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By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in

By J. R. Kyte, L. A. Rapoport

The material balance equation for partiai or complete 1:trter-drivc reser1,oir.s been re-arranged to include a pressure irrferferencr ternr. This pressure interfernce term was ohtained from the theory established hy Morinda. A .successful progranl deissed to solve the resrclritlg c,qrration in a few hours on a nleelitr .sizeti, digital compuier. No prior knowdelge of the properties of the eqrrifer is required in the solution. 7' ri~rl calculations areatle using various assumed con!binuiions of value of the constant expretsing the qquifer properties correspoinds to the best fit ohtained between observed and calculated field history. Details of the method of calculaion are illus trated by an example. INTKCDUCTICN A method 01' calculating the material balance equation for a partial water-drive reservoir completed in an aquifer has been described in the literature." Pressure interference i'rc,m other pools iocated in the same nquiucr is not taken into account in this solution. When present, the pres- sure interference effect must be included in order to make a complete performance analysis. A correction for this effect has been developed using the theory cstahlished by Mor-tada.' Manual calculation of the material balance for water-drive reservoirs is a formidable task. Such manual ca1culation when interference eflects are includcd would be impossible to completc in any reasonable time period. However, a medium-sized stored program, digltal conlputer can he used satisfactorily. The method is described in the following sections. THECKETICAL CONSIDEKATIOhS The material balance equation for a reservoir producing by partial or total water drive, as proposed by Van Everdingen, This relationship is linear for Z/a from which thc slopc, Z, and the intercept, N, can be obtained by the least-squares method from the data points. It is not necessary lo know the aquifer properties to uktain oplimum values tor 2nd IV. Various assumptions are made tor At,,: where 11 is production time, seconds (oilfield between the equal successive time intervals into which the history is divided. t,, h It, times the number of equal time periods from i.e.. the total dimen-sionless time interval from It is noted that the dinlensionless time interval, At,,, involves all the relevant aquifer properties. Accordingly, any assunlption of is an assumption of the combined aquifer properties which pertain to the solution of the equation. Deviations of the data points from a straight line arc calculated for each assumption of and the value of A, correspond ing to the minimunl deviation is chosen as the optimum solution. This method is described in Ref. 1 and 2. Thc material balance solution is usually made with an initial assumption that the reservoir being studied is located in an infinite aquifer from which there are no other withdrawals. Deviation of the points by amounts greater than can be attributed to inaccuracies in field data may be the result of: (1) boundary effects of a limited aquifer, (2) pressure interference from othcr pools completed in the .sarne aquifer, and (3) a combination of these effects. Differentiation of these effects can be made only on the basis of geologic data. Pressure interference from other fields will result in a pressure drop at the original oil-water boundary having an interference component, The measured instantaneous pressure drops at the oil-water

By E. J. Roberts

Hydrometallurgical operations and many processes in the chemical industry require the separation of dissolved material from solids. One of the decisions which has to be made in designing a plant for such an operation is how this separation shall be accomplished. It is the purpose of this paper to set forth the general principles involved in such separations in order that the optimum flowsheet and equipment may be selected. Countercurrent Decantation with thickeners, or C.C.D. as it is generally known, is, of course, only one way of separating dissolved material from undis-solved. Other unit operations such as Countercurrent Filtration (C.C.F.) and Countercurrent Classification (C.C.C.) are widely used. The same principles may also be applied to centrifugally assisted decantation, as with nozzle or solid bowl type centrifugals, and to separations using screens, either gravity or centrifugal type. Another form of countercurrent washing applicable to granular materials is practiced in continuous ion exchange operations. All of these operations depend on two basic principles, or combinations of these principles. In C.C.D. type operations the solids are concentrated into the smallest possible volume of liquor in each step and the resulting pulp then mixed with a more dilute liquor and recon cen trated, the liquors separated from the more dilute stages being advanced to dilute the more concentrated liquor in a previous solids concentrate, as is shown in Fig. I. This will be termed the solids concentration-solution dilution principle, or, for short, solution dilution. countercurrent decantation- type circuits. The second principle used in washing solubles from solids is that of solids concentration-solution displacement. Here the solids are restrained from movement while wash solution is forced through the interstices in a counter-current fashion, as in Fig. 2. In the simplest application of this principle, once the "cake" has been formed, it is not disturbed until the operation is completed. In continuous filters, the cake is merely moved under the successive washes and the displaced filtrates removed as in Fig. 4. Often, however, after one or two displacement washes, a repulping step is introduced, the cake reformed and washed again. This procedure brings the solution dilution principle into play as well as the solution displacement principle. Merely thickening ahead of filtration, which is often operationally advantageous, does not hybridize he circuit. It still can be a pure solution displacement operation from the washing

