys. From these results, the activity of copper in the alloys was determined at 146°, 1550°, and 1600°C. Calculations of the activity of iron were made from the results for copper. The activities of copper and iron show strong positive deviations from Raoult's law. KNOWLEDGE of vapor pressures of liquid metals has both practical and theoretical value. Fuming of metal baths is directly related to vapor pressure, and the data should bc particularly important to the technology of vacuum metallurgy. Theoretical applications include determinations of heats of vaporization, heats of solution, and activity coefficients in alloys. Methods for measuring vapor pressures of metals have been reviewed by Speiser and Spretnak.' High-vacuum procedures, such as the Langmuir and Knudsen methods, have been used most widely in recent years. However, these methods are not applicable to vapor pressures greater than lo-' mm Hg and often cannot be used in the temperature range of greatest interest. The purpose of this investigation was to develop a procedure for measuring vapor pressures of pure metals and alloys that would be applicable to pressures greater than lo-' mm Hg. The transportation or carrier gas method has been used. Copper was chosen for the initial work because its vapor pressure has been established fairly well and the reliability of the technique could be ascertained. Applicability to alloys was studied by determining the vapor pressure of copper over liquid Fe-Cu alloys. Experimental Procedure The tests were carried out in a graphite-spiral resistance furnace. The charge consisted of 50 g of metal contajned in a covered sintered-alumina crucible 1/2 in. deep and 13/8 in. ID. Two sintered-alumina tubes led from outside the furnace to within the crucible, passing through close-fitting holes in the crucible cover and radiation shield. The arrangement of the crucible and the two alumina tubes is shown in Fig. 1. The small-bore tube (1/16 in. ID by 5/16 in. OD) served as the inlet for the carrier gas. The tip of this tube touched the metal surface and the flow of gas imparted a rippling motion to the metal. In this manner the gas was brought into close contact with the metal and became saturated with metal vapor. In most of the tests the flow rate of the carrier gas was 560 ml per min, measured at room temperature. Approximately half of this saturated gas was allowed to escape from the crucible through the second alumina tube (3/16 in. ID by 5/16 in. OD) and was discharged to the atmosphere through a

Jan 1, 1957

By W. M. Albrecht, M. W. Mallett

The solubilities of hydrogen in titanium and several of its alloys were determined at 600 to 1000°C and pressures of 0.05 to 10µ of mercury. Solubility increases with increasing beta phase in the alloys. Factors found to affect degassing rates are specimen size and presence of thick surficial oxide. Removal of hydrogen by heating in vacuum and in flowing inert atmospheres was studied. Practical curves predicting minimum degassing times are presented. THE presence of hydrogen in titanium and titanium alloys has detrimental effects on the mechanical properties of the metal.'"," The hydrogen content of commercial titanium is sometimes of the order of 200 ppm by weight' and varies with alloy composition. As a consequence, titanium and some titanium alloys as normally processed are sometimes not ductile unless treated to lower the hydrogen content. The best known hydrogen-removal treatment is heating the material in a vacuum. The rate of removal (degassing) at a give temperature determines the duration of the treatment required to attain a satisfactory low hydrogen level.

Jan 1, 1959

By John G. Hall

The unstable metal market during 1949, with resulting lower metal prices, has focused every mine operator's attention on the problem of reducing operating costs. Improvement in mining, methods, use of modern mechanical mining equipment, and increasing the efficiency of the labor force are the tools with which we will have to work. Careful planning is necessary to coordinate all phases so that no one phase is overdone. A mine may become over-mechanized if, for instance, capital charges against new equipment exceed the savings in labor costs, or where a large enough tonnage is not produced. The cooperation, of labor is essential to any mechanization program. There have been too many instances where mechanization and improvements have done nothing more than make up for a decrease in labor efficiency, thus bringing the production of labor back to its old standard. The operator has gained little and labor has gained only a "softer job." In any mechanization program there are gains to be had by both the operator and labor. By the efficient application of modern equipment and improved mining methods the operator should gain by decreased costs, and labor may profit by receiving a share of these decreased costs.

Jan 1, 1950

By GUY C. RIDDELL

THE recent purchase by an American investment trust of a substantial block of shares in a British owned Venezuelan copper operation directs attention to mining activities that have been quietly gaining momentum in that country for a number of years. We hear so much of oil work in Venezuela that attention to its metal-mining activities is in most quarters casual. In gold and copper the country has made some interesting mining records, and two of the old districts are ,digging in for a come-back. Copper Copper production centers in the state of Yaracuy. The Aroa-Cumaragua mining region has had a long and eventful history. The Aroa mine itself, 50 miles from the coast in West-Central Venezuela, was discovered in 1605. First mined in 1632, owned at one time by Simon Bolivar, it has been reopened many times and is now , the basis of substantial operations by the South American Copper Syndicate, Ltd. of London. The latter has operated the property profitably, off and on, for a number of years, paying heavy dividends on a small investment-at times over 300 per cent annually.

