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By D. L. H. Forbes

The application of the cyanide process to complex sulphide ores for the extraction of the gold and silver is no longer a novelty; but, as an example showing modern teudencies in this direction, the following description of the new milling process at the Lucky-Tiger mine is offered: The extraordinary richuess of the ore in the upper workings of this mine made any thought of milling in its early days seem unnecessary. Its location in an almost inaccessible part of the rugged mountains just south of the Arizona boundary-line, and 60 miles from the town of Douglas, made the expense of bringing in machinery and sopplies a very serious consideration. But, after the property had been shipping high-grade ore on mule-back for a few years, there remained in the mine a considerable tonnage of vein-matter that mas too low in value to ship, but which it wag thought could be milled near the mine at a profit. The first milling-experiment consisted in the installation of Nissen stamps in conjunction with concentrating-tables and Frue vanners, but, as the ore from the upper workings contained most of its silver in the form of cerargyrite, this type of mill mas not successful. The proximity of the mine to the great copper-concentrating mills of Cananea and Moctezuma naturally made the influence of copper-milling ideas felt in the company's next instdlation. At considerable expense a stage-crushing concentrating-mill, with a capacity of 100 tons per day, was built. This mill was modeled along the lines of the most approved practice in copper-concentrators at that time, the main idea being that crushing by stages .in rolls was necessary in order to prevent losses from " sliming." Largely owing to the fact that, when the mill

Jan 1, 1913

By R. L. Rickett, S. H. Kalin, J. T. Mackenzie

Aluminum killed low carbon steel, § which is now used extensively for severe deep drawing or other difficult forming operations, is unusual in that its grain structure, after cold reduction and box annealing in accordance with conventional continuous sheet or strip mill practice, often is elongated, although at times it is equiaxed. Since this unusual structure has been found superior for many, but not all, severe forming operations, recrystallization of the steel, both at constant temperature and on continuous heating, was investigated and compared with that of rimmed steel in the hope that something might be learned about the mechanism of, and the factors controlling, the formation of such elongated grains. In this structure, the grains are elongated both in the lengthwise direction of the strip and transverse to this direction, even though nearly all of the extension in both hot and cold rolling is in the lengthwise direction. The grains are thus roughly pancake-shaped, being longer and wider than they are thick, as observed also by Burns and McCabe,1 and as illustrated by the typical structures shown in Fig 1. Fig la, representing a conventional longitudinal section, shows the length and thickness of the grains, whereas Fig Ib shows their length and width as seen by examining a section parallel to the sheet surface. Both illustrate the very irregular grain boundaries usually associated with the elongated grain shape. A finer equiaxed grain structure in this same grade is shown in Fig Ic. Either the elongated or the equiaxed structure may be present in the annealed product, and in rare instances the two types may coexist in a single specimen, as shown in Fig 1 d. Isothermal Recrystalliza-tion of Rimmed and Alamimum Killed Steel An aluminum killed steel known to have an elongated grain structure after conventional processing (Steel B, Table l), was selected for the initial recrystallization studies; for comparison, a rimmed steel, A in Table 1, was used. Samples of each in the form of hot rolled strip 0.075 and 0.095 in. thick, respectively, were cold rolled on a small laboratory mill in steps of about 0.010 in. per pass to obtain total reductions of 40 and 60 pct. Small pieces of the cold reduced strip were heated in lead at selected constant temperatures for one of several periods of time, then cooled in air. Rate of heating in the lead was, of course, very fast. Hardness of the cooled specimen was measured and a longitudinal section examined metallographically. Isothermal recrystallization curves for these two steels at 1050°F, based on hardness of the air cooled specimens, are shown in Fig 2 in which the amount of recrystallization corresponding to each plotted point is indicated. The marked difference in the behavior of these two types of steel is evident. After a corresponding amount of cold reduction, the rimmed steel recrys-tallizes in a much shorter time than the killed steel and the shape of its recrystallization curve, (plotted on a logarithmic time scale), is very different. The curve for rimmed steel indicates that recrystallization is analogous to isothermal transformation of aus-i.enite in that it proceeds at a progressively faster rate up to some 50 pct recrystallization, then at an increasingly slower rate. For the aluminum killed steel, however, the start of

