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By L. A. Weitzenkamp, N. M. Bashara

A study of the electrical conductivity of gold films less than 200 in thickness indicates a negative temperature coefficient of resistance and a thermal actiuatlon energy of less than 0.25 ev. The films consist of discrete metal islands of linear dimensions from a few angstroms to 1000A. Films were able to withstand applied fields up to 60,000 v per cm before breakdown occurred. A model for the conduction mechanism is proposed which involtes a Potential barrier due to work junction, irriage forces , and an electrostatic potential arising from separating an electron from a neutral island leaving behind a positively charged metal island. Activation energies of less than 0.25 ev ave consistent with this model, which includes a tunneling andor Thermal mechanism for conduction between the separate metal islands. An apparent satuvation effect in conductivity at high fields is observed experimentally. The saturation effect may be explained by the influence of the electrostatic contribution to the potential barriers for the transition through several islands adjacent to the original island which was activated to give up an electron. The proposed model gives Poor quantitative agyeement for the intermal electrical field between islands. ThIS paper will relate the structure of discontinuous metal films to the electrical properties and will emphasize the following topics: 1) the relation of the conduction mechanism to particle size and a comparison of particle size from electrical measurements with electron-microscope studies; 2) the saturation of the conductivity at high electric fields; and finally, 3) a comparison between the external field applied and the apparent field between particles. che- latter comparison points to a need for a modification in the model for the conduction mechanism first proposed by orter' and expanded by Neugebauer and webb2 which will be dealt with in the discussion. The paper is based on results on gold films on glass microscope slides. The clms were vacuum-evaporated and were about lOOA thick, thickness being measured by interferometry. It has been observed that metal films of this thickness do not exhibit bulk metallic conduction. Films thinner than some critical thiclmess, depending upon substrate temperature and other factors, have conductivities which increase with increasing temperature with thermal activation energies of less than 0.25 ev. Electron-microscope studies3 have shown that these films consist of discrete metal islands having linear dimnsions from a few angstroms to approximately 1000A. When the metal is being vacuum-deposited on the substrate, islands on the order of a few angstroms appear first. As the deposition continues the islands may tend to agglomerate into larger particles and may eventually grow together into a continuous film,3''' In our tests the conductivity of the gold films was found to be about ten orders of magnitude less than the bulk conductivity of gold. When oxygen was introduced into the test chamber the conductivity decreased by a factor of about one-third. This can be related to an increase in work function for gold caused by adsorption of oxygen, as reported by Oullet and Rideal.s Exposure to an atmosphere of water vapor caused an increase in conductivity by a factor of 2 or 3 when a low field was applied. When the films were exposed to water vapor under a high field the conductivity increased by as much as two orders of magnitude. The activation energies measured were much less than the work function for gold, 0.25 ev or less, with the smaller activation energies observed for thicker films. It will be shown that the activation energy is a function of particle size and spacing. In general the model for the potential between metal islands would include the effective work function, the image force, the applied field, and an electrostatic term. The electrostatic contribution arises from the potential required to separate an electron from a conducting sphere. According to Neugebauer and webb2 the maximum potential due to the field and the electrostatic term only is

Jan 1, 1967

By H. W. Mead, C. E. Birchenall

The rates of growth of graphite nodules in cast irons are calculated for a model of a growing graphite sphere surrounded by a shell of austenite through which carbon and iron are diffusing. The carbon is supplied by a cementite-austenite mixture at the outer edge of the shell. The calculated rates from carbon diffusion agree fairly well with the measured values, but the rates based on iron self-diffusion are much too low. Because the iron must be removed for the process to continue, o plastic deformation mechanism is suggested. THERE has been an unfortunate tendency in the literature of growth and dissolution reactions to identify the slope of a plot of the logarithm of the growth or dissolution rate vs reciprocal of temperature with the activation energies determined by diffusion measurements in chemically similar systems. If the solubility limits at the growing or dissolving phase interfaces change appreciably with temperature, such procedures may lead to serious errors in specifying the mechanisms controlling the rates of these processes. A reaction involving the simultaneous growth of graphite from and dissolution of cementite in austenite will be discussed here to show that substantial oversimplifications have been made in earlier studies of this process. From a dilatometric study of the overall y-range graphitization process, Bunin and Danil'chenko' found an apparent activation energy of 90 kcal per g-atom. They concluded that, since this value was much nearer the approximately 68 kcal per g-atom observed for self-diffusion in pure iron than it was to 32 kcal per g-atom for diffusion of carbon in iron, the rate-controlling process must be the diffusion of iron away from the growth interface to provide space for graphite to grow. Bunin and Salli' bolstered this agreement with the observation that graphite forms preferentially at surfaces, cracks, and pores where free volume is present initially. Ziegler, Meinhart, and DeaconQ ad found an apparent activation energy for graphitization of 98 kcal per g-atom. This value, like that of Bunin and Danil'chenko, applies to nucleation and growth occurring simultaneously. It is not generally assumed that nucleation is entirely diffusion-controlled. Treatments such as prior cold-working and prequenching, which strongly affect the rate of graphitization, would be expected to have little effect on diffusion processes occurring at the graphitization temperature. In any case 90 kcal per g-atom is not particularly close to the 54 kcal or lower to be expected for diffusion of iron which is carbon-saturated.' The presence of silicon in iron is said to reduce the activation energy for diffusion,' so its presence in cast irons would be expected to have a similar effect. The growth rates of nearly spherical graphite nodules have been studied by Brown and Hawkes." The initial rate of growth before impingement of adjacent carbon-depleted areas was found to be parabolic, and rate constants were measured at several temperatures. Their apparent activation energy for the growth process only was roughly 45 kcal per mol. Burke and Owen' made growth-rate measurements on several alloys, recording appreciable induction periods, initial nucleation rates, and average radial growth rates based on an assumed linear rate of radial growth. They found that increased silicon content increases the ovel-all reaction rate and the initial rate of nucleation, and decreases the induction period. Assuming 1) spherical nodules. 2) constant volume rate of nucleation, 3) austenite in equilibrium with cementite at positions where the cementite is not depleted, and 4) a constant diffusion distance during the growth of a nodule, they calculated an apparent overall activation energy of 68 kcal per mol, which was related to an activation energy for nucleation of 79 kcal per mol and activation energy

Jan 1, 1957

By Kenneth E. Gray

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton's equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?' lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.' It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By H. L. Hartman

