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By R. E. Zimmerman

Wide attention is being placed upon various methods for cleaning the fine sizes of bituminous coals. The author describes and analyzes the results achieved on wet concentrating .tables of modern design on unclassified feeds of - 1/2 in. particle sizes, including tests on high-sulphur coals.

Jan 1, 1950

By William L. Russell

A new instrument for measuring bulk and grain vol-urnes is described, and compared in accuracy with two modifications of Nutting's method, All three methods are reasonably fast, and in all three the probable error in the determinations of bulk volume can be kept down to about 0.1 to 0.2 per cent. INTRODUCTION The new pycnometer described in this paper is designed to give speed without sacrificing accuracy. Some time ago Russell1 described a somewhat similar appa-ratus; however, the instrument described in the present paper is more accurate. Nutting' designed the pycnom-eter shown in Fig. 1 (A and B), and Pirson3 has shown points like those of Fig. 1-D. The procedure described in this paper for using Nutting's pycnometer has been modified from that used by Nutting. CHOICE OF LIQUIDS The best liquids for measuring grain volumes are hydrocarbons or chlorinated hydrocarbons which evaporate slowly. Trimethylbenzene or mesitylene, triethylben-zene, carbon tetrachloride, and tertalin have been used for this purpose. Any of these liquids or mercury may be used for measuring bulk volume. PREVENTING ERRORS DUE TO INVASION OF LIQUID Errors due to the invasion of the porous, permeable bulk samples by the liquid of measurement may be prevented or greatly reduced by using mercury, by applying an impervious coating, or by soaking the bulk samples in the liquid of measurement until bubbles cease issuing from them. Errors are produced only by the invasion of the samples which occurs between movement when the samples are weighed in air and the moment the weight of liquid displaced by the sample in the pycnometer is determined. No error is produced by varying degrees of filling of the pore space of the samples by the liquid of measurement. The excess liquid should be wiped from the samples immediately before the weight in air W1, is determined, and they should be placed in the pycnometers immediately. OPERATION OF NEW INSTRUMENT The new pycnometer is shown in Fig. 2. It consists of two glass parts which fit together at a ground glass joint. The spaces J and D are connected by fine glass tubes E, and the space J must be larger than the space D by at least the volume of the largest sample to be tested. The projections H afford a grip for twisting when the two parts tend to stick together. The position of the sample in mercury is shown by I, and in other liquids by M. F is a permanent mark on the glass, and G is a tem-Some marker. In order to determine the position at which G should be placed, invert the instrument so that A is at the bottom, and fill space D. Place the cub K

Jan 1, 1958

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"' and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By AIME AIME

THE paper by C. H., Lieb on the "Economics of Oil-Producing Practice" (June issue, M. & M.) contains much food for thought. The engineers should be gratified that an executive with Mr. Lieb's. responsibility should recognize their standing in the industry. Yet after giving them that recognition, he proceeds to spur them on to greater accomplishments by pointing out that their job is only partly done and in some instances poorly done. The operating policies in this paper when applied to new pools with flowing wells are sound. Neither do I take exception to their application to pumping wells. But I do wish to comment on what lie says about price when applied to the many more wells that are approaching abandonment that is, the small producing wells. Mr. Lieb states in effect that higher prices would be detrimental from the long range viewpoint. I doubt that the present prices of crude will provide an ample return from the hundreds of thousands of small wells that have possibilities of substantial recovery by means of water-flooding, repressuring with gas, and air drive. Probably expenditure for experimental work can he justified, but at this time it must usually be considered as experimental. Recently I visited a property where it was estimated that $250,000 would be spent on a 160-acre tract for flooding purposes. The rate of r e t n r n and amount of profit at today's prices are uncertain. It can be argued that if this type of recovery is not economic with crude at $1 then it can he delayed as it is now possible to secure economically an ample supply of crude from our flush fields. But these old fields still retain large quantities of crude in a dormant state, and should not he abandoned per-

