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By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By Maynard H. Jameson

Earlier investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.l The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,' and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. Theory Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredgea determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities PO, p1, and p2 are involved, and the source I is located at the interface of the media Coo) and (p1). The perpendicular depth of the lower interface is h, 0 is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: EvEn Odd Ta — R r1 - [rl] - [RS + 4h(h + R sin 01½ r, = [r] =. [R1 + 4h cos 0)2(h + -R sin 0)1½ ri - [r3] ={r3} [R* + 4h(4 cos2 0 - i)1 (h + R sin 0)l½ r4 = [r4] = [R2 + 4h(4 cos $ cos 30)1 (h + R sin 0)]½ r, — [r4] - [R2 + 4h(4 cos9 R cos 20 + cos 48)2 (h + R sin 01½ I RI + 4h[2 cos 30(4 cos2 0 - I)12 (h + R sin 8)1 ½ rn - [r4] - [R2 + 4hlf(cOs 0)18(h + R sin R)l½ As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is 0, the angle measured from the horizontal to the first image is 28; to the second image it is 48, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1946

By T. Cantwell, N. C. Rasmussen, H. E. Hawkes

Beryl is a mineral that may be difficult to distinguish from quartz by casual field inspection. The easily recognized green color and hexagonal crystal form of coarse-grained beryl are by no means universal, even in beryl from pegmatitic deposits. If it occurred as a fine-grained accessory mineral in an igneous rock, it would almost certainly escape detection unless samples were submitted for petrographic or chemical analysis. There may be substantial deposits of some beryllium mineral, other than beryl, that has been overlooked because that mineral also closely resembles the common rock-forming minerals. A reliable and simple method of identifying beryllium minerals and determining the beryllium content of a rock would be helpful in exploration. This article describes preliminary experiments in applying nuclear reaction to the qualitative identification of beryl and to the semiquantitative determination of the beryllium content of rock samples. Gaudin,1,2 the first to apply a nuclear reaction in detecting beryllium minerals, developed a method that irradiates the sample with gamma rays, which react with beryllium nuclei to produce neutrons. The neutrons are then measured with standard equipment. The cross section for this reaction is about 1 millibarn. The cross section is a measure of the probability that a reaction will take place, for example, between a beryllium nucleus and an incident gamma ray or alpha particles.3-5 At 1-millibarn cross section for the reaction, satisfactory performance required a source strength of the order of 1 curie (3.7 x 10"' disintegrations per sec, where each disintegration releases one or more gamma rays). The reactions will not take place if the gamma radiation is below a minimum energy, in this case 1.63 mev. The size of the source and the energy of the radiation made heavy shielding necessary for these experiments, both to reduce the background count of the neutron counter and to safeguard personnel. The original discovery of the neutron by Chad-wick in 1932 resulted from experiments with another nuclear reaction, induced by bombarding beryllium with alpha particles in which the products are carbon-12 and neutrons. The equation for this reaction is as follows:' " ,Be" + ,He'? 6C12 + 8,n' [1] re-particle neutron In the above nuclear equation (Eq. 1), the sub- script number indicates the number of protons in the nucleus (the atomic number) and the superscript the total number of neutrons and protons (approximately the atomic mass). For the alpha-neutron reaction the cross section is about 250 milli-barns, or 250 times that of the gamma-neutron reaction used by Gaudin. The positively charged alpha particle is repelled by the positive charge of the beryllium nucleus; it must, therefore, have a certain minimum energy in order to approach close enough to the beryllium nucleus to react. For reaction with the beryllium nucleus, the lower limit of the alpha-particle energy is 3.7 mev. The alpha-neutron reaction, with polonium-210 as an alpha source, was selected for the present experiments. Alpha particles are emitted by polonium-210 at 5.30 mev, which is adequate for the reaction with beryllium. Furthermore, this isotope of polonium emits alpha particles with negligible associated gamma radiation, thus eliminating the necessity of shielding. The half-life of polonium-210 is 138 days. Inasmuch as alpha particles carry a possible charge and are large compared with most nuclear particles, their energy is rapidly dissipated in passing through matter. Their range in standard air is 3.66 cm,3 and they penetrate only a few tens of microns into a mineral sample. The short range in air can be minimized by preparation of a flat sample surface that can be brought very close to the alpha source during analysis. On the other hand, short range of alpha particles in air lessens the radiological health hazard and makes it possible to use this method without shielding. It must be emphasized, however, that the alpha emitters are potentially very dangerous if they enter the human body. Polonium must be handled with extreme caution. The literature has reported experiments on the yield of neutrons from reaction of alpha particles with beryllium nuclei. Feld" reports that in intimate mixtures of polonium and beryllium, 3 x 106 eutrons per sec are produced per curie of polonium. Elsewhere in the same reference it is stated that a sandwich-type source yields about one third as many neutrons as an intimate mixture. A table of neutron yields for full energy polonium alpha-particles on thick targets as reported by Anderson7 is the basis of Table I. From Table I it can be deduced that the elements most likely to interfere, i.e., those that also produce neutrons when bombarded by alpha particles, are boron and fluorine. These data also show that it will probably not be possible to determine very small quantities of beryllium in rocks because of the masking effects of the major elements, sodium, magnesium, and aluminum. The neutrons emitted in the alpha reaction are detected by another nuclear reaction. Either of the

