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By W. A. Tiller, W. C. Johnston

A high-temperature electromagnetic stirrer is described in which heating and stirring are accomplished by independently controlled power sources. The appavatus is suitable lor use at temperatures up to 1700°C in a variety of ambient atmospheres. Some typical examples of the homogenizatimz capabilities of the system are given. THERE are few processes in solidification that are not markedly affected by motion in the melt during freezing. In many instances, the mechanisms are diffusion-controlled, and the transport in the melt may be greatly accelerated by deliberately stirring the melt. In zone-refining, stirring1 assists the removal of rejected impurities from the interface, so the process proceeds at a faster rate. The transition from a planar to a cellular interface is caused by constitutional undercooling in the melt ahead of the interface: and stirring delays its onset. Stirring is valuable for homogenization of melts: and chemical reaction with sluggish kinetics may be accelerated. Finally, it has been observed that grain refinement is related to motion in the melt. Fine grain castings are usually produced by the addition of catalysts to the -melt,' catalysts which are thought to act simply as hetereogeneous nucleation centers. Even here motion is important. Richards and Rostoker 5 applied ultrasonic vibration to a solidifying A1-Cu alloy which had been innoculated with a catalyst and found that the grain diameter fell linearly with the amplitude, the peak acceleration and the power input to the melt from the transducer. Finally, mechanical and electrical stirring alone have been used to generate a fine-grained structure.6,7 Johnston ef a1.' have carried out a series of systematic investigations of grain refinement by electromagnetic stirring in a number of low melting point alloys. They found, for example, that the number of grains per unit volume in Pb-Sn alloys could be increased several orders of magnitude by stirring an undercooled melt at the moment of recalescence. In general, a relation AT .H = constant prevailed for a given grain size, where AT was the undercooling of the melt and H the field strength. In more recent work, deliberate homogeneous nucleation of slightly undercooled melts established that the mechanism of refinement must be one involving crystal fragmentation and subsequent multiplication, rather than a "shower" of nuclei effect.9 It is the purpose of this note to describe a stirring device suitable for use up to 1700°C. At low temperatures mechanical stirring and direct-current methods are feasible, but at high temperatures the problem of a protective atmosphere and of electrode corrosion rules out such procedures. The most convenient method for high temperatures is to use externally generated ac fields for both stirring and heating. With rf induction heating alone, considerable stirring and agitation can be achieved, but in general the penetration of field into the melt is small, and the stirring cannot be controlled independently of the heating. In the present experiments, separate power sources of different frequencies for heating and for stirring were used. A susceptor design was chosen so that the 450 kc rf heating field was completely absorbed in the susceptor. The stirring frequency, 400 cps, hereafter called the af field, was chosen so that a high penetration of the melt proper was achieved. EXPERIMENTAL APPARATUS The apparatus, Fig. 1, consists of a quartz tube and end plates, surrounded by an rf induction coil and six equally spaced af stirring coils, four of which are shown in full and a fifth in section. Each af stirring coil is a transformer of which the secondary is a single-turn water-cooled copper loop and the primary is composed of two 10 amp-117 v Variac cores as shown. These cores are cooled by forced air, as each of the six pairs will carry maximum currents of 15 amp for short periods. Each set of Variac windings are connected in series, but opposite sets are connected in parallel with a three-phase 400 cps 400-v source. By properly phasing the coils in this way, a rotating field is produced. Capacitors C1, C2, and C3 in Fig. 2 are used to match this inductive load to the generator. Fig. 3 shows a cutaway view of the quartz tube. The sample (1 in. diam by 1 in. high) is placed in a tapered alumina crucible. An axial W-26 pct Re thermocouple, enclosed by a protection tube, is provided. The cruci-

