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By Best W. N.

Discussion of the paper of W. N. BEST, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 104, August, 1915, pp. 1527 to 1537. WILLIAM A. WILLIAMS, San Francisco, Cal.-I would like to ask whether .Mr. Best ever had any experience with an oil burner that used neither air nor steam? W. N. BEST, New York, N. Y.-Yes. This type is commonly known as the "mechanical spray burner" and uses oil heated under high pressure to above its vaporizing point. These burners are not as efficient as the atomizing type for the following reasons: 1. They produce a round flame which; as with any other type of burner, must pass over a flat surface. A round flame cannot fit a flat surface. 2. They do not evenly distribute the heat, resulting in localized heat. 3. The outlet through which the fuel passes is very small; so all gravities of oil, especially oil containing sand, cannot be burned. 4. Their construction is such that they must be cleaned frequently, as the residuum in the fuel clogs the burner. 5. The oil opening being small, the capacity of each burner is small, so that many burners must be used in a boiler or furnace. (The fewer burners there are, the more accurately they can be regulated.) In marine boilers, these burners are largely used, because they do not require either steam or air for atomization. However, there are other methods by which this objection to other types can be eliminated, such as by the use of a rotary blower and steam turbine engine, the exhaust front the engine passing into the engine condenser, thus obviating loss of water. Mechanical burners are rarely used in shops. I know of but one power plant using them. With mechanical burners, the fuel must be maintained at a high pressure. On board naval vessels, some mechanical burners demand an oil pressure of from 100 to 6001b. It is advisable to reduce the pressure as much as possible, as fractured pipes or fittings are particularly dangerous, for the heated oil escapes as a vapor. In such cases there is liability of an explosion caused by spontaneous combustion.

Jan 12, 1915

By Robert E. Sorenson

EXPLORATION for deep-seated orebodies in the Silver Belt area of the Coeur d'Alene mining district is complicated by meager surface expressions of diagnostic criteria, lack of knowledge of the significance of specific alteration phenomena, and the great expense involved in the exploration for ore shoots, the tops of which often occur near sea level elevation or below and as much as 4000 ft or more below the surface. Except for the early studies of Ransome and Calkins in 1903 and 1904,' little geological work was done in the Coeur d'Alene district for many years, and it is only during the last 15 to 20 years that complete and careful geological mapping has been applied to most of the mines in the area. Much early information, which now would prove invaluable, is lost in hundreds of miles of caved and inaccessible mine openings not mapped by mining geologists. In more recent years mining geology has become a tool of greater use in the district, and some measurable progress is being made in the accumulation of observations that are adding gradually to the knowledge of ore deposits in the district. The recognition of alteration phenomena and related features by Hoyt S. Gale3 in 1935, followed by the work of Shenon and McConnel in 1936-37,4 changed many of the concepts formerly held and opened the way for more critical study and mapping of alteration effects. Mapping of these effects has been in progress for several years but no well-organized, careful, and complete laboratory study of the alteration has been made by mining companies or by government agencies. Recently, Thomas Mitcham of Columbia University has been occupied in the collection and study of specimens carefully selected from several producing mines in the Silver Belt as well as from several prospects exhibiting alteration effects. Mr. Mitcham and the writer have discussed some of the preliminary results of his investigations, which indicate that definite and interesting material is forthcoming from his studies. Work of this kind, aided by careful observation by district geologists, should advance the knowledge of the environment of Silver Belt ore shoots and establish additional criteria for recognizing meager shallow expressions of deep-lying orebodies. Structural details in the Silver Belt area are extremely difficult to decipher on the surface because the area is almost completely covered by a deep mantle of surface debris and soil. A dense growth of small trees and buck brush adds to a geologist's difficulties. Often large areas reveal only scattered small outcrops with great intervening areas where the underlying formations must be deduced from small altered rock fragments. Some considerable success in obtaining surface information has come from bulldozer roads and cuts in selected areas. As this type of work receives more attention, knowledge of the surface expressions of formations, alterations, faulting, and veining is expanding and giving more reliable information to guide deeper development. Lack of diagnostic marker beds in the district contributes to a geologist's difficulties in determining fault displacements. In the Silver Belt, known commercally important sulphide orebodies commonly are associated with siderite and quartz gangue. Some of the veins at shallow horizons above productive ore shoots are composed of quartz with light-colored carbonate minerals such as calcite, ferrocalcite, ferrodolomite, ankerite, and carbonates with variable amounts of manganese. The relation of these carbonates to commercial orebodies is a problem offering possibilities for research. Shallow exposures of veins composed of quartz and the light-colored carbonates, often with some associated barite, grade into quartz and siderite veins at deeper horizons. The vertical range of these carbonates has been partially established for some veins, but no reliable method has been devised for predicting where the change in a vein may take place. Careful observation and analysis of carbonates may make it possible to predict more closely where the change to siderite may be expected. In 1926 Shannon5 pointed out some of the characteristics of the carbonate veins of the district and included a few chemical analyses. Some of the Silver Belt ore shoots have small commercial outcrops, and very shallow development of some properties has led to the opening of small ore shoots." Several small ore shoots developed at shallow depths have not been explored at deep horizons, and some important ore shoots with no commercially significant exposures at shallow horizons have been developed. The greatest problem of the mining geologist working in the Silver Belt area is to find the all-important link between the very meager shallow expressions of mineralization and the rich ore shoots that may be found below. To develop criteria for use in the recognition of the weak upper expression of ore shoots, the experience of past development programs must be relied upon heavily. The investment of more than a million dollars in the exploration for such ore shoots requires some reliable criteria if these ore shoots are to be found. Management needs some assurance that the risk involved is justified by well-developed and acceptable geological inference. The richness of some of the ore shoots found thus far has contributed greatly to the justification for a bold approach, but many negative results of blind exploration programs would lead eventually to extreme caution on the part of management. Fortunately, recent experiences of development programs have been quite successful. It is hoped that added knowledge. of the environment of Silver Belt ore shoots will contribute greatly to the sureness of approach toward their development. The Coeur d'Alene mining district is located in the panhandle of Idaho in Shoshone County. The population of the county is either employed in the