Jan 1, 1960

By J. P. Hammond, C. J. McHargue

The wire textures for cold rolled and recrystallized iodide titanium and the sheet textures for this material produced by cold and hot rolling, and recrystallization at a series of temperatures were determined. &apos;The effect of the a + ß transformation on the sheet texture was noted. UNTIL recently it was believed that all hexagonal close-packed metals deformed by slip on the basal plane, (0001), and that rolling should tend to rotate this slip plane into the plane of the rolled sheet. The pole figures of cold rolled magnesium&apos; are satisfactorily explained on this basis. There is a tendency for the <1120> directions to align parallel to the rolling direction, and the principal scatter is in the rolling direction. Zinc% as a rolling texture in which the hexagonal axis is inclined 20" to 25" toward the rolling direction. Twinning is believed to account for the moving of the basal plane away from parallelism with the rolling plane. The texture of beryllium3 places the basal plane parallel to the rolling plane with the [1010] direction parallel to the rolling direction, and the scatter from this orientation is primarily in the transverse direction. Cold rolled textures reported for zirconium&apos; and titanium5 how the [1010] directions to lie parallel to the rolling direction and the (0001) plane tilted by approximately 25" to 30" to the rolling plane in the transverse direction. Rosi has recently reported that the mechanisms for deformation in titanium are distinctly different from those commonly reported for hexagonal close-packed metals. The principal slip plane is the prismatic plane, {1010), with some slip also occurring on the pyramidal planes, (1011). However, there is no evidence for basal slip. The slip direction is reported to be the close-packed digonal axis, [1120]. In addition to the twin plane commonly reported for metals of this class, {1012), Rosi found the twin planes (1122) and {1121), with the dominant twin plane being (1121). Information regarding the recrystallization and hot rolling textures of hexagonal close-packed metals is limited. Barrett and Smigelskas report that rolling beryllium at temperatures up to 800°C and recrystallization at 700°C produce textures not differing from the cold rolled sheet texture.3 McGeary and Lustman find that hot rolling at 850°C produces the same basic texture in zirconium as rolling at room temperature.&apos; These investigators also report that the texture for sheet zirconium recrystallized at 650 °C differs from the cold rolled orientation inasmuch as the [1120] direction, instead of the [1010] direction, is parallel to the rolling direction. In the case of titanium, it is not possible to deduce which direction is preferred in the recrystallized state from the pole figures presented by Clark." The purpose of this paper is to report an extensive investigation of the preferred orientations in iodide titanium. Since the deformation mechanisms for titanium are different from those commonly given for hexagonal close-packed metals, it is not surprising to find distinct differences between the textures of titanium and other metals of this class. Materials and Methods This investigation was carried out on iodide titanium obtained from the New Jersey Zinc Co. with an analysis as follows: N2, 0.002 pct; Mn, 0.004; Fe, 0.0065; A1, 0.0065; Pb, 0.0025; Cu, 0.01; Sn, 0.002; and Ti, remainder. The crystallities of titanium were broken from the as-deposited bar and melted to form 20 g buttons on a water-cooled copper block in a vacuum arc-furnace. Hardness tests conducted on the material before and after melting differed by only two or three Vickers Pyramid Numbers, indicating no or insignificant contamination. The buttons were hot forged, ground, and etched to sizes and shapes suitable for the rolling schedule, and vacuum annealed at 1300°F. Specimens for determination of the wire textures were reduced 91 pct in diameter to 0.027 in. in 24 steps using grooved rolls. In order for the orientation of the central region to be studied, portions of these wires were electrolytically reduced to a diameter of 0.005 in. using the procedure described by Sutcliffe and Reynolds.&apos; The sheet textures were determined on titanium cold rolled 97 pct to a thickness of 0.005 in. A reduction of approximately 10 pct per pass was used, and the rolling direction was changed 180" after each pass. Specimens used for determination of the recrystallized textures were annealed in evacuated quartz tubes at 1000°, 1300°, and 1500°F. The grain size of the 1000°F specimen was sufficiently small to give satisfactory X-ray patterns with the specimen stationary. However, it was necessary to scan the surface of the other recrystallized specimens. The microstructure of each annealed specimen was that of a recrystallized material. The diffraction rings all showed the break-up into spots typical of recrystallized structures.

