Search Documents

By J. J. Thomas, J. H. Nead

This investigation was undertaken to determine, if possible, the relation between static and dynamic tensile tests as measured by the work required to break test specimens slowly, in a tensile testing machine, and rapidly, by means of a falling weight. It was hoped that the investigation would throw some light on the role played by ductility under different rates of application of load. In problems of design, it is usually assumed that the moduli of elasticity of all steels are equal; viz., about 30,000,000. The stress-strain diagram within the elastic limit is a straight line, as shown in Fig. 1, where OA is the curve of a hard steel and OB that of a soft steel. If the modulus of elasticity is constant, as assumed, the slope of the line OC

Jan 1, 1922

By J. H. Nead, J. J. Thomas

This investigation was undertaken to determine, if possible, the relation between static and dynamic tensile tests as measured by the work required to break test specimens slowly, in a tensile testing machine, and rapidly, by means of a falling weight. It was hoped that the investigation would throw some light on the role played by ductility under different rates of application of load. In problems of design, it is usually assumed that the moduli of elasticity of all steels are equal; viz., about 30,000,000. The stress-strain diagram within the elastic limit is a straight line, as shown in Fig. 1, where OA is the curve of a hard steel and OB that of a soft steel. If the modulus of elasticity is constant, as assumed, the slope of the line OC

Jan 1, 1922

By Victor Rudenno

Feasibility studies for mining projects traditionally involve in their final stages a lengthy process of repetitive trial and error discounting, in calculating the discounted cash flow rate of return resulting from the respective yearly after-tax cash flows. Also, probability analysis and sensitivity analysis (in particular) require extensive additional calculations with each change of any project parameter . These inefficient repetitive procedures have two unacceptable results: 1. they are not flexible enough to allow ready analysis of dependent parameters , and 2. they require resort to high-capacity centralised computing facilities with their inherent impersonality, rather than a convenient and available desk calculator - a factor of particular importance to top mining management. Such problems can be overcome if the mining project can be represented by a reasonable straightforward mathematical economic model. The most flexible and appropriate model has been found to be one in which a maximum and minimum value for each of n parameters are supplied to a program which determines a large number of systematic combinations of parameter events and then statistically analyses them to determine the resulting coefficients of the model. In this paper the authors discuss the selection of the most appropriate type of model and outline the steps followed in its development and application.

Jan 1, 1977

By Walter H. Voskuil

Illinois supplies coal to seven states in the Upper Mississippi Valley —Illinois, Missouri, Iowa, Minnesota, Wisconsin, and portions of the Dakotas, Nebraska and Kansas. In this same area are marketed large quantities of coal from West Virginia, Kentucky, Pennsylvania, and elsewhere; fuel oil from the crude petroleum supplies of the Mid-Continent fields, and natural gas from Louisiana, Kansas and the Texas Panhandle. The boundaries of this "Illinois coal-market area" are determined by competition from other coal fields and from other forms of fuel. Within the area so described 90 per cent of Illinois coal is marketed. Thus in the Southwest, an abundance of fuel-oil supplies and natural gas dominates the market almost to the exclusion of coal. The westward movement of Illinois coal in Kansas, Nebraska and the Dakotas is met by an eastward flow of high-grade coals from Colorado, Wyoming and Montana. In the lake-shore counties of Minnesota and Wisconsin, the market is dominated by Appalachian coals, cheaply carried over the Great Lakes and reaching the ports of Lake Michigan and at the head of Lake Superior. Illinois coals find their largest market in the southern and western sections of these two lake states. Only small quantities of Illinois coals are shipped east of the state line. This market area is occupied entirely by the neighboring coal fields of Indiana and the Appalachian coal fields in Ohio, West Virginia, Kentucky and Pennsylvania. Illinois Coal-makket Area , With these factors in mind, the map of the Illinois coal-market area may be drawn. Within this boundary is the area that is logically and economically served by Illinois coal. However, this area is by no means exclusively dependent upon coal from Illinois mines. The preponderance. of Appalachian coal in Wisconsin and Minnesota has been mentioned. Appalachian coal, also, moves in large tonnages into Illinois itself, particularly the Chicago district. The Iowa and Missouri local coals share the market with imported coal from Illinois; throughout the market area, fuel oil and natural gas are important factors in the total energy supply.