Jan 1, 1952

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines' Monograph 7.' An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines' Monograph 7.' An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951

By W. van der Knapp

A theoretical and experimental ana1ysis is given of the change in volume of a porous medium due to changes in external and internal pressures. The result enable one to deduce directly the effect of large increlents in stresses. It is shown that the three-dimensional representation of the volume of a nonlinear porous system is a cylindrical rules surface, the generating lines of Which have a slope according to the solid rock compressibility. Analytical expression for such a ,surface is very simple. It follows that the bulk and pore compressihilities depend only on the difference between pore fluid and external hydrostatic pressure, i.e., the effective rock frame pressure. From measurements on a number of sandstones as well as limestones it can be conduded that for practical values of this effective frame pressure the pore compressibility falls in the range between the compressibility of water and that of undersaturated crude oil. In general, pore compressibility is found to be higher the lower the porosity. For a particular limestone reservoir pore compressibility and porosity could he related by means of a simple empirical formula. Results from the described study find a direct applicxtion in material balance calculations and in prob1ems of liquid flow through porous media. Since the elastic constants of the rock bulk material enter into equatiorls for velocity of acoustic waves, the results are also of importance for calculating rates of wave propagation in these media. It is shown for sandstones with 1.5 to -10 prr cent porosity that laboratory measured porosities may differ from those lender reservoir conditions by about I per cent of their value. The difference for low porosity limestotnes can be of the order of 10 per cent. The subsidence caused by elastic deformation of reservoir rock is shown to he very small. General formulas relating pore and bulk volume to external and internal pressure can be derived, as has been shown by Biot1, Gassmann2 and Geertsma.2 Their theories describe the differential change in volume caused by a variation in pore fluid tension and external hydrostatic tension. It has been known for a long timei that the stress-strain relations of a packing of spheres are essentially noninear. Our experiments show that for almost all reservoir rocks which arc elastically deformable the relation between volume and loading is also a nonlinear one, resembling that of a packing of spheres very closely. The behavior of these media is often described by using the linear stress-strain relations for small incremental stresses and strains in the vicinity of a pre-stressed condition." The present study differs from these considerations in that it enables one to deduce the effect of large increments in the stresses directly. In analogy to the stress tensor for a homogeneous body the stress tensor for a porous body can be written in the conventional way: where the tensor components, o, and t, represent the total forces acting on the faces of a unit cube of porous material. This tensor can be split into two parts. a hydrostatic and a deviatoric part, as follows2,3,1 where the component of the hydrostatic stress system, a. equals The hydrostatic stress causes a change in volume whereas the deviatoric stress system gives rise to a change in shape only. One of the difficulties in describing changes of volume occurring in reservoir rocks is that the relations connecting these volume changes with external and internal stresses are essentially non-linear. A complete description requires the bulk volume, V,,, as well as the pore volume,V,,. to be known as a function of both the changes in pore fluid tension (v) and the hydrostatic tension on the outer boundary.