Jan 1, 1936

By E. G. Deane

A METHOD of top slicing has been devised at the Miami Copper Co.'s mine at Miami, Ariz., which differs radically in some ways from the customary methods of top slicing. The area of that section of the orebody in which top slicing is used is about 800 ft. square. The ore, while for the most part soft, is, nevertheless, considerably harder than the capping. The latter is siliceous, seldom containing any clay or other binding material, and breaks into fine particles so that it runs like sand if given the opportunity. Because of these facts, and because the ore is above the average grade of the mine ore, it has been mined by top slicing. Haulage levels are opened up 150 ft. apart, vertically, with two sublevels between at 50-ft. intervals, to facilitate the building of ore chutes. These sublevels are used during slicing for distributing air in the ventilation system. On the haulage level the drifts are spaced on 50-ft. centers, and raises along these drifts are also spaced on 50-ft. centers, except the incline raises as hereafter noted. The raises are cribbed where necessary. Where the wear will be excessive, ¼ -in. iron plates are spiked to the top of every third set of cribbing, for its protection. When top slicing was first used, an attempt was made to carry a slicing face from fifty to several hundred feet long. Timber and other, supplies were brought in through long drifts from an auxiliary shaft. Great difficulty was experienced in keeping these drifts open, the side pressure breaking the posts and the top weight breaking, both caps and posts. Furthermore, the men could not work efficiently while these drifts were .being repaired. The slicing faces advanced irregularly, due to varying conditions, and in many ways the results were not all that could be desired. It was then decided to divide the slicing area into blocks 200 ft. square and this wins later changed to 250 ft. square.

Jan 9, 1916

WHEN the new sulphide plant started to roll at Chuquicamata last July, we broached the matter of looking in on this historic event to Burr Wheeler, then executive vice president of Chile Exploration Co. (Chilex executive offices are housed with the parent company, Anaconda, at 25 Broadway which is 23 hours and 15 minutes closer to the AIME office than the mine, counting air and automobile travel). Mr. Wheeler was at Chuqui when they turned the first shovelful of earth, has an understandable pride and affection in the mine, and kindly offered to make all arrangements. As a guest of Chilex, physical exam, injections, police clearance, passport, and airline reservations on the crack Panagra airline are procured swiftly and almost painlessly. Winter clothes were advised by Mr. Wheeler and D. M. Dunbar, who is the former's assistant and a seasoned Chuqui-ite. Both of these gentlemen obviously prefer Chuqui climate, with 364 days of sunshine, 1 ½ -in. rainfall, rare atmosphere of 10,000 ft elevation, Christmas-time earthquakes, and howling winds through June and July to the vicissitudes of New York weather. Panagra's de luxe DC-6 noses in toward land at Antofagasta, Chile, the supply and embarkation port for Chuquicamata. The Coastal Range, completely barren of green, thrusts a spur far out into the Pacific creating a crescent-shaped and protected harbor at Antofagasta. Beach gives way to pampa, to hills, and the only variation in scenery is in topographic relief. Chilex's reception committee in the person of the alert and amiable Bob Condit, assistant port agent, takes care of everything: immigration, interviews by the local press, baggage, transportation, and introduction to Chilean cuisine. The drive up to Chuqui takes about three hours, on the only two lane highway in northern Chile; hard surfaced, with a few kilometers of repair work in progress. We were fortunate to make the trip with manager Charles Brinckerhoff, who arrived the same day at Antofagasta from the seat of government at Santiago where he goes frequently to keep in touch with the company's Santiago office.

Jan 1, 1952

By E. Swartzman

THE free-swelling index, a numerical value for the free-swelling properties of coal, is being used to an increasing extent in specifying coal for burning in various types of equipment. The empirical standard ASTM method for determining this index uses, as a source of heat, a gas burner which requires frequent calibration because gas pressures are not constant, relatively small changes in gas pressure resulting in rather wide variations in the temperature attained in a crucible and thus in the resultant size of the coke button. Furthermore, the quartz crucibles specified for the test are not standard equipment, and relatively small variations in dimension and wall thickness from those specified often result in rather wide variations in the resultant size of the button.