Jan 1, 1936

By Walter H. Voskuil

Illinois supplies coal to seven states in the Upper Mississippi Valley —Illinois, Missouri, Iowa, Minnesota, Wisconsin, and portions of the Dakotas, Nebraska and Kansas. In this same area are marketed large quantities of coal from West Virginia, Kentucky, Pennsylvania, and elsewhere; fuel oil from the crude petroleum supplies of the Mid-Continent fields, and natural gas from Louisiana, Kansas and the Texas Panhandle. The boundaries of this "Illinois coal-market area" are determined by competition from other coal fields and from other forms of fuel. Within the area so described 90 per cent of Illinois coal is marketed. Thus in the Southwest, an abundance of fuel-oil supplies and natural gas dominates the market almost to the exclusion of coal. The westward movement of Illinois coal in Kansas, Nebraska and the Dakotas is met by an eastward flow of high-grade coals from Colorado, Wyoming and Montana. In the lake-shore counties of Minnesota and Wisconsin, the market is dominated by Appalachian coals, cheaply carried over the Great Lakes and reaching the ports of Lake Michigan and at the head of Lake Superior. Illinois coals find their largest market in the southern and western sections of these two lake states. Only small quantities of Illinois coals are shipped east of the state line. This market area is occupied entirely by the neighboring coal fields of Indiana and the Appalachian coal fields in Ohio, West Virginia, Kentucky and Pennsylvania. Illinois Coal-makket Area , With these factors in mind, the map of the Illinois coal-market area may be drawn. Within this boundary is the area that is logically and economically served by Illinois coal. However, this area is by no means exclusively dependent upon coal from Illinois mines. The preponderance. of Appalachian coal in Wisconsin and Minnesota has been mentioned. Appalachian coal, also, moves in large tonnages into Illinois itself, particularly the Chicago district. The Iowa and Missouri local coals share the market with imported coal from Illinois; throughout the market area, fuel oil and natural gas are important factors in the total energy supply.

Jan 1, 1936

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula p = 2paR [1] where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homo¬geneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity pi and a lower layer, extend-ing to infinity, of resistivity p2. It has been shown by Lancaster-Jones2 that the apparent resistivity, obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the form pa/p1 = 1 + 4F [2] where Pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 - p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between Pa/P1, h/a and k. Such a set of curves for the case when pi > P2 is given in Fig. 1.

Jan 1, 1937

By T. Sterry Hunt

IN my address on the " Geognostical Relations of the Metals," delivered before the Institute on the 20th of February last (Vol. I Transactions, p. 331), I spoke of the rocks in the vicinity of Thunder Bay, Lake Superior, where I indicated two series of uncrystalline rocks resting upon the Huronian schists, the lower one consisting of dark-colored argillites and sandstones overlaid, apparently in slight discordance, by nearly horizontal red and white sandstone and marls, which were compared with those of Sault Ste. Marie, and those of the Portage Lake district, on the south shore. These latter sand-stones, according to Brooks and Pumpelly, overlie unconformably the Keweenaw series of copper-bearing amygdaloids, sandstones, and conglomerates, and are in turn overlaid by the Trenton limestone. I then proposed to call this lower series of Thunder Bay, that is to say, the dark-colored argillites and sandstones which are traversed by the silver-bearing lodes of that region, the Animikie group. Shortly after the publication of that address I received an abstract of a paper on the geology of that region by Professor Robert Bell, read before the Montreal Natural History Society, February 24th. He there confirms the statement made in my address that the gold of Lake Shebandowan occurs in the Huronian, which is also seen to be cut by the silver-bearing lodes just mentioned. Professor Bell, in this paper, proposes to designate both what I have called the Animikie group, and the overlying red and white sandstones, by the name of the Nepigon group, for the reason that the upper series is best displayed about Lake Nepigon. This latter series is by Logan supposed to be overlaid by the copper-bearing amygdaloids with conglomerates and sandstones of the north shore (apparently identical with those of Keweenaw) ; and the whole together, including the Animikie group, constitute his Upper Copper-bearing group. These copper-bearing strata are by him supposed to be overlaid by the red and white sandstones of St. Mary, which are apparently the same with those sandstones which, according to Brooks and Pumpelly, overlie unconformably the similar cupriferous rocks of Portage Lake, and are, in their turn, overlaid by the Trenton limestone. Thus the sandstones which at Thunder Cape overlie the Animikie group are by Logan placed in the midst of the Upper Copper-bear-