By A. J. Griest, A. P. Young, P. D. Frost

A study was made of the effect of ß grain size on the tensile ductility of a-ß titanium alloys haet treated to strengths in the range 165,000 to 180,000 psi. It was concluded that the primary cause of $ embrittlement is the large grain size which is obtained so rapidly in many a-ß titanium alloys when heated into the ß field. It was also found that grain-boundary a and acicular intragranular a in the microstructure are not necessarily detrimental to the tensile ductility if the prior ß grain size is sufficientlv fine. BETA embrittlement occurs in a-ß alloys when the finish hot-working or stages of the subsequent heat treatment have been done at temperatures in the ß field. In order to avoid this embrittlement, for-gings must be finished at temperatures under the ß transus. For better workability, it would be desirable to forge at temperatures in the ß field. For this reason, research has been conducted to determine the cause of ß embrittlement. Although ß grain size has been considered as a possible contributing factor to ß embrittlement, only limited research has been done to evaluate its effect. The effect of addition elements on ß grain growth in unalloyed titanium has been studied by Liu.' Complete mechanical property data, however, were not obtained for correlation with grain size. Ogden and coworkers2 have investigated the effect of both a and ß grain size and grain shape in Ti-Cr-Mo alloys. Their data indicated that tensile ductility was relatively insensitive to ß grain size at annealed strength levels (140,000 psi ultimate). No study has apparently been made to determine the relationship between ß grain size and ß embrittlement in a-ß alloys heat treated to high strength (180,000 psi ultimate). The high-strength condition is that in which ß embrittlement is particularly severe. Beta grain size is not easily varied through the use of a range of annealing times and temperatures in the ß field, because of the rapidity with which ß grain growth occurs. Short-time heating techniques are needed to obtain the smallest ß grains. EXPERIMENTAL PROCEDURE In this research, the experimental procedure was as follows: 1) Tensile and microimpact specimen blanks were resistance heated to produce a range of ß grain sizes. 2) The tensile and microimpact blanks were then solution-treated in the a-ß field and aged to produce predetermined ultimate tensile strengths in the range 165,000 to 180,000 psi. Tensile and impact ductility were then correlated with a grain size for constant strength levels. Materials—The alloys Ti-6A1-4V, Ti-4A1-4Mn, and Ti-16V-2.5Al are representative of the heat-treatable a-ß types in which ß embrittlement can be severe. The compositions and ß transi of the heats studied are given in Table I. The Ti-16V-2.5Al heat was melted and fabricated to 1/4 in. round at Battelle; the other alloys were obtained as 1/4 in. round rolled from commercial heats. The micro-structures of the as-rolled alloys were fine a-ß mixtures. This structure is typical of titanium alloys hot-worked extensively in the a-ß field. Resistance-Heating Treatments to Establish ß Grain Size—For direit resistance heating, a 1/4-in.-diam s~ecimen was heated with a 3000-watt transformer rated for 1000 amp with adjustable secondary voltage. The apparatus included a spray quench fixture. Both heating and quenching periods could be automatically controlled. For temperature measurements, 28-gage Chromel-Alumel wires were tack-welded to the specimen at its midpoint. A high-speed recorder-controller was used to control the heating cycle.

