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By Walter S. McKee

Discussion of the paper of WALTER S. McKEE, presented at the New York meeting, February, 1916, and printed in Bulletin No. 108, December, 1915, pp. 2399 to 2411. J. W. RICHARDS, So. Bethlehem, Pa.-I regret that the author has overlooked the great usefulness of the electric furnace for the melting of ferromanganese in the manufacture of manganese steel. WALTER S. MCKEE, Chicago, Ill. (communication to the Secretary*)-In an article as brief as mine it was not possible to .fully cover the metallurgical field; this accounts for my not mentioning the electric furnace for the melting of ferromanganese in the manufacture of manganese steel, although the advantages of such an apparatus are fully appreciated by me. FREDERICK LAIST, + Anaconda, Mont. (communication to the Sec-retary?).-Manganese steel has proved very serviceable in our plant.. We are using manganese steel for the jaw plates on the 5-' by 15-in. crushers in the concentrator instead of cast-iron jaw plates which we formerly used. The manganese steel wears five times as long as the cast iron. We are also using manganese steel in our 8- by 20-in. crushers. In our primary crushers, which are 12 by 24 in., we still use cast iron because the manganese-steel plates wore unevenly and left shoulders which caused trouble in setting up the crusher. Another reason for preferring cast iron in these crushers is that they grip the ore better on account of wearing of the rougher surface. The surface of the manganese steel becomes polished and large pieces of ore fail to be drawn in. We recently tested 8- by 16-in. manganese-steel elevator buckets working on 2-in. undersize against malleable-iron buckets and found that manganese-steel buckets lasted two and one-half times as long as the malleable-iron buckets. We use manganese-steel screen plates on our 2-in. trommels and have found that they last about five times as long as cast iron. We also used manganese-steel wheels and rails under the 20-deck round table in our slimes-treatment plant. We first used cast-iron rails and wheels and found that these wore badly at the end of two or three weeks, while the life of the manganese steel seemed to be almost indefinite; we never had occasion to change any of the manganese steel rail sections or wheels in the year and nine months that the plant was in operation.

Jan 5, 1916

By F. V. Greene

This paper is based on my experience in the use of asphalt, for paving and other purposes, during the last ten years, part of the

Jan 1, 1889

By J. A. Herbst, K. Rajamani, Y. C. Lo

In spite of potential theoretical and economic advantages of large-diameter ball mills, many manufacturers elect not to build them owing to what is perceived as an excessively large design risk. This is because traditional predictions for mill scaleup to large diameters are not always accurate. Alternative methods of analysis and scale-up are required. Recent studies have shown that detailed population balance models which account for important grinding subprocesses (grinding kinetics, material transport, and classification) are capable of predicting the performance of small- and intermediate-diameter mills (up to 4.3 m, or 14 ft) from small-scale batch tests. These same models are used in the current study to predict the performance of a "borderline "large ball mill (4.7 x 5.5 m, or 15 x 18 ft) at Asarco's Sacaton operation, a ball mill (5 x 5.8 m, or 16.4 x 19 ft) at Kennecott's Chino operation, and one of the world's largest ball mills (5.5 x 6.4 m, or 18 x 21 ft) at Cities Service Pinto Valley operation. Model parameters required for scale-up have been estimated in a 380-mm-diam (15-in.-diam) batch mill. Predictions are compared with the results of detailed plant sampling in the three plants. For the Sacaton and Chino operations, the error of the predictions was found to be less than 2.5%, while the corresponding error for the Pinto Valley operation was less than 2.7%. It is concluded that proper representation of the major subprocesses of grinding in the model equations is the key to achieving accurate scale-up. Of special importance is the need to account for the size distribution of the grinding media and the influence of the size distribution environment in the mill on grinding kinetics.

Jan 1, 1986

By Robert C. Stephenson

In 1954, a year when general industrial production declined, it is significant that industrial mineral products continued in high demand. Phenomenal growth of the cement industry, increase in filler-fibre markets such as for asbestos and diatomite, expansion of the gypsum industry, and the increasing production of agricultural raw materials all illustrate the vitality of industrial minerals fields. Pioneer development of new industrial raw materials-wollastonite as a current example-requires keen foresight, hard work, and tremendous intestinal fortitude. The present-day requirements of industry for rigid quality control and uniformity of raw materials have resulted in highly specialized

Jan 3, 1955

Jan 1, 1892

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' 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'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'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' 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'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'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 H. W. Rogers

