Search Documents

By G. Rowan, M. W. Clegg

The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including: gravity drainage of depletion-type reservoirs; multiple well systems; well interference. INTRODUCTION A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages — the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov,1 who (a) postulated a disturbed zone in the reservoir, the radius of which increases with time, and (b) replaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following: 1. That the flow is irrotational. 2. That the formation is of constant thickness. 3. Darcy's Law is valid. 4. The formation is saturated with a single homogeneous fluid.

By C. G. Dunn

James, Jones, and Leak (JJL) conclude that growth-rate and orientation-distribution data obtained in a steep thermal gradient should be used with caution to account for isothermally produced recrystallization textures. I agree. However, it is not clear whether they conclude a) that the orientation dependence of rate of growth of secondaries in (commercial) silicon iron depends on both temperature and a temperature gradient or b) that, in applying rate data obtained in a steep thermal gradient, the isothermal annealing temperature must be close to the temperature for which the rate data apply. Also, it is not clear what tem-

Jan 1, 1967

By M. E. Gershon

A mixed-integer formulation of the mine scheduling problem is discussed and applied for the purpose of optimizing both the mine production sequencing and the mill blending and processing problem simultaneously. Previous attempts at solving these problem separately, although successful, fail to take into account the interrelationships between these problems. Project structure selves as the outline of this paper Generalized in its organization, this concept is useful for long, intermediate, and short range scheduling. Actual applications that show the concept also is applicable to mining a variety of ore are mentioned.

Jan 1, 1984

By Takahide Wakamatsu, Douglas W. Fuerstenau

Contact angles on alumina are related directly to the adsorption of alkyl sulfonates at the solid-water interface and thus are strongly controlled by the pH of the solution, the concentration of surfactant, and the number of carbon atoms in the alkyl chain. As the pH of the solution is increased above the point of zero charge, sulfonate adsorption ceases and alumina remains hydrophilic. However, in neutral and acidic solutions, contact angles increase markedly in magnitude when the adsorbed sulfonate ions form hemimicelles at the solid-water interface. Under a wide variety of solution conditions, a limiting value of the contact angle is attained at the point of reversal of the zeta potential. Finally, contact angle phenomena are empirically correlated with the sulfonate adsorption density through the work of adhesion.

Jan 1, 1974

By J. Rogers, H. F. A. Hergt, K. L. Sutherland

IN 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group -SO4- or _S03- are excellent collectors for cassiterite and promise to be selective.1 The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000gram Denver cell. EXPERIMENTAL METHODS Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously described.5-10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these tests determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver Submachines.--Melbourne tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By J. Rogers, K. L. Sutherland

THE relationships between collector and mineral, activator and mineral, and activator, collector and mineral will be considered herein. We propose to criticize current theories of flotation but we will not repeat the many pertinent arguments presented by Wark and Cox28 in 1937 in which the "chemical" or more strictly the "solubility" theory proposed by Taggart and co-workers22 is shown to be untenable. Recently Taggart, Arbiter and Kellogg24 have studied the long-chain aliphatic amines as collectors and have attempted to resuscitate the solubility theory for these particular collectors. Dean and Ambrose3 have felt that "we stumble over words" when we distinguish different mechanisms of adsorption. Our view is that nothing is more stultifying to the development of a science than attempts to force widely different phenomena into one classification. This oversimplification leads immediately to difficulties in the interpretation of results. EXPERIMENTAL PROCEDURE The response of minerals to activator and collector was determined by "captive-bubble" tests. The methods of preparation of specimens26 and of testing18 have been previously described. Results from captive-bubble tests were confirmed by flotation tests in glass-stoppered cylinders.25 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible by a cross and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, the experimental results being indicated on the figures by a square. The curves show the limits of composition of solution in which flotation in a cell would be possible. Many factors other than those considered in these tests determine recovery or grade of a given mineral in practice.