Jan 1, 1968

By C. A. Wright

Since the adoption by the U. S. Bureau of Standards several years ago of specifications for standard 100- and 200-mesh sieves, frequent requests have been received that this Bureau test and certify sieves of other sizes than these. With a view to the adoption of a series of standard testing sieves which might be of use to all industries making fineness tests, this Bureau for two years has been studying the question of such a standard screen scale. Various scales that have been proposed were considered, and information was sought of representative firms in the various industries interested as to their requirements. Manufacturers of sieves have also been consulted as to the desirability of different screen scales and the practicability of their manufacture. As a result of this study of the question, a conference was called at the Bureau of Standards, Apr. 20, 1916, of representatives of various committees of the American Society for Testing Materials, American Society of Civil Engineers, American Institute of Mining Engineers, American Foundrymen's Association, Mining and Metallurgical Society of America, American Water Works Association, American Institute of Metals and the American Spice Trade Association; also representatives of the Committee of Revision of the U. S. Pharmacopæia, the U. S. Geological Survey, the U. S. Bureau of Mines, the U. S. Office of Public Roads and Rural Engineering, the U. S. Office of Grain Standardization and the U. S. Bureau of Standards; also representatives of a number of private firms engaged in industries in which sieves are used, such as the glass, the drug milling, the abrasive, the asphalt, the mining, the spice, the chemical, and the graphite industries; also representatives of the firms in this country manufacturing wire cloth and sieves. This Conference, after considering the various screen scales either proposed or now in use, adopted as a Standard Screen Scale that given in Table 1, and recommends that it be adopted generally by scientific,

Jan 1, 1918

By Bryon W. Cheever

The greatest objection to be brought against the present methods for estimating phosphorus in iron and steel, is the time consumed in the operation. The following method, originated and perfected by Mr. E. D. Campbell, assistant in the chemical laboratory of the University of Michigan, will, 1 think, if carefully followed out, give results that are sufficiently accurate for technical purposes, and will give them in less time than they can be obtained by any other process. The process consists in comparing the color obtained by the action of stannous chloride upon a solution of the phospho-molybdate precipitate obtained from the solution of iron or steel, with that obtained from a standard solution of molybdie acid which represents a given amount of phosphorus. The operation is as follows : Take of ordinary steel 1 grm. and treat as in any of the wellknown processes until the phosphorus is precipitated as ammoniumphospho-molybdate. When precipitated, the phospho-molybdate precipitate is filtered out, thoroughly washed with an acid solution of ammonium nitrate, and, finally, twice with water, to remove most of the ammonium nitrate. The precipitate is then dissolved in about 1 c. c. of 10 per cent. potassium hydrate, which is let fall drop by drop on the filter till the precipitate is dissolved ; the filter is now washed with about 25 or 30 c. c. of water, and the potassium hydrate solution, which now consists of 25-32 c. c. of solution, is boiled until the peculiar frothy appearance, which first appears on boiling, is entirely gone. The solution is then cooled until perfectly cold, and about 10 or 15 c. c. of strong hydrochloric acid added ; if the solution is kept cold this will form no precipitate, but a light yellow or colorless solution. The solution is now ready for the addition of stannous chloride, and the subsequent comparison of color produced with that obtained from the standard molybdie acid. The comparison is made in tubes that are calibrated like carbon-tubes, but which are larger, about 5/8-inch bore, and graduated to 100 c. c.; this makes them about 18 inches long. To make the comparison of color, first transfer the now acid solu

Jan 1, 1886

By A. J. Weinig

IN the accompanying figure consider the classified AB in closed circuit with a ball mill, wherein T = Tonnage of new feed C = Ratio of circulating load Now consider that the circulating load is made up of two portions of ore. One portion is due entirely to the characteristics of the ball mill and the tonnage of new feed impressed on the ball mill. This portion of the circulating load in no way is to be blamed on the characteristics of the classifier and is all composed of oversize. Consider, for illustration, that this portion of the circulating load is handled in the A division of the classifier, assuming that the classifier is divided longitudinally into two divisions by an imaginary line. Because the classifier does not usually make a perfect separation of the undersize, a certain portion of the total circulating load is to be directly blamed on the efficiency of the classifier. Let this portion of the circulating load be considered as being handled in the B division of the classifier. Now if the classifier is operating perfectly (100 per cent efficient), the width due to the B division becomes zero and correspondingly the efficiency of the classifier diminishes as B becomes wider in proportion to A. If E is the mechanical efficiency, then

