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By R. L. Skaggs, D. T. Peterson

The effect of carbon in solid solution on the plastic behavior of thorium was studied by measuring the flow stress of Th-C alloys from 4.2" to 573°K and at several strain rates. Carbon was found to strengthen thorium primarily by increasing the thermally activated component of the flow stress. The strengthening due to carbon was directly proportional to the carbon content and decreased rapidly with increasing temperature up to 423" K. The flow stress also increased with increasing strain rate. The strengthening appears to be due to a strong short-range interaction between carbon atoms and dislocations. A yield point was observed in the Th-C alloys which increased with increasing carbon content. JTREVIOUS study of the mechanical properties of thorium has been confined largely to the measurement of the engineering properties. Work prior to 1956 has been summarized by Milko et al.1 who reported that additions of carbon to thorium sharply increased the room-temperature strength. In addition, the yield strength was observed to decrease rapidly over the temperature range from 25" to 500°C. In 1960, Klieven-eit2 measured the flow stress of thorium containing 400 ppm C. He found that over the temperature range from 78" to 470°K the flow stress was strongly dependent on temperature and rate of deformation. A drop in the load-elongation curve, or a yield point, was observed over most of the above temperature range. Above 470°K, the flow stress was nearly independent of temperature and strain rate. This strong temperature and strain rate dependence of flow stress is not generally observed in fcc metals. It is, in fact, more typical of the behavior reported for bcc metals. Bechtold,3 Wessel,4 and conrad5 have pointed out the striking difference between the commonly studied bcc metals and fcc metals in regard to the effect of temperature and strain rate on the flow stress. Zerwekh and scott6 studied the plastic deformation of thorium reported to contain 12 ppm C. They found that this material did not obey the Cottrell-Stokes law as expected for fcc metals. In addition, they found values of the activation volume smaller by an order of magnitude than expected for an fcc metal. They concluded that thorium was strengthened by a randomly dispersed solute. Thorium differs from many other fcc metals that have been studied extensively in that it shows a relatively high carbon solubility at room temperature. Mickleson and peterson7 report the solubility limit at room temperature to be 3500 ppm C. The lowest value reported is that of Smith and Honeycombe8 who report the limit to be 2000 ppm C at 350°C. The pres- ent investigation was a systematic study of the flow stress and yield point phenomenon of thorium over a broad range of carbon content, temperature, and strain rate. EXPERIMENTAL PROCEDURE The thorium used in this investigation was produced by the reduction of thorium tetrachloride with magnesium as described by Peterson et a1.' Chemical analysis of the original ingot after arc melting and electron beam melting is shown in Table I. Alloys were prepared by arc melting this thorium with high-purity spectrographic graphite. Threaded specimens with a gage length 0.252 in. diam by 1.6 in. long were used for the constant stress or creep measurements. These specimens were machined from rod which had been cold-rolled and swaged to % in. diam. Tensile specimens were prepared by swaging annealed 3/8 -in.-diam rod to 0.102 *0.001 in. The as-swaged wire was cut to lengths of 2 in., annealed, and the center 1-in. gage length elec-tropolished to 0.100 ±0.001 in. The specimens were gripped for a length of 3 in. at each end by a serrated four-jaw collet which was tightened by a tapered compression nut. No slipping occurred in the grips and negligible deformation was observed outside the 1-in. gage length. Both the creep and tensile specimens were annealed at 730°C under a vacuum of 1 x X Torr. The resulting structures consisted of equiaxed recrystallized grains with a grain size of 3200 grains per sq mm for the tensile specimens and 2200 grains per sq mm for the creep specimens. After the specimens were prepared, samples were analyzed for nitrogen, oxygen, and hydrogen. The results of these analyses are given in Table 11.