Jan 10, 1951

By J. A. Hren, C. M. Wayman

RECENT investigators have noted anomalous behavior in the electrical resistivity of vanadium below room temperature. Rostoker and Yamamoto1 in studying the vanadium-oxygen system hypothesized that the body-centered-tetragonal phase existing from 15 to 34 at. pet O at approximately 800°K was really a low-temperature allotrope of vanadium that was stabilized by oxygen. In measuring the electrical resistance of cold-swaged vanadium rod over a range of temperatures, a small discontinuity was observed at approximately 240°K, supporting their notion of allotropy. However, the magnitude of the observed discontinuity was extremely small. Loomis and Carlson2 in studying the ductile-brittle transition in vanadium also made resistance measurements and reported a discontinuity near 200°K. More recently, White and Woods3 showed that the electrical resistivity from room temperature to approximately 100 °K was not linear and at variance with the Bloch-Griineisen law. Instead of finding a discontinuity, they observed a deviation from linearity below 200°K. In discussing their results they pointed

Jan 1, 1961

By C. V. Millikan

New developments in air-gas lift practices in the Mid-Continent area since our Pall meeting in Fort Worth have done much to increase the efficiency of installations, and thus bring within economic limit of air-gas lift many wells which could not have been flowed profitably before. After the gas-lift had so thoroughly demonstrated its value in the Seminole field, its use spread to other areas and many installations were made of which the economy could be questioned. In the Seminole area, when production began to decline it was necessary either to increase the efficiency of the air or gas-lift or to put the wells on the pump, and pumping was not a process of lifting oil to which any operator looked forward with confidence. These conditions have resulted in the development of many practices which increase the efficiency and permit wells to be flowed with air or gas which earlier could not have been flowed economically, and wells which have been flowing to continue to a lower rate of production. The practices which have come into more common usage in the Mid-Continent area recently are mostly revivals of and improvements on practices which have been known in air-lift work for several years. Many arc peculiar to the individual well on which they are used. Intermittent Flowing Some interesting results are being obtained in Seminole and other districts by intermittent injection of gas. Gas is introduced during per-iods iods of 3 to 5 min. at a rate considerably over that necessary to acquire the production at a steady rate of injection, and is then cut off for a period of 3 to 15 min. Two to five wells are run from the same group of conlpressors. The total volume of gas required is sometimes reduced as much as one-third of that required when it is introduced at a constant rate, without changing the amount of oil production. The maximum pressure required is usually higher, but the average equal to or lower than that required for constant rate of flow. The effect on the wells is usually an irregular rate of flowing which may cause inconvenience where recycling is practiced. It would seem that this increase in efficiency is due to less slippage when the gas is introduced intermittently than when it is intro-

Jan 1, 1928

By R. B. Russell

SINCE Cahn's¹ paper on plastic deformation in orthorhombic (a) uranium an increasing amount of work is to be expected on orientation of single crystals and preferred orientation in this metal. It would seem desirable to have a table of angles between crystallographic planes (hkl) and (HKL). Table I shows these angles as distances from (loo), (0l0), and (00l), and in Fig. 1 as a standard (001) stereographic projection. Only the locations of poles whose diffracting planes produce Cu Ka reflections up to 0 = 70.5" (i.e. (154) ) are given." The relative reflection of these planes are represented by circle diameters. It is hoped that the projection may also be used in making inverse pole figures, originally suggested by Harris.' Values of 4 were calculated from the expression hH kK 1L cos = hH/a²+kK/b²-lL/c² where the lattice parameters a, b, c, and the spac-ings d were taken from the work of Jacob and Warren." (They report a = 2.852 kX (2.8578 A), b = 5.865 kX (5.8768 A), c = 4.945 kX (4.9550 A).) The parameters reported by them may be subject to revision,4,5 accordingly the interplanar angles are listed to only the nearest tenth of a degree. References ¹R. W. Cahn: Acta Metallurgica (1953) 1, p. 49. ¹G. B. Harris: Philosophical Magazine (1952) 43, p. 113. 3C. W. Jacob and B. E. Warren: Journal ACS (1937) 59, p. 2588. 4J. S. Lukesh: Acta Crystallographica (1949) 2, p. 420. ³ J. Thewlis: Nature (1951) 168, p. 198.

