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By M. E. Wadsworth, A. E. Lewis, R. L. Braun

Experimental results obtained in laboratory leaching studies of primary copper sulfide ore in sulfuric acid systems pressurized with oxygen are interpreted by a computerized geometric model involving the movement of a reaction zone through the ore fragments. Physical properties of the ore, including size, shape, and mineral content, are considered. The leaching mechanism involves mixed kinetics and includes a surface reaction within a moving reaction zone plus pore diffusion of dissolved oxygen through the reacted portion of the ore fragment to the reaction zone. The results are applicable to conditions that would exist in nuclear solution mining or similar processes in which the ore is converted into rubble and then inundated by a leach solution adequately supplied with oxidants. Experimental results at 90°C are correlated with the model, which includes temperature-dependent parameters.

Jan 1, 1974

By S. E. Piper, E. M. Buchalter, R. P. King, E. T. Woodburn

The problems involved in an optimum decision making model for flotation circuit are, first of all, to characterize the feed material in terms of parameters which can quantitatively describe the network flotation action in terms of a feasible set of control actions. Once the characterization has been postulated, it is then necessary to devise tests relating to parameter sensitivity, in order that credibility of the model predictions can be assessed. Once a credible model is available, the optimum control set is determined by a hill climbing technique. Details will be reported as to the credibility of model predictions using the stochastic flotation model on a network and further, computational problems associated with hill climbing for a complex objective function are reviewed. Discussion is presented on use of the Rosenbrock technique with constraints and use of a modified objective function with constrained derivatives when employing Fletcher and Powell technique.

Jan 1, 1969

By Eckley B. Coxe

IN the anthracite coal regions of Pennsylvania the custom has been to sight either at an open light (generally a mine-lamp), or at the string of a plumb-bob. If the station was intended to he a permanent one, a spud, as it is called, that is, a nail resembling a horseshoe nail with a hole in the head, is driven into the timbers over the station, or, if there be no timber, a hole is drilled in the coal or rock roof, into which a wooden plug is driven, which serves to hold the spud. The first operation in making a survey is to lay out the stations, that is, to mark the place where the holes are to be drilled for the plugs or the points on the timbers where the spuds are to be driven in. This should be done before any instrumental work is begun, as much labor can generally be spared, and the use of very short sights can often be avoided, by carefully laying out the stations beforehand. When the stations were laid out, a plumb-bob was hung from the innermost spud, which I will call No. 1, the instrument was put in position at No. 2, by plumbing down and putting a centre-pin under the spud, and then setting up over the centre-pin, and another plumb-bob was suspended from No. 3. If great accuracy was not required, a mine-lamp was set up under the plumbbobs, at No. 1 and No. 3, and the engineer sighted at them. If great accuracy was required, a lamp or some white sbface was held by an assistant behind the strings of the plumb-bobs. To work with any speed by the latter method (i. e., the accurate one), it was necessary for the engineer to have three assistants on whom he could rely even when the chaining was done afterwards; viz. : one to hold the light behind the string at No. 1, one at No. 3, and an assistant at the instrument to hold the light while levelling, reading the in

By A. S. Appleton

The diffusion of carbon in Fe-Co-C austenites was studied as a function of cobalt concentration up to 12 at. pet, using an autoradiographic technique. The diffusion coefficient was found to initially decrease and then increase with increasing cobalt concentration, the trends being more marked the higher the temperature of diffusion. These effects were paralleled by variations in the activation energy and the constant for diffusion which, however, were found to be dependent also on the carbon content. The results are compared with the previously available data and their significance is discussed in terms of the kinetics of solid-state reactions in this systern. THE influence of cobalt on the diffusivity of carbon in austenite was first studied by Smoluchowski,' his data being that most commonly cited in works

Jan 1, 1964

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By J. H. Brophy, J. Wulff, H. W. Hayden