Jan 1, 1969

A letter has been received by the Secretary of the Institute from Mr. C. W. Purington, Honorary. Secretary of the. American Committee of Engineers in London, whose offices are at 6, Copthall Avenue, London, E. C. 2, which will be of interest to any member who may be intending to go to England. Mr. Purington says: "A Committee of Americans has been formed here, consisting mostly of Mining Engineers, and those interested-in mining and allied industries. We should be very glad, among other duties, to give assistance to any American engineers arriving in England on official business connected with the war. This assistance would probably take the form of offering advice and hints as to saving time in approaching British official Departments, and generally in getting. about." This Committee of Engineers was organized with the approval of the American Ambassador to Great Britain, who has recommended its services to the United States Government in connection with the conduct of the war.

Jan 7, 1917

By Graham MacFarlane

The largest area of high-grade cannel coals known in America is doubtless found in eastern Kentucky. Notwithstanding the popular belief to the contrary, there is no reason to doubt that these eastern Kentucky cannel-fields, following the general rule, will be uncertain and treacherous. But, taken in the aggregate, their extent is very great. The principal service to which cannel coal can be put is enriching illuminating-gas. The electric light has, to a certain extent, created a demand for better gas, and has increased the market for gas-enrichers. Before the discovery of rock-oil, coal-oil was distilled from cannel coal and cannel shale. This business was getting fairly started when the cheaper rock-oil, or petroleum, overcame it, and the great distilleries went into disuse and ruin. Now, again, the chief competitor with cannel coal is oil, namely, the cheap oil of Lima, Ohio. Under proper treatment the vile odor of this oil can be removed.

Jan 1, 1890

(Under this heading will be published notes sent to the Secretary of the Institute of members or other persons introduced by members) Young mining engineer, and geologist, member, technical, graduate with four years' varied mining experience in the West and Southwest as miner, surveyor and engineer. Past 18 months, work in mine geology, mapping and examinations. Would prefer assisting consulting engineer or work with exploration company in foreign service. Unmarried. Age, 28. No. 331. Member; aged 35, married, with 10 years' experience in the Southwest, thoroughly competent to take full charge of mining and milling operations. Particularly fitted to handle either gold or tungsten producers. At liberty February 1. Will go anywhere. No. 340. A member wants a roving commission to examine old mines of the Mother Lode in. California, especially those which can be bought for their taxes. Some of these mines are reported to contain large quantities of low-grade ores which can now be treated at a profit. No. 341.

Jan 2, 1917

The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing. committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization and at a minimum of expense. J. V. W. Reynders is chairman of the Endowment Committee.

Jan 1, 1929

LUTHER B. EAMES, Pueblo, Colo. (written discussion*).-In reading Mr. North's interesting paper, several points have been noted that appear to warrant discussion. With a feed all through 20 mesh, I feel inclined to question the use of steel balls as large as 2 in. in a tube mill. I have seen balls as small as-3/4 in. used for the dry grinding of cement clinker, and surely many more points of contact would result from smaller balls. This would seem to be desirable in a mill as short as 6 ft. The heavy load in the classifiers would also indicate a high proportion of returned pulp. I hope that some discussion by Mr. North -and others may develop this point. The flow sheet on page 1181 shows the solution returning from the dam valued at 40 c. per ton being added to the last decantation tank. Theoretically, this solution should not be added to that of a lower value. As I calculate it, if this solution were added to tank X the solution finally discharged from tank Z would be reduced in value by nearly 4 c. per ton.

Jan 10, 1919

By L. G. Marshall

WHILE surveying in a small Western mine, the following problem was encountered: Two traverses had to be connected by running a traverse line down the main hoisting shaft, which was the only connection between the two levels. The shaft was inclined at about 80 deg. from the horizontal and measured 8 by 10 ft. The distance between levels was about 110 ft., measured on one side of the shaft. The surveying equipment consisted of a transit, tripod, level rod, 100-ft. chain, and plumb bobs. There were no side or top the- scope attachments with which to take large, vertical angles. Therefore, we were confronted with the problem of taking readings between two points, one of which could not be seen through the instrument when set up under the other point, owing to the obstruction of the horizontal plate, and of measuring the distance between these points with a chain that was too short. The method of a line of plumb bobs down the shaft was impractical because a setup would be needed part way down the shaft, which would call a halt to all hoisting operations for some time. After considerable experimentation the following method was used.