Jan 1, 1961

Jan 1, 1961

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers' knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

By G. W. Thomas

Jan 1, 1967

By B. E. Warren

Jan 1, 1965

By R. L. Whiting, H. J. Ramey

The basic study from which this paper was prepared was started as the result of the growing need throughout the world for increasing quantities of energy in all forms. Quite obviously, natural forms of energy that are readily available at low development cost are those in greatest demand. The underdeveloped countries — and particularly those having little or no petroleum resources — are the countries in which the most interest is being shown in the newer energy sources. One of the least expensive energy sources is natural geothermal steam.'-* Although this form of energy has been recognized for centuries, it has been only during the past 20 years that serious efforts have been made to harness it. Natural geothermal steam energy in Italy, New Zealand, Mexico, Japan, and California is now being produced through wells to drive turbines and generate electricity. Further, active exploration for natural geothermal steam is being conducted in Hawaii, Fiji, Taiwan, Chile, Russia, Greece, and Katanga. It is surprising to find that most geothermal steam exploration is in the "steam seep" stage. That is, surface studies are made and exploratory wells are drilled in the general area of steam seeps. However, in the larger geothermal steam areas, there have been efforts to apply the most modern geological and reservoir engineering principles in order to define the reservoir parameters, particularly those relating to estimates of reserves and future productivity. This paper is concerned with the development of appropriate equations and techniques to facilitate these estimates. Production of natural steam or hot water presents problems different from those experienced in the production of oil and gas. For example, steam or hot water systems may be essentially single-component systems, while hydrocarbon systems are most frequently multicomponent fluid systems. Heat effects are much larger for water than for hydrocarbon systems; and the natural steam production may or may not be isothermal, while production of petroleum reservoirs is considered normally to be isothermal. Petroleum reservoir engineering principles may be applied to natural steam or hot water reservoirs if the inherent differences in the systems are considered. The basic considerations involved in geothermal steam reservoir engineering are: thermodynamics, physical and thermal properties of water, materials and energy balances, fluid influx, and performance matching and predicting. Thermodynamics Fig. 1 is a pressure-temperature diagram for the liquid-vapor region for pure water, showing the critical point and five other points representing possible initial conditions for a geothermal steam reservoir. To generate a physical appreciation for the mechanics of natural steam production, it is helpful to consider