The estimation of the magnitude of pressure changes which occur in mine ventilation circuits is of primary importance to the mining engineer in making changes in an existing mine or in projecting the ventilation requirements of a new mine. It is a formidable task in many cases, because no adequate theory is available and empirical data are unreliable or even lacking. The common practice of increasing one's estimate of the mine static pressure by an arbitrary "safety factor" to compensate for the unknown is a poor substitute for accuracy. Generally little difficulty is encountered in calculating friction losses in mine airways. As long as the friction factor can be reliably estimated, the well-known Atkinson formula gives accurate results. However, it is in the determination of shock losses that the ventilation engineer encounters difficulty and is apt to resort to an arbitrary allowance. Shock losses may constitute as little as five or as much as twenty-five percent or more of the overall pressure drop in the mine, and such allowances are generally completely unsatisfactory. Since other shock losses have been covered by McElroy (1), this paper deals with a long-neglected source of shock and pressure change in ventilation circuits, divergence and convergence of airflows, here referred to by their more common mining terms, splits and junctions. PREVIOUS WORK There is practically no fundamental information available in ventilation literature on the splitting and junction of airflows, either in mining or mechanical engineering periodicals or handbooks. Fluid mechanics textbooks seemingly avoid the subject of divergence and convergence, except for brief empirical treatment. The only investigation reported for mine ventilation systems was by Weeks, et a1 (21), in 1933. Although applicable to the case of line brattices in coal mines, it cannot be applied to the general case of mine splitting and junctions involving change of direction with little or no area change. In dealing briefly with the subject of shock losses at splits and junctions, McElroy (1) suggests only that they be considered comparable to bends, with losses at junctions being increased 50 pct to allow for interference of merging streams. He recognizes the importance of quantity ratio but concludes that exact quantitative data are lacking to compute losses at splits and junctions. A very capable summary and analysis of the state of knowledge in industrial ventilation and fluid mechanics regarding losses due to divergence has recently been reported by Gilman (3). In considering all earlier work dealing with both air and water as fluids, he compares results on a common basis and obtains good empirical agreement. For divergent flow, the controlling variable in each branch is the quantity ratio, although the deflection angle is of secondary importance. Empirical equations are presented for straight and 90-deg branches with varying velocity ratios, assuming branches smaller than the main duct. These formulas are modifications of the Borda equation for abrupt contraction and expansion. The only information available on shock losses in convergent flow are approximate experimental data presented by Alden (4) and the Manual of Recommended Practice for Industrial Ventilation of the American Conference of Governmental Industrial Hygienists. Alden considers the effects of both quantity ratio and deflection angle. The data indicate an effect opposite to that observed in divergence, the shock loss varying directly with quantity ratio. SHOCK LOSS THEORY Because pressure losses due to shock have been found to bear a constant relation to the mean velocity of flow in a given conduit, they are frequently expressed as a dimensionless function of the velocity head, termed the shock loss factor. For airflow in ducts and mine airways, the shock loss may be represented by the formula (1): Hx - XHv, (1)

Jan 1, 1961

By L. F. Mondolfo, B. E. Sundquist

The crystallographic orientation relationships resulting when lead is nucleated from the liquid by Ni, Cu, Ag, and Ge were determined. For each nucleating agent several definite orientatioz relationships were found. These relationships seemed to be controlled by good symmetry relations and low crystallographic disregistry between mating planes. For any given nucleating agent the under colling for nucleation was found fairly constant and independent of the orientation relationship and consequent disregistry. It was also found that, upon re melting and refreezing the Pb, the orientation relationship was changed. These findings prove that crystallographic disregistry is not the controlling factor in heterogeneous nucleation from the liquid. The results of this investigation tend to confirm the theory presented in a preceding paper that heterogeneous nucleation starts with the formation of an adsorbed layer of nucleated metal on the nucleat-ing impurity. Evidence is given that cavities in the nucleating agent act as centers of nucleation. IT has long been known' that solid extraneous particles are active in catalyzing phase transformations that occur in a system, particularly condensation and crystallization. It is well established that these heterogeneities act as catalysts by providing surfaces upon which nuclei of the precipitating phase can form with activation energies smaller than those required for homogeneous nucleation. Numerous investigations have shown that in this process of heterogeneous nucleation: a) the nucleus forms with one, or several, definite crystallographic orientation relationships with the nucleating phase2-4 and b) that there is a small range of undercoolings or super saturations characteristic of the nucleation of a given solid on a given Substrate.5-10 Turnbull and vonnegut11 have developed a theory based on theories developed by Volmer12 and Turn-bull and Fisher1= for heterogeneous nucleation from gases and liquids, that relates the super saturation or undercooling required for nucleation to the dis-registry between the lattices of the nucleus and the nucleating agent. This theory predicts that nucleation should occur with the orientation relationship between the nucleus and nucleating agent that minimizes the disregistry. Further, it predicts that the undercooling or super saturation necessary for nucleation should be a function of the disregistry. Numerous investigations have dealt with the orientation relationships resulting from the condensation of vapors onto crystalline solid substrates2,3 and a few with the nucleation of one phase by a second phase in solidification4,14. Others have dealt with the supersaturation8-10 and undercooling5-7 associated with nucleation in condensation and solidification respectively. However, there is virtually no report that gives both of these factors for the same system. In this investigation a study was made of the undercoolings and orientation relationships resulting when Pb is nucleated from the liquid by Ni, Cu, Ag, and Ge. It was the purpose of this investigation to check the Turnbull-Vonnegut theory, i.e., the importance of crystallographic disregistry between nucleating catalyst and nucleated metal. The results indicate that disregistry is not an important factor in nucleation and that the nucleation process is probably somewhat more complex than current theories suggest. EXPERMENTAL PROCEDURE Small single crystals of nickel, copper, silver, and germanium were prepared from materials of four to five nines purity, and the Pb used was also 99.999+ pet pure. Cu and Ag single crystals were prepared by sealing small chips of Cu or Ag in an evacuated quartz capsule and heating the capsule at 2000°F for 1 hr before cooling. Nickel crystals of 200 diam were also prepared in evacuated quartz capsules, but melting was done by heating the capsules in an oxy-acetylene flame for a few minutes. These spheres were invariably polycrystalline so

