Search Documents

By F. Brons, W. C. Miller

Pressure information for use in material-balance calculations is obtained, where possible, from pressure build-up surveys in shut-in wells. Using proper extrapolation methods, static pressures are obtained which, by averaging, give the field static pressure. Often, particularly in fields with a large number of wells, only spot pressure readings are available. A graphical method is presented here which enables the determination of the corrections which must be applied to the spot readings to give an estinzate of the static pressure. Although the static pressures thus obtained are not so reliable as those from build-up surveys, they are more nearly correct than the spot readings themselves for use in material-balance calculations. INTRODUCTION The average static pressure in a bounded reservoir is determined from a number of individual-well pressure measurements. Where pressure build-up curves are available, extrapolation methods such as described in Ref. 3 may be used to determine the static pressure in the drainage area of each individual well. The possibility of using pressure build-up curves presupposes that each well being surveyed is closed in during a certain period and that, during this time, a pressure recorder is left suspended in the hole. For surveys in fields with a large number of wells, this is usually not feasible for economic and other reasons. Either a large number of pressure recorders would have to be used simultaneously or, using a limited number of recorders, the time interval needed to complete a field-wide survey would be too long. The data obtained for this incomplete coverage are insufficient to permit reliable averaging of the few calculated static pressures over the entire reservoir. In many such cases another type of pressure information is available, i.e., spot pressure readings. During this type of pressure survey all wells are closed-in simultaneously and, after a reasonable shut-in time (e.g., three days), pressure readings are taken by running the recorder in and out of each successive well. These surveys, which are less expensive, are often taken at regular intervals, say once or twice a year. In fact, such surveys are required by the state regulatory bodies in many portions of the united States. These spot readings are normally lower than the static (fully built-up) pressure due to the relatively short shut-in time. No direct means of extrapolating such a reading to the static pressure is available because no pressure build-up record is obtainable. Consequently, these data are inferior to pressure build-up information as a basis for estimating the stabilized reservoir pressure in the drainage area of a specific well. For the common case where abundant spot readings but only a few pressure build-up surveys are available, our studies suggest that it may be possible to design a program which will combine the two types of information and provide an estimate of the average reservoir pressure that is more reliable than that obtainable solely from either set of data. in time) gives a point marked p. The actual static pressure at the time the well was shut-in is marked by p.. The illustration shows that, even if a build-up curve is available and can be extrapolated, a correction

By R. S. Busk, E. G. Bobalek

The relation between gases and metals has been a subject of increasingly active investigation during the past years, principally devoted to the study of metal-hydrogen systems. It has been found that hydrogen is soluble in most molten metals to an appreciable extent and somewhat soluble in most solid metals.l,2 In every known case there is a sudden decrease in solubility at the melting point. Thus a freezing mass of metal containing hydrogen in excess of the solid solubility must in some way expel that excess during the freezing process. This leads to internal blowholes, and such effects as pinhole porosity. Gas trapped in metal that is to be fabricated by a working process such as extrusion or rolling may be the cause of blisters. For some cases, notably in copper and iron alloys, the presence of hydrogen can lead to extreme embrittle-ment of the metal. The aluminum-casting industry has long recognized the importance of hydrogen in its techniques. Excess gas in molten aluminum alloys often leads to the formation of "pinhole porosity" in the solid casting.= To prevent this hydrogen pickup it is necessary to avoid overheating the melt and to protect it from such sources of hydrogen as water. In spite of all precautions, it is sometimes necessary to extract hydrogen from the melt just before pouring by bubbling with a gas such as chlorine or nitrogen. Reccntly it has been found that somewhat similar effects are possible with magnesium alloys, in that the presence of hydrogen can induce or aggravate micro-p~rosity.4-6 This paper is primarily concerned with a presentation of some facts concerning the solubility of hydrogen in magnesium and its alloys, with some discussion of the significance of these facts in a practical sense. In any study of gas-metal systems it is important to bear in mind a clear distinction between adsorption on surfaces and absorption within the lattice.' Considerable attention has been directed toward determining whether hydrogen is truly soluble in any solid metal, or whether the gas extracted from a sample was present at surfaces (external and internal) only.7 Most present day evidence supports the idea of true solution in addition to adsorption. A second important factor when dealing with gas solubility is the dependence of such solubility on external pressure. For diatomic gases such as H², solubility in both liquid and solid metals apparently is proportional to the square root of the pressure, indicating a breakdown to a monatomic gas before diffusion into the lattice.= For true equilibrium values of solubility, therefore, the pressure at the the surface must be constant and, preferably, known. Very little has been published concerning the hydrogen-magnesium system. Winterhager has presented the most