Jan 1, 1934

Howard N. Eavenson, Gary, W. Va. (communication to the Secretary*):—For some time before the publication of Mr. Scholz's paper, I had been collecting data bearing upon its subject, and I now take pleasure in presenting to the Institute my results in the form of a discussion. It has long been a matter of common opinion among mining-men that mine-explosions are more frequent during the colder, or winter months, than during the warmer ones, and it is a matter of common knowledge among them that the air-ways and road-ways in most mines are much drier and are more inclined to be dusty during the winter than during the summer. In many mines, places which are wet and sloppy in the summer are dry and sometimes dusty during the winter. These changes, of course, can only be due to atmospheric conditions, and are caused by differences in temperature and humidity. Until recently, however, very little attention has been paid to the part that atmospheric conditions may play in mine-explosions, or, rather, to the effect they may have in rendering mine-conditions peculiarly dangerous, and in spreading and rendering more disastrous the effects of what otherwise probably would have been small explosions. To show the difference in mine-conditions during summer and winter months, I have tabulated in Table I. the results of 24 observations of hygrometric conditions in several different mines at different times of the year. Mines Nos. 1, 2, and 6 are located in the Pocahontas coal-region, in McDowell county,w.Va., the first one being a shaft-mine and the others drift. Mines 1A and 2A are drift-mines located in Logan county, W. Va. All of these are mines of fair size, but none of them has been in operation more than six years,

Jan 1, 1910

By Warren L. Howes

This paper deals primarily with an investigation of ball-mill liners that was conducted by the writer over a period of six years at the Mammoth mill in Arizona. The investigation covered a wide variety of designs of liners in both primary and secondary mills. The comparative results are presented herein as evidence of the extent to which design influenced liner life and mill performance. Flowsheet The feed to the Mammoth mill was a complex, oxidized, gold-silver-lead-molybde-num-vanadium ore with rhyolite, andesite and granite as gangue. Although the ore varied between stopes, the long-term average in character remained substantially the same. Capacity was 560 tons per day.† Fig. I shows an abbreviated flowsheet of the grinding section of the mill. Primary Ball Mill A 3-ft. Symons shorthead crusher in open circuit crushed to 1/4-in. maximum one-way dimension the feed to the 5 by Io-ft. Marcy open-end ball mill. The mill rotated at 80 per cent of critical speed and was charged with 4-in. forged steel balls. Cast balls were used for a few months at a slight reduction in ball cost, but breakage of the large balls reduced the ball size and grinding capacity to a point where the over-all costs suffered out of proportion to the saving in cost of balls. For metallurgical reasons, the finished product of the mill was maintained at minus 8-mesh. This coarse product, plus the very abrasive ore and the absence of fines in the feed, caused abnormally rapid wear of the mill liners. The resultant high operating cost led to the most extensive phase of the investigation. In order to clarify the difference in design of the various types of liners used, Fig. a shows the profiles with the arrangement in which grinding balls of maximum size would lie on the face of the liners. The results with each type of shell liner in the primary mill are shown in Table I. Since most of the testing was done with

Jan 1, 1943

By Warren L. Howes

This paper deals primarily with an investigation of ball-mill liners that was conducted by the writer over a period of six years at the Mammoth mill in Arizona. The investigation covered a wide variety of designs of liners in both primary and secondary mills. The comparative results are presented herein as evidence of the extent to which design influenced liner life and mill performance. Flowsheet The feed to the Mammoth mill was a complex, oxidized, gold-silver-lead-molybde-num-vanadium ore with rhyolite, andesite and granite as gangue. Although the ore varied between stopes, the long-term average in character remained substantially the same. Capacity was 560 tons per day.† Fig. I shows an abbreviated flowsheet of the grinding section of the mill. Primary Ball Mill A 3-ft. Symons shorthead crusher in open circuit crushed to 1/4-in. maximum one-way dimension the feed to the 5 by Io-ft. Marcy open-end ball mill. The mill rotated at 80 per cent of critical speed and was charged with 4-in. forged steel balls. Cast balls were used for a few months at a slight reduction in ball cost, but breakage of the large balls reduced the ball size and grinding capacity to a point where the over-all costs suffered out of proportion to the saving in cost of balls. For metallurgical reasons, the finished product of the mill was maintained at minus 8-mesh. This coarse product, plus the very abrasive ore and the absence of fines in the feed, caused abnormally rapid wear of the mill liners. The resultant high operating cost led to the most extensive phase of the investigation. In order to clarify the difference in design of the various types of liners used, Fig. a shows the profiles with the arrangement in which grinding balls of maximum size would lie on the face of the liners. The results with each type of shell liner in the primary mill are shown in Table I. Since most of the testing was done with