The first steam shovels used in this country were built by the Otis Company, of Boston, about 50 years ago, but as they were of very crude construction and rather unsuccessful only a few were built. For possibly 10 years prior to 1884 successful steam shovels were made and used on certain classes of work, but it was not until that time that they were manufactured in quantities and began to play an important part in all classes of excavation. From that time up to the present day there have been gradual but continuous improvements on the original shovel, not only in the mechanical construction, but also in the design of boilers and engines which are best adapted to this class of service. In proposing a change from steam to electric operation we have to deal with a steam equipment which has not only proved its worth but has probably reached its highest stage of development and efficiency. That the electric shovel is a possibility cannot be denied, as at present from 12 to 18 shovels are in operation in this country. These shovels may be divided into three classes: the friction electric, which is operated by a single constant-speed motor with friction clutches; the three or four motor direct-current equipment, and the three or four motor alternating-current equipment. It is the second and third classes that I wish to deal with, as the first class does not compare favorably with the steam shovel so far as speed is concerned, although it may be operated as cheaply. There is probably no other class of machinery that presents a duty cycle as severe as that of the shovel, which is very short, varying from 7 to 12 sec. on the hoist, from 7 to 12 sec. on the thrust, and from 10 to 18 sec. on the swing, making a complete cycle in from 17 to 30 sec., and the motor to meet these requirements must have a sufficiently low armature inertia to permit of rapid acceleration and quick reversals under small power. It should also be a motor of rugged design, as it must be subjected to severe overloads and shocks and frequent reversals. This is especially true of the hoist motors and, to a lesser degree, of the swing motor; the thrust motor being practically stalled during the digging operation, although it may revolve or overhaul, according to conditions, and is operated at full speed only after the hoisting operation is completed.

Jan 1, 1915

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'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 Edmund B. Kirby

This meeting marks the point at which the long-standing dissatisfaction with the mineral-land laws, the innumerable protests against them, and the many isolated efforts to obtain relief, have developed into a general movement for their revision. That part of the mining industry which is affected by these laws has three general organizations which are able to speak for it: the American Institute of Mining Engineers, the Mining and Metallurgical Society of . America, and the American Mining Congress; all of which are represented in this meeting. In the series of able and thoughtful papers presented here, prominent men have discussed the evils of the present laws and some of the reforms which should be made in them. We all appreciate fully the ultimate value of these studies; but we are also painfully aware of the fact that discussion of this kind has been going on for a quarter of a century without any other effect than a steady increase in the mass of printed records stored on library shelves. In order to get any practical result we Gust induce an indifferent government at Washington to act, and to do this we must unite in pushing some practical plan whereby it may act in a simple and effective way and with the least possible amount of criticism or opposition. The actual question before us is not whether the mining laws are bad; for their evils and absurdities are not only beyond discussion but also beyond the resources of a temperate and dignified vocabulary. It is not what particular changes ought to be made; for it is premature to make . specific recommendations until there is some one to listen to them. Moreover, we all know that there are wisdom and experience enough available, and awaiting that time, for the creation of a code which would be a model to the mining world. The practical question now is, how to obtain the revision; and since the American Mining Congress has of late restricted its attention to this phase of the problem I wish as one of its representatives here to present its views upon the matter.

Jan 1, 1915

By DR. RICHARD RATHBUN

ON behalf of the Regents and the Secretary of the Smithsonian Institution, it gives me great pleasure to welcome you to the National Museum; but it is to your own museum, since it belongs to you in common with all the people of the country. Still young in a life which has been beset with many difficulties, it has gathered strength and attained a growth quite unprecedented. In fact, it is this very growth which has been the chief cause of trouble, always leading far and away beyond the capacity for storage ; and to-day there is nearly as much material contained in outside buildings as is displayed in this one. You will, accordingly, find the collections crowded, the cases so close together that their contents are often difficult to view, and the arrangement generally lacking symmetry. You may, therefore, be inclined to regard us as poor custodians of the collections of a great nation, but I beg you to withhold your judgment for a while. From the beginning there has been abundant zeal and activity and a proper direction of affairs, but space and money have been lacking. There is now a prospect of better times. All about you here is a beautiful park, but without. a covering it is not adapted to museum purposes. Upon it, however, a new large building is going up, so extensive in its dimensions that technology can soon be given a fitting home, thus realizing one of the earliest aspirations of the Regents. Some sixty-five years ago the extensive returns of specimens from the famous Wilkes Exploring Expedition around the world began to reach Washington, where they were deposited in the Patent Office Building, and formed practically the first of the National Collections. Six years later the Smithsonian Institution, based upon the bequest of James Smithson, was