Jan 1, 1947

By R. S. Busk, E. G. Bobalek

The relation between gases and metals has been a subject of increasingly active investigation during the past years, principally devoted to the study of metal-hydrogen systems. It has been found that hydrogen is soluble in most molten metals to an appreciable extent and somewhat soluble in most solid metals.l,2 In every known case there is a sudden decrease in solubility at the melting point. Thus a freezing mass of metal containing hydrogen in excess of the solid solubility must in some way expel that excess during the freezing process. This leads to internal blowholes, and such effects as pinhole porosity. Gas trapped in metal that is to be fabricated by a working process such as extrusion or rolling may be the cause of blisters. For some cases, notably in copper and iron alloys, the presence of hydrogen can lead to extreme embrittle-ment of the metal. The aluminum-casting industry has long recognized the importance of hydrogen in its techniques. Excess gas in molten aluminum alloys often leads to the formation of "pinhole porosity" in the solid casting.= To prevent this hydrogen pickup it is necessary to avoid overheating the melt and to protect it from such sources of hydrogen as water. In spite of all precautions, it is sometimes necessary to extract hydrogen from the melt just before pouring by bubbling with a gas such as chlorine or nitrogen. Reccntly it has been found that somewhat similar effects are possible with magnesium alloys, in that the presence of hydrogen can induce or aggravate micro-p~rosity.4-6 This paper is primarily concerned with a presentation of some facts concerning the solubility of hydrogen in magnesium and its alloys, with some discussion of the significance of these facts in a practical sense. In any study of gas-metal systems it is important to bear in mind a clear distinction between adsorption on surfaces and absorption within the lattice.' Considerable attention has been directed toward determining whether hydrogen is truly soluble in any solid metal, or whether the gas extracted from a sample was present at surfaces (external and internal) only.7 Most present day evidence supports the idea of true solution in addition to adsorption. A second important factor when dealing with gas solubility is the dependence of such solubility on external pressure. For diatomic gases such as H², solubility in both liquid and solid metals apparently is proportional to the square root of the pressure, indicating a breakdown to a monatomic gas before diffusion into the lattice.= For true equilibrium values of solubility, therefore, the pressure at the the surface must be constant and, preferably, known. Very little has been published concerning the hydrogen-magnesium system. Winterhager has presented the most

Jan 1, 1947

By R. S. Busk, E. G. Bobalek

THE relation between gases and metals has been a subject of increasingly active investigation during the past years, principally devoted to the study of metal-hydrogen systems. It has been found that hydrogen is soluble in most molten metals to an appreciable extent and somewhat soluble in most solid metals.1,2 In every known case there is a sudden decrease in solubility at the melting point. Thus a freezing mass of metal containing hydrogen in excess of the solid solubility must in some way expel that excess during the freezing process. This leads to internal blowholes, and such effects as pinhole porosity. Gas trapped in metal that is to be fabricated by a working process such as extrusion or rolling may be the cause of blisters. For some cases, notably in copper and iron alloys, the presence of hydrogen can lead to extreme embrittlement of the metal. The aluminum-casting industry has long recognized the importance of hydrogen in its techniques. Excess gas in molten aluminum alloys often leads to the formation of "pinhole porosity" in the solid casting.3 To prevent this hydrogen pickup it is necessary to avoid overheating the melt and to protect it from such sources of hydrogen as water. In spite of all precautions, it is sometimes necessary to extract hydrogen from the melt just before pouring by bubbling with a gas such as chlorine or nitrogen. Recently it has been found that somewhat similar effects are possible with magnesium alloys, in that the presence of hydrogen can induce or aggravate microporosity.4-6 This paper is primarily concerned with a presentation of some facts concerning the solubility of hydrogen in magnesium and its alloys, with some discussion of the significance of these facts in a practical sense. In any study of gas-metal systems it is important to bear in mind a clear distinction between adsorption on surfaces and absorption within the lattice.1 Considerable attention has been directed toward determining whether hydrogen is truly soluble in any solid metal, or whether the gas extracted from a sample was present at surfaces (external and internal) only.7 Most present day evidence supports the idea of true solution in addition to adsorption. A second important factor when dealing with gas solubility is the dependence of such solubility on external pressure. For diatomic gases such as H2, solubility in both liquid and solid metals apparently is proportional to the square root of the pressure, indicating a breakdown to a monatomic gas before diffusion into the lattice .2 For true equilibrium values of solubility, therefore, the pressure at the metal surface must be constant and, preferably, known. Very little has been published concerning the hydrogen-magnesium system. Winterhager has presented the most