Jan 1, 1970

By A. W. Asman

The problem of balanced design in a belt conveyor has been under constant study. Increased use of this method of transport in recent years has stimulated investigations. Conveyor belt, power transmission and other machinery should be adequate to perform the required service. All components of the belt conveyor should work as an efficient unit moving its load continuously between terminals. As part of a long term research project on belt conveyors, Hewitt-Robins established in 1954 a 2-year grant at Pennsylvania State University. Under terms of the grant, certain fundamental phenomena were to be studied. This work evolved a new concept in belt conveyor power determination based on the principle of belt tension. The Penn State contract furnished the foundation for later more detailed studies. From these most recent investigations, more specific factors were defined. In the final analysis, all of the data collected has been worthwhile in belt conveyor design. Units now operate over long distances at speeds of over 800 fpm. Long high lifts are commonplace. Where vertical or inclined shafts were the rule, belt conveyors receive first consideration. Although belt conveyors have moved forward rapidly, the future will see a tremendous gain in their use. The ideal test belt conveyor would be several thousand feet in length and have a maximum tension of at least 70,000 lb., Also, this conveyor should be horizontai and have a variable feed rate of more than one material. Data from such a field belt conveyor combined with laboratory information would permit accurate analysis. Since this type of conveyor was not available, many field locations were visited: An alternate would have been to erect a closed circuit system in the laboratory. Either method had limitations and the first was selected as having the best possibilities. Manufacturers of conveyor belting and machinery basically have been using the same horsepower formula. As more information became available from field installations, factors in the basic formula were modified. Practically all conveyors are designed today by adding together the horsepowers required to move the empty belt, move the load horizontally, and elevate the load. In selecting size of drive motor, the first two elements are relatively unimportant if the last is large. However, it is the combination of

Jan 1, 1961

By C. Crussard, R. Tamhankar

It is the policy of The Metallurgical Society to provide, in the TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME, a prompt and accurate medium for publication of reports of significant new research in both the scientific and engineering aspects of metallurgy. Papers submitted to the Society are judged by competent reviewers accord-ing to established criteria for technical merit, accuracy, originality, and presentation. STAFF: Editor, Gerhurd Derge Carnegie Institute of Technology Schenley Park Pittsburgh 13, Pa. Editorial Assistant, M. A. Redmerski Staff Coordinator, James J. Burke THE METALLURGICAL SOCIETY: W. R. Hibbard, Jr., President; J. C. Kinnear, Jr., Past-President; John Chiprnan, Vice President; T. D. Jones, Treasurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: A. W. Thornton, Chairman; Dennis Carney, John Chip-man, J. C. Fulton, J. H. Hollomon, H. H. Kellogg, A. E. Lee, R. Maddin, J. D. Sullivan, and D. Swan. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extractive Metallurgy Division: T. B. King, Chairman; S. J. Dickenson, R. P. Hermsdorf, R. Schuhmann, Jr., and P. T. Stroup. Institute of Metals Division: Robert Maddin, Chairman, F. Lincoln Vogel, Jr., Vice-chairman, W. A. Backofen, R. W. Balluffi, J. H. Bechtold, M. B. Bever, R. S. Busk, C. G. Goetzel, Paul Gordon, C. D. Graham, .Jr., Robert F. Hehemonn, R. I. Jaffee, F. E. Jaumot, Jr., Irving R. Kramer, A. J. Lena, Harold Margolin, C. J. McHorgue, Russell A. Meussner, J. B. Newkirk, H. W. Paxton, G. E. Pellissier, I. S. Servi, Alan U. Seybolt, A. J. Shaler, and Jack Washburn. Iron and Steel Division: J. C. Fulton, Chairman; T. B. King, F. C. Langenberg, W. 0. Philbrook, and T. 0. Winkler. Published bimonthly by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., 29 West 39th Street, New York 18, N. Y. Telephone: PEnnsylvania 6-9220. Subscription $20 per year for non-AIME members in United States and North, South, and Central America; $25, foreign; $5 for AIME members. Single copies, $4.00, single copies foreign, $5.00. The AIME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1958 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AIME New York ... Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts... Second class postage paid at New Yark, N. Y., and Ann Arbor, Mich. Volume 212, Number 6.

Jan 1, 1959

By Ernst M. Cohn

The demonstrations of the "Silent Sentry" by Union Carbide Corp. in 1957 and of a special tractor-plow by Allis-Chalmers in 1959 ushered in the technology era of fuel cells. The idea for direct conversion of chemical to electrical energy, first published in 1801 by Davy in England and Ritter in Germany, has been kept alive by a few people through 150 years: Grove built the first hydrogen-oxygen fuel cell in 1839; Mond and Langer made electrolyte contributions around 1890 that are still used today; Baur worked on coal-based cells from 1900; Bacon started his work in the '30's, which resulted in the first multi-kilowatt unit in the '50's; Davtyan studied molten-salt electrolytes in the '40's, followed by Ketelaar in the '50's; and Justi developed highly active electrodes in the '50's, to name only some of the pioneers. Despite the tremendous increase in research and development of fuel cells, these direct energy converters are still in their infancy. They will find their functional application in space, where power density must be maximized and product water utilized. These early systems will provide valuable experience in system engineering and reliability.