Jan 1, 1936

By Harry W. Brown

This paper presents results of static capillary pressure measprements made both by the restored-state and by the mercury-injection methods, and of dynamic capillary pressure measurements made by the Hassler technique. The results indicate a variation from sample to sample of the factor used to convert capillary pressure obtained by mercury injection to those applicable to a water-gas system. Static capillary pressures measured by the restored-state method were found to be in close agreement with dynamic capillary pressures, indicating that data obtained from static measurements may be utilized with confidenre in the solution of dynamic problems of fluid flow. Experimental data are presented on the use of "J-curves" for the correlation of capillary pressure-saturation relations for a number of cores from a particular geologic formation. It is shown that the correlation was improved in some cases by reqtricting it to rertain lithologic classifications. INTRODUCTION The Meaning and Importance of Capillary Pressure The coexistence of two or more immiscible fluids within the voids of a porous medium, such as reservoir rock, gives rise to capillary forces. Because of the interfacial tension existing at the boundary between two immiscible fluids in a pore space, the interface is curved, and there is a pressure difference across the interface. This pressure difference is termed the capillary pressure. The magnitude of the capillary pressure between two immiscible fluids which together fill a porous medium depends upon several factors: the textural properties of the medium, the wettability of the medium, the interfacial tension between the fluids, the respective saturations of the fluids, and the manner in which these saturations are attained. For a given pair of immiscible fluids in a particular sample of reservoir rock, the capillary pressure is a unique function of the fluid saturation, provided that the saturation of the fluid which wets the rock has previously been decreased unidirectionally from an initially complete saturation. Similarly, for a given pair of fluids at a particular saturation which has been achieved by a

Jan 1, 1951

By Harry W. Brown

This paper presents results of static capillary pressure measprements made both by the restored-state and by the mercury-injection methods, and of dynamic capillary pressure measurements made by the Hassler technique. The results indicate a variation from sample to sample of the factor used to convert capillary pressure obtained by mercury injection to those applicable to a water-gas system. Static capillary pressures measured by the restored-state method were found to be in close agreement with dynamic capillary pressures, indicating that data obtained from static measurements may be utilized with confidenre in the solution of dynamic problems of fluid flow. Experimental data are presented on the use of "J-curves" for the correlation of capillary pressure-saturation relations for a number of cores from a particular geologic formation. It is shown that the correlation was improved in some cases by reqtricting it to rertain lithologic classifications. INTRODUCTION The Meaning and Importance of Capillary Pressure The coexistence of two or more immiscible fluids within the voids of a porous medium, such as reservoir rock, gives rise to capillary forces. Because of the interfacial tension existing at the boundary between two immiscible fluids in a pore space, the interface is curved, and there is a pressure difference across the interface. This pressure difference is termed the capillary pressure. The magnitude of the capillary pressure between two immiscible fluids which together fill a porous medium depends upon several factors: the textural properties of the medium, the wettability of the medium, the interfacial tension between the fluids, the respective saturations of the fluids, and the manner in which these saturations are attained. For a given pair of immiscible fluids in a particular sample of reservoir rock, the capillary pressure is a unique function of the fluid saturation, provided that the saturation of the fluid which wets the rock has previously been decreased unidirectionally from an initially complete saturation. Similarly, for a given pair of fluids at a particular saturation which has been achieved by a