Jan 1, 1946

By M. R. Pickus, I. W. Pickus

Ordinarily age-hardening is thought of as being associated with a limited solubility of one metal in another. Much less has been written about the type of age-hardening that attends the formation of superstructures. Solid solutions generally have a disordered or random arrangement of atoms; that is to say, in a unit cell, such as that of the face-centered cubic lattice, there is no distinction between atomic sites. Atoms of a given metal may occupy cube corners or face centers. Under certain conditions, however, some alloys develop what is known as an ordered structure. In this case, cube corners would be occupied by only one type of atom and face centers by another type. Associated with this ordering process are many interesting changes in physical and electrical properties. Moreover, in many instances the alloys become susceptible to age-hardening. From the evidence now to be described, it appears that age-hardening in 14-carat gold alloys is due to the formation of both a superstructure and a precipitate. Alloys of the metals gold, silver and copper were known in antiquity. The available knowledge regarding their constitution has been ably summarized and extended by Sterner-Rainer,' Jänecke,2 Carter,3 Wise,4 and Coleman.5 Despite the long familiarity with these alloys and the numerous investigations of their properties that have been made, there is still much that remains unexplained. It has been known for a long time that the hardness of these alloys is closely related to the rate of cooling. Similar changes have been observed in the binary gold-copper systemI6 one alloy of which corresponding to the formula CU³AU, has been the subject of a careful and competent report by the English investigators, Sykes and Evans.7 They have established the fact that the shift of atoms from the ordered to the disordered condition takes place in some critical temperature range. At temperatures above the critical range the structure is random, and at temperatures below it the structure is ordered. No difference between these two structures is revealed by the microscope. Both have a face-centered cubic lattice and complete solubility, so that there is no evidence to suggest that the changes in properties are associated with a phase change. The more slowly the alloy is cooled, the higher is the degree to which the ordering process proceeds and the more marked is the increase in hardness. As experimental data were accumulated on I4-carat gold alloys, several contradictions arose. Certain observations tended to confirm the existence of a superstructure, while other observations seemed to be inconsistent with such a transformation. Present Investigation As a focal point about which to develop this subject, it is expedient to consider first

Jan 1, 1943

By M. R. Pickus, I. W. Pickus

Ordinarily age-hardening is thought of as being associated with a limited solubility of one metal in another. Much less has been written about the type of age-hardening that attends the formation of superstructures. Solid solutions generally have a disordered or random arrangement of atoms; that is to say, in a unit cell, such as that of the face-centered cubic lattice, there is no distinction between atomic sites. Atoms of a given metal may occupy cube corners or face centers. Under certain conditions, however, some alloys develop what is known as an ordered structure. In this case, cube corners would be occupied by only one type of atom and face centers by another type. Associated with this ordering process are many interesting changes in physical and electrical properties. Moreover, in many instances the alloys become susceptible to age-hardening. From the evidence now to be described, it appears that age-hardening in 14-carat gold alloys is due to the formation of both a superstructure and a precipitate. Alloys of the metals gold, silver and copper were known in antiquity. The available knowledge regarding their constitution has been ably summarized and extended by Sterner-Rainer,' Jänecke,2 Carter,3 Wise,4 and Coleman.5 Despite the long familiarity with these alloys and the numerous investigations of their properties that have been made, there is still much that remains unexplained. It has been known for a long time that the hardness of these alloys is closely related to the rate of cooling. Similar changes have been observed in the binary gold-copper systemI6 one alloy of which corresponding to the formula CU³AU, has been the subject of a careful and competent report by the English investigators, Sykes and Evans.7 They have established the fact that the shift of atoms from the ordered to the disordered condition takes place in some critical temperature range. At temperatures above the critical range the structure is random, and at temperatures below it the structure is ordered. No difference between these two structures is revealed by the microscope. Both have a face-centered cubic lattice and complete solubility, so that there is no evidence to suggest that the changes in properties are associated with a phase change. The more slowly the alloy is cooled, the higher is the degree to which the ordering process proceeds and the more marked is the increase in hardness. As experimental data were accumulated on I4-carat gold alloys, several contradictions arose. Certain observations tended to confirm the existence of a superstructure, while other observations seemed to be inconsistent with such a transformation. Present Investigation As a focal point about which to develop this subject, it is expedient to consider first