Jan 9, 1964

By D. R. Cook

This paper is a case history of an exploration venture for base metals, begun by the Rocky Mountain District of Bear Creek Mining Company in 1952 and completed in 1954. The project was based on the idea of W. S. Burbank, U. S. Geological Survey, that commercial deposits of base metals might occur in Paleozoic sediments beneath hydrothermally altered volcanic rocks in the Southern Bonanza mining district, Colorado. Here, an area of andesitic rocks, four square miles in extent, has been argillized, pyritized, chloritized and silicified. Geological, geophysical and geochemical studies were followed by the diamond drilling of three holes totalling 6,220 feet. Further alteration ang geochemical studies were made on the cores from these holes. A brief review of the alteration and geologic mapping, colored aerial photograph interpretation, geochemical soil and rock sampling, magnetic, gravity and radio-metric surveys are presented together with some conclusions regarding this work. This paper is a case history of an exploration venture for base metals, begun by the Rocky Mountain District of Bear Creek Mining Company in 1952 and completed in 1954. Important contributions were made to the project by personnel of the Rocky Mountain District and the Geophysics Division. Individual acknowledgements to these people are made at the end of the paper. BASIS FOR THE PROJECT The project was based on the idea of W. S. Burbank (1947, p. 444) that commercial deposits of base metals might occur in Paleozoic sediments beneath hydrothermally altered volcanic rocks in the Southern Bonanza mining district, Colorado. Paleozoic sedimentary rocks, including the favorable Leadville limestone, are exposed three miles south of the altered area, and reason exists to believe that they might underlie it within a reasonable depth. Alteration of pre-mineral volcanic rocks has been used successfully as a guide to concealed orebodies in the Main Tintic and East Tin tic mining districts, Utah (Bill-ingsley, 1933, p. 120-122; Lovering et al, 1949; Howd, 1957, p. 124-134; Cook, 1957, p. 73) and could be a useful guide here. GENERAL GEOLOGY AND STRUCTURE The Northern and Southern Bonanza mining districts are northwest of the San Luis Valley in southern Colorado, just within the northeastern edge of the San Juan volcanic province. The districts are1ocated on the southern extension of the Sawatch uplift, a prorninent northwest-trending structural high. The highly productive mining camp. of Leadville, Gilman and Aspen are on the northeastern and northwestern flanks of this uplift where Paleozoic limestones have