Jan 1, 1954

By E. M. Murphy

(Presented by invitation at a meeting of the Spokane Local Section of the Institute, Feb. 17, 1912.) EIGHT years ago the Hecla mine, a lead-silver producer, situated at Burke, Idaho, was producing ore from but two levels, the 300- and the 600-ft. All hoisting was done with a 12- by 16-in. slide-valve, double-reel, hoist. The hoist was being worked to its capacity and was unsuitable for hoisting from greater depths. As the work of opening a new level was about to be started, it became necessary to remodel the then-existing equipment or install a new hoist. The recent advent of electricity from Spokane had made available a cheaper power than steam. By a series of tests conducted throughout the Coeur d'Alène district, it was found that it cost $109 per year to generate a horse-power with steam. Electric power was to be had for $50 a horse-power per year. It was decided to substitute for the engines a motor-drive, of sufficient capacity to operate from the 900-ft. level, and ultimately install an entirely new hoist. After disconnecting the engines, installing a new shaft, and making a few minor changes, a 300-h-p., 2,300-volt, 514-rev. per min., variable-speed motor of the induction type was geared to the reel-shaft. The reels were supplied with 3/8 by 4-in. flat rope, and the duty of the hoist was about as follows: Cage, 1,700; ore, 2,600; car, 1,400; rope, 2,250; total, 7,950 pounds. The Bristol ammeter chart, Fig. 1, shows the combined current-consumption of the hoist- and mine-motors. The large intermittent load is clearly shown ; this produced harmful fluctuations in the voltage of the long, lightly-loaded, 60,000-volt transmission-line from Spokane to the Coeur d'Alènes. The power company received no compensation for the increased cost of producing power for this intermittent or fluctuating load. In order to protect its system from similar excessive

Sep 1, 1912

By P. Barnes

These furnaces are of the ordinary Siemens type, and present no special peculiarities of construction. The bed of each is 8 feet by 20 feet clear inside of the walls and ports. The producers are placed at a distance of about 200 feet from the furnaces, and the gas is collected in an iron tube and led across the yard overhead. It then drops underground into the gas flue, and is distributed to the furnaces. A considerable weight of floor-plates over the valve-pits is included in account 39, but none of the general stock of floor-plates for the mill were charged to the furnaces. In Table No. 1 is shown the money cost of the furnaces as distributed to the several accounts named. In Table 2 is shown the proportion of each account due to each of the several items or classes of expenditure named.. It is thus rendered possible, almost at a glance, to determine the money value in this particular case of each of the items named. The regular work of three of these furnaces in heating steel blooms for the months of January and February, 1877, was 77 rounds per week of 60 blooms each, or 4620 30-foot rails per week. Each furnace will heat 8 14-inch ingots, for three rails each, at one time.