Jan 1, 1874

By Benjamin LeRoy Miller, Joseph T. Singewald

The ore deposits at Firmeza have been worked continuously since 1884; those at Daiquiri since 1895. It is surprising, therefore, that they have not been the object of careful geologic study until quite recently. It is true that considerable attention was paid to these deposits by A. C. Spencer, in 1901, in the report on the geology of Cuba, by Hayes, Vaughan, and Spencer,l but this was only incidental to a hasty general reconnaissance of the Island. As far as the Daiquiri deposits are concerned, this gap has been filled by the appearance of the two papers by Prof. James F. Kemp2 and by Prof. Waldemar Lind-gren and Clyde P. Ross respectively.3 Max Roesler, first holder of the Emmons fellowship, made a detailed study of the Firmeza deposits during the past summer, so that soon we can expect a full description of them. Consequently, there is no, demand at the present time for a description of the deposits from other sources, and that is not the purpose of this paper. The papers on Daiquiri, however, leave unsolved problems in regard to the age of the rocks of the district and certain phases of the genesis of the deposits, and it is with the hope of aiding in the solution of some of these problems that this contribution is offered. Kemp, and Lindgren and Ross agree in assigning these deposits to the type of contact metamorphic deposits. They disagree in part on the question of their localization. The deposits occur in an extensive area of diorite which includes numerous blocks of limestone, and sometimes are found in the contact zones between these blocks and the diorite, and in other instances are completely enveloped in the diorite, showing no apparent connection with the limestone. The latter class includes

Jan 1, 1916

By David Browne

THE literature dealing with the physical constants of nickel is so fragmentary and unrelated, that a synopsis presents unusual difficulties. It is only within the last few years that investigators have understood the importance of placing on record not only the determinations they have made but also the composition, physical treatment, and past history of the material investigated. For this reason much of the earlier literature is valueless. Determinations have been made of the same physical constants on samples differing widely in origin, composition, and treatment, and the results differ widely among themselves. In the first place nickel is almost as flexible a term as steel. Its physical properties are widely influenced by its composition and treatment. It absorbs large quantities of gases and is exceedingly difficult to prepare in a state of chemical purity comparable to gold, silver, or copper. It is vitally affected by thermal and mechanical treatment. Hence in the following pages the recorded literature, where quoted, must be accepted with a certain reserve and used, as far as possible, as a check on later observations, in which these important factors are noted. In every case where new determinations are given, an attempt has been made to record all available information concerning the composition and treatment of the material used so that the data may serve as steppingstones toward a wider knowledge of the properties of the metal. As this synopsis is an attempt by men of metallurgical training to do what should long before have been clone by physicists, it is to be expected

Jan 9, 1919

By R. W. Raymond

THE situation in 1872, from the standpoint of the prospector, the locator, the possessory claimant, and the patentee of mineral land under Federal statutes, cannot be understood without a knowledge of the situation prior to 1866, and between 1866 and 1872. The Situation before 1866 The western public domain acquired by the United States through treaties, as the result of conquest or purchase, was invaded after Marshall's re-discovery of gold in California, by an overwhelming multitude of prospectors and miners from all parts of the world. The mineral lands of the whole Pacific slope were practically unsurveyed. Congress, disgusted with the experiment of leasing mineral lands; which it had tried for 40 years, and abandoned in 1847, enacted no laws for the management of these public mineral lands, and the pioneers made their own laws governing mining titles. These local regulations applied at first to gulch-mining in the auriferous river-beds only; and they constituted a simple and practical system, adapted to the needs and means of primitive communities-significantly called "camps." They had the means of measuring distances, but not angles; they knew no -property except personal property in the form of pickaxes, pans, supplies, camp-equipage, horses or mules, and mining rights. The earliest codes which they developed expressed what might be called the law of the lariat. With the lariat they measured the distance assigned to each miner along the gold-bearing gulch-a double portion to the discoverer, and a single portion to his successors, in the order of their coming. With the lariat, they hung, after such due process of law as was available, the rascal who stole a horse, or a bag of gold-dust, or a; mining claim, or killed another man without giving him fair notice and a chance to defend himself. In these pioneer codes, adopted in mass-meetings and enforced by the same authority, two features concern us most:

Jan 4, 1914

By Carl Trischka

During fifty-three years of mining operations in the Warren mining district, the mineralization has been found to cover an area roughly 2 miles long by 155 miles wide. Ore extraction from the richer portions of this area has been closely followed by surface subsidence. At the western end of the district, where the ore outcrops at the surface and oxidation is more complete over a wide area, intense surface disturbance is visible in the form of closely spaced open cracks and escarpments. As work has progressed toward the east, more unoxidized ore-bodies have been found and mining has been at increasing depth, for which reasons surface subsidence is less intense and subsidence blocks become larger and in general are bounded by open cracks, which persist over long distances. There may also be traced on the surface what appears to be a boundary crack, running in a northwest-southeast direction, marking the present southerly limit of subsidence of the district as a whole. It is not completely developed, and has not as yet appeared over the very deep mining operations in the extreme easterly portion of the district. Check surveys show that vertical and horizontal dislocation is still taking place. All of the various mining operations, including open-pit work in porphyry ore and underground mining of limestone replacement and porphyry ores, have had their influence in disturbing the surface. As these influences frequently overlap, and because the surface disturbance is continuous over practically all ore occurrences, it is virtually impossible to choose an area sufficiently isolated to ascribe the amount of subsidence to any definite volume of ore removed. After due consideration of all factors, there has been selected for discussion an area 1400 ft. long by 1200 ft. wide, which will be referred to as the Queen Hill block. It is bounded on all four sides by faults, which tend to limit subsidence disturbance to that caused by ore mined from within the block, and likewise to prevent subsidence cracks due to mining outside of the block from entering the area.

Jan 1, 1934

By C. H. Li, R. J. Stokes, T. S. Liu

Poly crystalline silver chloride specimens having different micro structures were prepared by extruding monocrystals or precompressed powder at varying temperatures. Extrusion at high temperature (370°C) produced a Fully recrystallized equi-axed material which was brittle and fractured by simple cleavage below its transition temperature (60°C for notched specimens). Extrusion at low temperatures (down to -196°C) produced an extremely tough cold-worked material with grains elongated in the extrusion direction. This material fractured below its transition temperature (which varied from —20" to —200°C) by an intergranular mode. It is concluded that cold work increases the resistance to transgranular cleavage. Fracture is then de-flected to propagate intergranularly ouer surfaces making an angle with the tensile axis with a corresponding improvement in notch toughness. This deflection is greater for extruded powder than for extruded monocrystals because of the extremely elongated grain shape. PREVIOUS work1,' on the fracture properties of fully recrystallized silver chloride under notch impact conditions has indicated that the fracture behavior is rather invariant. Thus polycrystalline materials originating from a number of sources ranging from relatively pure Harshaw single crystals to commercial-purity powder and prepared by hot extrusion at 370°C all fracture by simple cleavage with a ductile-brittle transition at 60°C, see Fig. 1. This behavior is also typical for fully annealed single crystals and appears to be fundamental to silver chloride for the particular loading conditions and notch configuration adopted. One way in which this characteristic fracture behavior can be modified is by the dispersion of alumina particles in the silver chloride matrix.' Then, particularly when the alumina particles are in the shape of spheres, the duc tile-brittle transition is much less sharply defined and occurs over a range of temperature, the transition temperature is lowered considerably and the fracture mode changes from simple cleavage to a fibrous or shear mode. The reason for this change is believed to be partly due to the nucleation of cavities in the region of the dispersed alumina particles which influences the state of stress locally and the distribution of plastic constraint at the root of the notch. It is emphasized however that this is not the sole factor responsible for the increase in toughness. In extruded materials it is reasonable to expect that the resultant grain size, texture, and the residual cold work will be influenced by the presence of a dispersed phase. The present experiments were initially designed to determine the extent to which cold work influenced the fundamental ductile-brittle transition temperature and fracture mode of silver chloride. They were stimulated by the discovery that silver chloride could be extruded at temperatures as low as -25°C when commercial-purity powder was used and as low as -196°C when single crystals were used. This working temperature was far below that previously used (370°C) and it was found that such extruded material was exceedingly tough. The reasons for the enhanced toughness and its relation to the previous work on silver chloride-alumina compacts will be discussed. EXPERIMENTAL PROCEDURE Materials Used. Two forms of silver chloride were used in this study: i) silver chloride powder