Jan 1, 1961

By R. G. Turner, M. G. Hubbard, A. E. Dukler

Gas phase hydrocarbons produced from underground reservoirs will, in many instances, have liquid phase material associated with them, the presence of which can affect the flowing characteristics of the well. Liquids can come from condensation of hydrocarbon gas (condensate) or from interstitial water in the reservoir matrix. In either case, the higher density liquid phase, being essentially discontinuous, must be transported to the surface by the gas. In the event the gas phase does not provide sufficient transport energy to lift the liquids out of the well, the liquids will accumulate in the wellbore. The accumulation of the liquid will impose an additional back pressure on the formation that can significantly affect the production capacity of the well. In low pressure wells the liquid may completely kill the well; and in the higher pressure wells there can occur a variable degree of slugging or churning of the liquids, which can affect calculations used in routine well tests. Specifically, the calculated bottom-hole pressures used in multirate backpressure tests will be erroneous if the well is not removing liquids on a continuous basis, and gas:liquid ratios observed during such a test may not be correct. Several authors1,3,8,14 have suggested methods to determine if the flow rate of a well is sufficient to remove liquid phase material. Vitter14 and Duggan' proposed that wellhead velocities observed in the field would be adequate for keeping wells unloaded. Jones8 and Dukler3 presented analytical treatments resulting in equations for calculating, from physical properties, the minimum necessary flow rate. An analysis of these studies indicates the existence of two proposed physical models for the removal of gas well liquids: (1) liquid film movement along the walls of the pipe and (2) liquid droplets entrained in the high velocity gas core. Although there probably is a continuous exchange of liquid between the gas core and the film, they will be treated separately for the purposes of this study. The development and comparison of these separate models with experimental data will permit the determination of which, if either, is the controlling mechanism for the removal of liquids from gas wells. The Continuous Film Model Liquid phase accumulation on the walls of a conduit during two-phase gas/liquid flow is inevitable due to the impingement of entrained liquid drops and the condensation of vapors. The movement of the liquid on the wall is therefore of interest in the analysis of liquid removal from gas wells. If the annular liquid film must be moved upward along the walls in order to keep a gas well from loading up, then the minimum gas flow rate necessary to accomplish this is of primary interest. The analysis technique used follows Dukler2 and Hewitt5 and involves describing the profile of the velocity of a liquid film moving upward on the inside of a tube. The minimum rate of gas flow required to move the film upward is then calculated.

Jan 1, 1970

By J. E. House, J. L. Drobnick, R. R. Swanson, D. W. Agers

The paper describes an improved process for the recovery, purification, and concentration of copper values from acidic dump leach liquors. The process employs a new liquid ion exchange material (LIX® 64 reagent) capable of separating copper values from iron and other impurities common to dump leach liquors in the typical pH range of 1.4-3.0. Properties and performance of the reagent are discussed. Design scale-up information for both pilot plants and commercial installations, including preliminary economics, are presented. Economic considerations include the production of electrolytic copper from the purified copper aqueous concentrate. INTRODUCTION Since the commercial acceptance of the liquid ion exchange process in the mineral processing industry, it has been predicted that a wide selection of chemical reagents to efficiently and economically separate many metals in solution under a wide range of conditions would be commercially available. Several years ago, General Mills began a basic research and development program to determine if it were possible to develop a reagent to extract economically metallic ion from existing process streams. Progress toward reaching this objective was reported in late 1963, when development of quantities of LIX -63 reagent, a highly selective reagent for the extraction of copper, was introduced. The properties of this reagent are described in a previous paper.' The development work with this reagent indicated that perhaps the largest potential application for a copper extractant, the treatment of acidic dump leach liquors, would not be economically possible with LIX-63 because of limitations of the reagent to extract copper below a pH of 3.0. The relatively small pH adjustment required with LIX-63 would result in a significant processing cost and the undesirable precipitation of ferric hydroxide from the liquor. This pointed to the need for another copper extractant which would extract copper from dump leach liquors without pH adjustment. General Mills was successful in synthesizing a molecule which does not have the pH limitation of the LIX-63, yet possesses the selectivity-solubility properties required of a metallic extractant. The resulting LIX-64 reagent broadens the pH range from which copper can be effectively extracted and separated from other metallic impurities. Of special significance is the fact that the reagent, LIX-64 was developed by combining the technical requirements of a specific problem in hydro-metallurgy with theoretical organic and physical chemical principles.