Jan 1, 1951

By K. E. Brown, G. H. Fancher

An 8,000-ft experimental field well was utilized to conduct flowing pressure gradient tests under conditions of continuous, multiphase flow through 2 3/8-in. OD tubing. The well was equipped with 10 gas-lift valves and 10 Maihak electronic pressure recorders, as well as instruments to accurately measure the surface pressure, temperature, volume of injected gas and fluid production. These tests were conducted for flow rates ranging from 75 to 936 B/D at various gas-liquid ratios from 105 to 9,433 scf/bbl. An expanding-orifice gas-lift valve allowed each flow rate to be produced with a range of controlled gas-liquid ratios. From these data an accurate pressure traverse has been constructed for various flow rates and for various gas-liquid ratios. A comparison of these tests to Poettmann and Carpenter's correlation indicates that deviations occur for certain ranges of flow rates and gas-liquid ratios. Numerous curves are presented illustrating the comparison of this correlation with the field data. Poettmann and Carpenter's correlation deviates some for low flow rates and, in particular, for gas-liquid ratios in excess of 3,000 scf/bbl. These deviations me believed to be mainly due to the friction-factor correlation. However, Poettmann and Carpenter's correlation gives excellent agreement in those ranges of higher density. This was as expected and predicted by Poettmann. He pointed out that their method was not intended to be extended to those ranges of low densities whereby an extreme reversal in curvature occurs.l As a result of these experimental tests, correlations using Poettmann and Carpenter's method were established between the friction factors and mass flow rates which are applicable for all gas-liquid ratios and flow rates. Definite changing flow patterns do not allow any one correlation to be accurate for all ranges of flow. INTRODUCTION The ability to analytically predict the pressure at any point in a flow string is essential in determining optimum production string dimensions and in the design of gas-lift installations. This information is also invaluable in predicting bottom-hole pressures in flowing wells. Although this problem is not new to industry, it has by no means been solved completely for all types of flow conditions. Versluys,2 Uren, et al, 3 Gosline,4 May,5 and Moore, et al,6,7 were all early investigators of multiphase flow through vertical conduits. However, all of these investigations and proposed methods were very limited as to their range of application. Likewise, many are extremely complicated and therefore not very useful in the field. Only in the last decade have any significant methods been proposed which are generally applicable. The most widely accepted procedure in industry at the present time is a semi-empirical method developed from an energy balance, proposed by Poettmann and Carpenter8 in 1952. Their correlation is based on actual pressure measurements from field wells. Accurate predictions from this correlation are limited to high flow rates and low gas-liquid ratios. Although this method will be discussed in detail later, it should be pointed out that two important parameters, namely the gas-liquid ratio and the viscosity, were omitted in their correlation. The viscosity was justifiably omitted since their data was in the highly turbulent flow region for both phases, and most wells fall in this category. The gas-liquid ratio was incorporated to some extent in the gas-density term. In 1954, Gilbert9 presented numerous pressure gradient curves obtained from field data for various flow rates and gas-liquid ratios for the determination of optimum flow strings. However, no method is presented for predicting pressure gradients except by comparison to these curves. Baxendell, et al,10 proposed a method based on Poettmann and Carpenter's procedure

By L. Burris, C. H. Stockman, I. G. Dillion

Zone melting is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Equations are presented which 1—predict the concentration profiles after successive passes of the zone and 2—give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing in the last zone length. These equations were solved numerically using an electronic computer, and the concentration profiles are presented as a function of the solute distribution coefficient and the ratio of molten zone to total bar length. ZONE MELTING is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Separation occurs if the solid freezing from a solution at any moment has a composition different from that of the liquid from which it is freezing. Solutes which lower the freezing point will tend to remain in solution and will be moved in the direction of zone travel. Solutes which raise the freezing point will preferentially freeze out, and they will be moved in a direction opposite to that of zone travel. After repeated unidirectional passage of a molten zone through a bar of material, impurities will be concentrated in the ends of the bar. A limiting concentration gradient will be reached in the bar after a large number of passes of the molten zone. Both the magnitude of this limiting concentration gradient and the rate of movement of solute in any pass depend on the zone length and on the equilibrium concentrations of solute in the liquid and solid phases. The basic theory of zone melting was thoroughly covered by Pfann.1 The purpose of this paper is to extend the theory of zone melting by presenting 1—equations which relate the concentration profiles in successive passes of the zone and 2—equations which give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing* in the last zone length concentration of a given solute in the solid to the concentration of the same solute in the liquid. Analytical methods for determining the concentration profiles after any pass have been developed by Lord2 and Reiss. The method developed by Lord does not take into account normal freezing in the last zone and also becomes very complicated when the number of passes becomes large. The method developed by Reiss enables the direct calculation of the complete concentration profiles (including that in the last zone) after any pass for values of k close to unity (0.9 < k < 1.1). Both methods are useful and provide valuable insight into the zone melting process. The equations given in this article are based on the same assumptions used by Pfann. These are: 1—uniform composition in the liquid, 2—negligible diffusion in the solid, 3—constant distribution coefficient, 4—constant length of the liquid zone (except at the ends), and 5—solubility of the solute in the melt is not exceeded at any point. Equations for Concentrations in Successive Passes For a melted zone of length 1 at the left-hand end of a bar of uniform unit cross-section, the amount of solute in the liquid is J0Cn-1(x) dx [1] where the subscript is the number of the pass. Cn-1(x) represents the concentration (expressed as weight per unit volume) obtained in the previous