Jan 1, 1964

By Mahesh C. Jha

Arsenical gold ores occur in many parts of the world, including numerous mines in Canada and the western United States. Free gold is often finely disseminated in the grains of sulfide minerals, arsenopyrite, pyrite, orpiment and realgar. Generally a sulfide concentrate is produced by flotation. Arsenical ores or concentrates are not amenable to direct cyanidation and therefore are considered refractory. A wide variety of roasting equipment and conditions have been used by the mills to remove arsenic and sulfur from these concentrates. The resulting calcine is easy to cyanide and gold is recovered from the cyanide solution by zinc dust cementation. Room-temperature potential-pH diagrams and high-temperature phasestability diagrams are presented to discuss the chemistry of the gold cyanidation, cementation, and roasting steps in the presence of arsenic. The environmental aspects of arsenic discharge are also included.

Jan 1, 1984

By D. Walton, W. C. Winegard, W. A. Tiller, J. W. Rutter

It is shown that the cellular substructure observed in binary alloy crystals grown from a melt of known concentration can be eliminated by the proper choice of growth conditions. For a given solute concentration, there exists a critical ratio of temperature gradient G in the melt to the rate of solidification R of the crystal, i.e., of G/R, which must be exceeded before the cellular structure can be eliminated. A secondary substructure is observed which is related to the cellular substructure. IN crystals grown from the melt, a prismatic substructure has been observed by Buerger,1 Pond and Kessler,2 and Rutter and Chalmers." This structure is columnar in the direction of growth and appears as a network of hexagonal cells in the plane of the solid-liquid interface. Rutter and Chalmers3 have shown that this substructure occurs as a result of the presence of a layer of high impurity concentration in the melt adjacent to the solid-liquid interface. The formation of the substructure is accompanied by a redistribution of this impurity in the neighborhood of the interface. The structure can be controlled by proper adjustment of the variables in the solidification process such as a rate of solidification and the temperature gradient in the liquid. The redistribution of solute during the solidification of metal crystals has been treated theoretically

Jan 1, 1956

By G. M. Ritcey

Purification of solutions can involve various treatment methods. In the normal sequence of metals recovery by hydrometallurgy, the ore is initially prepared for leaching by grinding to the desired optimum mesh size as dictated by the leaching parameters. Following leaching and liquids- solids separation, the resultant solution is ready for purification. The use, or introduction of solvent extraction into a plant, can be either a major or a minor part of the metal recovery process as shown by the following list where solvent extraction is normally considered: a) recovery of a metal by a simple leaching of the broken ore, e.g., copper from dump leaching where there are only the three main steps of leaching, solvent extraction, and electrowinning (1);

Jan 1, 1978

By E. H. Jr. Dix

THE importance of aluminum-silicon alloys in the light alloy field is now generally recognized. Where silicon was once considered detrimental to the properties of aluminum, useful alloys now contain as much as 13 per cent. Furthermore, silicon is present as an impurity in aluminum of even the purest grades. Iron is another important impurity in aluminum and like silicon is found in small quantities in the purest aluminum available today. The manner of occurrence of iron and silicon in commercially pure aluminum and many of its alloys exerts, a very pronounced influence upon their properties. The effect of large quantities of iron in aluminum-silicon alloys is so detrimental that it has been found necessary to limit the allowable maximum percentage to as low a figure as is consistent with quantity production and satisfactory physical properties. The intimate relation existing between iron and silicon in aluminum and aluminum alloys makes necessary a more complete knowledge of this ternary system. This paper is divided into two principal parts, dealing respectively with aluminum-silicon solubility equilibria and the constitution of aluminum-iron-silicon alloys.