Jan 1, 1929

By E. A. Gulbransen, K. F. Andrew

Thermodynamic information on the solubility of hydrogen in exothermic metals is limited. Thus, the overall solubility decreased as the temperature rose, which suggests the heat of solution of hydrogen in the metal is negative; yet the terminal solubility in the metal phase increased, which suggests an endothermic reaction. A thermodynamic analysis, therefore, was made of the several equilibria involved when hydrogen dissolved in the metal. Equations were derived expressing the solubility, terminal solubility, and decomposition pressures of hydrogen in terms of the heat, entropy, and free energy of solution of hydrogen in the given phase. The relations between the thermodynamic functions for the a-zirconium and 8-hydride phase were developed. The thermodynamic quantities were determined experimentally by the measurement of the decomposition pressures over a broad composition and temperature range. Two new methods of analyzing the experimental data were developed for determination of the terminal solubility. STUDIES', ' of the impact strength of zirconium at room temperature indicated that small quantities of hydrogen, of the order of 10 parts per million, embrittles the metal. Micrographic' and X-ray diffraction' studies showed this embrittlement to result from the precipitation of a second phase upon slow cooling. These studies suggested that the terminal solubility of hydrogen in the metal phase increased with increase of temperature. This behavior appeared to contradict the effect of temperature on exothermic hydrogen occluders such as zirconium. For these metals, the solubility of hydrogen should decrease with increase of temperature. Before these facts could be understood, a thorough analysis of the several equilibria was essential. It was the purpose of this paper to consider the several equilibria involved when hydrogen was reacted with zirconium from both the theoretical and experimental points of view. Since the overall solubility of hydrogen in the metal has been considered by a number of workers, it was proposed to study the composition range 0 to 6 atomic pct H in detail. Literature Schwartz and Mallett' determined the terminal solubilities of hydrogen in the metallic phase from diffusion studies. They extrapolated concentration-penetration curves to the boundary between the solid solution phase and the hydride phase at the surface. Their results showed values of 2.6 atomic pct at 400°C and 5.2 atomic pct at 500°C. Extrapolations of the data to room temperature suggested very low values for the terminal solubilities. This study confirmed the hydrogen embrittlement results and indicated that the terminal solubilities increased as the temperature was raised. The solution of hydrogen in zirconium over the complete concentration range was studied by Hall, Martin, and Rees3 and by others. The results showed that hydrogen was absorbed up to a maximum composition of 66 atomic pct or ZrH This composition represented the t-hydride phase. The maximum amount of hydrogen absorbed increased with pressure and decreased with temperature. Due to this temperature behavior, zirconium was classed as an exothermic occluder." In 1930 Hägg studied the crystal structures of the Zr-H alloys over a broad composition range. Four hydride phases were found. However, the range of homogeneity of the several phases was not studied. Gulbransen and Andrew" recently studied the phase diagram of this system by X-ray diffraction methods and by a thermodynamic method based on decomposition pressure measurements. The results showed that only two hydride phases existed for low temperatures, the 6 and the .-phases of Hagg.' Both phases had broad regions of homogeneity. The lower limit of the two-phase region of a and d-phases suggested a terminal solubility of 4 atomic pct at 500°C. This value was in agreement with the results of Schwartz and Mallett.' To avoid hydrogen embrittlement at low temperatures, it was necessary to heat the metal in high vacuum at elevated temperatures. To choose the conditions of temperature and high vacuum, it was