Jan 1, 1967

By R. B. Booth, W. F. Linke

The continuous interest of the American Cyanamid Company in producing superior polymeric flocculants and dispersants for the mining industry has resulted in a broad, general study of the physical chemistry of mineral-polymer systems. The aim of this program has been to establish a sound theoretical basis on which practical problems could be analyzed, and which would lead to the development of new and improved flocculating and dispersing agents. This study has required the cooperative effort of physical, analytical, and polymer chemists, as well as engineers familiar with mining problems. This report summarizes the results of some of our investigations over the past two years. Further studies along these and other lines are in progress and will be reported in the near future. MEASURING FLOCCULATION IN THE LABORATORY The foremost problem in studying flocculation in the laboratory has been to establish reproducible methods of comparing and evaluating the effectiveness of various reagents. Previous workers have measured settling -rates 1,8 filtration rates2 , and sediment volumes3 . Direct observations of the floc size, or the clarity of the supernatant liquid, can also be used. AIthough these parameters are all interrelated, they do not always measure the same physical properties of the suspensions, and hence are not equally useful or reliable. Whatever the method of comparison selected. the testing procedure must be carefully defined and standardized. The results must be satisfactorily reproducible, and for practical purposes must accurately reflect the results obtained in mill use. In order to compare the data obtained in these various types of test, the physical nature of the flocculated system must be examined in some detail. In an unflocculated system, only the larger or denser particles (the "sands") settle at a useful rate. The sediment can be observed to build up from the bottom of the cylinder, while the fines remain in suspension for a long period of time. If the system is not disturbed, even the microscopic fines can be seen to classify themselves as they fall over a period of days. When a high molecular weight polymer is added to the system, the colloidal particles are tied together randomly in flocs, and the sands and fines settle together. The line of demarkation between solid and liquid phases moves downward from the top of the cylinder. The settling rate of the flocs depends on their size and on their effective density. For a given mineral sample, the larger the flocs, the faster the settling. Since the large flocs cannot pack as closely as small ones, they produce a sediment with more pore spaces, and hence of larger volume, which is easier to pump and to agitate. Although it is nearly impossible to measure individual floc sizes, it is relatively easy to determine settling rates and sediment volumes. Of these two, the settling rate is simpIer to measure, and hence generally more practical. Reproducible sediment volumes can only be obtained by allowing the solids to pack for a rather long period of time (e.g., hours to days), and although the volumes thus observed are directly related to the degree of flocculation (average floc size), it is often impractical to wait so long for the results.

Jan 1, 1961

By E. J. Ripling, M. W. Toaz

Tensile tests were conducted on pure magnesium and on four commercial alloys over a variety of temperatures and strain rates. The high positive slope of the ductility vs testing temperature curves that is found over a short range of testing temperatures for these materaturerials was shown to result from the fact that the microstructure was not stable at these testing temperatures. Pure magnesium did not display a transition temperature, although its sub-room temperature ductility was low. This poor ductility resulted from a grain boundary weakness. The aluminum-bearing commercial magnesium alloys had a higher ductility than the pure magnesium. ness.Thealuminum-bearingcommercialThese alloys did exhibit a transition temperature and grain boundaries that were stronger than the grain material. Both pure magnesium and the commercial alloys began initiating cracks at strains equal to one half of their fracture strain. MAGNESIUM base alloys' enormous potential as structural materials lies in their high strength to weight ratios. At present, the high strength magnesium base alloys such as AZ-80, which will be discussed later, have about as high a tensile strength to specific gravity ratio as the highest strength wrought aluminum alloy, 75s-T6, and, of course, a much higher strength to weight ratio than structural steel. Further, since the magnesium base alloys develop their high strength to weight ratios with moderate strengths and extremely light weights, the ratio of load carrying capacity to the weight of many structures is relatively higher for the magnesium base alloys than their strength to weight ratios would indicate. This results because judicious increases in section size, such as increasing the depth of bending members or adding reinforcing ribs, can frequently increase the weight of a structure linearly while the strength and stiffness increase as the second or third power of the added weight. Strength and rigidity must be designed into lightweight structures by those techniques which establish multiaxial stress states. Consequently, strong, lightweight structures frequently also possess a greater propensity toward brittle failures. In order to insure against these catastrophic failures, an extra premium must be placed on ductility and toughness in light alloys. Current knowledge of the ductility and toughness behaviors—notched behaviors—of magnesium base alloys is limited.* Most of the magnesium base alloys * The state of present knowledge regarding the effect of testing temperature on mechanical properties has recently been summar-ized by Pritchard.' crystallize in the hexagonal system, so that they are expected to exhibit a tough and ductile to brittle transition temperature. Actually, a transition temperature behavior has been reported for commercially pure magnesium in the literature, but the characteristics of this transition temperatureh uggest that it may not be a transition in the usual meaning, but simply the onset of some thermal softening, a performance much like that which face-centered-cubic lead might exhibit slightly below room temperature. If transition temperatures do exist, such important questions as the manner in which they are affected by internal variables such as chemical composition and grain size, or the effect of external variables such as rate of straining or notch severity have never been investigated. The investigation reported upon herein was undertaken in order to define some of the mechanical behaviors of the magnesium base alloys better, to gain a better understanding of the influence of some of the above listed variables, and particularly to understand their effect on ductility and toughness better. Material and Procedure Material-—Pure magnesium and four commercial alloys were used in this investigation. The alloys were selected so that chemically they made up a series with approximately the same minor alloying