Jan 1, 1943

By H. A. Sawin, C.M. Romanowitz

Placer dredging as we know it today, especially gold dredging, is an industry about 40 years old, dating from the beginning of this century, when a few mining men in California saw the possibilities in adapting earlier dredging methods to California placer fields in and immediately adjacent to streams. At first it was thought that dredges must be operated in existing stream beds, but experience soon pointed the way to dredging alluvial deposits of old stream beds, operating on landlocked dredging ponds. Within the first five or six years of modern dredging, experience was gained so rapidly that dredges to dig 60 ft. below water level were *designed and built. This depth was believed by many operators to be the maximum at which successful dredging could be carried on. Alluvial deposits of gold, suitable for dredging, were readily handled by equipment available and developed early in the industry's history. Much of the gravel was easily dug and if deposits were cemented, contained large boulders, or for some other reason could not be handled by a dredge, the ground was abandoned in favor of other deposits that could be handled easily. Many failures, adversely affecting the dredging industry, resulted from attempts at that time to extend the scope of placer dredging with equipment not suited to the formation being dredged. Dredging ground suited to early equipment was exhausted eventually, but many supposedly undredgeable alluvial fields containing gold in commercial quantities were found and became known to dredgemen. Improved equipment was needed to work deposits known to exist at great depths or associated with unusual obstructions. Operating companies looked to dredge manufacturers and metallurgists, particularly manganese-steel foundries, for improved designs and materials. Experience developed in California has spread throughout the world, and dredges of improved types have been adapted to the mining of platinum and tin as well as gold. Space will not permit a description of all the improvements in dredging since the early days, but a few of the recent developments are worthy of note, because they make possible the dredging of placer deposits of great depth, those having hard, irregular bedrock or containing large boulders in great quantities, and compacted or cemented gravel deposits. Deep Dredging At Hammonton, calif., yuba consolidated Gold Fields has, within= the past two years, built its dredge No. 20. The company has operated continuously in that field since 1904, digging successively at maximum depths of 60 ft., 80 ft., 112 ft., and now 124 ft. below water level. The first dredges were equipped with buckets of 6 and 7½-cu. ft. capacity; six dredges operating in the field today have 18-cu. ft. buckets, digging now 65 to 124 ft. below water level. Some ground near Hammonton has been dug for the third time, owing to the devel-

Jan 1, 1943

By C. M. Romanowitz, H. A. Sawin

Placer dredging as we know it today, especially gold dredging, is an industry about 40 years old, dating from the beginning of this century, when a few mining men in California saw the possibilities in adapting earlier dredging methods to California placer fields in and immediately adjacent to streams. At first it was thought that dredges must be operated in existing stream beds, but experience soon pointed the way to dredging alluvial deposits of old stream beds, operating on landlocked dredging ponds. Within the first five or six years of modern dredging, experience was gained so rapidly that dredges to dig 60 ft. below water level were *designed and built. This depth was believed by many operators to be the maximum at which successful dredging could be carried on. Alluvial deposits of gold, suitable for dredging, were readily handled by equipment available and developed early in the industry's history. Much of the gravel was easily dug and if deposits were cemented, contained large boulders, or for some other reason could not be handled by a dredge, the ground was abandoned in favor of other deposits that could be handled easily. Many failures, adversely affecting the dredging industry, resulted from attempts at that time to extend the scope of placer dredging with equipment not suited to the formation being dredged. Dredging ground suited to early equipment was exhausted eventually, but many supposedly undredgeable alluvial fields containing gold in commercial quantities were found and became known to dredgemen. Improved equipment was needed to work deposits known to exist at great depths or associated with unusual obstructions. Operating companies looked to dredge manufacturers and metallurgists, particularly manganese-steel foundries, for improved designs and materials. Experience developed in California has spread throughout the world, and dredges of improved types have been adapted to the mining of platinum and tin as well as gold. Space will not permit a description of all the improvements in dredging since the early days, but a few of the recent developments are worthy of note, because they make possible the dredging of placer deposits of great depth, those having hard, irregular bedrock or containing large boulders in great quantities, and compacted or cemented gravel deposits. Deep Dredging At Hammonton, calif., yuba consolidated Gold Fields has, within= the past two years, built its dredge No. 20. The company has operated continuously in that field since 1904, digging successively at maximum depths of 60 ft., 80 ft., 112 ft., and now 124 ft. below water level. The first dredges were equipped with buckets of 6 and 7½-cu. ft. capacity; six dredges operating in the field today have 18-cu. ft. buckets, digging now 65 to 124 ft. below water level. Some ground near Hammonton has been dug for the third time, owing to the devel-