Jan 1, 1927

By W. W. Anderson

John Griffen—The author has called attention to an important phase of coal cleaning since there has been considerable loose thinking regarding efficiency formulae and particularly inaccurate application of ones that have been advanced. The unanimous acceptance of an efficiency formula has been prevented because the issue has been beclouded by the fact that the objective of cleaning—-the control of chemical characteristics of the coal such as ash or sulphur content—is attained by an indirect rather than a direct method. The indirect method is usually to effect separation according to differences in specific gravity. Such separation relies on the fact that the desired chemical qualities are roughly inversely proportional to the specific gravity of the particles being separated. However, the sulphur content of the materials found in raw coal usually exhibit a far from straight line relationship with their specific gravities. Mr. Anderson meets this issue squarely by basing his formula on the efficiency of separation according to specific gravity only. It is true that machines that effect primarily a specific gravity separation are in no way directly influenced by the chemical analysis of the materials being handled and it can be argued that it is illogical to measure their efficiency by any criterion other than that of separation according to specific gravity. For the moment, let us accept this basis and analyze the application of the efficiency conception and formula proposed by Mr. Anderson under conditions which he has not considered but that will readily be found. Let us take the separation shown in his table III as an example. He terms this an example of a high order of quantitative efficiency. We will show the weight distribution of the various gravity fractions as between clean coal and refuse in table XV. Only in the gravity range of 1.50 to 1.70 has material been misplaced and, on the assumption that the cleaned coal and refuse are equal in weight, Anderson shows a quantitative efficiency of 99 pet. The gravity of separation is 1.60 and one third of the 1.50 to 1.60 sp gr fraction is misplaced in the refuse while one third of the 1.60 to 1.70 sp gr fraction is misplaced in the cleaned coal. Let us now see what effect the gravity distribution of the total products has on the quantitative efficiency calculated by his formula. Still using the data in table

Jan 1, 1951

By W. W. Anderson

John Griffen—The author has called attention to an important phase of coal cleaning since there has been considerable loose thinking regarding efficiency formulae and particularly inaccurate application of ones that have been advanced. The unanimous acceptance of an efficiency formula has been prevented because the issue has been beclouded by the fact that the objective of cleaning—-the control of chemical characteristics of the coal such as ash or sulphur content—is attained by an indirect rather than a direct method. The indirect method is usually to effect separation according to differences in specific gravity. Such separation relies on the fact that the desired chemical qualities are roughly inversely proportional to the specific gravity of the particles being separated. However, the sulphur content of the materials found in raw coal usually exhibit a far from straight line relationship with their specific gravities. Mr. Anderson meets this issue squarely by basing his formula on the efficiency of separation according to specific gravity only. It is true that machines that effect primarily a specific gravity separation are in no way directly influenced by the chemical analysis of the materials being handled and it can be argued that it is illogical to measure their efficiency by any criterion other than that of separation according to specific gravity. For the moment, let us accept this basis and analyze the application of the efficiency conception and formula proposed by Mr. Anderson under conditions which he has not considered but that will readily be found. Let us take the separation shown in his table III as an example. He terms this an example of a high order of quantitative efficiency. We will show the weight distribution of the various gravity fractions as between clean coal and refuse in table XV. Only in the gravity range of 1.50 to 1.70 has material been misplaced and, on the assumption that the cleaned coal and refuse are equal in weight, Anderson shows a quantitative efficiency of 99 pet. The gravity of separation is 1.60 and one third of the 1.50 to 1.60 sp gr fraction is misplaced in the refuse while one third of the 1.60 to 1.70 sp gr fraction is misplaced in the cleaned coal. Let us now see what effect the gravity distribution of the total products has on the quantitative efficiency calculated by his formula. Still using the data in table