Jan 1, 1962

By F. P. Bullen

Empirical relationships between fracture stress, orientation angle, and diameter of crystal have been determined at 77°K. Orientation ranges of markedly different behavior were found—a law of constant normal stress&apos; of value a (diameter)-1/2 for the fracture of ductile crystals, and a condition of shear stress (or strain) for more brittle crystals. The observations are not consistent with current theories. An interpretation is advanced which is also applicable to observations on the effect of prestrain at room temperature on the subsequent fracture stress at 77°K and to the effect of cyclic stressing on the cleavage strength.&apos;&apos; The law of constunt normal stress&apos; and the brittle ductile transition are also explained. The interpretation is more consistent with the initiation of cracks by intersecting dislocations than with theories based on stress -concentration by dislocation arrays. ZINC single crystals are particularly suited to the study of cleavage because fracture occurs on the basal plane over a wide range of crystal orientations. Analysis of the conditions of stress and strain at fracture in crystals of different orientations should indicate which parameters control the cleavage process. Unfortunately, controversy has arisen over the correct empirical relationship between tensile fracture stress and orientation. Schmid&apos;s observations1,2 favored a &apos;law of constant normal stress&apos;, as observed in other materials.2 For zinc, however, the observed values are far below the theoretical strength and cannot represent the true limit of cohesion between neighboring atomic planes. Hence, the interpretation of such a &apos;law&apos; is not straightforward. Deruyttere and Greenough3,4 found a complex variation between tensile fracture stress and orientation; this variation did not agree with a &apos;law of constant normal stress&apos;. Two theories have been advanced to account for their observations: a) the propagation of cracks from low-angle boundaries,5 and b) the release of energy from piled-up dislocations during crack-propagation.4 The present work resolves the apparent discrepancy between the observations and shows that neither of the above theories are applicable to the tensile fracture of zinc single crystals. A phenomenological explanation, along the lines suggested by Gilman,&apos; is advanced and successfully applied to previously unexplained effects. EXPERIMENTAL DETAILS &apos;Crown Special&apos; redistilled zinc was used, except for one comparison series op tests using &apos;Tadanac&apos; electrolytic zinc. Crystals of 1 mm diam, subsequently called &apos;1 mm crystals&apos;, were grown from the melt in vacuo in precision-bore Pyrex tubes internally coated with graphite. Several specimens 1 in. long were cut from each crystal and chemically polished. Jigs were used to minimize handling strains, and crystals were mounted in the Polanyi machine the day prior to testing to allow recovery from any such strains. One-mm crystals were chemically polished for long periods to obtain 0.1 mm (approx) crystals. One-mm crystals were cemented into miniature gimbals by &apos;Araldite&apos; casting resin. The Appendix gives the reasons for using gimbals and the results obtained by other methods. More complete details of all techniques are given elsewhere.7 The symbols and terminology used are as follows: X = orientation angle (angle between tensile axis and line of greatest slope in the basal plane). T = tensile stress (on true cross-section) S,N = shear and normal stress (components of T with respect to the basal plane) ? = shear strain D = crystal diameter. The subscript &apos;f&apos; will be used to denote values at fracture. PART I-ANNEALED CRYSTALS EXPERIMENTAL OBSERVATIONS One-mm crystals were used to establish the variation of fracture stress at 77°K with orientation at fracture (Xf), Fig. 1. For 18 deg = Xf = 55 deg, a &apos;law of constant normal stress&apos; was observed. For Xf > 55 deg, the fracture condition approximated to a constant shear stress. At Xf< 18 deg, twinning occurred before fracture so that the results were not typical of homogeneous single crystals,4,8— such specimens will not be considered herein. The dependences of fracture stress upon Xf were of similar type for 6 mm,* 1 mm, and 0.1 mm crystals,

Jan 1, 1963

By J. J. Taber

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton&apos;s equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?&apos; lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.&apos; It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By R. P. Alger, C. A. Doh, M. P. Tixier

The principle, the equipment and field operation of sonic logging are described. The tfio-receiver system produces logs independent of hole size and mud. Field experience is given and forms the basis for the interpretation of the log. The derivaiion of porosity values from measured velocities is discussed, according to the type of formations (hard formations, compacted sands, and unconsolidated formations). The time-average equation proposed by M. R. J. Wyllie, A. R. Gregory and L. W. Gardner is uscd as a basis for the computation of porosity in limestones, cemented sandstones and compacted sands. Variations in the lithologic character of limestones do not seem to change the porosity calibration markedly. The compaction of sands is related to the compaction of shale adjacent to them; and, thus, the shale velocity is used for the establishtnent of empirical relations for the computation of porosity in un-consolidated formations. Various forrnu.las are tentatively presented to account for shale and fluid content. Field experience demonstrates that considerable attenuation of sonic energy takes place in unconsolidated formations, particularly when gas bearing, and in fractrured formations. Unusually large attenuation produces skipped cycles, a feature easily recognized. The application of sonic logging to structura1 studies is featured, showing its possible integration with the dipmeter. Correlation and its application to the irrterpretation of seisrmic surveys are reviewed. The paper is illustrated with field examples. Sonic logging is the recording of the time required for a sound wave to traverse a definite length of formation. Sonic travel-times are inversely proportional to the speed of sound in the various formations. The speed of sound in subsurface formations depends upon the elastic properties of the rock matrix, the porosity of the formations and their fluid content and pressure. Below the "weathered" or low-velocity layer extending from 50 to 100 ft or so below the surface, sound velocities may range from about 6,000 ft/sec in shallow shales to as much as 34,000 ft/sec in dolomites. In hard formations (well cemented and/or compacted), the sonic log reflects the amount of fluid in the formations; hence, it correlates well with their porosity. In unconsolidated formations, which are usually of fairly high porosity, the sonic log gives an approach to porosity determination, when its readings are corrected for lack of compaction, shaliness, and fluid content. In such formations the sonic log may also indicate the presence of gas and may distinguish between oil- and water-bearing beds. Field experience with the sonic log in soft formations is more limited than that in hard formations. As a result, interpretation in soft formations is not as well developed at the present time. In all types of formations the sonic log is of considerable value for correlation and for the more detailed and accurate interpretation of seismic data. EQUIPMENT AND PRINCIPLE FIELD OPERATION The basic features of the sonic log" are a two-receiver system and two available short spacings. The log is recorded on film using a standard field unit. An SP curve is run along with the sonic curve to give a more interpretable log and to establish absclute depth control for comparison with other logs run in the same well. If desired, a gamma-ray curve may be recorded simultaneously with the sonic curve. Fig. 1 shows the sonic-gamma ray combination sonde. The sonic portion consists of a sound transmitter and three receivers mounted 3, 4 and 6 ft from the transmitter. When the first and second receivers are used, a sonic log of I -ft spacing (distance between receivers) is obtainea. Use of the first and third receivers provides a 3-ft spacing. The transmitter emits pulses at the rate of l0/sec. After the transmission of a pulse the first arrival of sound energy at each receiver triggers its response system. The differ-