Jan 1, 1956

By E. C. Dominguez, H. B. Scharf

THE Sparrows Point plant of Bethlehem Steel Co., southeast of Baltimore, is the largest Bethlehem plant, with an annual rated capacity of 6.2 million ingot tons. There is considerable diversity of product, but a high percentage is sheet, tin plate, galvanized sheets, and rod and wire. The large amount of light-weight end product requires a number of pickling installations that necessarily consume large quantities of sulfuric acid. In the coking operations sulfuric acid is also consumed in recovery of ammonia as ammonium sulfate and in treatment of recovered light oil derivatives. Total sulfuric acid consumption in the plant is currently approaching 10,000 tons per month, of which 55 to 60 pct is required for pickling. In 1951 the acute sulfur shortage caused grave concern as to future sulfuric acid supply for the Sparrows Point plant. Raw materials for acid making were already at hand in the form of hydrogen sulfide and pyrites sufficient to produce nearly half the sulfuric acid required at that time. It was also known that the Bethlehem mining activities would produce additional pyrites in the future. Late in 1951 Bethlehem management decided to build a 250-ton sulfuric acid plant at Sparrows Point to utilize these raw materials. The plant was built and put in operation in May 1953. The steel plant has expanded considerably since 1951, and it is now necessary to operate the acid plant far over rated capacity in order to supply plant demand. Production of acid in 1954 amounted to 93,000 tons. Raw Materials for Acid Making: Coking operations at Sparrows Point produce a residual fuel gas in large quantity which has a net heating value of 525 to 545 Btu. Prior to 1950, plant surplus coke oven gas was sold to the local utility company. In

Jan 1, 1957

By B. Haimson, C. Fairhurst

A criterion is Proposed for the initiation of vertical hydraulic fracturing taking into consideration the three stress fields around the wellbore. These fields arise from (1) nonhydrostatic regional stresses in earth, (2) the difference between the fluid pressure in the wellbore and the formation fluid pressure and (3) the radial fluid flow through porous rock from the wellbore into the formation due to this pressure difference. The wellbore fluid pressure required to initiate a fracture (assuming elastic rock and a smooth wellbore wall) is a function of the porous elastic constants of the rock, the two unequal horizontal principal regional stresses, the tensile strength of the rock and the formation fluid pressure. A constant injection rate will extend the fracture to a point where equilibrium is reached and then, to keep the fracture open, the pressure required is a function of the porous elastic constants of the rock, the component of the regional stress normal to the plane of the fracture, the formation fluid pressure and the dimensions of the crack. The same expression may also be used to estimate the vertical fracture width, provided all other variables are known. The derived equations for the initiation and extension pressures in vertical fracturing may be employed to solve for the two horizontal, regional, principal stresses in the rock. INTRODUCTION Well stimulation by hydraulic fracturing is a common practice today in the petroleum industry. However, this stimulation process is not a guaranteed success; hence, the deep interest shown by the petroleum companies in better understanding the mechanism that brings about rock fracturing, fracture extension and productivity increase. Geologists and mining people became interested in hydraulic fracturing from a different point of view: the method may possibly be employed to determine the magnitude and direction of the principal stresses of great depth. Numerous articles in past years have dealt with the theory of hydraulic fracturing, but they all seem to underestimate the effect of stresses around the wellbore due to penetration of some of the injected fluid into the porous formation.1-4 Excellent papers on stresses in porous materials due to fluid flow have been published5,6 but no real attempt has been made to show the effect of these stresses in the form of a more complete criterion for vertical hydraulic fracturing initiation and extension. This paper is such an attempt. ASSUMPTIONS It is assumed that rock in the oil-bearing formation is elastic, porous, isotropic and homogeneous. The formation is under a nonhydrostatic state of regional stress with one of the principal regional stresses acting parallel to the vertical axis of the wellbore. This assumption is justified in areas where rock formations do not dip at steep angles and where the surface of the earth is relatively flat. This vertical principal regional stress equals the pressure of the overlying rock, i.e., S33 = —pD, where S33 is the total vertical principal stress (positive for tension), p is average density of the overlying material and D is the depth of the point where S33 is calculated. The wellbore wall in the formation is considered to be smooth and circular in cross-section. The fluid flow through the porous elastic rock obeys Darcy&apos;s law. The whole medium is looked upon as an infinitely long cylinder with its axis along the axis of the wellbore. The radius of the cylinder is also very large. Over the range of depth at which the oil-bearing formation occurs, it will be assumed that any horizontal cross-section of the cylinder is subjected to the same stress distribution, and likewise that it will deform in the same manner. STATE OF STRESS PRIOR TO DRILLING OF WELLBORE At a depth D from the earth surface within the oil-bearing strata, it is assumed that the following are 1References given at end of paper.