Jan 1, 1947

By H. F. A. Hergt, K. L. Sutherland, J. Rogers

In 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group — SO4- or — SO3- are excellent collectors for cassiterite and promise to be selective. The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000-gram Denver cell. Experimental Methods Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously de- scribed.5,10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these the determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver SUbmachines,—Melboume tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By J. Rogers, H. F. A. Hergt, K. L. Sutherland

In 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group — SO4- or — SO3- are excellent collectors for cassiterite and promise to be selective. The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000-gram Denver cell. Experimental Methods Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously de- scribed.5,10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these the determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver SUbmachines,—Melboume tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By K. L. Sutherland, J. Rogers

The relationships between collector and mineral, activator and mineral, and activator, collector and mineral will be considered herein. We propose to criticize current theories of flotation but we will not repeat the many pertinent arguments presented by Wark and Cox28 in 1937 in which the "chemical" or more strictly the "solubility" theory proposed by Taggart and co-workers22 is shown to be untenable. Recently Taggart, Arbiter and Kellogg24 have studied the long-chain aliphatic amines as collectors and have attempted to resuscitate the solubility theory for these particular collectors. Dean and Ambrose3 have felt that "we stumble over words" when we distinguish different mechanisms of adsorption. Our view is that nothing is more stultifying to the development of a science than attempts to force widely different phenomena into one classification. This oversimplification leads immediately to difficulties in the interpretation of results. Experimental Procedure The response of minerals to activator and collector was determined by "captive-bubble" tests. The methods of preparation of specimens26 and of testingin have been previously described. Results from captive-bubble tests were confirmed by flotation tests in glass-stoppered cylinders.26 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±o.2 pH units and ±5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible by a cross and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, the experimental results being indicated on the figures by a square. The curves show the limits of composition of solution in which flotation in a cell would be possible. Many factors other than those considered in these tests determine recovery or grade of a given mineral in practice.

Jan 1, 1947

By J. Rogers, K. L. Sutherland

The relationships between collector and mineral, activator and mineral, and activator, collector and mineral will be considered herein. We propose to criticize current theories of flotation but we will not repeat the many pertinent arguments presented by Wark and Cox28 in 1937 in which the "chemical" or more strictly the "solubility" theory proposed by Taggart and co-workers22 is shown to be untenable. Recently Taggart, Arbiter and Kellogg24 have studied the long-chain aliphatic amines as collectors and have attempted to resuscitate the solubility theory for these particular collectors. Dean and Ambrose3 have felt that "we stumble over words" when we distinguish different mechanisms of adsorption. Our view is that nothing is more stultifying to the development of a science than attempts to force widely different phenomena into one classification. This oversimplification leads immediately to difficulties in the interpretation of results. Experimental Procedure The response of minerals to activator and collector was determined by "captive-bubble" tests. The methods of preparation of specimens26 and of testingin have been previously described. Results from captive-bubble tests were confirmed by flotation tests in glass-stoppered cylinders.26 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±o.2 pH units and ±5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible by a cross and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, the experimental results being indicated on the figures by a square. The curves show the limits of composition of solution in which flotation in a cell would be possible. Many factors other than those considered in these tests determine recovery or grade of a given mineral in practice.

Jan 1, 1947

By James C. M. Li, J. Weertman

James C. M. Li (United States Steel Covp.)—The author has discovered a single analytical relation between the minimum, or the steady-state, creep rate and the applied stress confirming a statement made earlier by orn" that such relation should exist and should reduce to the power law at low-stress levels and to the exponential law at high-stress levels. However, as pointed out by the author, all the available theories of creep are not adequate to explain such a single relation. Inspired by such a statement, I have made a suggestion concerning a possible explanation13 of the new relation. This is based on the concept that the rate-controlling step is the cooperative motion of a short dislocation segment. The nature of and the reason for the cooperation have been discussed13 as well as the reason why the motion of the dislocation could be controlled by the mobility of the short segments. A natural short segment has been proposed13 to be the node formed at the intersection of two dislocations. The reason why the node may contain only a few atoms has not been discussed and the application of the proposed model to all the metals and alloys reported in this paper has not been attempted. It seems appropriate to include these in this discussion. The model was partly inspired by the substructure recently observed in the electron microscope on creep specimens. One such example is shown in Fig. 48 in Darken's Campbell Memorial Lecture. The substructure is a collection of dislocation intersections and irregular networks. No pileups have ever been observed in such specimens. A closer look at the network indicates that one set of dislocations is more straight than the other set sug- gesting that the other set may be mobile in the plane of the net. Since, for the network to survive the creep deformation, some dislocation reaction has to take place at the intersection of the two sets of dislocations, the mobile dislocation, even if it can slip in the plane of the net, will have difficulty in moving at these intersections. To illustrate, an idealized network is shown in Fig. 9. The thin lines represent the set of dislocations which are mobile and can slip in the plane of the net except at the nodes which are formed at the intersection of the two sets of dislocations. The other set of dislocations, represented by the thick lines, may have a Burgers vector which is not parallel to the plane of the net, and therefore may be immobile. Because of this nonparallel Burgers vector, the Burgers vector of the node, which is avectorial sum of the Burgers vectors of the two sets of dislocations, will also be nonparallel to the plane of the net. Therefore, the node cannot slip in the plane of the net and the set of mobile dislocations will have to drag the node along as indicated in Fig. 9. Now the problem is how many atoms could be involved in the nodes. Exact calculation of the length of the node is a difficult task especially since the length should be a steady-state length and not an equilibrium length. An estimate of the equilibrium length can be made by balancing the line tension of all the dislocations. The results would be a small fraction of the length 1 between nodes as shown in Fig. 10. In some instances such a calculation shows that the node will not be formed. But, since the calculation is only approximate, it does not rule out the possibility of the formation of a short node. In other instances the equilibrium length of the node is an appreciable fraction of I. Such a node would