By O. D. Gonzalez, R. A. Oriani

A thermo-osmosis technique has been used to measure the heat of transport, Q* , of hydrogen and of deuterium dissolved in a iron and in nickel, and of hydrogen in Feo.6Nio.4 in the tempevature range 400° to 600°C. For all these systems, Q* is negative and has a large temperature coefficient; an isotope effect can be established for the solutes only in nickel. The magnitude of Q* is considerably larger than the activation energy, E , for migration in the case of these isotopes in a iron, so that all variants of the Wirtz model must be rejected. The phenomenological definition of Q* is developed to show that Q* is related to the mechanisms by which the activation energy is dissipated back into the lattice, and that Q*/E is a function of the ratios of the mean free paths of electrons and of phonons to the distance of jump of the diffusing atom. A correlation is shown to exist between the sign of Q* in thermal diffusion and that of the effective charge in electro migration, and may be understood as due to the large ratio of the mean free path of electrons to that of phonons. THE study of nonisothermal diffusion in the solid state is of interest because certain aspects of the mechanism of diffusion are made manifest which remain concealed though still present in the isothermal case. The thermodynamics of irreversible processes characterizes nonisothermal diffusion, known as thermal diffusion or as the Ludwig-Soret effect, by a quantity, Q*, called the heat of transport, which essentially measures the sign and the magnitude of the steady-state concentration gradient produced by the imposed temperature gradient. The problem then is to understand the quantity Q* at the atomistic level. There does not exist a theory for the atomistic interpretation of the heat of transport. There are, however, two classes of simple models which seem to afford some physical insight into Q*. Wirtz&apos;s model1, z and its subsequent generalizations partition the activation energy, E, for the migration of the atom spatially about the region of the migrating atom, so that Q* is the difference between the portion of the activation energy centered about the original site of the jumping atom and that portion about the arrival site. Clearly, the magnitude of Q* cannot on this model be larger than the activation energy for migration. The model of Oriani3 also considers the spatial distribution of E not only before but also after the atomic jump, and Q* is related to the variation of the spatial distribution of E that is produced by the jump. The simplest kind of system with which to compare the consequences of these ideas is the interstitial solid solution, since one may easily choose a temperature at which only the interstitial component moves, the solvent lattice serving as a completely satisfactory frame of reference. Thus, one avoids complications arising when both species in a binary system move. In addition, one avoids the necessity of knowing the energy for the formation of a vacancy, something which is needed for the analysis of thermal-diffusion data on metals which diffuse by the vacancy-exchange mechanism. However, the number of well-measured interstitial systems is extremely small, and, in particular, there are almost no data in the published literature for the temperature dependence of the heat of transport. If one works with solutes which are gases in the pure state at ordinary temperatures, one may use the technique of thermo-osmosis4 which permits thermal diffusion to be measured over a small temperature difference so that the temperature dependence of Q* can be more easily determined. The choice of dissolved hydrogen in iron and nickel was based on these considerations as well as on the desire to look for an isotope effect associated with localized

Jan 1, 1965

By J. A. Herbst, D. W. Fuerstenau

This paper examines the zero order production phenomenon in the context of the size discretized batch grinding model. A restrictive interrelationship between the selection and breakage parameters of the model, which is mathematically sufficient to ensure zero order behavior, is delineated. Based on this interrelationship, a scheme is developed for predicting the values of the selection and breakage parameters for all size fractions from a minimum of experimental data. To test this scheme, dolomite was ground in a laboratory batch ball mill. Successful simulation of the comminution behavior of this system was achieved using the batch grinding model with the parameter values obtained from the proposed scheme. Historically, a preponderance of comminution research has centered on attempts to relate breakage energy to the performance of comminution machines. Concomitantly, grinding data were interpreted almost exclusively in terms of inherently empirical energy-size reduction relationships1-3 or "laws of comminution"4- 6 which were based on highly oversimplified descriptions of the fracture process. In some instances, these relationships provide a crude basis for the correlation of experimental data, but, invariably, this approach is inadequate for meaningful process simulation. The control and optimum design of comminution circuits require a mathematical model capable of depicting the size reduction behavior of every size fraction for grinding conditions of technological importance. Energy-size relationships do not provide this detailed information. For example, an energy-size analysis for batch ball-milled dolomite has recently been completed in the authors&apos; laboratories.7 This analysis provided a satisfactory correlation between the hypothetical size modulus, which characterizes only the finer portion of the size distribution, and the input energy. However, this relation did not constitute an adequate description of the complete system. In general, one of two distinct viewpoints toward simulation has been adopted in recent comminution research. The first approach focuses on the fracture of single mineral specimens, with the essential aim of representing the over-all process in terms of the breakage characteristics of individual particles and the characteristics of the stress field which the particles experience within the particular size reduction device. As illustrated by Harris&apos;s review,&apos; the actual incorporation of single-specimen fracture information into a description of the behavior of a multiparticle comminution system has seldom been attempted. The only model to accomplish this incorporation was the one developed by Schönert.8 The Schonert model treats single-passage grinding machines in terms of a distribution of effective loads acting on a particle, a distribution of required particle breakage energies, and the breakage product distribution. However, the use of single-particle fracture behavior to derive models of the size reduction process is at present limited to machines in which the particle residence time is approximately equal to the time required to apply stress. As a result, Schönert&apos;s analysis cannot be used to advantage to simulate the complex environment which prevails within a tumbling mill. For multiple-passage systems a second approach to the description of comminution processes has been more fruitful. This approach entails the formulation of a mathematical model which is phenomenological in nature in that it lumps together the entire spectrum of stress-application events which prevail in a system under a given set of operating conditions. The appropriately defined average of these individual events is then considered to characterize the over-all breakage properties of the device. Thus, to analyze the performance of a tumbling mill, the manner in which the particles of a particular size (or size fraction) are stressed need not be distinguished. Instead, a single parameter is assumed to represent the resistance of that size to fracture, given the average grinding environment which exists in the mill. The isolation of such a parameter and a related set of quantities, which constitute the breakage product size distribution for the average event in this size fraction, allows the formulation of physically meaningful descriptive equations capable of yielding precise and detailed information for simulation.