Jan 1, 1960

By F. A. Crossley

The additions: o, Sn, Zr, Cb, Mo, and V were studied for their effects on the a/a + Ti3A1 boundary of Ti-A1 base ternary alloys. These additions were chosen because of their importance to commercial titanium alloy practice—oxygen as the major impurity (in terms of influence on mechanical properties) and the others as major alloying additions. The composition and temperature ranges of investigation varied according to the system as shown in Table I. The principal means of investigation was light-microscopy. The basis of the ternary studies was the recently determined titanium-rich end of the Ti-A1 system.' MATERIALS, METHODS, AND PROCEDURES Ingots were prepared in 15 g size for all alloys except those of the Ti-Al-Mo and Ti-A1-V systems which were prepared in 20 g size. These alloys were prepared from high-purity, electrolytically refined titanium obtained from the Bureau of Mines, Boulder City Metallurgical Laboratory, Boulder City, Col., and Chicago Development Corp., Riverdale, Md., for the 15 g and 20 g ingots, respectively. The alloying additions were obtained from commercial sources, and were at least of 99.9 pct purity, except the V-15 wt pct A1 master alloy for vanadium additions. This alloy was of 98.2 pct purity; the major impurities were 0.37 wt pct Fe and 0.38 wt pct Si. The ingots were prepared by multiple melting in a nonconsum-able-electrode arc furnace. The ingots were covered with Markal coating "CR-T22" (Markal Co., Chicago) to protect them from scaling. Markal coating is applied as a slurry of solids in a volatile carrier liquid. The coated article is air dried. Upon heating to the hot working temperature the coating fuses to form a glassy, protective film. The ingots were heated to 1000°C and rolled to 0.16 in. thickness, reheating after each pass. The glassy film was removed by sand blasting. Ten mils were removed from all surfaces by grinding and/or pickling (3 pct HF, 30 pct HN03, balance water). Grinding was always followed by pickling to remove traces of the grindmg medium. Hydrogen removal was accomplished by vacuum annealing at 1000°C for 2 hr to a final pressure of about 0.02 µ Hg. This was followed by annealing in evacuated Vycor bulbs (800°C, 2 hr, ice brine quenched (IBQ)) in order to maximize ductility. The materials were then lightly pickled and cold rolled to 0.12 in. thickness or cracking, whichever occurred first. After rolling, 1/2 by 1/4 in. specimens were cut for the equilibration anneals given in Table 11 and carried out as previously described.1 Final polishing of the specimens for metallographic examination was done by electrolytic means. Specimens were first examined without etching under bright field and polarized light illumination, for this is the only means of detecting the "two-phase" phenomenon.1,2 The term "two-phase syndrome" refers to Ti-A1 al-loys which appear on the bases of their chemical, phys-ical, and mechanical properties, to be two-phase, but are actually single phase and inhomogeneous in composition. Since processing and heat treatment of the alloys of the first group were completed before the two-phase syndrome was discovered, a number of the specimens were found to exhibit this phenomenon—80 pct of those of the Ti-Al-Zr system, 5 pct of those of the Ti-Al-Sn system, 30 pct of those of the Ti-Al-Zr system. The affected specimens were homogenized by heating above the ß transus temperature and quenching. The heat treatment and working schedules to accomplish this are given in Table 111. After rolling, specimens were pickled (3 pctHF, 30 pct HNO3 in water) to remove 1 to 2 mils from the

Jan 1, 1970

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.'" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase 'Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By Luiz C. Correa da Silva, Robert F. Mehl