Jan 1, 1963

By J. A. Snyder, W. L. Finlay

SEVERAL notable studies of the effects of sub- stitutional solutes have been reported. Outstanding among these for its elucidation of general principles, is the summarized work of Hume-Rothery and coworkers.1 For a systematic study of the effects of substitutional solutes on the mechanical properties of the solvent lattice, the work of Brick, Martin, and Angier² on copper; of Frye and coworkers³,4,5 on copper and silver; and of Lacy and Gensamer6 and of Austin7 on iron may be mentioned. Titanium is one of the few elements offering the possibility of a similar study of interstitial solutes since, unlike most metallic elements, it exhibits extended solid solubility for most of the interstitial solutes—hydrogen, boron, nitrogen, oxygen, and carbon. This paper reports a survey of the effects of dilute solutions of nitrogen, oxygen, and carbon on the mechanical properties of high-purity alpha titanium. Previous Work: Van Arkel and De Boer showed" that high purity titanium was quite ductile and De Boer, Burgers and Fast established".' that not only were oxygen and nitrogen very soluble in solid titanium but that, long before the limit of solid solubility of either had been reached, these interstitial solutes rendered the metal brittle. Their electrical resistance data as a function of

Jan 1, 1951

By K. A. Kiselev, V. I. Zelentsov, V. P. Nebera

INTRODUCTION Most works on flotation of ions and precipitates from solutions have been summarized recently (1-3). Flotation is more desirable than thickening or centrifuging because of higher recovery, productivity, simplicity of apparatus and better economics in general. Electrolytic flotation that utilizes gases is more favorable than other flotation processes because of the following: higher dispersity of gas bubbles, low coalescence of the bubbles, possibility of gradual regulation of the dispersity and other parameters of flotation (4-5). Flotation from solutions is mostly based on the use of alkaline reagents as precipitants (5). Flotation from acid solutions is less common. We used multicomponent solutions with more than 2-3 components, unlike previous research methods. Acidic flotation allows recirculation of solutions to previous operations such as leaching, etc. REAGENTS FOR PRECIPITATION Electroflotation was studied over a wide range of pH with the addition of ferrocyanide, oxyquinoline, hydroxide and carbonate precipitants. In recent works (1,2,6,7) on flotation of Ni, Cu, Zn from alkaline solutions, mostly ferrocyanides were applied. Our choice was oxyquinoline because of the following: 8-oxyquinoline is a nonspecific reagent for many metals, it is readily soluble in acids and alkalis, oxyquinolates of the studied metals are in soluble compounds, the reagent works over a wide range of pH, it is widely available, oxyquinolate precipitates are stable when exposed to air, are readily floatable, and are easily converted to oxides of the metals by sintering.

Jan 1, 1980

By Fred C., Bond

IN CYANIDE milling, little attention has been paid to the effect of the viscosity of the mill solution on the extraction speed. The viscosity of the solution varies with the amount of dissolved salts present as impurities. These salts build up to a maximum depending on the character of the ore, the grade of cyanide used, the lime and salts added, and the impurities originally in the water. The viscosity will change from month to month and week to week as these factors vary; and that this variation affects the extraction is unquestioned, although methods for calculating it are lacking. The character of the ore is probably the most important of the four factors, as the amount of minerals present that are soluble in cyanide solution will vary constantly, and each variation affects the viscosity of the mill solution. When the cyanide consumption increases as the character of the ore changes, the viscosity of the solution will increase and the extraction will decrease, for the cyanide consumption is usually a measure of the impurities dissolved from the ore. In other words, as the difference between the total and free cyanide increases the extraction will decrease, other factors remaining constant.