The mickel-activated sintering of tungsten occurs in two stages of densification. A kinetic analysis of the second stage has been based on an appropriate model of the process. As in the first stage, the rate-controlling mechanism for the second stage is also the solution of tungsten in the nickel carrier phase. The transition from the relatively rapid first-stage results from the spherozdization of pores and the initiation of grain growth. Finer grain size due to higher-nickel content leads to more rapid and higher degrees of densification 1 HE sintering of tungsten is accelerated by small additions of nickel, cobalt, and iron.' Experimental evidence in detail has shown that nickel-coated, hydrogen-reduced tungsten powder may be sintered to more than 90 pet of theoretical density at l100o C.2, 3 Simultaneously, a kinetic analysis of the process showed that it took place in two distinct stages. In the first stage, nickel evidently served as a carrier phase through which tungsten atoms could move. This stage was kinetically similar to the "solution-precipitation" step postulated when the carrier phase is a liquid,4 although in the Ni-W case, there is no evidence of the existence of a liquid phase either in equilibrium phase relationships or in microstruc-tures at the temperatures under consideration. It has been shown that this stage corresponds to a process which is rate controlled by a phase boundary reaction.3 More recent evidence has been presented5 showing that after the initial rapid stage of sintering, densification continues in the final stage but at a slower rate, although no mechanism for this stage of densification was defined. An analysis of later stages of densification in solid state sintering has been presented,6 but it is not directly applicable in the present case of activated or carrier phase sintering. It is the purpose of this investigation to study the final stage of nickel activated tungsten sintering in greater detail The effect of varying nickel content has been examined, and a possible kinetic mechanism defined. EXPERIMENTAL PROCEDURE AND RESULTS Commercial hydrogen-reduced tungsten powder from Wah-Chmg Corp., having a nominal particle size of1 µ and a B.E.T. specific surface area of 5500 sq. cm per g was mixed with aqueous solutions of hydrated nickel nitrate in proportions sufficient to produce nominal compositions of 0.25, 1, 3, and 5 wt pet Ni. This solution was then evaporated to dry-ness at approximately 150" C for 15 hr. Following evaporation, the resulting powder cake was broken with a mortar and pestle and reduced in hydrogen at 800oC for 1 hr. Following reduction, the powder

Jan 1, 1962

By Arthur C. Simmons

The State of Pennsylvania produces approximately 60 per cent of the total production of Pennsylvania Grade oil, and naturally represents the dominant factor in the area producing that grade. The producing area comprises the states of New York, Pennsylvania, West Virginia, and a small part of Ohio. The importance of this area is too commonly neglected because it produces only 2 per cent of the total amount of crude produced in the United States. It is, of course, unimportant in its percentage of total crude production, but extremely important for its production of lubricating oil. The lubricating fraction from a barrel of Penllsylvania Grade crude oil represents about 22 per cent of the total, whereas the lubricating fraction from the total United States production represents only about 2.5 per cent of the crude oil. The Pennsylvania Grade area produces about 6,000,000 bbl. of lubricants, which is 15 to 20 per cent of the total produced in the United States. All Pennsylvania Grade lubricants are classified as "high-grade," and with a production of 15 to 20 per cent of the total lubricants, it appears probable that the Pennsylvania Grade area accounts for 25 to 50 per cent of the high-grade lubricants produccd in the United States. Production Bradford Field The production figures quoted in Table I apply only to the part of the Bradford held that lies wholly within the state of Pennsylvania; approximately 15 per cent of the Bradford field is in Cattaraugus County, New York, and 10 per cent of the production is obtained from that sector. The Bradford-field production in 1941 was 12,729,900 bbl. as compared with a production in the year 1940 of 12,748,279 bbl., or a reduction of 18,379 bbl. The year 1941 represents the fourth successive year in which production in the Bradford field has declined. All of the production from the Bradford field is obtained by water-flooding methods and increases or decreases in production are due more to economic factors than to any physical limitations of the pool, inasmuch as additional drilling of water-intake and producing wells would increase the total production of the field. It is apparent that increased drilling of oil and water-intake wells does not take place except under stimulps of a favorable price; and while oil prices during 1941 were moderately favorable, they were not sufficient to prevent a mild decline. Too many wells were drilled in the Bradford field in 1937, but this was compensated by subnormal drilling activities in 1938 and 1939 and a large increase in 1940, The increase in 1941 over 1940 was about 7 per cent. The effect of new drilling is becoming less pronounced on a per well basis because more properties yielding less per acre are being drilled than were drilled in former years. Central and Southern Pennsylvania The production in central and southern Pennsylvania amounted to a total of