Jul 1, 1905

By A. Eilers

A MARKED peculiarity of most of the smelting-works of the Far West is the looseness with which accounts of the operations are kept. Indeed, probably over half of the works do not keep any detailed accounts at all, the yearly gross statement of profit or loss being considered sufficient for all purposes. The reasons for this must apparently be sought in the as yet unsettled state of all business relations, and in the deplorable fact that only in isolated cases educated metallurgists are in charge of the smelting-works. Continual and regular assays of the ores, by-products, and slags, are almost unknown, so that it is impracticable to ascertain, even approximately, the losses in the smelting processes. Of cases where regular accounts are kept of the quantities of ore smelted, of the composition of charges, and of the fuel consumed, I know only two or three. Under these circumstances it is extremely difficult to collect figures which cover the operations for a considerable length of time, and which are so valuable for the metallurgist, who wishes to get an insight into the economy of smelting operations, as shown by practice. Figures obtained by personal observation, which can of course cover only the brief space of the visit of the travelling metallurgist, must, therefore, be made to replace the more valuable data. The writer has had occasion, during the last and the preceding summer, to visit the larger number of the Western lead-smelting works, and offers, in the following pages, such data relating to the economy of lead-smelting in the blast furnace at various works, as he has been able to obtain. The only object in doing so is to place these figures on record, so that they may be from time to time supplemented with other data, which are now wanting. I. EUREKA CONSOLIDATED COMPANY'S SMELTING-WORKS. These works smelt the ores from the mines of the same company on Ruby Hill, Eureka, Nevada. The supply is almost unlimited,

By Albert Roberts

Summary In response to a growing intolerance towards ground vibrations and noise as environmental pollutants the engineer must consider the effects of his operations as they are likely to be judged subjectively by the public at large. Much work has been done on the study of vibration damage to structures, but the damage criteria normally applied do not take into account any resonance effects, nor do they embody any subjective criterion. Mu1tiple criterion techniques of subjective appraisal have proven to be of value .in the assessment of environmental comfort in relation to ventilation, air conditioning, and lighting. One such scale, the Reiher-Meister Scale, has also been applied to ground vibrations and noise, and an attempt has been made to correlate this scale with objective criteria, using the parameters of frequency and displacement. This paper quotes examples and compares ground vibrations resulting from blasting, the operation of, vibrating and impact-hamner pi1e drivers, forge hammers, and railway and road traffic. The Reiher- Meister Scale was applied to a subjective-objective correlation in relation to vibrations from railway traffic and gave results which did not conflict with experience.

Jan 1, 1971

By J. L. Bray

IT is well known that iron markedly improves the physical properties and casting characteristics of aluminum bronzes. The use of 1 to 4 per cent iron as the principal modifying addition has become common practice in many foundries melting aluminum bronzes. Although the beneficial effects of iron are unquestioned, there is some uncertainty regarding the structural changes caused by it in the basic copper-alumi-num system. It is agreed that a new constituent appears in abundance when the iron content reaches 2 to 4 per cent. This constituent, which frequently occurs in shapes resembling clover leaves, is sometimes assumed to be an aluminum-iron intermetallic compound. If this were correct we might expect a change in the structural relationships of the matrix in the direction of decreased aluminum content. On the other hand, it has been reported that iron has a negligible effect in altering the fundamental relationships of copper-aluminum alloys1. Others2,3 have reported an additive coefficient. Apparently it will be necessary to know the equilibrium relationships between the phases of the copper-aluminum-iron alloy system to establish any such theory as fact. When this has been done it may very well be that a further revision in the structural relationships may be necessary to describe the changes to be expected in commercial cast alloys. It was with this latter problem before them that the authors attempted to

Jan 1, 1936

By W. H. W. Husband

Rock salt has been solution mined for many years in many countries. Attempts have been made in the past in Canada and various other countries to produce potash by the same method. However, only Kalium Chemicals Ltd. has been successful, possibly because the conditions in Saskatchewan are the most favorable to be found so far for the development of a solution-mining method for potash. In view of the fact that few studies of solution mining of potash have been attempted, only one company has succeeded in using the method, and no information has been released by this company, the application of solution mining of potash ore bodies has to be presented on the basis of available theory, past small-scale studies, and recent patents. A simple mining method is outlined and possible methods of recovering the potash from the brine are discussed. Dissolution data pertaining to solution mining of potash, flowsheets, and material balances are presented. The available information is brought together in a cost analysis to show capital and product costs in terms of 1966 dollars.