Jan 1, 1969

By Leslie C. Richards

The competitive position of producers of industrial minerals depends upon the delivered price of their product. Freight charges are a major factor in the sales to consumers. A comparison of freight rates on movements of limestone and silica rock in the Pacific Northwest shows a wide variance in mills per ton mile for like hauls, thereby favoring some localities over others. Introduction: Sooner or later the potential miner of industrial minerals reaches the conclusion that of the various factors he must consider, the marketing of his product is. the most important. The sooner he realizes this the better, as successful industrial mineral producers .will confirm. Herein lies a difference between i.ndustria1 mineral mining and metal mining. Often in the latter, technical problems of mining or concentrating are equal to or even surpass those of marketing. This is not meant to imply that there are no problems in mining and beneficiation of industrial minerals, but these usually are outweighed by the problem of marketing. Recentlv. an official of a nationally known corporation :i the elecl.ro-metallurgical industry made an industrial mineral survey in the Pacific Northwest. In the course of his investigation he interviewed producers and potential producers of the various industrial minerals scheduled for use in the plant now being constructed in this area. He stated that he was interested in only three factors: namely, (1) Can your product meet our specifications? (2) Are you able to supply our tonnage requirements? and (3) What will be the delivered price? If there are several sources of supply of sufficient grade and tonnage, as is often the case in the Northwest, then the third factor becomes the important and deciding one. While industrial minerals are usually sold f.0.b. cars with the freight being paid by the buyer, it is the delivered and riot the f.0.b. price that determines the competitive position of the producer and his industrial mineral product. Unfortunately for both the consumers and producers of industrial minerals in the Northwest, the sources are generally a considerable distance from the markets. This necessitates long rail hauls, for which transportation charges make up the largest share of the delivered cost and the delivered price of the product. Is it any wonder then, that rail rates play such an important part in the marketing of industrial minerals? In order to sell his product, the producer must be able to deliver to the market at a competitive price. It must be remembered that his largest cost factor is rail transportation, and that he is limited to markets that he can reach competitively. Since the cost of rail transportation is so important, let us compare various freight rates in the Northwest and attempt to determine their influence on marketing. A study of all rates on all industrial minerals transported in this area, is beyond the scope of this paper. For the purposes of comparison, let us consider limestone (broken, crushed, or ground), and silica rock. These are widely used industrial minerals, and are carried by several different rail routes from.the sources of supply to the centers of consumption in the Pacific Northwest. Markets and Sources of Supply: Limestone has a number of uses in western Oregon and Washington. Among them are agricultural lime for the soils of the Willamette Valley and southwestern Washington; paper rock for the mills in such cities as West Linn, Oregon City, Newberg, St. Helens, and Salem, Oregon, and Camas and Everett, Wash.; chemical and metallurgical-grade limestone for the metallurgical plants centering around Portland, and the Tacoma-Seattle areas&apos;; and sugar rock for the sugar refineries at Toppenish, Wash., and Nyssa, Oregon. Since limestone for cement manufacture is generally processed near the quarry, transportation

Jan 1, 1951

By H. A. Shaw, H. G. G. Whitton

This paper describes the use of the electric-arc furnace for the production of tough-pitch, horizontal cast copper shapes and the production of copper anodes from tank house anode scrap. This installation is the only one of its kind in the United States. SINCE the initial use of electric-arc furnaces for refined copper melting on a commercial scale at Copper Cliff in 1936, this type of melting has been of extreme interest to everyone in any way connected with copper casting and fabricating. Early in 1948, Kennecott Copper Corp. decided to build an electrolytic copper refinery at Garfield, Utah. One of the major decisions to be made at that time was the type of furnace to be used for melting cathodes for casting into refined copper shapes and for melting anode scrap for the production of anodes. Based on the results obtained from arc furnaces by the Tnternational Nickel Co. of Canada, at Copper Cliff, and by the American Smelting and Refining Co., at Baltimore, coupled with certain important economic factors such as having an adequate amount of relatively cheap power available at the Magna Central Power Plant, high cost of poles and oil in the Salt Lake District, and the lack of natural gas at that time, the final decision was to install electric-arc furnaces rather than the standard type of rever-beratory furnaces. Experience has shown certain parts of the original installation to have been inadequate or in need of modification. Although the present status of arc-furnace melting at the Utah Refinery is far from perfect, nevertheless substantial progress has been made. At the Utah refinery, copper is melted in three 15-ft diam, size "M" Lectromelt furnaces, two of which are used for melting cathodes and one for remelting anode scrap. Each furnace is energized from a 13,800-225 v, 3-phase, 60-cycle, 6000-kva (at 40°C rise) oil-immersed water-cooled transformer. Auxiliary equipment for each refined copper furnace includes a charging machine, launders, ladle, 40 ft diam Walker-type casting wheel, bosh, and inspection conveyor. The anode furnace differs in that it is charged by hand from an elevated platform and the anodes are picked off the 24-ft diam casting wheel by a takeoff hoist and loaded directly into specially designed trailers, Figs. 1 and 2. Electrical Equipment Electric power to operate the arc furnaces is generated at the Kennecott-owned Magna Central Power Station two miles distant and transmitted to the Refinery outdoor substation at 44,000 v. At this point it is stepped down to 13,800 v and carried through concrete-lined underground tunnels to the switchgear and then to the primary side of the furnace transformers. The power is conducted from the Y-connected secondary bus bars of the transformer to the electrode arms by means of 22 flexible copper cable conductors per phase. Each cable has a cross-sectional area of 1,750,000 circular mils, giving a total area of 38,500,000 circular mils per phase. The power is carried from these cables to the three individual electrode holders by means of water-cooled copper bus tubing. The electrode clamps are incorporated in the electrode holders and are released by air pressure working against a spring in the clamp control cylinder. The movement of the electrode arms is either automatic or manual. The automatic control is used during melting and is regulated by three Westing-