Jan 1, 1956

By B. G. Matson, M. A. Whitfield, G. R. Dysart

This paper describes the development of u computer program to calculate changes that occur in the length of tubular goods due to temperature and pressure changes during stimulation operations. Due to the numerous variables involved and the uncertainty of all static and dynamic conditions that could exist, it becomes a staggering task for individuals charged with completions to perform the necessary mathematical calculations. The computer program permits advance calculations for several sets of conditions. INTRODUCTION In the Delaware basin of West Texas alone, 50 wells were contracted or drilled to 15,000 ft or deeper in 1965. Deep well activity is continuing in this and other areas on an expanding scale. Many of these deep wells require extensive stimulation for successful commercial production, and during these operations, pressures and temperatures are encountered that have a pronounced effect on the length of tubular goods. This length change during a large-volume, high-pressure stimulation treatment utilizing fluids considerably cooler than bottom-hole temperature can be of such a magnitude that permanent damage to casing and tubing will result unless mechanical design, pressures and fluid temperatures are evaluated and controlled. These pressure and temperature effects can be calculated. However, the process lends itself well to computer solutions because of the mathematical nature of the problem and the calculating hours involved in arriving at an answer. The engineering-hour demand becomes more severe as tapered strings are involved. On initial treatments on a given well, surface pressure and injection rate conditions are unknown, and offset well conditions have not proven to be a reliable method for making predictions. For these reasons, it has become rather standard procedure for operators to compensate for these uncertainties by placing unnecessary pressure and fluid temperature restrictions on stimulation design. On a number of occasions treating fluids have been preheated to as much as 160F as a means of compensating for thermal contmction resulting from pumping cool fluids. The maintenance of packer seals has been treated by Lubinski, Althouse and Logan',' and the problem of therma1 effects on pipe has been explored by Ramey." These works were expanded and the results made applicable to everyday oilfield terminology before submitting them to computer programming. The pressure and temperature effects on tubing movement previously mentioned occur simultaneously as fluid moves through the pipe. The pressure changes, for purposes of explanation, are categorized here as to the various effects these pressures have on a tubing string. These divisions are (1) the piston-like results of forces acting on horizontal surfaces exposed to pressure, (2) swelling or ballooning of the tubing along its entire length due to the forces of pressure acting against the tubing walls, (3) the elongation of tubing due to frictional drag and (4) corkscrewing of the pipe due to internal pressure. Thermal changes are also of great importance, as their results may be more significant than any of the pressure effects. Steel is an excellent conductor of heat and the earth is a relatively poor conductor. It has been calculated that pipe temperatures at depths of more than 20,000 ft approach within as little as 25" the temperfature of the surface fluid after pumping for 2 hours, or a drop in temperature in some treatments of more than 220F. The equations presented in this paper were developed for computer programming and simplicity of input information; therefore, numerical constants such as Young's modulus for steel (28 X 10\ si), the coefficient of thermal expansion of steel (6.9 X 10."IF) and Poisson's ratio for steel (0.3) are included with unit conversion factors. The moment of inertia of tubing cross-sectional area with respect to its diameter was changed to a constant times (D' — d') where D is outer diameter and d is inner diameter. Units in the equations are length in feet, diameter in inches, density in pounds per gallon, pressure in psi, rate in barrels per minute and time in hours. PISTON-LIKE REACTIONS A change in tubing internal dimensions and the exposure of other horizontal surfaces to different pressures on the inside and outside of the tubing result in a reaction much like a piston under pressure. Such is the case when the internal diameter changes in a combination string of pipe, when seals of a slick joint assembly are subject to pressure and in the end effects of a tubing string. The change in tubing length due to the piston effects of a slick joint packer is affected by the various diameters involved, the tubing pressure Ap,, the casing pressure ,Ap,, length of pipe L, densities of fluid in the tubing before and during pump-

By R. G. Hudson, H. W. Paxton

The activities of iron and chromium in their binary system have been measured by the Knudsen orifice technique. The system is close to ideal at 1200- 1250 C with slight positive deviations. The effect of this on the liquidus and solidus is discussed and these are calculated for two limiting assumptions. The vapor pressure of pure iron, pure chromium, and one alloy is compared with that obtained by the Langmuir free-evaporation technique. The results agree, indicating a vaporization coefficient close to 1. HERE are no reported data on the thermody-A namic activity of iron and chromium in the solid portions of the phase diagram. It is generally assumed'.' that the liquid solutions of iron and chromium obey Raoult's law. Chen and Chipman" have inferred that the liquid solution obeys Raoult's law. The minimum' in the solidus-liquidus curves for the iron-chromium system shows that there are deviations from ideality in either the solid or liquid or both. Because of the importance of developing reliable techniques for obtaining activity data in alloy systems at high temperatures and of the data so obtained, an investigation of the activity of iron and chromium in the binary at 1200-1250 C was undertaken using the Knudsen cell. Experimental The apparatus and experimental procedures used in this investigation were described in a previous paper." The various materials used for the construction of the Knudsen cell are listed in Table I. The metal used for the determination of the vapor pressure of chromium was 99.9 pet pure, obtained from A. D. Mackay, Inc. The iron was obtained as electrolytic grade from Fisher Scientific Company. The Fe-Cr alloys used are shown in Table 11. The largest error and controlling factor in the accuracy in the experiments reported here are introduced because of temperature uncertainty, which is estimated to be ±3 deg C. This introduces an uncertainty of 26 pet in the measured pressure. Experimental Results and Calculations The vapor pressures of pure iron and pure chromium were calculated from the measurements by the Knudsen equation3 on the assumption that only Cr or Fe atoms were present in the gas phase. For metal vapors, at the high temperatures and low pressures involved in these measurements this should be a reasonable assumption. Whitman" corrections for the cells were made. The data and results of pressure calculations are presented in Table I, and are plotted in Fig. 1. In addition the heat of vaporization at the absolute zero, ?E°°, has been calculated for chromium. These calculations are summarized in Table 111. The data used in these calculations are as follows kelley13 (F° - E°°/T ) Speiser, et al H (F° - E°°/T ) 010 where F" — standard free energy at temperature T It was necessary to calculate the total pressure above the alloys from the total weight loss W of the cell during a run, because of the fact that all attempts to collect and analyze the chromium and iron vapor effusing from the cell in the apparatus available failed. The failure resulted from the re-

Jan 1, 1959