Jan 1, 1943

By GUY C. RIDDELL

THE recent purchase by an American investment trust of a substantial block of shares in a British owned Venezuelan copper operation directs attention to mining activities that have been quietly gaining momentum in that country for a number of years. We hear so much of oil work in Venezuela that attention to its metal-mining activities is in most quarters casual. In gold and copper the country has made some interesting mining records, and two of the old districts are ,digging in for a come-back. Copper Copper production centers in the state of Yaracuy. The Aroa-Cumaragua mining region has had a long and eventful history. The Aroa mine itself, 50 miles from the coast in West-Central Venezuela, was discovered in 1605. First mined in 1632, owned at one time by Simon Bolivar, it has been reopened many times and is now , the basis of substantial operations by the South American Copper Syndicate, Ltd. of London. The latter has operated the property profitably, off and on, for a number of years, paying heavy dividends on a small investment-at times over 300 per cent annually.

Jan 1, 1929

By D. M. Dunbar, H. C. SCHLILTZ

HE Chile Exploration Co.'s mine and reduction plant are at Chuquicamata, Chile, on the eastern edge of the Atacama Desert, 163 miles northeast of Antofagasta, 80 miles from the Pacific Ocean, and 70 miles from the Bolivian border and at an altitude of 10,000 ft. Guggenheim Brothers started prospecting in -4pri1, 1912, and purchased the main property, in October of that year; the property is now controlled by the Anaconda Copper Mining Co., which acquired it in January, 1923. The orebody strikes north 10" east, and has a dip of about 64" west. The length, as far as developed, is approximately 1% miles; the width averages sightless than mile.

Jan 1, 1925

By L. W. Kempf

THE thermal expansion characteristics of aluminum alloys have been examined by several investigators, among whom may be mentioned Shakespear,1 Schulz,2 Hidnert,3 Hidnert and Sweeney4 and McCullough.5 Shakespear compared the expansion of a series of aluminum alloys containing 14 per cent copper, with separate additions of about 1 per cent each of manganese, tin and zinc with that of pure copper. Schulz examined the expansion of aluminum and zinc and some aluminum-zinc alloys. Hidnert determined with a high degree of precision the expansion characteristics of pure aluminum, some aluminum-copper, aluminum-zinc, aluminum-silicon and some commercial alloys. Hidnert and Sweeney examined the expansion characteristics of aluminum-beryllium alloys. McCullough, by an interferometer method, determined the expansivity of some aluminum-copper, aluminum-magnesium, aluminum-iron, aluminum-nickel, aluminum-silicon and aluminum-manganese alloys. Incidental to an investigation carried out during the past six years and leading to the development and exploitation of an aluminum piston alloy of relatively low thermal expansivity, the expansion characteristics of a wide variety of alloys were examined. Some of the data which might be of general interest are gathered in this paper.