Jan 1, 1957

By E. H. Boswell, E. M. Cushing

The Mississippi embayment east of the Mississippi River is part of a vast geologic and hydrologic province. The abundance of water available is largely responsible for the agricultural history of the area and is perhaps the key factor in the rapidly accelerating trend toward industrialization. The multiple artesian aquifer systems that underlie the region and the alluvial aquifer along the Mississippi River are virtually undeveloped sources of fresh water in that they are yielding only a fraction of the water available. The potential yield of the 12 aquifer systems is estimated to be about 25,000 mgd (million gpd) of which only about 600 mgd is presently being withdrawn. The amount of water in storage in these systems is about 1600 trillion gal. Ground water having a dissolved-solids content of less than 500 ppm is generally available at depths of less than 1000 ft, and water having a dissolved-solids content of less than 1000 ppm is available in some places to depths of more than 3000 ft. Iron is the most common troublesome chemical constituent in the ground water. Water in varying amounts is also available from streams within the region. The amount of water which originates within the region and which leaves it as streamflow during a year averages about 50 million acre-ft (about 45,000 mgd). An additional 375 million acre-ft (about 340,000 mgd), which originated outside the region, leaves the region as streamflow during an average year. Some streams have considerable flow during periods of no precipitation and the water during these periods generally has a low dissolved-solids content. Large quantities of water from streams and waterbearing sands (aquifers) are available in the Mississippi embayment east of the Mississippi River. Most of the region is underlain by aquifer systems that will yield large quantities of water to wells, making ground water the most readily available source of fresh water. About 90% of the water used in the region is obtained from wells. Streams have been used primarily to dispose of, and dilute, wastes that have been dumped into them. The Mississippi, Ohio and Tennessee rivers, and the lower parts of the Tombigee and Yazoo rivers also serve as a means of transportation. This nominally water-rich region receives from 48 to 56 in. of precipitation in average years and is crossed by several large rivers. The largest, the Mississippi River, is the western boundary of the region discussed in this paper. The economy of the region is basically agricultural, but industry has become increasingly important since World War 11. The diversification and mechanization of agriculture have resulted in a surplus of manpower, most of which is being absorbed by the expansion of industry. Further industrial expansion probably will occur because of the available manpower, natural resources and economical transportation. Increasing demands on available water supplies will be made and the future economic growth of the region will be largely dependent upon wise utilization and management of the water resources.