Jan 1, 1942

By Arthur C. Simmons

The State of Pennsylvania produces approximately 60 per cent of the total production of Pennsylvania Grade oil, and naturally represents the dominant factor in the area producing that grade. The producing area comprises the states of New York, Pennsylvania, West Virginia, and a small part of Ohio. The importance of this area is too commonly neglected because it produces only 2 per cent of the total amount of crude produced in the United States. It is, of course, unimportant in its percentage of total crude production, but extremely important for its production of lubricating oil. The lubricating fraction from a barrel of Penllsylvania Grade crude oil represents about 22 per cent of the total, whereas the lubricating fraction from the total United States production represents only about 2.5 per cent of the crude oil. The Pennsylvania Grade area produces about 6,000,000 bbl. of lubricants, which is 15 to 20 per cent of the total produced in the United States. All Pennsylvania Grade lubricants are classified as "high-grade," and with a production of 15 to 20 per cent of the total lubricants, it appears probable that the Pennsylvania Grade area accounts for 25 to 50 per cent of the high-grade lubricants produccd in the United States. Production Bradford Field The production figures quoted in Table I apply only to the part of the Bradford held that lies wholly within the state of Pennsylvania; approximately 15 per cent of the Bradford field is in Cattaraugus County, New York, and 10 per cent of the production is obtained from that sector. The Bradford-field production in 1941 was 12,729,900 bbl. as compared with a production in the year 1940 of 12,748,279 bbl., or a reduction of 18,379 bbl. The year 1941 represents the fourth successive year in which production in the Bradford field has declined. All of the production from the Bradford field is obtained by water-flooding methods and increases or decreases in production are due more to economic factors than to any physical limitations of the pool, inasmuch as additional drilling of water-intake and producing wells would increase the total production of the field. It is apparent that increased drilling of oil and water-intake wells does not take place except under stimulps of a favorable price; and while oil prices during 1941 were moderately favorable, they were not sufficient to prevent a mild decline. Too many wells were drilled in the Bradford field in 1937, but this was compensated by subnormal drilling activities in 1938 and 1939 and a large increase in 1940, The increase in 1941 over 1940 was about 7 per cent. The effect of new drilling is becoming less pronounced on a per well basis because more properties yielding less per acre are being drilled than were drilled in former years. Central and Southern Pennsylvania The production in central and southern Pennsylvania amounted to a total of

Jan 1, 1942

By Paul E. Richardson, Edwin E. Maust

Cyclic voltammetry and surface potential (photovoltage) measurements have been carried out on galena electrodes in sodium tetraborate solutions with added HC1 and NaOH to adjust the pH over the range 2 to 13. The first technique shows that the surface species formed on moderate anodic polarization and reduced on subsequent cathodic polarization are the same over the entire pH range. At anodic potentials, a soluble metal species and excess sulfur are formed; at cathodic potentials, sulfur is reduced to a soluble species. More importantly, excess surface sulfur is formed spontaneously under zero current conditions in alkaline solutions. This has been shown to occur on both polished surfaces and on virgin surfaces produced by in situ cleavage under the electrolyte. The photovoltage gives some insight into the charge and potential distribution at the galena surface. This is found to depend on past electrochemical history and the n- or p-type semiconducting character of the electrode and is interpreted in terms of changes in the surface stoichiometry that occur during reduction or oxidation. The effect of surface stoichiometry on subsequent xanthate interactions is discussed.