Jan 1, 1950

By E. S. Machlin, A. J. McEvily

HE results of an experimental investigation by McEvily and Machlin have indicated that a strong relationship exists between the processes of cross slip and fatigue. Whenever dislocations can cross onto an intersecting plane and expand thereon, as in AgCl crystals, the usual type of S-N behavior is obtained, but when such a process is difficult, as in NaCl crystals, fatigue does not occur in its usual manner, if at all. MgO, because of its crystal structure (NaCl type) and slip systems ({110}<110>) would not be expected to fail in fatigue. However, Cornet and Gorum2 have found something akin to the usual type of fatigue behavior for MgO crystals. The purpose of this note is to attempt to resolve this apparent discrepancy. In Cornet and Gorum&apos;s work as-cleaved crystals were tested under cyclic axial loading, whereas in McEvily and Machlin&apos;s work chemically-polished crystals were tested in reversed bending. Because of the difference in specimen preparation, the major effort of the present work was directed toward comparing the behavior of as-cleaved as opposed to chemically-polished specimens. The effect of type of loading seemed less important, but a check was made on this also. Eighteen bend tests and one axial load test were made. The specimens were cleaved from Norton magnorite blocks, and measured 1 by 3/16 by 1/8 in. To avoid failures in the grips, the thickness of the bend specimens was reduced from 1/8 in. near the ends to 0.04 in. in the central portion. This reduction was from one side of the crystal only. Twelve specimens were polished in orthophosphoric acid to remove the damage due to cleavage. The other six specimens were not chemically polished so as to maintain the as-cleaved condition of the crystal faces which had not been reduced. The axial-load specimen was reduced from both faces to a thickness of

Jan 1, 1962

By Carl Swartz

IN the course of a recent investigation1 to develop a more satisfactory white-metal. bearing alloy, a number of alloy systems were studied. The cadmium-nickel system showed characteristics desirable in a bearing alloy, and the system was therefore studied in some detail. EXPERIMENTAL METHOD Alloying cadmium with nickel offered no serious difficulty. After melting the cadmium, clean sheet nickel was added while the temperature was maintained at 500° to 600° C: A few crystals of ammonium chloride2 served to clean the nickel when the latter did not "wet" readily. In preparing the individual alloys for thermal and microscopic investigation, a "hardener" containing about 10 per cent nickel was used.

Jan 1, 1933

APPROXIMATELY 90 per cent of the steel that is melted and refined in the United States and poured into ingots is made in basic open-hearth furnaces, as shown in Table 1-1. The annual ingot capacity of the steel industry reported January 1,1950, by the American Iron and Steel Institute8* was 99,040,160 tons, of which the basic open-hearth process accounted for 85,896,580 tons, 86.7 per cent of the total. The capacity of the individual furnaces varies over a wide range, a large majority falling within limits of 50 to 200 tons (Fig 1-1). Most of the units constructed [ ] since 1942 are in the larger size groups, between 175 and 225 tons capacity.

Jan 1, 1951

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system&apos;s behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell&apos; have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine&apos; have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.&apos; A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By Norman D. Fitz Gerald

The lack of a continuous operating balance in petroleum refining, which is analyzed in this paper, is by no means a feature solely of this division of the oil industry. Serious disequilibria of a capital as well as an operating nature exist both in the producing and marketing departments, while problems in the former and to some degree the latter are complicated by political involvements. Attention has previously been directed to the unstabilizing influence of present proration formulas in stimulating unnecessary drilling.&apos; While equilibrium in petroleum refining operations has been fairly well maintained in the past decade, examination of departures may prove fruitful. Economic analysis is the application of time and motion study to the functioning of management, rather than labor. Properly applied it may reveal changes in policies that would increase the utility of the properties and facilities of the industry for stockholders, employees and the public, while contributing a stabilizing influence to the general economy. The study of economic equilibrium is essentially one of measurement and interpretation, requiring adequate data and the development of a technique of analysis that employs statistical and mathematical methods as a supplement to the broad descriptive phase of economics. Economic equilibrium in petroleum refining is a dual concept. It embraces both the over-all balance between total storage and total demand for major products and the internal balance between the demands and inventories of the various products. The latter is the more complex of the two for it is concerned with proportionating the supplies of the several products stemming from the joint source to the demands for the individual products which are subject to wide variations. All the products are essentially nondurable goods, and they are used both by producers and consumers but in varying proportions. Motor fuel is very largely a consumer&apos;s good, while residual fuel oil is almost entirely a producer&apos;s good, the other products falling between these extremes. The peculiar-