Jan 1, 1943

By M. T. Worley

This paper reports investigative work conducted to develop a method of estimating the groundwater influx from a homogeneous permeable formation into a vertical mine shaft during sinking. A method of analysis was developed using data obtained from pumping tests and a modification of the Theis non-equilibrium interpretation technique. Excess influx of groundwater into mine shafts has long been one of the more important problems encountered in the development of a mining property. Much work has been done on methods of preventing such influx and on pumping schemes to control inflow if preventive measures fail. The fundamental aspects of the problem, on the other hand, seem to have been neglected. The purpose of this paper is to review the fundamentals of groundwater flow and to propose a rapid method of analyzing hydrologic data in order to estimate influx from a homogeneous permeable formation into a mine shaft. Such an estimate of the quantity of water to be encountered is of value in planning grouting, pumping and other programs designed to control that influx. It is emphasized that the proposed method of analysis should be regarded only as a tool to be used in evaluating the problem before investing the capital necessary to begin development of a property. FUNDAMENTALS OF GROUNDWATER FLOW In order to effectively approach the problem of estimating influx into a mine shaft, a knowledge of the fundamentals of fluid flow through a porous medium is necessary. Darcy, in 1856, developed an empirical relationship to explain the flow of water through sand filters. This relationship V = k (dh/dl), is the basis for all other flow formulae. It has been shown that Darcy's relation is a solution of the Laplace equation and thus is analagous to other natural phenomena such as heat flow. Theis, using the analogy of heat flow by conduction, developed an expression for determining the transient or time-dependent groundwater flow through a homogeneous, isotropic medium. The resulting equation Was also derived by Jacob using hydrologic considerations alone.' The individual terms in the equation are described in Table I. It is important to understand the assumptions upon which this equation is based. 1) The medium through which the fluid flows is infinite in areal extent, homogeneous and isotropic. 2) The well into which the fluid discharges completely penetrates the medium. 3) The characteristics of the medium remain constant at all times. 4) The initial pressure surface is horizontal. 5) The confining media are impervious and horizontal. 6) Fluid is removed from storage instantaneously by a decline in pressure. 7) The diameter of the discharge well is infinitesimal with respect to the drainage radius of the medium.

Jan 1, 1962

By C. M. Romanowitz, H. A. Sawin

PLACER dredging as we know it today, especially gold dredging, is an industry about 40 years old, dating from the beginning of this century, when a few mining men in California saw the possibilities in adapting earlier dredging methods to California placer fields in and immediately adjacent to streams. At first it was thought that dredges must be operated in existing stream beds, but experience soon pointed the way to dredging alluvial deposits of old stream beds, operating on landlocked dredging ponds. Within the first five or six years of modern dredging, experience was gained so rapidly that dredges to dig 60 ft. below water level were designed and built. This depth was believed by many operators to be the maximum at which successful dredging could be carried on. Alluvial deposits of gold, suitable for dredging, were readily handled by equipment available and developed early in the industry's history. Much of the gravel was easily dug and if deposits were cemented, contained large boulders, or for some other reason could not be handled by a dredge, the ground was abandoned in favor of other deposits that could be handled easily. Many failures, adversely affecting the dredging industry, resulted from attempts at that time to extend the scope of placer dredging with equipment not suited to the formation being dredged. Dredging ground suited to early equipment was exhausted eventually, but many supposedly undredgeable alluvial fields containing gold in commercial quantities were found and became known to dredgemen. Improved equipment was needed to work deposits known to exist at great depths or associated with unusual obstructions. Operating companies looked to dredge manufacturers and metallurgists, particularly manganese-steel foundries, for improved designs and materials. Experience developed in California has spread throughout the world, and dredges of improved types have been adapted to the mining of platinum and tin as well as gold. Space will not permit a description of all the improvements in dredging since the early days, but a few of the recent developments are worthy of note, because they make possible the dredging of placer deposits of great depth, those having hard, irregular bedrock or containing large boulders in great quantities, and compacted or cemented gravel deposits. DEEP DREDGING At Hammonton, Calif., Yuba Consolidated Gold Fields has, within the past two years, built its dredge No. 20. The company has operated continuously in that field since 1904, digging successively at maximum depths of 60 ft., 80 ft., 112 ft., and now 124 ft. below water level. The first dredges were equipped with buckets of 6 and 7 1/2-cu. ft. capacity; six dredges operating in the field today have 18-cu. ft. buckets, digging now 65 to 124 ft. below water level. Some ground near Hammonton has been dug for the third time, owing to the devel-