Jan 1, 1933

By E. L. Spain

The deposits described in this paper occur over much of Wayne County and in the southeast portion of Hardin County, Tennessee, and in the northeast and northwest portions of Mississippi and Alabama respectively. The presence of tripoli in this region has been known for some time and descriptions of various occurrences in Tennessee have been made by Jewelll and Miser2, while Hilgard3, Lowe4 and Logan5 have treated the deposits that occur in the adjacent portions of Alabama and Mississippi, but there has not been a 'general survey of the entire field summarizing completely the geology of the deposits with respect to their origin and stratigraphic relationships. During 1934, while engaged in surveys of mineral resources through this region for the Tennessee Valley Authority, the writer collected data with this in mind, and has assembled them in this report. He is indebted to H. S. Rankin and N. A. Rose, of the Tennessee Valley Authority Geology Division, for field assistance. Location of Tripoli Deposits Fig. 1 shows the locations of deposits of tripoli in a long belt that extends from northeast Wayne County southwestward into northwest Alabama and thence passes into Mississippi, where the formations carrying it are finally covered by Cretaceous sand and gravel of the Mississippian Embayment. Occasional deposits occur also in the southeastern corner of Hardin County, Tennessee. While tripoli is found at nearly all points along this axis where the related formations are exposed, the largest deposits are grouped about three different centers. Waynesboro-Collinwood District.—In the area between Waynesboro and Collinwood, in Wayne County, Tennessee, tripoli of various grades outcrops in the valley of Green River and in tributary valleys on either side. This district is roughly 12 miles long in a northeast-southwest direction and has a maximum width of 5 miles at its northern end. Exposures are found in road cuts, highway chert pits, in the beds of some of the streams, and on hillsides. The greatest number of high-grade

Jan 1, 1938

By E. L. Spain

The deposits described in this paper occur over much of Wayne County and in the southeast portion of Hardin County, Tennessee, and in the northeast and northwest portions of Mississippi and Alabama respectively. The presence of tripoli in this region has been known for some time and descriptions of various occurrences in Tennessee have been made by Jewelll and Miser2, while Hilgard3, Lowe4 and Logan5 have treated the deposits that occur in the adjacent portions of Alabama and Mississippi, but there has not been a 'general survey of the entire field summarizing completely the geology of the deposits with respect to their origin and stratigraphic relationships. During 1934, while engaged in surveys of mineral resources through this region for the Tennessee Valley Authority, the writer collected data with this in mind, and has assembled them in this report. He is indebted to H. S. Rankin and N. A. Rose, of the Tennessee Valley Authority Geology Division, for field assistance. Location of Tripoli Deposits Fig. 1 shows the locations of deposits of tripoli in a long belt that extends from northeast Wayne County southwestward into northwest Alabama and thence passes into Mississippi, where the formations carrying it are finally covered by Cretaceous sand and gravel of the Mississippian Embayment. Occasional deposits occur also in the southeastern corner of Hardin County, Tennessee. While tripoli is found at nearly all points along this axis where the related formations are exposed, the largest deposits are grouped about three different centers. Waynesboro-Collinwood District.—In the area between Waynesboro and Collinwood, in Wayne County, Tennessee, tripoli of various grades outcrops in the valley of Green River and in tributary valleys on either side. This district is roughly 12 miles long in a northeast-southwest direction and has a maximum width of 5 miles at its northern end. Exposures are found in road cuts, highway chert pits, in the beds of some of the streams, and on hillsides. The greatest number of high-grade