A. D. Le Claire and R. S. Barnes (Atomic Energy Research Establishment, Harwell, Didcot, Berks., England)-—This much awaited paper admirably confirms that the Kirkendall effect is a true diffusion phenomenon and likely to be found in all diffusing systems. The most likely explanation put forward so far to account for the shift of interface is that the two components of the system, diffusing in opposite directions, do so with unequal rates so that there is a net loss of material from that half of the diffusion zone rich in the more rapidly diffusing component. This loss is accompanied, and at least partly compensated for, by a closing up or decrease in volume of this latter half of the diffusion zone and an expansion of the other half so as to tend to keep constant the overall volume per atom. This is manifest as a movement of the original interface. If this is a true picture of what is taking place then there are at least two important matters requiring further study."1—The quantitative relating of the observed shift with the independently measured separate diffusion coefficients of the two diffusing species."2—A detailed study of the mechanism and characteristics of the closing up process."We would like first to make a few remarks pertinent to these topics. In connection with the first of these, it is a pity that more and detailed measurements were not made on the Au-Ag system, the only one for which the separate diffusion coefficients of the two species have been measured.'" One of us (A. D. Le C.) has calculated from Johnson's results the shift to have been expected in samples D.2 and D.3. Darken4 showed that the velocity v with which the markers move is related to the separate diffusion coefficients Dau, Dag, by the eauation:"dN"v = (Dag — Dau "dx"dN"where .is the concentration gradient at the mark-ax"ers. Under certain conditions,4, 20 it can also be shown that:"Xm"v = "2t"where x, is the total marker shift after time, t:"dN". . xm = 2t (Dag — Dau) [9]"dX"Johnson measured Dag and DAu in a chemically homogeneous alloy and so his reported figures represent the true or ideal diffusion coefficients"; the same quantities in eq 9 represent the actual diffusion coefficients as would be measured in the presence of a chemical concentration gradient, so we need to multiply Johnson's reported values of Dag and Dau by the"1 before insert-dlogN "ing them in eq 9. 7 is the activity coefficient of Ag at the concentration prevailing near the markers which we shall assume to be - 50 pct. The values of the thermodynamic factor for N = 0.5 and the temperatures at which D.2 and D.3 were annealed were obtained from thermodynamic data quoted by Darken.' aN/ax was computed from the coefficient of inter-diffusion of Au and Ag given by Johnson on the assumption that in the samples D.2 and D.3, the concentration distance curve could be represented by the standard equation:""No is the original difference in concentration between the two halves of the couple, and + is the error or probability function."aN/ax at x = 0 is then given by:"adN/dx "2/nDt"and we assume that this represents the concentration gradient at the markers, although it is probable that the figure is slightly high."When all the appropriate quantities are inserted in eq 9, we find that the expected shifts are: for D.2, 0.0134 cm and for D.3, 0.0119 cm."The agreement between these results and those