Jan 1, 1941

By A. Berghezan, E. Bull Simonsen

A simple and general method is described for melting and zone refining refractory metals by induction heating on a specially shaped water-cooled copper crucible. The crucible is the essential part of the apparatus and is placed horizontally. It consists of either a copper plate, or a flattened tube, or of several parallel small diameter tubes all water cooled. The charge lies on the crucible, or whenever possible, is suspended above it. This assembly goes into a transparent quartz tube and the whole is passed through the coil of a radio frequency generator. Vaarious atmospheres can be used. No contamination is detected from the copper crucible. purification is obtained both by selective evaporation of impurities and by zone refining. METHODS of melting and refining relatively large ingots of all reactive and refractory metals as well as some semiconductor materials have been developed in this laboratory during the past several years using induction heating and cold crucibles. These methods are simple and permit the use of a variety of starting materials in preparing ingots of suitable shapes. Among these methods, two are of particular interest. One deals only with the problem of melting without contamination. In this method the induction coil has a specially designed shape and acts simultaneously as heating element and crucible. The second goes one step further, being designed for both melting and further purification of the refractory metals. The aim of this paper is to describe the second method which is of more general interest and of greater applicability to metallurgical problems. A) THE PRINCIPLE OF THE MELTING AND PURIFICATION METHOD As originally proposed by one of us1 the method consists of heating a charge of any refractory metal or semiconductor material to the melting point on a water-cooled copper crucible by passing both the charge and the crucible through the induction coil of a radiofrequency generator. Although both are subjected to the same induction field, one achieves the melting of a refractory metal on a copper crucible even when the refractory metal has a melting point of more than 2000°C above that of the crucible. This seemingly "odd" method works effectively for the following reasons. Because of its high electrical and thermal conductivity as compared with the material being melted, copper can be used as the crucible and kept at a low temperature while the material is heated by induction to its melting point. With water Silver and other highly conducting materials can also be used. If a nonconducting material is contemplated, e.g. SiO or a high polymer, a very thin wall should provide efficient cooling. cooling through ducts in the crucible its temperature can be kept between 40" to 70°C; thus its electrical resistivity is kept low, while the resistivity of the charge increases rapidly as its temperature is increased. B) APPARATUS The crucible is the essential part of the apparatus. It has been designed in various shapes depending on the atmosphere used, whether vacuum or an inert gas or hydrogen. In all crucible designs an effort was made to reduce its volume to "nothing but the cooling water" in order to avoid shielding the ingot from the induction field. In practice it is either a

Jan 1, 1962

By E. F. Sturcken, J. W. Croach

A grain orientation distribution function, P(u,F), was developed for use in predicting physical properties in oriented metals. Examples are given of the use of the function to predict thermal expansion coefficients in rolled uranium rods and plate. The P(u,F) function was synthesized from X-ray difpaction intensity measurements, Ii, norrnally used to plot inverse pole figures. The symbols u and F specify the angles that the crystallographic axes of the grain make with the normal to the sample surface and P(u, F) gives the number of grains oriented in each direction, (u,F). P(u,F) is obtained from a least squares fit of the Ii to an orthonormal set of spherical harmonic functions. The P(u, F) function was also used to define a quantity, J, which is a measure of the departure of the orientation distribution from unifomzity (or "randomness"). The J parameter may be used to follow, quantitatively, the amount of preferred orientation induced as a function of mechanical working or heat treatment. An example is given of the application of the J parameter to prefevred orientation studies of hot- and cold-rolled uranium rods and hot-rolled uranium plate. Because P(u,F) is derived from relative intensity measurements by the powder diffraction technique, it is applicable to material with large absorption coefficients and/or grain size and is particularly suitable for characterizing the preferred orientation of large numbers of samples such as fuel elenzents for a nuclear reactor. IN general the physical properties of an oriented metal depend on the direction in which the properties are measured. Hence to predict physical properties the grain orientation must be known as a function of the direction of the specimen. The conventional methods of expressing preferred orientation measurements are the pole figure1 and the inverse pole figure.2-8 Both methods are difficult to use for predicting physical propertiess because they are graphical and because they are stereographic projections and hence are not "area-true." In the present report a quantitative orientation distribution function, P(u,F), is synthesized from pole density measurements normally used to plot inverse pole figures. For inverse pole figure plots the pole densities, pi, are obtained by powder dif-fractometer intensity measurements of their reflections from a flat surface of the sample, normal to the direction of interest. Each pole density, pi, represents a single orientation, i, and is proportional to the volume of material with orientation, i; hence a set of pi gives an approximation for the general orientation for the sample direction measured. The expression8'7 for calculating the pole densities, pi, from the diffraction measurements was previously