Jan 1, 1938

J. W. Tomlison—It seems probable that the author's conclusion, that the conductivity of the slags decreases with increasing content of FeO, is erroneous due to the method of plotting the data. Thus, the results of other workers2,3,13,15 show that the conductivity of molten oxide slags increase with increasing temperature, indicating that the trend of the curve shown by the authors is due to the fact that the data for the slags containing relatively small amounts of FeO are at higher temperatures than those for the slags containing relatively large amounts of this oxide. In this connection the work of Wejnarth2 may be mentioned in which in an investigation of a series of iron silicate slags, the conductivity was found to increase with increasing content of FeO; the fact that the author's slags contained TiO2 probably does not affect the issue since it has been shown15,16 that, at least as far as conductivity is concerned, this oxide behaves essentially the same as silica and that mixtures of the oxide with silica have a very low conductivity of the order of 10-4 mhos at 1750°C. In connection with the experimental technique it may be noted that bubbles of carbon monoxide would probably be produced at the surface of the graphite electrodes in contact with the melts thus rendering the accuracy of the measurements somewhat open to question. J. L. Wyatt (author's reply)—Dr. Tomlinson makes reference to works by Martin and Derge, which indicate that slag systems containing no TiO2 are characterized by an increase in conductivity with an increase in temperature. Further, I have cited his examples, which indicate a drastic increase with small temperature change. The results of Dr. Derge's work have no bearing whatsoever on the results of this paper, since the slags under study here contained up to 70 pct TiO2 One cannot generalize on slag systems as a whole on the basis of any one family, for there are definite compounds of ionic nature formed in each system, and the ionic mobilization of these is something that cannot be determined without actual experimentation. Dr. Tomlinson makes reference to an unpublished work which, he claims, shows that titanium dioxide behaves the same as silica in regard to conductivity. Since I have not had 'an opportunity to see the paper I cannot make any comments, but unless the same slag system was studied there can be no specific comparison of results. If the decrease in conductivity of the slag was due entirely to temperature phenomena, as Dr. Tomlinson indicates, then one is without an explanation of the values shown in the paper for slags containing from 10 to 20 pct FeO. I cannot agree that the deviation in findings was appreciably related to temperature change; further, I believe this point was completely covered in the paper. References 13 Endell and Hellbrügge: Glasstech. Ber. (1942) 20, 277. 14 Bockris, Kitchener, Ignatowicz and Tomlinson: Faraday Society. Discussion (1948) 4, 265. 15 Tomlinson: Thesis, London 1949. 10 Bockris, Kitchener, Ignatowicz, and Tomlinson: Unpublished work.

Jan 1, 1951

By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat' has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. 'The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953

By Ralph Sherman

IN these days of intense competition for the domestic fuel market much is heard of the low efficiencies with which solid fuels, and most particularly bituminous coal, are burned in domestic heating equipment. In contrast to the every-day operating efficiencies of 85 and 90 per cent in large, central, electric-generating stations, efficiencies of 50 per cent and lower are cited for the hand-fired home furnace. Just as the miles per gallon of gasoline is only one of the factors that determine the cost of operation of an automobile, so the thermal efficiency is only one factor in the cost of domestic or other heating. The purpose of this paper is to analyze the total costs of domestic heating by various fuels and types of equipment, to determine the relative importance of efficiency and other factors, and to discuss what this signifies relative to the future of the use of fuels in the home.

Jan 1, 1933

By C. W. Allen, B. D. Cullity, H. S. Choi

The torsional deformation of aluminum and magnesium crystals is investigated, with particular reference to the dependence of proportional limit on crystal orientation. The proportional limit is found to be governed by the average value of the resolved shear stress on the most highly stressed slip systems, but the proportional limit does not strictly obey a critical-resolved-shear-stress law. The behavior of a cylindrical single crystal stressed in tension is well known: plastic flow begins when the resolved shear stress on the most highly stressed slip system reaches a critical value. There is much less understanding of the effect of torsion on such a crystal and on the way in which the critical-resolved-shear-stress law should be applied to torsional deformation. In the present paper particular attention is paid to the dependence of plastic yielding on crystal orientation and lesser attention to the mechanism of flow after yielding has occurred. New work on aluminum and magnesium crystals is presented, and previous results obtained in this laboratory on magnesium1 are re-examined. STRESS DISTRIBUTION The problems involved in torsional deformation of single crystals are due entirely to the complexity of the stress distribution. In tension, if loading conditions are perfect, the shear stress on any particular slip plane is completely uniform over the entire area of that plane. In torsion, on the other hand, the stress on any selected plane in a particular direction varies not only from center to edge of the specimen but also around its perimeter. It is convenient to express the stress at any point in terms of t0, which is the shear stress acting at the surface of a cylindrical specimen on a plane normal to the axis and in a direction tangential to the cylinder. At point P of Fig. 1 this stress acts in the direction of axis 2 and is given by To = 2T/pr3 [1] where T is the applied torque and r the specimen radius. This stress can be resolved on any chosen slip system, and details are given in the Appendix. Let P be the point on the specimen surface where the stress is to be evaluated; P is defined by its angular distance A from an arbitrary reference line through 0 normal to the axis. his line is usually taken as the direction of incidence of the X-ray beam used to determine the crystal orientation.) Then the shear stress t, acting at P in direction Dona plane whose normal is N is given by Ts/TO = sin ? 0, cos ?d sin (?0, - ?) + cos ?, sin ?d sin (?d - ?) [2] where 0, and Od are the angles between N and D, respectively, and the axis, ?0 and ?d are the angles between the projections of N and D, respectively, on the transverse plane and the reference line through 0. By means of Eq. [2], the stress 7, acting in any given slip direction can be computed. In the previous work on magnesium1 only gross slip tangential to the specimen surface was considered, and this