By G. H. Enzian

THE effects of phosphorus and nitrogen on the properties and behavior of low carbon steels are important considerations to both the manufacturer and the user of such material. For one thing, these two elements are the principal points of distinction between the chemical compositions of Bessemer and open-hearth grades. Further, open-hearth steels themselves may vary considerably in nitrogen content depending on the raw materials and ..practice used. In addition, appreciable amounts of rephosphorized open-hearth steels are being used at the present time in some low alloy, high strength grades and in certain other cases. For these and other reasons, it was felt desirable to obtain more complete knowledge of the effects of simultaneous small variations in phosphorus and nitrogen content on such properties of low carbon steel as tensile strength, impact toughness, sensitivity to cold work, and strain aging. A long range investigational program designed to furnish such information, was carried out, and the present paper summarizes some of the data currently obtained. General Discussion The strengthening effect of relatively small amounts of phosphorus in steel has been recognized, and to some extent utilized, for many years. A number of investigators have pointed out, from time to time, that under proper conditions of control, phosphorus can be a useful alloying element in low carbon steels.1-3 Nevertheless, in spite of the volume of data on the subject, the use of phosphorus for this purpose has always been handicapped by widespread feeling that its presence makes the steel brittle, difficult to cold work, and unreliable at low temperatures. This belief on the part of some steel users is not entirely justified in many cases, and often stems from early experience with acid Bessemer steels which have appreciably higher phosphorus (and nitrogen) contents than basic open-hearth grades. Nitrogen in steel, and its effect on properties, has also received considerable attention in the literature.4 In 1906, Braune5 ascribed the brittleness of Bessemer rails to the nitrogen content, and proposed a schedule of nitrogen limits for steels for various uses. This was one of the first papers to recommend directly the use of nitrogen content as a quality control measure, but it did not meet with much favor or support; as a matter of fact, the Jernkon-toret was rather sharply criticized for publishing the paper. In the intervening years a number of papers have been published on the subject of nitrogen in steel. As a result, it is now generally recognized that nitrogen can have an important effect on the properties and behavior of steel and that the presence of this element should be considered in any systematic study of factors affecting steel quality. In 1932, Graham6 introduced the concept that the quality of various steels could conveniently be evaluated and compared in terms of "sensitivity", which was defined as "the characteristic reaction rate of a piece of steel toward brittleness or hardness." This concept formed the basis for a broad research program into factors causing variations in the quality of commercial steels. At an early stage of this work, it became apparent that the observed effect of either phosphorus or nitrogen on the sensitivity of steel depended, in no small measure, on how much of the other of these two elements was also present. Indeed, the combined effect of phosphorus and nitrogen in steel may often be more important than the specific effect of either. With a few exceptions, it is not possible to predict accurately the effect on steel properties of a change in the amount of either phosphorus or nitrogen in the steel without also specifying the approximate amount of the other element. It seems desirable, at this point, to discuss briefly the distinction between strain-sensitivity and strain aging as used in this paper. In the early stages of its development, the work-brittleness test7 (which will be described in more detail later) was used