Jan 1, 1879

By Arthur S. Dwight

THE professional career of Thomas Septimus Austin, who died at El Paso, Tex., August 23, 1906, was contemporaneous with the growth of the silver-lead smelting-industry of the Far West, to which his talents and zeal contributed in no small degree. Born at Stratford, Conn., December 7, 1853, he was the seventh son in a family of thirteen. His parents were well-to-do; and he received a thorough preliminary training at the Hopkins Grammar School, New Haven, Conn., passing thence to the Columbia School of Mines, in New York, where he was graduated in 1876. His first professional work was that of analytical chemist with a Cuban sugar company. In this position he spent a year, and, whatever else of benefit he may have acquired during that year in Cuba, he gained a facility of speech in the Spanish language which was of inestimable value in his subsequent work in Mexico and the southwestern United States. In 1877, he went to the Rocky Mountains, and, under the firm name of Murphy & Austin, opened an assay-office in Leadville, Colo., which was just then coming into public notice as a rich silver-lead camp. The next year, however, he entered the service of the Germania Smelting & Refining Co. at Salt Lake City, Utah, where he remained until 1882, first as assayer and chemist, and later as Assistant Superintendent. The Germanic bears the honorable distinction of being one of the first of the large " custom " lead-smelters erected in the West. Its founders may be called the pioneers of the modern lead-smelting practice, and the Germania served, to a large extent, as a model for the many plants that sprang into existence during the next few years in Utah, southern Idaho, Colorado and other lead-producing districts. The formulation, for the first

Jan 1, 1908

By Albert F. J. Bordeaux

Discussion of the paper of Albert F. J. Bordeaux (Bi-Monthly Bulletin, No. 23, September, 190S, pp. 629 to 640). A. H. BROMLY, Zihuatanejo, Guerrero, Mexico (communication to the Secretary*) :-The following criticism of what "is offered as a summary which may be found useful by mining engineers," is not dictated by any captious spirit, but in the interest of historical and scientific accuracy. The States of Queretaro and Oaxaca have produced sufficient silver to warrant more extended notice. Referring to Pachuca, State of Hidalgo, the somewhat loose and. inexact statement is made that "the ore-deposit is an andesite, intermixed with quartz-veins, rich from the surface." A better description would be,-the ore-deposits consist of quartz-veins in andesite. It is notable that many of the rich shoots worked in recent days did not come to surface. In consequence, Pachuca, is often quoted by the ill-informed as a camp in which values improve with depth, the truth being that the veins carry shoots, or clavos, some of which were exposed at surface and some not. The name of " electric plow," applied to the mechanical stirrer of recent use, is certainly not to be recommended. The stirrer, or agitator, consists essentially of a traversing gang-plow, operated by power through shafting, drums, and wire-rope. The fact that in certain plants the motive-power used is electricity does not make it an electric plow. Such a name suggests a machine of which the motor is an essential and integral part; which is not so in this case. A lathe in a factory driven by water-power is not called a hydraulic lathe. My experience agrees with Dr. Raymond's note as to azulaque, which in sortie districts is also applied to blue copper carbonate. The El Oro, Esperanza, and Mexico mines should be allocated to the State of Mexico; the Dos Estrellas being in Michoacan, as stated. The El Oro quartz certainly does not appeal to me