Jan 1, 1926

By D. T. Peterson, F. A. Schmidt, J. D. Verhoeven

The velocity of mig-ration of these solutes in thorium metal due to a high amperage dc current was measured at several temperatures. All three solutes migrated in the same direction as the electron flow. Diffusion coefficients were combined with the migration velocities to predict the steady-state concentration profile. Electrotransport was shown to be an effective method of removing carbon, oxygen, and nitrogen from thorium and resistance ratios several times larger than for crystal bar thorium were achieved. However, the maxirnum attained purification was well below the predicted values, apparently due to some form of contamination. THE migration of solutes in metals when a high current density dc current is passed has been known for many years. This phenomenon has been the subject of a number of reviews published in recent years.l~* Many of the earlier investigators of electromigration of interstitial solutes interpreted the direction and velocity of migration on the basis of a charge on the solute particle. This interpretation is unclear because, in a given experiment, one cannot separate the contributions to the force moving the solute which arise from the charge on the solute in an electric field gradient and the momentum transfer from the scattering of the electrons or holes. There have been only a few quantitative measurements of interstitial migration velocities and some of these have been characterized by poor accuracy or by errors in the analysis of the experiment. The electrotransport mobilities of carbon, nitrogen, and oxygen in thorium were determined by observing the rate of movement of a discontinuity in the concentration profile. This method was used by Carlson el a~.~ to determine the mobilities of interstitial solutes in yttrium and its advantages are discussed in that paper. The specimen is essentially a pair of semi-infinite, bar-type diffusion couples. The electro-transport velocity was measured by observing the displacement of the mean concentration point in a measured length of time. The diffusion coefficients were calculated by the Grube method from the concentration profile. The transport mobilities and diffusion coefficients can be used to predict the concentration profile in an electrotransport experiment of a given time, current density, and specimen length. At long times a steady state will be reached such that the natural logarithm of the concentration of each solute varies linearly along the bar with a slope which is equal to the velocity of the migrating solute divided by its diffusion coefficient. The estimation of the purification potential of electrotransport is discussed by ~erhoeven.' A comparison of the concentration profile and the purification which should be expected from known solute velocities and diffusion coefficients with that which is obtained in an experiment can be very useful in indicating whether the maximum possible purification has been achieved. EXPERIMENTAL METHOD The apparatus used in this study consisted of a sample chamber which was equipped with two electrodes, a sight glass, and a flange for mounting to a high-vacuum system capable of obtaining pressure of 2 x lo-? Torr. The chamber was made of stainless steel and was 4 in. in diam and 6 in. long. The seal between the electrodes and the chamber was made with "0" rings and compression bushings. The thorium specimens were threaded and screwed into tantalum "U"-shaped adapters attached to the ends of the electrodes. This arrangement is shown in Fig. 1

Jan 1, 1967

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*

By R. A. Spurling, C. G. Rhodes

SATISFACTORY metallographic sample preparation of very soft metals, such as lead and its alloys is generally difficult. The prime requisite of any technique must be that the result gives an undis-torted microstructure for the microscopist to examine. A small amount of mechanical polishing followed by a chemical or electrolytic polish is usually the most desirable way to obtain an undis-torted surface. Several chemical-4 and electrolytic3-' polishing solutions have been developed for dilute lead alloys. Perchloric acid mixtures (with acetic anhydride, ethyl alcohol, or water) are among the most prominent electropolishing solutions used for lead; however, the presence of bismuth in the alloy precludes the use of any perchloric-containing solution. The other solutions1-7 were found to be unsatisfactory on alloys ranging from 10 to 65 wt pct Bi in lead. With increasing bismuth content, the microstructure shows a lead (terminal solid solution), 0-6 mixture, E (peri-tectically formed hexagonal phase), and E bismuth mixture (eutectic at 56.7 wt pct Bi).9 The metallographic samples were mounted in "Araldite" epoxy (the heat generated during polymerization does not alter the microstructure), ground by hand on well-waxed silicon carbide papers (400 and 600 grit), and polished with 3- and 0.25-CL diamond paste on billiard and microcloths, respectively. The use of the various polishing and etching solutions reported in the literature resulted in the formation of irremovable reaction products on the sample surface when applied to "as-ground" or "as-polished" surfaces. The E phase was the most difficult to clean chemically and in the development of an etchant for this system several solutions which satisfactorily etched the bismuth or a phase were unacceptable because of their reaction with the E. It was found that a mixture of 50 ml lactic acid 30 ml nitric acid 20 ml (30 pct) hydrogen peroxide (Solution #1) was a satisfactory etchant for the a-matrix alloys. The samples were prepared as before and etched after 1 min of polishing with 3-p diamond paste. The etchant was applied by swabbing (light pressure) for 30 sec to 1 min and the sample was then rinsed in running water. The E has a slight stain and the a is fairly bright, Fig. 1.