Jan 1, 1976

By J. E. Berry

AII evaluation is made of the acoustic velocity log for measurement of formation porosity. Plots of field-observer1 velocities vs core-measured porosities of sandstones and limestotnes with inter intergranular porosity show that the velocity log gives a useful measure of porotity, in agreement with published data. A new method of plotting electrical and velocity log data makes it easier to recognize hydrocarbon-water coritnct~ from log darn and to make serni-quantitative estinlates of hydrocarbon saturation. Two examples of this interpretation technique are given. This paper also discusses the various factors that affect acoustic velocity and shows how corrections can be made for some of these factors. INTRODUCTION Although the continuous velocity log was developed primarily as an aid to seismic interpretation, it is finding widespread use for measurement of porosity. The purpose of this paper is to evaluate this use of the log. Results are presented for the velocity-porosity relationship in many sandstones and one limestone. Practical applications of porosity values derived from the velocity log to improve interpretation of electrical surveys are presented. Various parameters which affect velocity in porous media are considered. Porosity, composition, cementa-tion, pressure difference (overburden pressure minus fluid pressure), fluid saturation, and wellability are discussed. Some of the ideas are opinions based on general considerations of well logging problems while others are supported by published data and our own observations. Major conclusions from these studies arc given in the body of the paper and detailed discussions of some of the various factors affecting porosity are given in the Appendix. POROSITY Sandstones The primary factor affecting the velocity of sound in porous media is porosity. Wyllie, et al,1 have reported a time average equation for the relationship between velocity and porosity.* This has found considerable acceptance in the industry. Other relationships between velocity and porosity have been proposed, none of which are entirely satisfactory. It is doubtful that any one relationship will completely describe all situations. We have tried an empirical relationship based on correlating log velocities with core-measured porosities. Measured porosities were averaged over a depth interval equal to the spacing used in recording the velocity logs. The depth range for the information used was from 2,000 to 12,000 ft. Velocity measurements were normalized for the effects of depth and overburden pressure. A detailed discussion of the basis for this normalization is given in the Appendix. The change is usually insignificant and when working with individual formations it can be neglected. All velocity measurements were normalized to a depth of 10,000 ft. The velocity-porosity data for sandstones in Fig. 1 came from 20 wells scattered throughout the Mid-Continent and Gulf Coast areas. The scatter of the data points is attributed to three causes: 1. There is no theoretical basis for expecting an exact velocity vs porosity relationship and it is not possible to correct precisely for the effects of such factors as impurities, grain shape, manner of cementation, etc. Some of these factors are discussed in the Appendix. 2. Porosities measured by core analysis are not necessarily representative of what the velocity log "sees". 3. Inaccuracies appear in the velocity log reading. This is particularly true of velocities from one-receiver logging tools.*" A linear-time curve (time-average equation) is plotted in Fig. 1 along with the best straight line through the points. Velocities used for the linear-time curves were 19,500 ft/sec for the matrix velocity (zero porosity) and 5,500 ft/sec for fluid velocity. For clean sandstones with velocities greater than 10,000 ft/sec, there is little difference between the velocity-porosity and the time-porosity curves. Both curves are well within the scatter of data points. The data points in Fig. 1 were restricted primarily to clean sandstones, using the SP and/or gamma-ray logs as clues to the lithology. Where a lithologic de-

By Donald D. Smythe

This paper describes briefly the topography and geology of the region where the mica-bearing pegmatites are found and discusses prospecting, the quality of the mica, its preparation, and evaluation of the deposits. Muscovite mica occurs in a number of widely separated localities in Brazil, but production has come largely from deposits in the southeastern and eastern part of the State of Minas Gerais (Fig. I). There the deposits form a discontinuous zone, which starts at a point go km. north of the city of Rio de Janeiro and extends north for some 500 km., roughly parallel to the coast. A maximum width of 180 km. is reached along the Rio Doce. To the west in Minas Gerais, and extending east into the states of Espirito Santo and Rio de Janeiro, the mica zone proper is fringed by areas in which there are scattered occurrences of mica-bearing pegmatites. A few of these outlying deposits have produced commercial mica, but most of them are unimportant. To the southwest, in the State of Sao Paulo, there are a number of mines, which at one time produced a very considerable amount of sheet mica, largely as a byproduct of kaolin mining. These deposits, and a few others lying between them and the main productive areas to the northeast, appear to be the southwestern continuation of the strong Minas Gerais mica zone. In the vicinity of Conquista, just north of the Minas Gerais boundary in the State of Bahia, and still farther north, near Jacobina, there are several known mica deposits. Their location indicates that they may be the northern continuation of the main mica zone. The major part of Brazilian mica production has come from four areas within the mica zone proper; from north to south, Governador Valadares, Raul Soares, Espera Feliz, and Muriaé.. The first is go km. from north to south and reaches a maximum width of 180 km. The Raul Soares area extends 135 km. from northeast to southwest, and in places is 80 km. wide. The Espera Feliz area is 100 km. from north to south, and reaches a width of 35 km. The Muriai. area extends 150 km. from northeast to southwest and its width reaches 40 kilometers. Between the known productive areas, and in the areas directly to the southwest and to the north of them, little mica has been produced. These gaps, as well as certain irregularities in the outline of the mica zone itself, are to be ascribed either to lack of prospecting or to conditions preventing the discovery of mica, rather than to its nonexistence. Elsewhere in Brazil mica has been reported from eastern Goiaz, Ceará, Pernambuco, Rio Grande do Sul, Matto Grosso, and Amazonas. Production from these sources is negligible at present. Because of the inferior quality of the mica from the more accessible of these localities, and the operational difficulties occasioned by the remoteness of others, it is improbable that they will become important producers for some time to come.