Jan 1, 1972

By C. W. George, Bruce Chalmers

The authors enumerate the factors which appear, from their observations and practical experience of failure of aircraft components in Great Britain, to be responsible for causing a metal or alloy to fail by stress corrosion. The essential conditions for promoting failure by stress corrosion are: (I) tensile stress at the surface of the component, (either residual or applied), and (2) an attacking medium that may be a solution or a liquid metal. Particular attacking agents are effective only on certain metals. In all instances of stress-corrosion failure experienced, cracking of an intercrystalline form has occurred and examples of such failure in aluminum alloy, steel and copper alloys are described and illustrated. The relation between microstructure and stress corrosion is mentioned and methods of investigating the susceptibility to stress-corrosion failure of metallic materials are described. The precautions to be taken in selecting materials for particular aircraft components and the importance of adequate protection against chemical attack are considered. The authors have given a factual survey of stress corrosion and have made no attempt to advance any scientific explanation of the phenomenon.

Jan 1, 1945

By Gerald Edmunds

THE development of "fiber" or preferred orientations, during the plastic deformation of metals, and the relation of such structures to the anisotropic characteristics of worked metals has become a subject of common knowledge among metallurgists. Very little has been published, however, relative to variations existent throughout the cross-sections of rolled strips,1 and the influence that such variations may have. This paper presents such a study on a rolled zinc alloy.2 The significance of small differences in surface structure is shown in relation to bending properties. Experience with zinc and its alloys has shown that the outer radius of the bend, which is subject to tensile deformation, is the common region of failure. In considering relations of structural characteristics to bending properties it will suffice, therefore, to consider the ease and possible extent of tensile deformation resulting from various orientations. It is necessary in this connection to assume that on the average the individual crystals of a polycrystalline material act substantially as if their movements were unobstructed by the surrounding grains. This assumption is not strictly valid, but the error involved is unlikely to affect seriously the qualitative conclusions derived from its use. The mechanism of the plastic deformation of zinc crystals has been described by Mark, Polanyi and Schmid3 and by Mathewson and Phillips,4 and is regarded as ' being accomplished by block movements or

Jan 1, 1931

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By Alexander Coucoulas

FABRICATION of thin-film circuits deposited on glass substrates requires the formation of permanent electrical contacts. Since thin films are in the order of a few thousand angstroms thick and are deposited on nonconductive surfaces such as glass, new methods of lead attachment are being pursued in the microelectronics industry. Ultrasonic welding is being considered in thin-film technology since joining can be accomplished between a wide variety of dissimilar materials.l,' Ultrasonic welding is accomplished by a transducer-coupling-tip system which converts high-frequency electrical energy into mechanical vibrations and delivers it into the weld region. During the process the tip oscillates in a direction parallel to the surface of the weldments, inducing shear stresses in the work pieces which are clamped between the tip and anvil. Though the basic bonding mechanism is not clearly understood, it has been described as closely akin to friction welding. In the course of an investigation concerned with ultrasonic we!ding of aluminum wires to tantalum thin films (1400A) deposited on glass, low weld strengths were related to glass failure. Upon investigating this condition, an improved method of bonding was developed where the aluminum was held at a temperature where a minimum amount of strain hardening occurred during the introduction of ultrasonic energy. Experimental Procedure. Aluminum wires (0.015 in,) were bonded to tantalum thin films with an optimized set of welding parameters (power, time, clamping force) employing a commercial 100-w 60-kc ultrasonic welder. Forty-five degree shear-peel tests, where the lead is pulled at a 45-deg angle with respect to the substrate at 0.2 in. per min, produced a large variation from zero to the strength of the wire, Table I. Inspection of the weld region generally revealed: glass cracking before and after testing; the removal of glass nuggets from the substrate by the lead during testing, Table I; thin-film penetration. In an effort to improve the shear-peel strength, the aluminum between the tip and substrate was heated above ambient temperature through an argon gas media prior to and during welding with the same parameters employed above. With the addition of heat: wire deformation was increased; shear-peel tests all failed at the weld-wire junction, leaving the bonded portion undisturbed; no evidence of glass cracking or film penetration prior to or after testing was observed. In order to prevent failure at the weld-wire junction due to excessive wire deformation, 0.035-in. aluminum wires were welded to tantalum thin films with an optimized set of welding and heating parameters. As

Jan 1, 1967