Jan 1, 1963

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By S. W. Poole, J. A. Rosa

The object of this investigation was to determine the distribution of chemical elements within a large, killed alloy-steel ingot, by sulphur printing and quantitative chemical analysis. With regard to segregation in steel ingots, the factors of melting practice, pouring temperatures, mold design, etc., and the mechanics of solidification and its attendant functions, have been the subject of intensive study over a period of years by many investigators. Notable among these is the Sub-committee of the No. 5 Committee of the British Iron and Steel Institute. For an exposition of the many problems awaiting the researcher on the heterogeneity of steel ingots, the methods of attacking these problems, together with some of the answers, the reader is referred to the nine reports and numerous papers of that committee and its membership. Steelmaking Data Melt.—The heat was made in a 70-ton direct arc-type basic electric furnace. Furnace charge consisted of nickel-chromium-molybdenum steel, most of it in the form of heavy mill scrap. All of the scrap was charged cold. The standard double-slag method was employed, the heat being finished under a strong carbide slag. Aluminum was used as the deoxidizing agent. Tapping tempera- ture, as observed with an optical pyrometer, was 3000°F. Detail of Mold and Ingot Size.—Details of the ingot mold and the ingot itself are given in Fig. I. Teeming.—Teeming temperature of the subject ingot as observed with an optical pyrometer was 2830°F. The ingot was top-poured directly through a 1 1/2-in. nozzle and required 7 min., 44 sec. to fill up to the hot top. An additional 2 min., 30 sec. were required to fill the hot top. The ingot was stripped hot and charged with the remainder of the heat into an annealing furnace. There it was given the standard annealing cycle used for these ingots. Subsequent heat-treatments are described elsewhere in this paper. Sectioning and Preparation for Sulphur Printing Because of previous favorable experience in sectioning ingots up to 21 1/2 in. square with an oxyacetylene torch, it was decided to use this method to section the subject ingot. The ingot was preheated to 900°F. for 12 hr. It was then placed on a steel bed in a horizontal position so that the longitudinal axis was level and parallel to the track of the motor-driven torch carrier. Two cuts were made, one 2 in. above the longitudinal axis and the other 2 in. below. The time required to make each cut was approximately 75 min. The cutting operation is shown in Figs. 2 and 3. The 4-in. thick slab was mmediately charged into a furnace standing at 1200F.

Jan 1, 1945

By J. E. Burke, Y. G. Shiau

SEVERAL attempts have been made to account for the fact that grains in a fully recrystallized metal will coarsen on annealing Two fundamentally different hypotheses have been advanced; with several variations of each. One school considers that the cause of grain growth is the surface energy of the grain boundary The theory of Jeffries1 that grain size and grain size contrast control growth is an example The second school considers the primary cause to be a difference in the lattice energy on either side of the grain boundary The more perfect grains are considered to grow at the expense of their less perfect neighbors, with a decrease in free energy, and a consequent increase in the stability of the system. Burgers2 presents the case for the strain or lattice imperfection theory of grain growth quite completely The latter theory is attractive, since there is no doubt that differences in lattice energy or lattice perfection can cause grain boundary migration A recrystallization nucleus grows for this reason as was beautifully demonstrated by van Arkel and Ploos van Amstel3 Although it is generally stated that grain growth does not precede recrystallization, several workers4,5 have shown that small strains may induce a single crystal in an aggregate to grow, or at least may cause some' grain boundary migration The origin and nature of the imperfections that are considered to be responsible for normal grain growth have never been clearly described, but it is generally agreed that they are a consequence of the difficulty of atomic reorientation in the solid state, and that they do not seriously differ from the type of imperfection that-can be introduced by mechanical deformation An object of the present work was to determine whether the introduction of mechanical deformation would cause grain growth in a specimen which would not otherwise show it under the conditions used It was also planned to determine the effect of such deformation the rate of growth in a specimen which would show - growth in the unstrained condition Recently Maddigan and Blank6 have indicated that slightly strained specimens of alpha brass can undergo considerable growth prior to recrystallization if annealed at low temperatures French7 has reported that at deformations less than 17 pct it is very difficult to detect the beginning of recrystallization in the same material. It was therefore planned to broaden this work to include a complete study of the microscopic behavior of alpha brass under conditions of temperature, time, grain size and deformation such that recrystallization would not occur or would occur to only a small extent EXPERIMENTAL PROCEDURE The brass was prepared by melting cathode copper and commercially pure zinc

Jan 1, 1947

By B. M. Larsen, L. S. Darken

Some years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general, our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2) by a high concentration of active (or "free") lime and of manganese oxide dissolved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. Distribution 02 Manganese between Slag and Metal at Equilibrium On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction FeO + Mn -& MnO + Fe [A] slag metal slag metal the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as K,, _ aMnO' afe aFeO ' aMn where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term afe may be combined with K" to give a new constant K'. Making these changes, 7

Jan 1, 1942

By B. M. Larsen, L. S. Darken

Some years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general, our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2) by a high concentration of active (or "free") lime and of manganese oxide dissolved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. Distribution 02 Manganese between Slag and Metal at Equilibrium On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction FeO + Mn -& MnO + Fe [A] slag metal slag metal the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as K,, _ aMnO' afe aFeO ' aMn where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term afe may be combined with K" to give a new constant K'. Making these changes, 7