May 1, 1909

By Jack L. Taylor

Single crystals of tungsten grown from powder -metallurgy swaged rod by high-temperative annealing were deformed in tetzsion at temperatures from 2500 to 5000 OF. Orientation of specittzen tensile axis, strained ratrix, and defortnation bands was determined optically by reflections from {110} etch pits. Slip traces meve analyzed and slip directiorz determined. Results indicate that {110}(111) , {112){111}. and {123}{111} type slip occur in tungsten over the terpe,atuve rutge investigated. Slip is orientation-dependent occuvring on tCuzt cowzbitzation oj slip plane and direction which has the highest critical resolved shear stvess. Overshooting appears to be a general occurrence between 2500' and 5000°F. Dejornatiotz bands show rotation in a directiorz opposite to the yotation of tire tensile axis. DEFORMATION in bcc metals has been reviewed by Maddin and Chen,' Keh and eissman,' and most recently by Nabarro, Basinski, and olt. From these reviews it is apparent that some disagreement exists concerning the crystallography of plastic deformation in bcc metals. There is evidence of noncrystallo-graphic slip, the crystal slipping on or near a noncrys-tallographic plane in the (111) zone for which the resolved shear stress is greatest. There is also evidence to indicate that crystallographic slip occurs in the planes of the same zone. On the other hand, there is agreement that the close-packed direction ( 111) is the slip direction in bcc metals. Further, in pure bcc metals4 and alloys the operative crystallographic slip systems are strongly dependent on temperature. Both crystallographic and noncrystallographic slip have been reportede8 in tungsten, a group VIA bcc metal. The number of slip families which operate in the case of crystallographic slip, however, has been in question. The earliest study by oucher' of single-crystal tungsten tested at temperatures of 1800 to 5000°F led to the conclusion that only {112)( 111) type slip operated. Raymond and eumann recently reached the same conclusion studying deformation by rolling of plasma-flame single crystals at 1800°F; however, only [loo] and [110] orientations were studied. Work at high temperatures by Leber and Pughs on tungsten and Chen and Maddin9 on molybdenum suggests that conjugate slip on nonparallel (110) planes may account for the slip on (112) and (123) planes found by others working with bcc metals. The present paper presents evidence of three families or modes of slip in tungsten in the temperature EXPERIMENTAL PROCEDURE Material. Standard microtensile specimens, 0.160 in. diam by 0.640 in. gage length, were ground from commercial powder-metallurgy swaged tungsten rod, type MK. Specimens were heated for 10 min at 5150°F or 6 hr at 5400°F in vacuum of 1 x 105 Torr or less to produce single crystals. At the lower temperature an average of two out of seven specimens heated in a group developed single crystals throughout the specimen length as shown in Fig. 1, the rest remaining wholly poly crystalline. At the higher temperature, three or four out of seven specimens became single crystal. Other than to note that Laue X-ray photographs generally showed sharp, well-defined spots, no attempt was made to assess crystal perfection or measure dislocation density. Two tungsten single crystals grown from the melt by the plasma-arc process were also used for this study.

Jan 1, 1967

By W. C. Hagel

In 1952, Hauffe and pfeiffer1,2 reported that parabolic rates of nickel oxidation are decreased by factors of two and four at 1100° and 1000°C, respectively, when Li2O vapor is present. Hauffe 's3 explanation was that monovalent lithium enters the crystal lattice of p-type NiO to decrease cation-vacancy concentration and, hence, diffusion of Ni2+ ions across the growing oxide. After first succeeding in adding lithium directly to molten nickel, the purpose of this investigation was to determine whether alloyed lithium is a more effective oxidation inhibitor than the external vapor. Seven 650-g heats were prepared by melting carbonyl nickel inductively under 1 atm of argon. Various amounts of lithium were added by dropping small chunks into the melt. Only about 10-pct recovery was achieved with the remainder lost by spattering and volatilization. Nominal and actual

Jan 1, 1965

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

By Walter Renton Ingalls

IN SEVERAL papers and addresses during the past two years, I have dwelled upon some of the economic consequences of the war. The fundamental thought that I have sought to convey is that the world became immensely poorer by the war, not only in material wealth and population, but also in the psychology and morale of the people. I do not see how there can be any intelligent dissent from that statement. All the ideas of post-war prosperity were manifestly fallacious, manifestly fallacious from the outset. If there had been any truth in them it would have followed logically that a great war, with all its destruction of wealth, health and life would be a good thing. Therefore, let us have a great war every ten years or so. Such an idea would be both monstrous and absurd. Assuming then the acceptance of my premise, I have tried to show that the losses by the war could be made good in a short time, i.e., in a relatively short time, only by doing things a great deal better than formerly, and that the accomplishment of such a result called for greater transparency in industry, for industrial cooperation, for thinking in terms of industries as a whole, and for the greater exercise of engineering functions. All of this introduced, of course, the position and psychology of labor. I say frankly that I do not look for labor to contribute any constructive thought to the upbuilding. I neither expect it nor hope for it. This is a pity, for it could do so much for its own economic advancement if it would. However, it never has done so, but rather has benefited only from the exercise of the talents of the few, and the main hope now is to bring it into a passive state, dispelling the resistive fallacies that developed during the war. Let us briefly examine the nature of these.