Jan 1, 1939

By Norman D. Fitz Gerald

The lack of a continuous operating balance in petroleum refining, which is analyzed in this paper, is by no means a feature solely of this division of the oil industry. Serious disequilibria of a capital as well as an operating nature exist both in the producing and marketing departments, while problems in the former and to some degree the latter are complicated by political involvements. Attention has previously been directed to the unstabilizing influence of present proration formulas in stimulating unnecessary drilling.&apos; While equilibrium in petroleum refining operations has been fairly well maintained in the past decade, examination of departures may prove fruitful. Economic analysis is the application of time and motion study to the functioning of management, rather than labor. Properly applied it may reveal changes in policies that would increase the utility of the properties and facilities of the industry for stockholders, employees and the public, while contributing a stabilizing influence to the general economy. The study of economic equilibrium is essentially one of measurement and interpretation, requiring adequate data and the development of a technique of analysis that employs statistical and mathematical methods as a supplement to the broad descriptive phase of economics. Economic equilibrium in petroleum refining is a dual concept. It embraces both the over-all balance between total storage and total demand for major products and the internal balance between the demands and inventories of the various products. The latter is the more complex of the two for it is concerned with proportionating the supplies of the several products stemming from the joint source to the demands for the individual products which are subject to wide variations. All the products are essentially nondurable goods, and they are used both by producers and consumers but in varying proportions. Motor fuel is very largely a consumer&apos;s good, while residual fuel oil is almost entirely a producer&apos;s good, the other products falling between these extremes. The peculiar-

Jan 1, 1939

By J. L. Jernegan

In a former paper laid before the Institute, entitled Lead and Silver Smelting in Chicago, I endeavored to give a description of the manner in which argentiferous lead ores from the far West were treated in that city, and also described the method employed in the desilverization of the silver-lead produced from the ores. It will perhaps be remembered, that very siliceous ores, principally from the Emma mine, Utah, containing over 40 per cent. of silicic acid, were then being treated at the works of the Chicago Silver Smelting and Refining Company in the reverberatory furnace, with the use of metallic iron, in the form of borings, as a precipitating medium for the lead ; and that the extraction of the silver from the resulting bullion was effected by the Balbach process. The Swansea Works, also the works at Brighton, just outside of this city, and those of S. P. Lunt, were at that time treating ore of a similar character by the same method. The inadequacy of the process for the ores then under treatment was, in a manner, pointed out by me in the paper above referred to. Since the time of its writing, many and important improvements have been made in the metallurgical treatment of western ores in Chicago. Most ores are now roasted previous to reduction, and the latter operation is conducted in the shaftfurnace instead of the reverberatory. Such is the fact at least at the Swansea Works, the largest in the city, and here it was where the first steps were taken in this direction. In selecting these works as the subject of this paper, I am in hopes that the description given of the varions metallurgical operations, as they are there now conducted, will serve to give an idea of the improvements introduced

By K. P. Wang

Under the Communist regime marked industrial progress has been achieved on the China mainland. Within a decade, the country has been transformed from an economy primarily agricultural to one bristling with industrial possibilities. The industrial capacity of Communist China is beginning to approach that of Japan and will probably surpass it by 1962, the last year of the Second Five-Year Plan. The slogan already is Beat the United Kingdom by 1972, a goal which most observers feel will be achieved ahead of schedule. During the early years of the industrialization program in Communist China, emphasis has been placed on basic goods; hence additional time will be needed to make large quantities of the more complicated products. However, regardless of the current stage of industrial development, it is apparent that the necessary forward momentum has been created. The many capital construction projects being brought into production and the additional projects being initiated confirm this observation. The accuracy of Communist China&apos;s industrial statistics can be questioned, but their order of magnitude is clear. To properly evaluate the industrial capability of the country, differentiation must be made between the absolute quantities that reflect overall strength and the per capita quantities that reflect living standards. While Communist China is well on the road to becoming a world power, its living standards will remain below European levels for many years to come.