Jan 1, 1952

By Henry Leidheiser, Melvin C. Jr. Hobson

The rate of formation of the intermetallic compound, indium antimonide, at the interface between iudium and antimony at 100°C is greatly increased when a composite electrode of indium electrode -posited on antimony is made the cathode in an electrolytic cell. The amount of indium antimonide formed during electrolytic treatment at constant potential appeared to he proportional to the square root of time, but the scatter of the data, particularly at long times, makes it impossible to state this conclzlsi1:ely. The rate constant for the electrochemical synthesis was estimated to he 1.5 x 10-12 sq cm per sec. A similar- set of experiments was conducted in the absence of an applied potential but under otherwise similar conditions. The rate constant lor the thermal synthesis was less than 2 x 10-14 sq cm per, sec, at least two orders of magnitude less than obtained during electrolytic treatment. In a series of electrochemical studies it was observed that intermetallic compounds formed on the surface of polarized electrodes.1'2 The possibility of using this technique for the electrochemical preparation of intermetallic compounds was investigated and subsequently applied to the synthesis of the semiconducting III-V compounds. Gallium antimonide, indium arsenide. indium antimonide, and indium bismuthide were successfully formed by electrodepositing the Group III element from a boiling acid solution onto an electrode made of the Group V element. The following kinetic studies were undertaken on indium antimonide to obtain quantitative information on the rate of formation of this representative III-V compound under a potential gradient. EXPERIMENTAL The electrolytic cell for these experiments was a modified, three-neck, round-bottom, 500-ml distillation flask. Sealed into the side of the flask was a Luggin probe which monitored the surface of the working electrode and extended out of the flask to a small reservoir containing a saturated calomel electrode. The counter electrode was platinum. The three electrodes were connected to a Wenking po-tentiostat which maintained a preselected constant potential near the surface of the working electrode with reference to a saturated calomel electrode. All potentials noted in this paper are with reference to a saturated calomel electrode at 45° ± 5°C. The potential and the current were both monitored using Sargent Model MR recorders. The antimony electrodes were cast in graphite molds to form spheres about 15 mm in diameter with a shank 6 mm in diameter and 10 mm long. A heavy copper wire (12B & S gage) was soldered to this shank. Collodion was applied for protection to the shank and the connecting part of the copper lead. A snug-fitting O-ring was slipped over the shank and the electrode was then fitted into a teflon holder such that only the spherical portion was exposed. The electrode surfaces were cleaned and chemically polished prior to assembly and introduction into the electrolyte by etching in a modified CP-4 solution (50 parts glacial acetic acid, 10 parts concentrated nitric acid, 2 parts 48 pct hydrofluoric acid). The electrolyte was 10-2 M In+3 in 1 MH2So4 and its temperature was held constant by refluxing. The reflux condenser was open to the atmosphere and no temperature correction was made for changes in barometric pressure. The indium concentration in the electrolyte was checked from time to time by the analytical method outlined below for the determination of the amount of indium antimonide formed electrochemically. A schematic of the recorded potential is shown in Fig. 1. At point A the antimony electrode was introduced into the cell and the open-circuit potential recorded. At point B the potentiostat, preset at the desired potential, was switched on. It was switched off at point C and the potential fell to the open-circuit value of the electrodeposited indium. The

Jan 1, 1965

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

Jan 1, 1905

By Harlan A. Walker

Rock-drill steel has an important bearing on costs in many mining operations, both directly and indirectly. Direct factors include such items as shop expense, steel consumed per ton of ore produced, cost of distribution and the dust hazard. The latter, although no specific amount may be assigned to it, is an ever-present problem, and is receiving increased attention as the science of mining progresses. Indirectly drill-steel performance affects consumption of compressed air, maintenance of drills and drilling speed. The latter, in turn, increases or retards the tempo of mining and development. These factors, while not all inclusive, are preponderant in their importance. Thus it is evident that in an extensive operation drill-steel expense may run to many thousands of dollars and that thoughtful research leading toward more efficient practice is warranted. Experimental Work During the late spring of 1939, experiments were undertaken at Homestake in reducing changes in drill-steel gauge from ? in. to 1/16 in. In drifts and crosscut headings mounted machines were set up and holes were drilled with ?-in. bit-gauge changes and other holes a few inches

Jan 1, 1940

By R. B. Gavert, David J. Mack

ROOM- and elevated-temperature compression tests were made on the binary 3/2 electron compounds AuZn, CuAu, AgZn, AgMg, AuCd, and NiA1. These compounds possess either the B2 CsC1-type ordered structure or the A2 bee disordered structure represented commonly as ß and ß on equilibrium phase diagrams. In testing at room temperature, cylindrical specimens 0.508 cm by 0.330 cm diam were seated directly on an instron compression load cell (CF 0 to 10,000 lb). At elevated temperatures, testing included a special apparatus with a furnace heat source and a protective atmosphere.' The specimens were strained at a rate of 1 pet per min. The compounds were prepared from 99.99 pet or better high-purity elements. Vacuum and/or argon cover gas was used throughout the mixing, melting, and specimen drawing processes. The generally equi-axed specimen grains varied in size from 0.5 to 1.5 mm for the five different compounds. The stress-strain curves in compression showed