Jan 1, 1954

By Charles L. Guettel

The temperature coefficients of electrical resistance of 31 alloys in the nickel-rich corner of the Ni-Cr-Fe system were determined. The results indicate that a range of binary Ni-Cr alloys has lower temperature coefficients than a specific region of Ni-Cr-Fe alloys which has been reported and quoted by others as providing the lowest coefficients in the ternary system. DESIRABLE properties of resistivity and temperature coefficients of resistance have been the basis for the successful commercial application of various Ni-Cr and Ni-Cr-Fe alloys. In particular, low or negligible temperature coefficients of resistance are necessary for wire used in precision wire wound resistors and potentiometers involved in closely controlled electrical and electronic circuitry. Alloys most successfully applied to this purpose basically have not been ternary Ni-Cr-Fe alloys but rather heat-treated Ni-Cr alloys in the region of approximately 73 to 79 pct Ni and 20 pct Cr with significant additions of other elements such as aluminum, silicon, iron, copper, manganese, and cobalt. While the addition elements play a vital role in the nature and control of the temperature-resistance curve of any one of these alloys, the inherent relatively low temperature coefficient of the binary Ni-Cr base composition itself in the approximate region of 80 pct Ni and 20 pct Cr contributes fundamentally to the eventual negligible temperature coefficient obtained with the applied alloys. W. A. Dean 1 has reported mean temperature coefficients (20&apos; to 100oC) of as-cast samples for the Ni-Cr-Fe system, the nickel corner of which is given in Fig. 1. Dean had to use as-cast samples because alloys from a considerable region of the system were unworkable. Dean refers to the work of Hunter and sebast2 who used annealed wire samples to show that, for chromium contents of 10 to 25 pct, the temperature coefficient increases as the iron content is increased at the expense of nickel. Although the data of Hunter and Sebast were limited in the nickel-rich areas to eight samples of 60 to 91 pct Ni with only four samples containing iron, the possibility that no Ni-Cr-Fe alloy has a lower temperature coefficient than certain binary Ni-Cr alloys should have been given serious consideration. However, Dean&apos;s work has been referred to by J. S. Marsh,3 who, quoting Dean, states that for the temperature coefficients "the smallest values-about 0.0001 per oC (100 ppm)—were found for alloys containing about 55 pct Ni and 20 pct Cr" (balance iron). A region such as that reported by Dean would be significant to those trying to develop alloys for the applications described. Therefore, a series of three-pound laboratory open-air induction melts of Ni-Cr and Ni-Cr-Fe alloys were melted, conventionally processed to 0.005 in. diam wire, and continuously strand annealed at 1900° F. The basic Ni-Cr compositions, with balances essentially iron other than usual minor impurities, and the corresponding temperature coefficients of resistance and resistivities are given in Table I. The resistivities are approximate and are not to be considered as a basis for relating them to their position of composition in the ternary system. The wire diameters were determined with a micrometer, and not by weight and density measurements which would be required for accurate resistivity values. However,

Jan 1, 1963

By R. G. Charles, E. A. Gulbransen, S. Barnartt

KINETICS of the reaction of zirconium with pure oxygen at elevated temperatures have been studied by several workers for periods of time up to 6 hr.1-1 In two cases,3-4 . the experimental values of oxygen uptake, w, as a function of time, t, were best fitted to the parabolic rate law w2 = kPt + constant. In others,3,4 the cubic rate law w3 = kot + constant, showed better agreement. The most recent data of Gulbransen and Andrew4 indicate that the choice between the parabolic and cubic laws for empirical representation of the data will often be arbitrary. This is particularly true if the first few minutes of the reaction with a clean zirconium surface is attributed to a different oxidation mechanism, for deviations from either rate law were found primarily during the initial period. Thus, the kinetics of this reaction have been too uncertain to permit safe extrapolation to oxidation periods of practical interest (many hundreds of hours). The data to be described are of interest, for they indicate that the cubic rate law applies over long oxidation times. The reaction of zirconium with oxygen at 1 atm pressure was followed at 350" and 450°C for 500 and 200 hr, respectively. Abraded test specimens of pure zirconium sheet&apos; 3.0 X 2.0 X 0.012 cm in size were oxidized by the procedure previously described,3 which included periodic cooling to room temperature for weighing. The surfaces were polished to a 4/0 finish using polishing paper wet with kerosene, then wiped with petroleum ether and washed in redistilled acetone. Fig. 1 shows plots of log ? vs log t. Each curve represents the average of duplicate measurements, and deviations from the average were generally less than 3 pet. The cubic rate law (slope = 1/3) is closely followed. The rate constants, 5.2, x 10 -6 and 2.4, X 10- (mg cm-2)3 per hr at 350" and 450 oC, respectively, are plotted as log k, vs 1/T in Fig. 2, together with cubic constants calculated from the data of Gulbransen and Andrew4 for abraded specimens from the same lot of zirconium. Their data refer to runs of 6-hr duration at a pressure of 0.1 atm 0 and under conditions of uninterrupted heating. In spite of these differences, the latter data yield a straight line which appears to apply equally well to the new extended time data. The energy of activation for the oxidation process, calculated from the slope of this line, i.s 38 keal per mole. This may be compared with the value of 47 keal per mole found by Belle and Mallett3 at higher temperatures. It may be concluded tentatively that extrapolation of short-term oxidation data for zirconium to obtain the long-term behavior is best done through the cubic equation ?3 = kpt + constant. References &apos; E. A. Gulbransen and K. F. Andrew: AIME Trans., 1949, vol. 185, p. A.515; JouRNal OF Metals, August 1949. &apos;D.p. Cubicciotti Journal Amer Chemical August1949.Soc., 1950, Vol. 72, P. 3 V. Belle and M. W. Mallett: Joulnal Electro chemical Soc., 1954, &apos; E. A. Gulbransen 339.and K. F. Andrew: Oxidation of Zirconium Between 400" Gulbransenand 800&apos;C.and AIME Trarzs.. 1957, vol. 209, p. 394; JOUR-Nal of Metals, April 1957. IS Barnartt, B G. Charles, and E. A. Gulbransen: Oxidation of 50 weight pet uranium-zirconium alloy, Journul Electrochemical SOC., 1957, vol. 104, p. 218.