Jan 8, 1960

By R. Kossowsky

BRIDGMAN has listed five possible transitions in bismuth at 25°C which were observed as volume changes. He was unable however to detect the last three transitions by electrical-resistivity changes. Kennedy and LaMori have verified the pressures at the Bi 1-11 and Bi 11-111 transitions. They suggested however that the 125-kbar transition previously reported by Bundy3 actually corresponds to the 90,000 kg per sq cm transition observed by Bridgman.1 Jura4 reported a well-defined drop in resistivity at 92 kbar obtained by a four-lead method. The Bi 111-IV and Bi IV-V transitions have not been reported in any of the above-mentioned references.&apos;-&apos; Bundy3 observed a small dent in the low-temperature boundary of the Bi Vll region which is consistent with the presence of a 111-IV boundary. Zeitlin and Bray-man5 were the only ones to report small but well-defined drops in resistance of bismuth at 44.0 and 63.8 kbar, corresponding to Bridgman&apos;s 111-IV and IV-V transitions, respectively. High-purity (99.99 pct) 0.020-in.-diam 0.5-in.-long bismuth wire was used to calibrate the Uniram tetra-hedral high-pressure apparatus used in the present work. The bismuth phase changes at 25°C were correlated with changes in electrical resistance as a function of pressure. The output of a sensitive bridge constructed of carbon resistors and kept at a constant temperature of ±°C during the measurements was fed to the Y axis of a MoseleyX-Y recorder and the X axis was used for time scans. Specimens were pressurized using a hydraulic press with maximum capacity of 200,000 lb. Load was applied in increments of 2000 lb and held for about 3 min. The resistance was recorded at the end of this time period. Good contact was established below 20,000 lb. Typical recorder charts are reproduced in Figs. 1 and 2 which show that resistance fluctuations were practically nil during each time scan. Well-defined discontinuities in resistance were observed at 58,000 and 82,000 lb, Fig. 1. Two small but definite "blips" are noticed at 92,000 and 122,000 lb, Fig. 2. At 156,000 lb another drop is observed which

Jan 1, 1967

By W. W. Odell

Once it was believed that anthracite or coke were the only fuels generally available and suitable for the generation of water gas, particularly so when this gas was made in the generators of standard carburetted water-gas sets such as are commonly used in the manufacture of city gas. During the past 8 years, practice has changed considerably and it is now common to find gas plants operating without anthracite or coke and using bituminous coal in the generator. This change in fuel has appreciably increased the marketability and sales of certain coal producers&apos; products; accordingly it is of interest to coal operators and others to know the reason for this change, the present trend in practice and the adaptability of various coals for generation of water gas. This paper briefly discusses these conditions and some of the factors relating thereto. Bituminous Coal not Ideal but Cheaper than Coke In spite of many changes which have been made in both process and generating apparatus for using bituminous coal as generator fuel more efficiently, in general it is not an ideal fuel for this purpose. It is supplanting coke because it costs less; it is so much cheaper per ton delivered at the gas works that water gas made therefrom costs less per unit-volume than that made from coke, even though the quantity of generator fuel consumed per therm (100,000 B. t. u.) of gas made is greater with coal. This is the reason why so many city gas plants, as well as others, are using bituminous coal instead of coke. Conditions Favoring Change from Coke to Coal The conditions which have made it possible and feasible, as well as economical, to supplant coke with coal may be summarized as follows: (1) Changes in methods of operating and alteration in generating apparatus; (2) lowering of the calorific standards for city gas, and (3) availability

Jan 1, 1927

By B. Barlin

Introduction The development of metallurgical practice at lambia Broken Hill is directly related to the change in mineralization of the deposits as mining progressed from the open pits to underground. The ore consists of a mixture of lead and zinc sulphide minerals, together with abundant silicates, carbonates and other oxidized minerals of these metals. The irregularity that characterizes the shape of the orebodies applies equally to their mineral content, which makes ore reserve calculations and the maintenance of a balanced feed to the metallurgical plants, problems of some magnitude. History The Rhodesia Broken Hill Development ,Company was formed in 1904 after an Australian prospector, T. G. Davey, discovered the outcrops in 1902. In the early years zinc ores were calcined for shipment but this proved uneconomic. Cerussite outcrops were then smelted directly in blast furnaces for the production of lead until 1929 when ore above the water level was exhausted.