Jan 1, 1968

By Harlan A. Walker

Rock-drill steel has an important bearing on costs in many mining operations, both directly and indirectly. Direct factors include such items as shop expense, steel consumed per ton of ore produced, cost of distribution and the dust hazard. The latter, although no specific amount may be assigned to it, is an ever-present problem, and is receiving increased attention as the science of mining progresses. Indirectly drill-steel performance affects consumption of compressed air, maintenance of drills and drilling speed. The latter, in turn, increases or retards the tempo of mining and development. These factors, while not all inclusive, are preponderant in their importance. Thus it is evident that in an extensive operation drill-steel expense may run to many thousands of dollars and that thoughtful research leading toward more efficient practice is warranted. Experimental Work During the late spring of 1939, experiments were undertaken at Homestake in reducing changes in drill-steel gauge from ? in. to 1/16 in. In drifts and crosscut headings mounted machines were set up and holes were drilled with ?-in. bit-gauge changes and other holes a few inches

Jan 1, 1940

By David J. Mack

A survey and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on. mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CalculatioX oP YouNg's Modulus from Theoretical or Empirical CoNsidera-tions Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Souther-land (1891), but Fess'enden4',~ made extensive calculations a few years later and arrived at the relationship: £ = 78.TOw(i)* where V is the atomic volume. In 1923, Peczalski, working from the same standpoint but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: where B is a constant of value about 8 . 107, p is density and mis atomic weight; the atomic volume, of course, being ml p. Portevind4 immediately pointcd out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: F- KT" where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson. Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff.50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium, 18

Jan 1, 1946

By Morris Cohen

STAFF: Editor, Gerhard Derge Acting Editor, Paul G. Shewmon Carnegie Institute of Technology Schenley Park Pittsburgh 13, Pa. Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Karl L. Fetters, President; J.S. Smart, Jr., Past-President; R. C. Cole, Vice President; R. L. Hennebach, Treasurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: W. O. Phil-brook, Chairman; H. L. Bishop, R. C. Cole, J. N. Hobstetter, W. A. Krivsky, E. R. Morgan, F. C. Langenberg, R. E. Lund, Paul Queneau, L. L. Seigle, R. L. Smith, and T. V. Wainwright. Review and selection of manuscripts is under the supervision of the following Publicotions Committes: Extractive Metallurgy Division: R. E. Lund, Chairman; M. E. Wadsworth, Vice Chairman; D. H. Baker, Jr., G. M. Bell, R. E. Grace, W. A. Krivsky, R. A. Lewis, Charles O'Neill, A. W. Schlechten, R. E. Shinkoskey, and W. W. Stephens. Iran and Steel Division: T. V. Wainright, Choirman; H. L. Bishop, R. E. Boni, T. E. Dancy, D. W. Murphy, Johannes M. Uys, J. B. Wogstoff, and R. G. Ward. Institute of Metals Division: J. N. Hobstetter, Chairman; P. A. Beck, J. J. Becker, G. F. Bolling, J. 0. Brittain, J. B. Clark, R. S. Davis, A. E. Dwight, R. W. Fountain, L. R. Girifolco, J. C. Gurland, H. S. Kalish, E. L. Harmon, J. J. Heger, A. A. Hendrickson, L. Himmel, J. P. Hirth, H. H. Johnson, Jr., R. R. Nosh, T. N. Rhodin, R. H. Richman, H. C. Rogers, W. Rostoker, C. Sherby, C. W. Spencer, L. Slifkin, J. K. Stanley, R. Steinitz, H. C. Stumpf, and R. Swalin. Published bimonthly by the Americon Institute of Mining, Metallurgicol, and Petroleum Engineers, Inc., 345 East 47th Street, New York 17, N. Y. Telephone PLaza 2-6800. Subscription $30 peryear for non-AIME members in United States and North, South, and Centrol America; $32, foreign; $30per$7.50 for AlME members. Single copies, $6.00, single copies foreign, $6.50. The AlME is not responsible for any stotement made or opinion expressed in its publications ... Copyright 1962 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AlME New York . . . Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts . . . Second class postage paid at New York, N. Y., and Ann Arbor, Mich. Volume 224, Number 4.