Jan 1, 1959

By J. S. Lasater

Resu1ts of experinmental measurernents of heat capacities and thermal conductivities of some typical porous rocks are presented. Measured heat capacities agree closely with va1ues calculated front known chenlical . compositions of the rocks. On the basis of this agreement, heat capacitir.7 of fluid-satttrated rocks were calc~ililted. Therrnal conductivities of the rock samples were measured under varioits conditions of fluid saturation. From these data therrnal dif-fvsivities were calculated. A significant variation of thermal diflusivity with trnlperature is indicated. Knowledge of the thermal characteristics of fluid-bearing porous rocks has become increasingly important with the development of thermal oil-recovery processes. Reliable thermal data for petroleum reservoir rocks are not available and approximate values are generally assumed for reservoir calculations. &apos;The effects of temperature, pressure and fluid saturation on thermal properties of porous rocks have not been carefully studied. The purpose of the present work was to measure and report the thermal characteristics of some typical porous rocks. A group of eight sedimentary rock samples, including limestone, shale, sandstone and silt-stone, was selected for the study. Properties reported include heat capacities, thermal conductivities and thermal diffusivities. The effect of fluid saturation on these properties was also considered. Determinations of thermal properties require precise measurements which are time consuming and difficult to reduce to a routine basis. Methods have not been developed for measurement of thermal proper-ties under conditions of pressure, temperature, and fluid saturation, which may be encountered in thermal recovery processes. As one approach to these problems, some preliminary work on methods of estimating thermal properties from other more readily measurable characteristics of the rock-fluid system is reported. The samples selected for the studies were oilfield cores from within, or closely associated with oil-productive zones. Descriptions of individual samples are given in Table 1. Clay minerals present in the samples were determined by differential thermal analysis (DTA). Quartz content was estimated from DTA cooling curves. For all but the thermal conductivity tests, a representative 200-gm sample of each core was disaggregated, thoroughly extracted in diox-ane and oven dried at 100°C. The cleaned and dried sample was care- fully split into appropriate portions for the several tests. Chemical analyses of the samples were obtained to permit calculations of heat capacities by methods which are outlined later. Resuits of chenlical analyses are given in Table 2. Heat contents of the test samples were measured by a Runsen-type calorimeter. The heat content of the unknown sample is measured relative to the known heat content of platinum. The apparatus is referred to as a relative error type because of the comparative measurements, and has the advantage of canceling systematic errors. Experimental results are reproducible within 0.5 per cent. A temperature base of 298.16 K is taken for heat content measurements. Measurements were made at five temperatures (260, 440, 620, 800 and 980° F). It was necessary to preheal the sample above the maximum experimental temperature to eliminate volatile constituents. Assuming the weight loss on pre-heat, ing was mostly water, a correction to the observed heat content was made to account for the water originally present in the sample. This latter procedure was followed in the determination of calculated heat contents as will be described later. The apparatus and the method of measure-

By W. I. Duvall

A brief review of the resonant frequency and ultrasonic pulse methods for obtaining elastic constants of rock samples shows that the equations for an iso-tropic elastic solid commonly used to calculate Young&apos;s modulus, modulus of rigidity and Poisson&apos;s ratio can result in appreciable error if the rock is even slightly anisotropic. Consideration of the equations that relate bar velocities and free medium velocities to elastic constants for orthotropic, transversely isotropic and isotropic solids shows that a combination of the two methods can be used to determine average elastic constants for a single sample of rock. The determination of elastic constants in different directions requires a large number of tests on oriented samples. The use of both the resonant frequency and ultrasonic pulse methods is recommended so that the determination of both Young&apos;s modulus and modulus of rigidity is independent of the determination of Poisson&apos;s ratio. The dynamic elastic constants of rock can be determined in the laboratory from measurements on small samples which may be in the form of right circular cylinders (diamond drill core). Either the resonant frequency6 or ultrasonic pulse method1 can be used to determine the longitudinal and shear velocities in the same specimen. The resonant frequency method provides a measure of the longitudinal bar velocity, V,, and the torsional bar velocity Vt; whereas the ultrasonic pulse method provides a measure of the free medium longitudinal velocity, Vp, and the free medium shear velocity, V, . The elastic constants (Young&apos;s modulus E, modulus of rigidity G, and Poisson&apos;s ratio v) are calculated from the density of the specimen, p, and one of the pairs of velocities by means of equations from isotropic elastic theory. For the resonant frequency method the equations are: It should be noted that Eq. 5 is derived from Eq. 4 and 6 and the relation between the elastic constants for an isotropic solid as given by the first part of Eq. 3. The in situ determination of dynamic elastic constants is accomplished by generating a complex seismic pulse in the rock and measuring the arrival times for the longitudinal and shear phases of the pulse at two distant points.5 From these travel times and the distance of the travel path both Vp and Vs are determined. The density of the rock is determined from samples in the laboratory, and Eq. 4 to 6 are used to calculate the elastic constants. These three methods involve the assumption of isotropy and perfect elasticity, and require the use of the relation v = (E/2G) - 1, which holds only if the elastic constants are the same in at least two directions. The calculation of v by means of Eq. 3 introduces considerable error, as a 1% error in V, and V, results in a 20% error in v. If frequencies for samples with a length-to-diameter ratio greater than four and a length greater than 8 in. are measured carefully, the experimental error can be kept to 1%. However, it is not unreasonable to expect that the variation in Vb and Vt with direction may exceed 1%. Thus, for even a small percentage of anisotropy the use of Eq. 3 can result in considerable error in v. The calculation of v by Eq. 5 also involves some uncertainty as a 1% error in Vs and Vp can result in a 6% error in v. By means of the pulse method both

Jan 1, 1965

By Stanley L. Lopata, Eric B. Kula

The problem of preferred orientation has been considered in quantitative phase analysis by X-ray diffraction techniques. The average intensity of a diffraction peak can be obtained by integration over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. For rod or wire, where the pole figure shows rotational symmetry, the intensity is measured along a radius of the pole figure. Where no symmetry is present, rotational symmetry is imparted by rapid rotation of the sheet around its surface normal during measurement. These methods are applied to the determination of aus-tenite in an Fe-31 pct Ni rod and Fe-28 pct Ni sheet. X-RAY diffraction techniques are frequently used for quantitatively determining the relative amounts of two or more phases present in a structure.1,2 Briefly, the method requires a measurement of the intensity of a Bragg reflection for each phase. The method is based on the principle that the intensity of a Bragg reflection, IA, is directly proportional to the volume fraction of the given phase present, CA: T KRACA/2µ [1] where K is a constant independent of the diffracting phase, RA can be calculated and depends on the Bragg angle ? and the particular reflection measured, and µ is the linear absorption coefficient of the mixture.&apos; For a mixture of two phases A and B, IA = RAcA [2] IA/IB=RAcA/Rbcb and CA+ CB = 1 [3] This allows the volume fraction of a phase to be calculated directly from the measured integrated intensities of the two phases present. This method is frequently used for quantitatively determining retained austenite in steels, but can be used for the quantitative determination of in titanium alloys, as well as phases in other alloy systems. The intensities are generally measured by diffracting only from planes whose normals are perpendicular to the specimen surface, with the implicit assumption being made that this intensity is typical of reflections from planes whose normals lie at other angles to the surface. If the specimen contains a texture or preferred orientation of the crys- tallographic planes by virtue of previous mechanical working, however, this measured intensity is correct only if the intensity level fortuitously is one times random. Examination of pole figures for actual rolled sheet shows that the intensity level at the center of the figure is seldom at the random level, and can very easily differ by a factor of five or more, leading to a commensurate error in the calculated amount of the phases. Textures have been commonly found in materials which are cold-rolled or recrystallized after cold rolling. This problem is becoming of greater importance since structural materials in use today, such as the high-strength stainless steels, frequently are further strengthened by cold rolling, and hence contain textures. Although high-strength carbon-containing alloy steels generally do not contain textures, some of the newer thermomechani-cal treatments will impart a texture even in these cases. In the case of hexagonal metals, such as titanium, probably every wrought sample will show some anisotropy. Since the standard X-ray techniques are inapplicable in all these cases, there is a clear need for some method of taking this anisotropy into account. The specific problem is to obtain the integrated intensity of a Bragg reflection for each phase, averaged over all orientations of the sample with respect to the X-ray beam. This can be done either by purely mechanical means or by a mathematical averaging. Mechanically, a small spherical speci-