Jan 1, 1969

By W. T. Malone, J. R. Williams, R. L. Tiner, J. M. Tinsley

Hydraulic fracturing methods for production stimulation have become a common procedure in the oil and gas industry. Fracturing treatments are performed on wells of various potentials to help increase the production rate. In addition to the desire for increased production is the need to predict what increase might be expected. This knowledge is useful in economical treatment planning to accomplish the desired production goals for the well. Theoretical production increases due to horizontal radial fractures may be calculated using equations developed from mathematical analyses and electrical models.1,2,6 It also is possible to predict theoretical production increases due to vertical fractures using curves developed from electrical3 and mathematical models.8 However, these studies assumed that the vertical fracture height and the formation height were equal, which may not be true." In addition, the final fracture height through which fluid is produced may not be equal to the created height. The development of vertical fracture proppant transport relationships has made unrealistic the assumption that propped fracture height is equal to created fracture height. Through the use of published proppant transport equations,4'12 it is possible to calculate the height of a bed of propping agent deposited in a fracture of a given height. Assuming that the fluid flowing in the fracture moves through only the propped portion of that fracture (i.e., that the un-propped part of the fracture heals) it becomes essential to know how production increase varies with the ratio of propped fracture height to formation height. It should be recognized that future investigation may determine that the fracture does not heal completely and that a highly permeable channel exists over the deposited bed of proppant. The effect of this channel was not considered for the present study. The following analysis of experimental data allowed development of curves to determine theoretical production increases considering fracture height as a variable. Discussion In designing a fracturing stimulation treatment a number of variables must be considered. The size of the treatment, type of proppant used, proppant concentration, treatment fluid properties and well conditions are all factors affecting the dimensions and permeability of the fracture. Production increase due to a vertical fracture is affected by propped length, height, width and permeability of the fracture for a given set of formation conditions. Production increase may be defined as the ratio of production rate after fracturing to the production rate before fracturing at the same pressure differential, pe — pw. The producing rate in an

Jan 1, 1970

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 L. A. Roe

Magnetic separation of iron ores is one of the fastest-growing segments of the minerals beneficiation industry. The tonnage of taconite ores processed annually by magnetic separation will, in a few years, reach 100 million. Magnetic separation occupies an attractive position in the field of ore beneficiation. It is a simple yet effective method, used for some 150 years and steadily growing more important. This type of beneficiation orginated in 1792, when William Ful-larton was issued a British patent covering the separation of iron ore by magnetic attraction. What is magnetism, and why are some materials capable of being magnetized and others not The study involves many unknowns, and even a partial answer to these questions would be a dissertation in solid state physics and perhaps other fields of science. But the last two decades have revealed basic facts as to why certain materials are magnetic and what happens to them when they are magnetized. Some of the newer studies in solid state physics have developed a theory that can be applied to studies of magnetism. It is claimed that magnetism stems fundamentally from the spin of electrons in atoms that tend to go in pairs, spinning in opposite directions. The atom as a whole can act as a magnet only when there is an imbalance of electronic spin. Whenever an atom has an odd number of electrons, therefore, this imbalance exists. This neutralizing effect explains why a piece of material that contains atomic magnets is not necessarily magnetic. The physicists tell us that iron is composed of many small magnetized regions called domains, which consist individually of millions of atoms. The piece of iron becomes magnetized when an external force lines up these domains in the same direction. Fundamental data developed by physicists working in fields far removed from minerals beneficiation are now available for developing better magnetic separators for ore processing. More Data Needed on Magnetic Properties of Minerals: There is less information on magnetic properties of minerals than there is for certain aspects of magnetic separator design. When the data on magnetic properties is available, it is often directed toward the study of powders for tape recorders and other highly scientific endeavors that are of little use to the beneficiation engineer. W. R. Crane's table of tractive forces, published in 1902, is still a guide in the study of magnetic minerals. Bits of other information regarding electrostatic conductivity, dielectric constant values, and permeability of various minerals have also appeared but are of small practical value in magnetic separation of ore. It is extremely important to obtain pure mineral specimens for making investigations and to record results that may be of use in studies of magnetic processes. Reference to the large volume of data developed by those concerned with analysis and design of permanent magnets soon reveals that these people have extensively evaluated the effect of various impurities on magnetic properties. Much of the science of the ferrite industry is based upon spinel-type structures which are varied by substitution of selected elements or even subtraction of elements, leaving vacant sites in the space lattice. Magnetic separators are used to beneficiate a wide variety of industrial minerals. In this application the relatively large volumes of nonmagnetics are usually the commercial products. The amount of mag-

Jan 1, 1959