Jan 1, 1970

By P. W. Guild

DURING 1956 the application of geology and related scientific disciplines to the search for new mineral deposits went forward on an ever widening front. Spurred on by record-breaking consumption of many of the established commodities and new uses for minerals and metals that were hardly known a few years ago, the profession is figuratively leaving no stone unturned in the effort to insure that adequate raw material supplies will be avail- able for the future. More money was spent and more people were engaged along more lines of research than ever before. A huge project to map much of the Canadian Shield area by photogeologic methods stands at one extreme; application of isotope ratios to ore finding stands at the other; between them the more traditional techniques are being increasingly refined. In the Fiftieth Anniversary volume of Economic Geology, published late in 1955, Alan Bateman sketches the development of fundamental concepts as recorded in the pages of the journal over the first five decades. An additional 24 review articles cover individual aspects of the field and constitute a base for further advances.

Jan 2, 1957

By H. Gisser

Recent experimental work has demonstrated (1)2 that ammonia and oxides of nitrogen are formed during the aging of smokeless powder. This is significant in connection with the problem of "season cracking," or stress corrosion of brass cartridge cases in view of other work(1) indicating that stressed and "stress- relieved" cases stored with small quantities of added ammonium nitrate crack on firing. The deterioration of stressed brass by ammonia has been known for some time(z) and it appears therefore that stress- corrosion cracking of brass cartridge cases is intimately associated with the so-called "powder volatiles," ammonia and oxides of nitrogen, both of which are decomposition products of smokeless powder. Working on the hypothesis that any barrier which prevents the powder volatiles from reaching the brass surface will reduce the incidence of stress-corrosion cracking, it was considered desirable to investigate the use of organic resin films to accomplish this purpose. The possibility of formation of ammonia within the nitrocellulose powder charge and by reduction of nitrogen oxides on the surface of the brass case requires that the barrier film be resistant both to ammonia and oxides of nitrogen. The film must also be impermeable to ammonium salts, either solid or in solution, since these salts and water necessarily appear within the powder charge. The usefulness of the

Jan 1, 1945

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By R. G. Ward, D. R. Gaskell

Using the maximum bubble pressure technique, the densities of iron silicates at 1410°C have been measured blowing helium, nitrogen, and argon. By ensuring equilibrium between the melt and the blowing gas with respect to oxygen potential and by minimizing tempcrature cycling of the furnace, iron precipitation in the melt has been prevented. Thus the previously reported effect of blowing-gas composition on the densities of the melts has been eliminated. Consideration of the oxygen densities of the melts gives an indication of the structural changes accompanying composition change. The density-composition relationship of iron oxide-silica melts in contact with solid iron has been the subject of several investigations1-7 and considerable disparities exist among the various results obtained. Of these investigations, all except one5 have employed the maximum bubble pressure method. In the most recently reported of these investigations1 the density-composition relationship obtained blowing nitrogen differed from that obtained blowing argon. The measured densities obtained under nitrogen were greater than those obtained under argon, the difference being a maximum at the pure liquid iron oxide composition and decreasing with increasing silica content. This observation rationalized the disparities existing among the results of the earlier investigations, showing that two lines, one for nitrogen and the other for argon, could be drawn to fit all the earlier results. No explanation for this phenomenon could be offered. Chemical analysis of rapidly quenched samples of melt for dissolved nitrogen, and direct weighing measurements, excluded solution of nitrogen in the melt from being the cause of the increase in density. The range of blowing gases was extended by Ward and Hendersons who measured the density of liquid iron oxide bubbling helium, nitrogen, neon, argon, and krypton. The measured density was found to decrease smoothly with increasing atomic number of the bubbling gas. The work reported here is a continuation of the program initiated by Ward and Sachdev7 to study the densities in multicomponent melts in which the iron oxide-silica system is the solvent. As such it is necessary to explain or eliminate the anomalous densities of iron silicates under different atmospheres, and the present rede termination was carried out towards this end. EXPERIMENTAL The maximum bubble pressure method of density determination was again employed and the experimen- tal apparatus used was essentially the same as that used by Ward and Sachdev.7 A molybdenum-wound resistance furnace heated an ingot iron crucible of internal diameter 1 in. containing a 2-in. depth of melt. The bubbling gas was blown through a 1/4 -in.-diam mild steel tube onto the end of which was welded a 2-in. extension of 1/4 -in.-diam ingot iron rod, drilled out to 5/32 in., and chamfered to an angle of 45 deg. The blowing tube was introduced to the furnace through a sliding seal and its position was controlled by a vertically mounted micrometer screw which allowed the depth of immersion to be determined with an accuracy of ± 0.01 cm. A Pt/Pt-10 pct Rh thermocouple was located below the crucible and temperature control was effected initially by means of an on-off controller and later by a saturable core reactor. The bubble pressure was determined by measurement of a dibutyl phthalate manometer using a cathetometer. PREPARATION OF MATERIALS Iron oxide was produced by melting ferric oxide in an inductively heated iron crucible in air. The liquid was quenched by pouring onto an iron plate. Silica was prepared by dehydrating silicic acid at 650°C for 12 hr. RESULTS Before any measurements of the density of a melt were made, the density of distilled water at room temperature was measured bubbling helium and argon. Both gases gave the density as 1.00 ± 0.01 g per cu cm which showed that the density of the manometric fluid (dibutyl phthalate) was not affected by contact with the blowing gas. With the furnace controlled by an on-off temperature controller an attempt was made to measure the density of pure liquid iron oxide by bubbling argon. The furnace atmosphere gas and bubbling gas were dried over magnesium perchlorate and deoxidized over copper turnings at 600°C. It was found that the pressure required to blow a bubble at a given depth increased slowly with time, and thus it was impossible to obtain a unique value for the density of the melt. Inspection of the blowing tube after removal from the furnace showed that rings of dendritic iron had precipitated from the melt onto the immersed part of the tube. This is shown in Fig. l(a) where the various "steps" correspond to different depths of immersion. The precipitation of iron was considered to be due to one or both of two possible causes: i) The composition of the liquid iron oxide is that of the liquidus at the temperature under consideration and can be expressed by the equilibrium