Jan 1, 1965

By David C. N. Cockburn

INTRODUCTION This paper analyses certain of the financial considerations which will commonly apply in relation to the following questions: - what equity structure or project vehicle should be adopted for the exploration and/or exploitation of a project by more than one unrelated participant? - what vehicle should be adopted by a participant for its participation in a multiparty project? Due to local, politically motivated laws in certain jurisdictions, or due to the overriding requirements of a dominant participant, there may be little choice of the underlying multiparty structure which may be adopted for the exploration, appraisal and/or development phases of a project. Nevertheless, even in such circumstances, attention should be given, at least in the preparation of the related documentation, or in considering methods of participating or funding the project, to certain of the points discussed below. This discussion of financial considerations in the context of the more commonly adopted multiparty structures concentrates primarily on fiscal, financial accounting, financing and funding aspects. TYPES OF PROJECT VEHICLE FOR MULTIPARTY INTERESTS The well known types of vehicle adopted for the participation in a project by more than one participant (assuming that the participants are effectively unrelated) are as follows. Joint Venture (unincorporated joint venture) By far the most commonly adopted structure for mining ventures, a joint venture is usually defined and documented in terms to distinguish it from a partnership for important tax and legal reasons. In essence, this is a contractual association of more than one participant to carry out a specific commercial project or purpose. The relationship between the separate participants and their respective rights, interests, obligations and liabilities are agreed between the participants in one or more contracts (viz Joint Venture Agreements or Joint Operating Agreements together with ancillary documentation). Unlike other project vehicles of participation, in most jurisdictions there is no specific body of law governing joint ventures. The participants thus enjoy contractual freedom to negotiate whatever deal they may wish between themselves. Jointly-Owned Project Company (corporate joint venture) A very familiar vehicle, this is a separate and distinct legal and tax entity incorporated under the company laws of the place of incorporation to undertake specific objects, and granted specific powers, in relation to the Project. Although certain rights, interests and obligations may be circumscribed in the governing corporate instruments by the promoter participants, the corporation laws of the relevant place of incorporation, and the selection of such governing laws (assuming freedom of choice) and future political changes in such corporate laws, should be carefully considered. The use of a company in a multiparty structure may be peripheral to the project itself as a specific purpose vehicle (for example, a joint sales agent or marketing company or a joint borrowing vehicle) or it may form a central function such as in the case of a tolling company which will own the project for legal and taxation purposes and raise financing with the backing of the shareholder participants commonly by the adoption of take-off, throughput and/or user agreements. Partnership This is a legal relationship, subject to the often wide-sweeping restrictions of the relevant local partnership laws, under which the participants have agreed to carry on a business venture together with a view to profit. The effect of the relevant partnership laws, as well as the various types of partnerships and the

Jan 1, 1985

By John R. Caldon

INTRODUCTION Leasing has become a major industry in many countries because of the advantages it affords. Whilst the accounting, legal and tax treatment of leasing varies from country to country, there is far more similarity than difference. The general approach to the subject is largely the same. This paper looks to the basic financial considerations in the decision to lease or buy. TYPES OF LEASES Before embarking upon the subject, it would seem appropriate to define a "lease". A lease may be defined as: "an agreement granting one party the right to use, for a specified period of time, property owned by another party in return for a series of payments of rental by the user to the owner&apos;&apos;. Ownership, of course, generally entitles the owner to unrestricted use of the asset over its useful life in contrast to a lease which gives the lessee use over a limited period. The distinction between the status of owner and a lessee often is fairly small. In this case we are dealing with what is generally termed a "finance lease". A finance lease is one which substantially transfers the risks and benefits of ownership from the legal owner to the lessee. For example, a finance lease would exist where the lessee enters into a lease of an asset for most of its useful life and has an option to buy the asset at the end of the lease for a price which takes cognisance of the rentals already paid. Where a lease does not substantially transfer the benefits and risks of ownership to the lessee, i.e. those benefits and risks remain with the owner and lessor, the lease is termed an "operating lease" and is an agreement for the renting and usage by the lessee of an asset owned by the lessor for a limited period. An example of an operating lease might be where a tenant leases a building for a defined period say 6 years with the rent and occupancy subject to renegotiation at the end of the lease term. The economic consequences of the distinction between a finance and an operating lease is very important. With a finance lease, the lessee has a de facto economic interest in the asset and the alternative to a finance lease is some form of purchase; with an operating lease, the lessee does not have a basic economic interest in the asset and consequently a comparison with a purchase option involves far more than simply a funding comparison. Some of the principal differences between finance and operating leases can be summarised as follows: (a) finance leases: -the risks and benefits of ownership are substantially transferred to the lessee; -the lessor normally recovers his investment during the term of the lease; -the lessor in entering into the transaction is relying more on the creditworthiness of the lessee than the underlying value of the asset; - the lease is either non-cancellable or a large penalty will apply for unilateral cancellation by the lessee; (b) operating leases -the risks and benefits of ownership remain essentially with the lessor; -the lease rental income would not normally cover the recovery of the lessor&apos;s investment; -the lessor evaluates his risk in terms of the underlying value of the assets;

Jan 1, 1985

By S. A. Hovanessian

Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. INTRODUCTION Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. perrinel in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et a1,2 discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle3 gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et a1,4 applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant-pressure 01 no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection 01. production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. I.), having a single source or sink of strength (2, can be written*