Jan 1, 1965

By F. A. Forward, V. N. Mackiw

The paper relates to the laboratory and pilot plant studies that have been carried out by Sherritt Gordon Mines Ltd., Metallurgical Research Div., in developing the ammonia pressure leach process for extracting copper, nickel, cobalt, and sulphur from high grade nickel concentrate produced from Lynn Lake ores, and describes in some detail the chemistry of the process. IT is well known'.' 2 that copper, nickel, cobalt, zinc, ferrous iron, and a number of other metals combine with ammonia in aqueous solution to form complex ions of the form [Me(NH,)x]"+. The stability and solubility of these ions depend on the concentration of the metal ion in solution, on the amount of NH, present, and on the amount and type of anions present, e.g., OH-, C0;-, NO,, C1-, SO;-. If ammonia is partially or completely removed from such solutions, for example by boiling, the soluble ammines tend to decompose and the metals precipitate as basic salts. These properties of metal ammines have found practical application in the commercial recovery of copper, nickel, and cobalt from a variety of ores. In an operation formerly conducted at Kennecott"" the mill tailing containing 0.80 pct Cu as copper carbonate was leached by percolation with an ammonia-ammonium carbonate solution to dissolve the copper as the ammine. At Calumet and Hecla0-" With a mill tailing containing about 0.4 pct Cu as metallic copper, it has been found necessary to aerate the ammonia-ammonium carbonate leach solutions between stages to oxidize the solubilized copper. At Nicarol"-" where nickel and cobalt occur as oxides and silicates which are not soluble in ammonia, the ore is heated to decompose silicates and to selectively reduce the nickel and cobalt to metal, leaving the iron as Fe,O,, and is then leached with ammonia-ammonium carbonate solution accompanied by aeration to dissolve nickel and cobalt as ammines. In each of these leaching operations, the anion present is CO, and the metals can be precipitated from the leach solution as oxide (copper) or hydroxide and carbonate (nickel and cobalt) by boil- ing off NH, and C02 both of which are recycled to treat a subsequent ore charge. The products-—oxide, hydroxide, or carbonate—can be treated by conventional smelting, calcining, or electrolytic methods to convert them to refined metals. Thus the procedures mentioned utilize the properties of the ammines to extract copper, nickel, and cobalt from nonsulphide ores and separate them from the leach solutions. These processes have the advantage that they can be carried out in closed vessels at atmospheric pressure, that the leaching solutions are specific for the desired metals, that the metals can be recovered as relatively pure compounds by the boiling operation, and that the NH, and CO, can be recycled. Also, as the leach solutions after boiling and filtration are substantially free of metals, NH,, and CO,, they can be discarded, thus facilitating the control of the water balance in the leaching circuit. When, as is the case with Sherritt Gordon concentrates, sulphides are treated with ammonia solution in the presence of oxygen, the leach solution contains SO,--, and an entirely different set of conditions is encountered. The ammine sulphates (of nickel, for example) are more soluble than the carbonates and can be only partially decomposed by boiling. The SO, and NH, in the solutions can not be recovered by boiling. Thus, despite the more favorable leaching conditions resulting from high solubility of the ammine sulphates, the recovery of metals, NH,, and SO, from the solutions must be effected by other means. Sherritt Gordon Nickel Concentrate Treatment The Ni-Cu-Co flotation concentrate produced at Lynn Lake'" contains 12 to 16 pct Ni, 1 to 2 pct Cu, 0.2 to 0.5 pct Co, 33 to 40 pct Fe, 28 to 34 pct S, 8 to 20 pct insoluble, and less than 0.02 oz per ton precious metals. The nickel is present chiefly as pentlandite, the copper as chalcopyrite, and the iron as pyrrhotite and pyrite. Most of the cobalt is thought to be present in pentlandite, although it is known that a small amount occurs as Co-Ni-pyrite.

Jan 1, 1956

By M. B. Ramachandra Rao

THIS paper records the results of the earth resistivity surveys made in the Godavari river in connection with the Ramapadasagar project. After describing the topographical and geological features of the area, the results of the investigation at the several sites have been mentioned. Further, a detailed account has been given of the resistivity methods adopted, the apparatus used and the interpretation of the curves. The resistivity measurements carried out over the water course have been specially outlined, and a review of the verification of the electrical indications by drilling in a number of cases, has also been presented.

Jan 1, 1947

Jan 1, 1970