Jan 1, 1948

By Donald D. Smythe

This paper describes briefly the topography and geology of the region where the mica-bearing pegmatites are found and discusses prospecting, the quality of the mica, its preparation, and evaluation of the deposits. Muscovite mica occurs in a number of widely separated localities in Brazil, but production has come largely from deposits in the southeastern and eastern part of the State of Minas Gerais (Fig. I). There the deposits form a discontinuous zone, which starts at a point go km. north of the city of Rio de Janeiro and extends north for some 500 km., roughly parallel to the coast. A maximum width of 180 km. is reached along the Rio Doce. To the west in Minas Gerais, and extending east into the states of Espirito Santo and Rio de Janeiro, the mica zone proper is fringed by areas in which there are scattered occurrences of mica-bearing pegmatites. A few of these outlying deposits have produced commercial mica, but most of them are unimportant. To the southwest, in the State of Sao Paulo, there are a number of mines, which at one time produced a very considerable amount of sheet mica, largely as a byproduct of kaolin mining. These deposits, and a few others lying between them and the main productive areas to the northeast, appear to be the southwestern continuation of the strong Minas Gerais mica zone. In the vicinity of Conquista, just north of the Minas Gerais boundary in the State of Bahia, and still farther north, near Jacobina, there are several known mica deposits. Their location indicates that they may be the northern continuation of the main mica zone. The major part of Brazilian mica production has come from four areas within the mica zone proper; from north to south, Governador Valadares, Raul Soares, Espera Feliz, and Muriaé.. The first is go km. from north to south and reaches a maximum width of 180 km. The Raul Soares area extends 135 km. from northeast to southwest, and in places is 80 km. wide. The Espera Feliz area is 100 km. from north to south, and reaches a width of 35 km. The Muriai. area extends 150 km. from northeast to southwest and its width reaches 40 kilometers. Between the known productive areas, and in the areas directly to the southwest and to the north of them, little mica has been produced. These gaps, as well as certain irregularities in the outline of the mica zone itself, are to be ascribed either to lack of prospecting or to conditions preventing the discovery of mica, rather than to its nonexistence. Elsewhere in Brazil mica has been reported from eastern Goiaz, Ceará, Pernambuco, Rio Grande do Sul, Matto Grosso, and Amazonas. Production from these sources is negligible at present. Because of the inferior quality of the mica from the more accessible of these localities, and the operational difficulties occasioned by the remoteness of others, it is improbable that they will become important producers for some time to come.

Jan 1, 1948

By Richard Zinszer

Application of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (1) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable correc- tions for sand thickness. The proceduer in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory. In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 ft., 16 ft., and 24 ft. thick, and found the observed resistivity Of the 8-ft. sand to be approximately

Jan 1, 1943

By Richard Zinszer

Application of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (1) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable correc- tions for sand thickness. The proceduer in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory. In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 ft., 16 ft., and 24 ft. thick, and found the observed resistivity Of the 8-ft. sand to be approximately

Jan 1, 1943

By Kichizo Niwa, Toshio Yokokawa, Mitsuo Shimoji, Yoshihiko Watanabe, Satoshi Kado

A LTHOUGH a systematic research on diffusion in liquid metals has not been carried out, partial studies have been developed by various workers in several systems. A few recent papers among them have shown that this line of approach is quite useful for understanding the structure of the liquid state. Furthermore, it has been found in kinetic