Jan 1, 1942

By B. M. Larsen, L. S. Darken

SOME years ago we collated all laboratory data then available to us on the distribution at equilibrium of manganese and of sulphur between metal and simple slags, and used the results in setting up an equation, which proved to be in accord with determinations of the distribution ratio of manganese and of sulphur between liquid steel and open-hearth slag, over a wide range of operating conditions. We now present an outline of our calculations and inferences on these two closely related questions, which are of especial importance because of the advisability of conserving manganese wherever possible. In general. our results show that in the open-hearth furnace equilibrium between metal and slag, with respect to both manganese and sulphur, is substantially attained during the finishing period of the heat, or in about a half hour to an hour after any additions were made. This implies that the end result will be identical whether manganese is added as alloy or metal to the liquid steel or as oxide to the slag. The proportion of total manganese retained by the steel is favored: (I) by use of the minimum amount of lime, consistent with other operating limitations, required to give a lime-silica ratio of about 2.4, which usually corresponds to a minimum practical slag volume; (2) by a high concentration in the slag of MnO relative to FeO; (3) by high operating temperature. Absorption of sulphur by the slag from the liquid metal is favored: (I) by large slag volume; (2-by a high concentration of active (or "free") lime and of manganese oxide dis) solved in the slag; (3) by low concentration of silica, iron oxide, and phosphate dissolved in the slag. DISTRIBUTION OF MANGANESE BETWEEN SLAG AND METAL AT EQUILIBRIUM On the basis that the distribution of manganese between liquid steel and slag is controlled by the reaction [FeO + Mn ;7± MnO + Fe [A] slag metal slag metal] the distribution at equilibrium, at a given temperature, is expressed by the equilibrium constant for this reaction, which is defined as [K" aFPI OFeO ? aMn] where a is the activity of the molecular species denoted by the subscript. The activity of each of the several components, although it is not known precisely, is approximately equal to the concentration of each component expressed as its mol fraction; that is, as the ratio of the number of mols of the given component to the total number of mols of all the molecular species present in the metal or slag, as the case may be. Moreover, since the activity, or concentration, of iron in the liquid metal is in fact substantially constant, the term aFe may he combined with K" to give a new constant K'. Making these changes.

Jan 1, 1942

By V. H. Wilhelm

The year 1941 in the California oil industry was marked by an increased market demand, drilling activity, and production of crude oil. Although seven new oil fields and two gas fields were discovered during the year, additions to reserves from these discoveries, as well as extensions and revaluations of previous discoveries, were approximately 100 million barrels, as against estimated withdrawals of 230,233,000 barrels. The year was remarkable for the very great increase in domestic demand for all products, which more than compensated for the loss in shipments to Japan, which averaged 60,041 bbl. Per day during 1940. Demand in terms of crude during 1941 was 648,967 bbl. per day as against 632,647 for the same period in 1940. This abnormal increase in demand is due to increased industrial activity, and especially increased railroad activity. Gasoline consumption for 1941 was 241,011 bbl. per day as against 217,744 in 1940. Demand for fuel oil increased from 259,806 bbl. per day in 1940 to 285,896 in 1941, and caused a withdrawal from stocks of more than 7,473,000 barrels. During 1941, total oil storage declined 9,153,000 bbl., but additions to storage of 1,754,000 bbl. of light oil and light oil products were offset by a withdrawal of 10,907,000 bbl. of heavier products. Production during the year is estimated at 230,233,000 bbl. as against 222,784,386 bbl. for 1940. TraNsportation For a short time, California was affected by lack of transportation due to the diversion of tankers. This shortage affected the movement of oil from the Sari Joaquin mated to the refineries, since a large percentage of this production is moved to the coast through pipe lines, and thence by tankers to Los Angeles and San Fran-,iSco, Return of the tanker fleet, which may be temporary, indicates that there is a possibility of ample supplies of petroleum products in the Pacific Northwest. Drilling Activity Contrary to general opinion, drilling activity increased in 1941 over the pre-vious Year, 942 wells being completed in 1941 as against 890 in 1940, an increase Of 6 per cent. This increase was due to the increased demands for fuel oil, and also to the decreased drilling costs, which made many former marginal locations economic. The main activity caused by increased demands for fuel oil was in the Mt. Poso, McKittrick, Midway and Santa Maria Valley oil fields. Dry-hole footage in 1941 was 655,354 ft. as against 583,537 ft. for 1940. Curtailment Voluntary curtailment succeeded in holding production considerably below demand, although it was above the state quota. During the year the top allotment

Jan 1, 1942