Jan 1, 1951

By J. P. Heller, H. B. Bradley, A. S. Odeh

A potentiometric model technique is presented for determining the areal sweep efficiency of a five-spot well pattern, at and beyond breakthrough. A sharp interface between displaced and displacing fluids is assumed. Although the prototype svstem is referred to as a waterflood operation, obvious changes in the notation and computations will adapt the results to other displacement processes. The results of the study include the following. 1. Areal sweep efficiencies for a five-spot well pattern, at and beyond breakthrough, for mobility ratios (displacing to displaced fluid) of 4:1, 2:1, 1:1 and 1:4. 2. Extension of potentiometric analysis to the investigation of the areal sweep efficiency beyond breakthrough in a five-spot pattern by the application of conformal mapping and conductive-solid models. 3. The use of layers of conductive fabric in representing mobility ratio changes in potentiometric models. 4. The development of a probe mechanism for probing conductive solids. The results obtained by conductive-cloth models agree with earlier areal sweep efficiencies at breakthrough obtained by Aronofsky and Ramey 1 on the potentiometric analyzer using electrolytic-tank models. Results beyond breakthrough differ from those obtained by the X-Ray Shadowgraph technique. Data from this study show that, for mobility ratios greater than one, water cut rises rapidly as fluid is produced after breakthrough. However, for mobility ratios smaller than one, a large increase in area swept resulted with only a small increase in water cut. INTRODUCTION In calculating reservoir performance of waterflood-ing operations and other fluid-injection programs, it is necesssary to estimate the areal sweep efficiency * before and after injected-fluid breakthrough into production wells. Influence of mobility ratio on oil-production history, before and after breakthrough for a five-spot well pattern, has been studied by X-Ray Shadowgraph techniques 2-5 and by gelatin models.6 In none of these investigations was the transition zone controlled experimentally. Steady-state anaiog techniques assume that a vertical and discrete interface exists between the displacing and displaced phase. Thus, when using a potentiometric analysis, it is assumed that no transition zone exists. To determine the areal sweep efficiency beyond breakthrough for a five-spot well pattern using the potentiometric analyzer, four principal problems had to be resolved. These were the following. 1. The laborious method of representing changes in mobility ratio in electrolytic tanks by means of contoured wooden blocks. 2. Vapcrization of the electrolyte solution during the study causing concentration changes and, thereby, variable conductivity. 3. The scale-limitation problem 7 that is accentuated by abrupt eiectrolyte depth changes. 4. A wellbore geometry problem. EXPERIhlENTAL EQUIPMENT AND PROCEDURES CONDUCTIVE-SOLID MODEL The theory, equipment and procedural techniques of the electrolytic-tank potentiometric model have been treaced excellently by Lee8 and by Muskat.9 By the use of a conductive solid to represent the fluid conductivity of the porous media, the need for contouring wooden blocks to represent mobility ratio was eliminated. It was found that a carbon-black coated fabric, Uskon D-16,** could be employed as a fairly uniform conductive media. This material, when stacked in appropriate layers and pressed together, can be used to represent changes in mo-

By B. L. Averbach, Morris Cohen, S. A. Kulin

The martensitic transformation can be initiated by elastic stresses at temperatures above M. in a steel containing 20 pct Ni and 0.5 pct C. Shear strains and normal tensile strains acting on a potential habit plane promote the transformation but compressive strains oppose it. THE strain sensitivity of the martensitic transformation has long been recognized. It is now well known that martensite formation can be induced by plastic deformation at temperatures below, and not too far above, the M, point.' However, the exact role of elastic vs. plastic strains and of the concomitant stresses has proved to be a very elusive matter. Many investigators2-' of the steel hardening reaction have made use of the stresses resulting from volume changes to account for such observations as the existence of retained austenite and its variation across the section of a bar, the change in the amount of retained austenite with quenching rate, and the self-stopping nature of the transformation when the cooling is stopped. The effect of applied strain as an independent variable has been studied in 70 pct Fe-30 pct Ni alloys by Scheil7 and McReynolds.8 Some data are also available for lithium and Li-Mg alloys,9 Cu-Zn,10 Cu-Sn and Cu-A1 alloys," and aus-tenitic stainless steels."-" It has been found that martensite formation can be induced isothermally, even at temperatures above M,, by mechanical deformation of the parent phase. The competitive nature of plastic yielding by slip and by the martensitic reaction has been depicted by Scheil.7 Basically, Scheil postulated that: 1—at temperatures not too far above M, (where austenite is less stable than martensite), a critical resolved shear stress (within the elastic range) is required to promote the transformation to martensite; 2—at and below M,, the austenite lattice becomes mechanically, as well as thermodynamically, unstable and shears over spontaneously into martensite without the application of external stress; and 3—at temperatures sufficiently far above M8, the critical resolved shear stress for martensite formation increases to a level above that required for slip, and plastic flow then supersedes the transformation when external stress is applied. Scheil's concepts were tested by McReyno1ds8 ho found no change in the elastic moduli (measured both statically and dynamically) of 71 pct Fe-29 pct Ni alloys in the vicinity of the M, temperature. Since the moduli did not approach zero or become negative on cooling to M,, it was concluded that the austenite lattice does not become mechanically unstable at M2, as postulated by Scheil. McReynolds also reported that M, is not raised by elastic stresses. Accordingly, plastic deformation was considered to stimulate the transformation by generating martensite nuclei in the distorted regions of the parent phase. The above issues with regard to the role of applied stress require clarification, if a basic understanding of the martensitic transformation is to be obtained. For example, in the reaction-path theory,'"," it is postulated that strain embryos exist in the austenite that provide part of the activation energy for the nucleation process. These embryos are visualized to be regions of localized strain in which the atoms in the austenite lattice are displaced part way along the path to their ultimate positions in the martensite. Consequently, it would

Jan 1, 1953