Jan 1, 1958

By Grover J. Holt

A DETAILED description of the many variations in iron mining and transportation practice in Minnesota would require much space. Since a fairly detailed description of the practices then in use was published in the guidebook issued in connection with the meeting of the Institute on the iron ranges in I920, and subsequent developments have been described by E. E. Hunner,1 M. H. Barber,2 and A. E. Anderson, J. M. Riddell and G. J. Holt,3 it will not be necessary here to do more than review the highlights of current practice. Details on any points of interest can be obtained through correspondence with the operators involved. [T] The iron ores of Minnesota, which have been formed through enrichment of the iron formation in which they occur, largely by the removal of silica, are usually covered by a blanket of glacial drift known locally as "surface." Surface material, including sand, clay, hardpan and boulders, makes up the greater portion of the stripping in open-pit operations. In some instances, stripping also includes taconite and "paint rock," directly below the surface material and overlying the ore. Taconite is the iron formation, a ferruginous chert with interbedded slate layers. "Paint rock" is a local term for oxidized slate layers interbedded in the iron formation, high in phosphorus, alumina and moisture. The iron ores fall into two classes: (I) direct shipping (merchantable ores or ores requiring no treatment except possibly crushing or screening to make an acceptable sized product), and (2) ores requiring beneficiation (such as sintering, drying, washing, jigging, high-density treatment, or magnetic separation in the case of magnetite). The Mesabi Range produces chiefly soft Bessemer and non-Bessemer ores. The Cuyuna Range produces mainly low-manganese brown ore and high-manganese black ores, with some iron ore. The Vermilion Range yields mainly Besse¬mer and non-Bessemer iron ore, with some hard or lump ore that finds use in the open hearth. Open-pit mining is limited to the Mesabi and Cuyuna Ranges but underground mining is done on all three. The choice of mining methods is determined by the relative economics of overburden¬-removal and shaft-mining costs. STRIPPING PRACTICE Common practice has been to remove the bulk of the overburden during the winter season and to mine during the summer. In the present emergency many operators are forced to forego the economies attained by year-round utilization of equipment and to equip for, and carry on, stripping and mining simultaneously. In the normal years or lean years to come, most properties probably will be over-equipped and high depreciation charges will have to be absorbed.

Jan 1, 1942

By David Cornell, Yusuf K. Sukkar

The fundamental differential equation for fluid flow has been rearranged, integrated numerically for natural gases, and the results presented in tabular and graphical form suitable for the direct calculation of vertical gas flow problems. The integration is rigorous except for the use of a constant average temperature. Both static and flowing bottom-hole pressures may be calculated by (his method without resort to trial and error procedures. INTRODUCTION Bottom-hole pressures can be determined either by direct measurement with a bottom-hole pressure gauge or by calculation. Since measurement with a bottom-hole pressure gauge is costly, calculation of bottom-hole pressures is to be preferred when possible. Calculation involves knowledge of the wellhead pressure, the properties of the gas, the depth of the well, the flow rate, the temperature of the gas, and the size of the flow line. These quantities must be combined in a suitable equation for vertical flow. Several equations have been developed for the purpose of calculating gas flow through both horizontal and vertical pipes1,2,4,5,6,7,8,9 These equations all have the basic differential equation for flow as their starting point. They differ only in the assumptions which are made in order to simplify the integration step. The bottom-hole pressures calculated using any of the better known equations are in good agreement with bottom-hole pressures calculated by a more rigorous but considerably more tedious stepwise integration method. All of these methods, however. require a trial and error solution for the calculation of flowing bottom-hole pressures. The purpose of this paper is to present a method which provides a direct solution of static and flowing bottom-hole pressures without use of a trial and error solution. At the same time the method involves fewer simplifying assumptions than any of the previous methods used, except lor the lengthy stepwise method. The derivation of any practical flow equation begins with the basic differential equation which is rigorous for almost all flow problems. The five terms in Equation 1 represent the potential energy, the potential energy of position, the kinetic energy, the shaft work done, and the energy losses due to motion of the fluid respectively. Equation 1 reduces to Bernoulli's theorem for the case of horizontal flow of an incompressible fluid, no work done, and no energy losses due to friction. In the present case, the term (v) (dv)/(g,.) can be shown to be quite negligible compared to the other terms, and is therefore neglected in the derivation. The term — dws includes work done by a pump or turbine in the system and is zero in this case. The frictional losses in the pipe are included in the term — d(lw) which is expressed in terms of the Moody friction factor as in Equation 2. (f) (v2) (dL) d(lW) = (f)(V2) (dl)/(2) (g) (d) The specific volume of a gas can be expressed in terms of the temperature, pressure, molecular weight, and compressibility factor. The velocity of the gas can be expressed in terms of the weight rate of flow, the specific volume, and the dimensions of the pipe.The reduced pressure Pr is to be used because z can be expressed as a function of Pr and Tr alone for most natural gases:

Jan 1, 1956

By C. M. Wayman, J. F. Breedis

The crystallography of the martensitic transformation in the Fe-30 Ni alloy was reinvestigated. The scatter in the habit Plane as determined from measurements on the mid-rib plane was smaller than reported previously, and the orientation relationship was determined from a martensite plate having known direction cosines. From agreement with crystallographic theory and from observations of the morphnlogy of the martensite plates, it is suggested that the mid-rib plane represents the starting region of the transformation. THE crystallography of the martensitic transformation in the iron-nickel system has been the subject of many investigations.&apos;-7 However, for iron alloys containing approximately 30 wt pct Ni, a wide scatter in the reported habit planes exists. In only one instance has a Laue determination of the orientation relationship been made, but the habit plane of the martensite plate studied was not determined experimentally. Because the most successful thermodynamic and kinetic analyses8 of the martensite transformation have been based on Fe-30 Ni alloys, it was considered desirable to reinvestigate the crystallographic features of the transformation in this alloy. Lieberman9 suggested that the most significant information for use in a theoretical treatment involves the determination of all the crystallographic observables from a single plate of the product phase. This was first done in essence by Greninger and Troiano10 for Fe-22 wt pct Ni-0.8 wt pct C, and is the method followed in this investigation. Some theoretical approaches11-13 in describing the martensitic transformation consider the overall transformation distortion to be comprised of a Bain distortion, or lattice deformation (PI, which produces the structure change, and a lattice invariant deformation (G), such as twinning, which together leave the interface or habit plane un-distorted. The incorporation of a rigid body rotation (R) results in a transformation distortion (E) such that the interface plane is left both undistorted and unrotated. In matrix notation, E = RPG where the lattice invariant deformation has "taken place" in the austenite. Bowles and Mackenzie14-16 in formulating a theoretical approach proposed an adjustable scaler quantity, denoted as 6, which represents a uniform dilation in the interface plane. This dilation acts to adjust the lattice spacings of the parent and product structures at the plane of contact. Using the dilation parameter as a variable, these authors were able to account for a continuous variation of habit planes in steels along a curve in the stereogram between {225}A and {259}A. she invariant line strain14 of the transformation is 6 RP, and the corresponding transformation distortion is E/6.) With the dilation parameter known, the invariant line is computed as the triple coincidence of the habit plane, the shear plane of the lattice invariant deformation, and the initial Bain cone.14 The contraction axis for the Bain distortion can be taken9&apos;17 as [010]A, and the correct permutation of the habit plane indices used. Kelly and Nutting 18 have established the shear plane (of twinning) in the tetragonal martensite of Fe-22 Ni-0.8C to be {112)M by means of transmission electron microscopy. The reasonable shear system is then {112}M which is equivalent to {011}A <01l>A. The as-