Jan 1, 1963

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation' can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation' in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

By C. C. Hawes

SILICA is the main impurity in iron ore. It is intimately associated with the iron oxide, sometimes free but more often in the combined state, as a mineral silicate. Its separation and purification sometimes present difficult problems to the analyst. In the absence of any definite knowledge to the contrary, orthosilicic acid. H4SiO4, is supposed to be the only silicic acid made, all other forms, such as metasilicic acid, H2SiO3, representing different degrees of its dehydration. These acids are exceedingly weak but form the most stable compounds found in nature. They are known as the silicate minerals and are formed by the combination of the different metallic oxides

Jan 1, 1936

W. S. GRESLEY, Erie, Pa.: Mr. Henrich's Fig. 1 and reference thereto remind me of a section of sand, gravel, clay, etc., which I sketched near Hellesylt on Stor Fjord, Norway, some years ago. Vertical Section of Glacial Morainic Material, containing Angular Masses of Banded Sand. Observed June 29, 1887, about 14 English miles south of Hellesylt, at head of Stor Fjord, near Aalesund, Norway. The accompanying figure reproduces my sketch. It was the angular and tilted blocks of sand in this glacial débris, or moraine, that particularly attracted my notice. The sand was moist; and I could only account for the phenomenon of blocks of sand

Jan 1, 1897

By K. P. Chong

Introduction One of the requirements of processing oil shale or other energy bearing rocks is to optimize particle sizes and permeability distributions in fragmentations as indicated by Hommert (1984). Basic to the understanding and planning of in situ fragmentation and ex situ mining of oil shale are the mechanical properties. During the past six years, an innovative and unique program was established by Chong et al. (1979, 1980a, 1980b, 1982a, 1982b) that developed an efficient methodology for standardized and simplified mechanical testing of the western oil shale. The experiments include precise, representative, and duplicable sample preparation; uniaxial static compression testing; "modified" split cylinder testing; uniaxial creep and relaxation testing under extended periods of time; dynamic testing with varying strain rates; and 3-D constitutive relationships. However, as far as the fracture mechanics is concerned, as Edl (1980) pointed out, there is still a lack of understanding "of the fundamental explosive rock breakage mechanisms," which "has necessitated extensive reliance on very costly empirical approaches." Fracture mechanics of rocks and oil shale (Costin, 1981; Schmidt, 1977; Abou-Sayed, 1977; and Barker, 1977) has been based on conventional fracture mechanics using regular notched samples with limited variations of oil yields and assuming the material to be isotropic and elastic (Kobayashi, 1975; Caddell, 1980). A cylindrical double cantilever beam (DCB) specimen with a "V" slot, known as a short rod specimen, has been used by Barker (1977) to determine fracture toughness of rock materials. The inherent geometric stability of the reinforced DCB specimen makes it suitable to be used with all brittle materials. Due to its remarkable stability for the initial crack growth, the DCB specimen can be used for dynamic fracture toughness testing as well. This specimen is more suitable for the evaluation of fracture toughness at high strain rates than most other fracture specimens. However, Barker's DCB specimen is not very well adaptable for short cores or layered rocks since the specimen contains numerous layers (say in a 100-mm (4-in.) long specimen), and the rock properties change from layer to layer. Schmidt (1977) studied the fracture mechanics of oil shale with two oil yields, using notched beams. Using several independent established testing methods, Costin (1981) pioneered the investigation of the static

Jan 1, 1986