Jan 1, 1951

By B. W. Frazier

At a recent meeting of the North of England Institute of Min ing and Mechanical Engineers, during a discussion upon the com pression of air, attention was called to an apparent anomaly in the phenomena attending the compression. At a subsequent meeting this apparent anomaly was explained by Prof. Herschel, and all the facts observed shown to be strictly in accordance with the laws of thermodynamics. Upon reading the report of the discussion in the published transactions of the society, it occurred to me that an attempt to determine mathematically the amounts of energy (whether in the form of heat or of work) expended and absorbed in compressing air, and causing it to perform work by expansion, might prove of use to some who have not access to any treatise upon the application of the laws of thermodynamics to the compression of air, and who have not the time or the inclination to make such application for themselves. The apparent anomaly noticed was this: If air be compressed, and at the same time, by the sufficient application of a cooling medium, kept at a constant temperature, the indicator diagrams in the

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

By R. D. Russell, R. M. Farquhar

ISOTOPIC tracers have become an important aid in following the progress of chemical processes in the laboratory. It has recently been found possible to utilize a system of naturally existing isotopic tracers to obtain information about the geo- logical history of lead ores. Common lead, such as is found in lead deposits, is a mixture of four stable isotopes having atomic weights 204, 206, 207, and 208. Of these, the last three are identical with the lead isotopes produced as stable end products of the radioactive decays of uranium and thorium: the first, lead-204, is not known to be produced on the surface of the earth by any process. Since uranium and thorium occur in the surface regions of the earth in amounts comparable with lead, and since the half-lives of uranium and thorium isotopes are of the same order as the age of the earth, they produce the radiogenic lead isotopes in amounts com- parable to the amount of nonradiogenic lead present. Every significant exposure of a sample of lead to uranium and thorium will therefore lead to the permanent alteration of the lead isotope ratios in that sample.

Jan 5, 1957

By Janshi Sen

Vertical-intensity magnetometers, for instance the Hotchkiss Superdip and the Askania vertical field balance, are now widely used, because vertical-intensity charts give definite information for the location of upper pole, dip and strike, and approximate shape of the deposit. Again, a slow and steady increase of dip over a large area indicates a large deep-lying deposit, while a large dip limited to a small area and falling away rapidly suggests a small and shallow one. The complication comes more from the richness of the ore. A large body of lean ore near the surface might produce the same vertical-intensity chart as a rich ore at depth. This paper presents a method for calculating the maximum depth of a single-pole deposit and another for a two-pole mineral body, by utilizing data of both vertical and horizontal intensities as obtained by a Thalen-Tiberg magnetometer. As shown on the left side of Fig. I, lean ore, rich ore and a single pole produce the same magnetic field. The depth of the pole, where G is the vertical intensity at point A due to the pole; F, the horizontal intensity of the same; and a, the distance from the point of maximum vertical intensity or the vertical projection of the pole on the surface to the point of observation A. If an entirely covered deposit is indicated by magnetic measurements and boring cost estimated from the calculated depth is so reasonable as to encourage drilling, the ore should be struck somewhere within the limit of the calculated depth by the borehole. A number of such points as A should be taken for calculation, erratic results should be rejected and the average figure used for cost estimation.