Jan 1, 1962

By J. K. Stanley

Knowledge of the diffusivity of carbon in the low temperature form of iron (alpha iron existing below 910°C) is at the moment of considerable interest in the study of the decomposition of austenite and martensite, the elastic after-effect,123 the magnetic after-effect4 and the decarburization of steel below 910°C. Information on the solubility of carbon in iron, and to a lesser extent its diffusion, is also important in consideration of such phenomena as blue-brittleness, temper-brittleness, "magnetic" aging, quench-aging, strain-aging, and possibly the yield point. In order to obtain more information on these subjects more fundamental knowledge is necessary. It is the purpose of this work to present data on the diffusion and solubility of carbon in the alpha iron. The high temperature form of iron (gamma; face-centered cubic) existing above 910°C is capable of dissolving relatively large amounts of carbon, up to 1.7 pet at 1130°C, while the low temperature form (alpha, body-centered cubic) existing below 910° dissolves only a limited maximum amount of less than 0.02 pet carbon at 725°C, according to data obtained here. Since the solubility of carbon in the face-centered or gamma iron is large, relatively speaking, no great analytical difficulties have been encountered in the determination of the solubility lines5 or of the diffusion of carbon.0 The limited solubility of carbon in alpha iron offers difficulties because experimental procedures and analytical methods for low carbon contents below say 0.01 pet have to be more refined than techniques used for work with gamma iron. Because of the difficulties of applying conventional methods to the determination of the diffusion of carbon in alpha iron, virtually no work has been done on this subject. However, by proper refinement of the analytical method for small amounts of carbon, the determination of the diffusion coefficient can be made readily using modified procedures. The solubility of carbon in alpha iron has been determined over a temperature range by various investigators, but the agreement among them is poor. The present investigation establishes the limits quite accurately. Information of this kind is useful in establishing the correctness of equilibrium diagrams but, more significantly, such information on maximum solubilities, especially when extended to alloyed ferrites, should be extremely important in the study of aging and related phenomena. Literature The literature existing on the diffusion, in particular, and on the solubility of carbon in alpha iron is not extensive. The data which exist are not of a high order of accuracy, much of them being in the realm of conjecture. THE DIFFUSION OF CARBON IN ALPHA IRON Whiteley7 made the qualitative ob- servation, using metallographic techniques, that the rate of diffusion of carbon at the A1 (725°C) point was very rapid and that its diffusion was still rapid at 550°C. Snoek,4 studying the magnetic aftereffect in high purity iron, arrived at the conclusion that the after-effect could be explained by the presence of small amounts of carbon diffusing under the influence of magnetostrictive strain (lattice distortion due to magnetic interaction). In later work, Snoek8 made an estimate of the ratio of carbon diffusion in alpha to its diffusion in gamma iron, and concluded that for a temperature of 910°C the ratio of Da/D? was 2600. Polder,9 basing his calculations of D on relaxation phenomena in the elastic after-effect, estimated that Da is about 1/3 of D? at 910°C (1183°K) and is about 1/12 of Dy at 727°C (1000°K). Polder&apos;s equation for the diffusion of carbon in alpha iron was calculated to be 18000 D = 5.2 X 10-4 e-RT cm2 per sec Ham10 obtained data for the diffusion and solid solubility of carbon in alpha iron at two temperatures by using one technique similar to that employed in this study. He found a D of 8.0 X 10-7 cm2 per sec at 702°C and of 2.7 X 10-7 at 648°C. THE SOLUBILITY OF CARBON IN ALPHA IRON Although pearlite is absent in steels containing 0.06 pet,11 0.05 pet,12 or 0.045 pet C,13 it appears that the carbon in these steels cannot be in solution in ferrite. The solubility of carbon at the A1 (725°C) point was first determined by Scott14 on the basis of cooling curves, and was found to be between 0.03 and 0.04 pet C. Tamura15 by interpolating between the solubility of carbon in delta iron at 1400°C and in alpha at room temperature (assuming zero solubility) ar-

Jan 1, 1950

By H. Reginald Hardy, Y. S. Kim

Recent studies of inelastic behavior and acoustic emission in geologic materials further validate the concept that such materials may be considered to consist of an elastic media containing an array of pores and cracks. In the present paper this concept is investigated further by experiments in which the mechanical behavior of a number of geologic materials were studied in detail at low stress levels using ultrasonic pulse methods. Experiments were carried out on cylindrical test specimens of Indiana Limestone, Tennessee Sand- stone and Barre Granite under relatively low confining pressures (0-5000 psi). Analysis of data from these experiments indicated that there existed a low-level critical stress at which there appeared to be a transition in the mechanical behavior of the material. Under triaxial stress, results indicated that the differential critical stress was relatively independent of confining pressure, i.e., the mechanism responsible for the transition in mechanical behavior was governed by a maximum shear stress criteria.

Jan 1, 1971