Jan 1, 1921

The following list comprises the names of those persons who became members during the period May 10, 1916, to June 10, 1916: ARCHIBALD, JOHN CHRISTIE, Min. Engr., Supt. of Cyanide Plant, Guanajuato Reduction Mines, Guanajuato, Mex. BRUNEL, FRANK P., Cons. Min. Engr Mitchell & Brunel, Ajo, Ariz. CALVERT, WILLIAM ROBERT, Cons. Geol. ...225 Kearns Bldg., Salt Lake City, Utah. CHAMPION, J. R., Supt The Yak Mining, Milling & Tunnel Co., Leadville, Colo. CHARLES, LAVERN JOHN, Construction Engr., Elephant Butte Dam, Elephant Butte, N. M. CHASTEL, ANDRE, Min. Engr., Societe Miniere & Metallurgique de Penarroya, 12, Place Vendome, Paris, France. CHRISTIE, WALLACE H., Vice-Pres. and Mgr., Alt. Bert Gold Dredging Co., 604 Mission St., San Francisco, Cal. CLARK, RONALD ..Hardinge Conical Mill Co., 120 Broadway, New York, N. Y.

Jan 7, 1916

By K. K. Clark, W. H. Somerton

The feasibility of reducing pressures needed to fracture formations by heating the borehole intensively has been investigated on a laboratory scale. Reductions in fracture pressures of heated Bandera, Berea and Boise sandstone cores were observed at various confining pressures, simulating reservoir stress conditions to a depth of 5,000 ft. Both permeable and impermeable borehole boundary conditions were tested. Three heating conditions were used in the tests. One group of samples was heated in a furnace to a temperature of 600C, cooled to room temperature., and then tested for fracture pressures. Two other groups of samples were heated with a borehole heater to maximum borehole wall temperatures of 625 and 792C, then cooled and tested. In all cases, heated samples showed substantial reductions in fracture pressures compared to unheated samples. The higher temperature borehole heated samples showed the greatest reduction, amounting to 70 per cent in the extreme case. In actual application to wells, it was concluded that fracture pressures may be reduced by 20 to 50 per cent by intensive borehole heating before fracturing. INTRODUCTION Hydraulic fracturing of oil and gas wells is an accepted and effective technique for increasing well productivity in many areas, but is notoriously unsuccessful in other areas. The technique becomes less interesting for production stimulation purposes when excessive fracture pressures are necessary. Formations which do fracture but require high pressures, probably form horizontal fractures. There is good evidence to indicate that some formations do not fracture at all, but yield plastically under high pressure. Thus, any technique which will make formations easier to fracture or will reduce fracture pressures is potentially interesting to petroleum producers. Horizontal fractures generally occur in planes of weakness, such as bedding planes, and at pressures equaling or exceeding the effective overburden stress. In the unusual case where planes of weakness do not exist, a slightly higher pressure must be applied to overcome the tensile strength of the rock. In general, high fluid-loss fracturing fluids are conducive to the formation of horizontal fractures.1 Vertical fractures, when they do occur, are initiated at pressures generally lower than overburden pressure and are favored by low fluid-loss fracturing fluids or impermeable boreholes. The pressure necessary to create a vertical fracture in an impermeable, elastic medium can be predicted from the so-called "thick-walled cylinder" equation: Pf = 2 or+ st.............(1) where pf = fracture pressure or = radial stress st = tensile strength of medium. This equation indicates that to fracture it is necessary to overcome a tangential compressive stress, induced by and equal to two times the radial confining stress, plus the tensile strength of the medium. If the above equation held strictly true for rocks, very little could be done to reduce fracture pressure. The tensile strength of the rock might be reduced somewhat, but any change in st would be small compared to the magnitude of the tangential stress at reasonable subsurface depths. Laboratory tests have shown that actual fracture pressures exceed values predicted from Eq. 1 by factors of 1.4 to 28.6.1,2 Eq. 1 thus does not properly describe the

Jan 1, 1966