Jan 1, 1946

By Janshi Sen

Vertical-intensity magnetometers, for instance the Hotchkiss Superdip and the Askania vertical field balance, are now widely used, because vertical-intensity charts give definite information for the location of upper pole, dip and strike, and approximate shape of the deposit. Again, a slow and steady increase of dip over a large area indicates a large deep-lying deposit, while a large dip limited to a small area and falling away rapidly suggests a small and shallow one. The complication comes more from the richness of the ore. A large body of lean ore near the surface might produce the same vertical-intensity chart as a rich ore at depth. This paper presents a method for calculating the maximum depth of a single-pole deposit and another for a two-pole mineral body, by utilizing data of both vertical and horizontal intensities as obtained by a Thalen-Tiberg magnetometer. As shown on the left side of Fig. I, lean ore, rich ore and a single pole produce the same magnetic field. The depth of the pole, where G is the vertical intensity at point A due to the pole; F, the horizontal intensity of the same; and a, the distance from the point of maximum vertical intensity or the vertical projection of the pole on the surface to the point of observation A. If an entirely covered deposit is indicated by magnetic measurements and boring cost estimated from the calculated depth is so reasonable as to encourage drilling, the ore should be struck somewhere within the limit of the calculated depth by the borehole. A number of such points as A should be taken for calculation, erratic results should be rejected and the average figure used for cost estimation.

Jan 1, 1946

By J. H. Jackson, P. D. Frost, C. H. Lorig, L. W. Eastwood, A. C. Loonam

R. S. BUSK*—I wish first to congratulate the authors of this paper both for the work done and the presentation of that work. We have also been working on this type of alloy development, but any technical contribution I might have is better reserved for a separate paper which is planned in the near future. However, I would like to insert a word of caution. The alloys described in this paper are still very much in the laboratory stage. There still remains the quite vexing problem of property stability at slightly elevated temperatures which must be solved before the properties quoted can be effectively utilized. These alloys are extremely interesting and I am confident that the problems can be solved. However, the present existence of those problems must not be overlooked. I have one question with regard to the work-hardening test. If the work harden-ability of magnesium is compared to aluminum using a more standard test such as the Meyer Analysis the magnesium is found to work harden the more rapidly. Is the test developed for this work truly a work-hardening test or a measure of something else ? J. H. JACKSON (authors&apos; reply)—I am sure we appreciate the comments of Mr. Busk and we are pleased that the Dow Chemical Co. has also undertaken work in this field. It is a big field. We, of course, are continuing our research for the Navy Bureau of Aeronautics, since, as clearly shown in the paper, the alloys are not completely developed. With regard to Mr. Busk&apos;s comments on the relative work-hardenability of aluminum and magnesium, the comparison we cited in the paper was intended merely to show that the results obtained by our method of testing were independent of the yield strength of the materials. We believe that this test method afforded a rough indication of the work-hardenability of the magnesium-lithium base alloys. It is not known whether this method affords greater or less accuracy than the Meyer Process, which is based upon a hardness-test impression. It is quite possible, since work-hardenability is a function of metal purity, that our results, obtained for commercial aluminum and magnesium, would be different if high-purity metals had been used. A. C. LOONAM—Lithium has some very interesting effects on magnesium. The paper showed that even small percentages increased ductility. These small amounts changed the axial ratio of the hexagonal magnesium from 1.624 in the pure metal to 1.606 in the saturated alpha solution, a value close to that of titanium, which has a ratio of 1.601. You will recall an article in the January, 1949, issue of the Journal of Metals where it was stated that titanium can be cold-rolled over 90 pct without any significant edge cracking. At 4.9 or 5 pct lithium, a change begins in crystal structure—from a hexagonal close packed to body centered cubic. There are two phases over a short range of lithium content, but at 10 pct the structure becomes completely cubic. The melting points of alloys in this range of lithium content are relatively high. Alloys even up to the six ratio have melting points above 500°C; this represents a relatively small reduction in melting point from pure magnesium itself. The magnesium-lithium system has a number of very interesting characteristics. This is only a very small part of the story. J. H. JACKSON—I would like to remind you that Mr. Loonam is one of the authors of this paper, and the fact is that this work is based on many of his ideas. I am sure we appreciate his additional comments in this discussion. R. LEITER*—I am interested in Fig 19 in which Mr. Jackson compares

Jan 1, 1950