Jan 1, 1962

By P. G. Winchell, R. J. Russell

The distribution of displacements of originally plane surfaces by an invariant-plane strain has been analyzed statistically. The displacement ratio (the magnitude of the displacement of a point originally a unit distance from the invariant plane) can be determined from an analysis either of tilts of random surfaces or of displacements of random scratches scribed on a randowz surface. In either case the mean of the tangent of the observed displacement angle is related to the displacement ratio, and the number of observations used in determining the mean is related to the confidence limits placed on the estimate of the displacement ratio. In estimating the effect of applied stress on a phase transformation whose displacement effects can be approximated as an invariant-plane strain,* the dis- placement ratio of the invariant-plane strain is of primary importance. Two procedures for determining such displacement ratios are considered here. In the tilt method the measured quantity is taken to be the angle through which a random polish plane is rotated by the invariant-plane strain. In the scratch method the measured quantity is taken to be the angle between the original direction of a random scratch in a random polish plane and the projection of its final direction in the polish plane. In order to obtain precise results from either of the methods, it is necessary to measure the relative volume change associated with the strain in a separate experiment. TILT METHOD A locally homogeneous invariant-plane strain, P, with displacement ratio, S, may be written&apos; where ; and < are unit vectors indicating the displacement direction and invariant-plane normal, respectively, as pictured in Fig. 1. Eq. [I] describes a uniaxial strain if the direction of displacement is parallel to the invariant-plane normal and a pure shear strain if the displacement direction is perpendicular to the invariant-plane normal. The original orientation of the random polish plane relative to the invariant plane and to the displacement direction is shown in Fig. 2. The angle 03 between < and u is related to the relative volume change, ?V/V, and to the displacement ratio by As a result of the invariant-plane strain, the polish plane is rotated about its intersection with the invariant plane by the angle y, which is always taken to be positive. The tangent of this angle in terms of the above parameters is

Jan 1, 1967

By Riki Kobayashi, D. L. Katz

The conditions at which methane and water form solid hydrates have been extended from 4,000 to 11,200 pounds per sq. in. The curve at high pressure had been in doubt because of Villard&apos;s report of a critical decomposition temperature. The paper explains the nature of the hydrate curve at high pressure and its dependence on fluid phase behavior. Extropolation of the methane hydrate curve indicates a pressure of 40,000 pounds per sq. in. will cause hydrates to form at a temperature of 100" F. INTRODUCTION The conditions under which natural gases form hydrates when liquid water is present have been studied by several investigators up to pressures of about 4,000 pounds per sq. in. The early work by Villard on hydrates of methane and ethylene13, ethane&apos;&apos;, and propane14 included references to critical decomposition temperatures of the hydrates. Villard&apos;s work raised the question as to whether the pressure-temperature curve for methane-water hydrate continued above a temperature of 70.7°F. or whether this was the maximum temperature at which hydrates would form. This paper extends the experimental data on methane hydrate to 11,200 pounds per sq. in. A discussion of phase relations in the hydrate region for the hydrocarbons and of the methane-water system at high pressures is included. PREVIOUS WORK Villard suspected that methane hydrates could not be formed at temperatures above 21.5°C. (70.7°F.)la irrespective of the pressure of the liquid-vapor system. However, he was limited in his studies by his apparatus in 1888 to pressures not greater than 300 atmospheres (4,410 pounds per sq. in.) so that there has remained some doubt as to the existence of such a maximum temperature in this region. For the case of ethylene hydrates, however, Villard does specifically state the occurrence of what he terms a "critical temperature for the decomposition of the hydrates"13. Fig. lB shows a pressure-temperature projection of the three-phase locus, hydrate-ethylene rich liquid-vapor (H-L2-V) terminating at the critical locus in which L² and V assume similar properties. Throughout this paper the following phase designations will be used: H for hydrate, Ll for the water rich liquid. L2 for the

Jan 1, 1949