Jan 1, 1968

By Toshihisa Adachi, Shosei Serata, Shunsuke Sakurai

The present state of knowledge of three-dimensional rock properties does not provide an adequate basis for evaluating the safety of under- ground structures in situ. Most of the triaxial studies reported in the past have dealt with crushing strength, but have failed to consider the intergranular behavior and triaxial strain state of rocks. Without this information, the structural competence of rocks cannot be accurately assessed. The absolute three-dimensional testing method (ATT) was conceived for the purpose of analyzing the three-dimensional states of stresses and strains in aggregate rocks under conditions commonly encountered in underground structures. In-situ stress-strain states are not simple, even in the simplest possible form of opening, excavated in a homogeneous and isotropic rock medium. In general, there are four basic stress-strain states which are present in underground openings, regardless of the complexity of their geological conditions. They are the yielded, brittle-fractured, stress-relieved, stress-concentrated states, as illustrated in the schematic diagram, Fig. 1. The ATT machine was designed to create and study all these states in the laboratory. A theory describing the aggregate behavior of rocks under these diversified states is essential to evaluate the safety of underground structures. The Griffith theory is limited to tensile failure of ductile materials and therefore does not apply to behavior of aggregate rocks under compression. The Griffith theory also fails to consider the grain boundary characteristics of aggregates, which is the determining factor of rock behavior. The Mohr-Coulomb theory of failure ignores the importance of the intergranular behavior of rocks. An application of the continuum theory to

Jan 1, 1972

By C. Schlumberger

IN the course of the past few years the authors and their associates have had different opportunities to study the electrical phenomena which accompany the oxidation of pipe lines. The causes of such phenomena are very similar to those which have been described under the name "spontaneous polarization" with reference to metallic orebodies,1 and can be investigated in the same manner. These investigations, however, until recently were of a scientific and theoretical character, and had not found any important practical application. During the year 1931, however, the authors treated several industrial corrosion problems for public utility companies. These problems usually had to be studied in towns or in densely populated areas, where it was well-nigh impossible, or very expensive, to dig pits and trenches in order to make electrical measurements on the pipe itself. The authors were thus led to evolve a method and apparatus permitting the study, from the surface, of the direction of the currents flowing from pipe lines. The purpose of the present paper is to discuss the results obtained in the course of these investigations. However, in consideration of the importance and interest of the work carried out by other scientists along the same lines, a separate chapter will be devoted to a summary of the results achieved up to the present time in the study of pipe line corrosion.

Jan 1, 1932