Jan 1, 1954

Here are the details . . . . . of how a $2.5 million research gamble, now backed by five years of intensive development in cooperation with the Chemical Construction Corp. resulted in a hydrometollurgical process that yields pure metal powders from sulphide concentrate - a process that offers potential savings of $2.5 million a year.

Jan 6, 1953

By D. E. Norquist, J. E. Moeller

The results of wear on marked balls, 4, 31/2, 3, and 2 in. diam are given. All balls were forged steel of practically the same chemical analysis and hardness. The results indicate that balls in a given mill for a given length of time will have equal diameter losses, regardless of size.

Jan 6, 1950

By I. L. Dillamore

I. L. Dillamore (University of Birmingham)—The different textures developed in various fcc metals have long awaited satisfactory explanation and it has now become clear that these differences are related to parallel differences in the deformation characteristics of the metals. Liu is correct, therefore, in seeking to account for the observed textures in terms of the flow mechanisms but I believe, for the reasons outlined below, that the particular interpretation of flow mechanisms proposed by Liu is open to substantial objections. By considering the forty-eight possible designations of the twelve octahedral slip systems found in fcc metals as distinct and separate deformation modes, Liu has fallen into the error of assuming that only positive glide dislocations associated with each system are present. In fact both positive and negative dislocations will be present and the only difference between for instance the systems B4 and B4&apos; (in Liu&apos;s notation) is that under a stress of given sign the direction of motion of a dislocation is reversed on changing from B4 to B4&apos;. For both orientations positive and negative dislocations will be present. In considering possible dislocation interactions it is, therefore, inadmissible to differentiate between R4 and R4&apos; as Liu does. Liu considers those dislocation interactions which give the biggest reduction in energy to be the most favorable and neglects, on the grounds that they will form strong barriers to slip, interactions between dislocations with perpendicular Burgers vectors. Setting aside interactions between positive and negative dislocations of the same slip system, which must occur regardless of the combination of slip systems chosen, the biggest reduction in energy occurs for the Lomer-Cottrell interaction and it is Lomer-Cottrell barriers which are thought to provide the stronger dislocation obstacles. On the other hand the intersection of dislocations with perpendicular Burgers vectors is thought to be a low-energy process which contributes only a fairly small temperature-dependent part of the total work hardening. On this basis it seems doubtful whether the reduction in energy through possible dislocation interactions provides a reasonable criterion for choosing the operative slip systems. From the point of view of texture development it is unsatisfactory to ignore the slip rotations leading to an end position and to neglect to consider the stability of the chosen end point. It is also unsatisfactory to treat the two stress axes as interchangeable since, if the stress system is idealized as biaxial, one stress is compressive and the other is tensile. For the same reason the rotations of the two stress axes are not made compatible simply by assuming that the same slip directions are responsible for the rotations of the two stress axes. It is, in short, essential to treat the two stress axes as acting together on the same slip systems. Turning to the question of the difference between the copper-type and the brass-type texture, there now remains little doubt that the difference is attributable to differences in stacking-fault energy (y), as noted by Liu, but it is doubtful whether the temperature dependence of the texture in copper and in silver is due to increasing stacking-fault energy with increasing temperature. The results of Swann and Nutting42 cited by Liu were obtained in Cu-A1 alloys and the apparent increase in stacking-fault energy on raising the temperature may be influenced by short-range ordering. In pure metals such effects are absent and the only data available on the variation of y with temperature are those of Buhler et a1.43 for silver. They report a minimum at 200°C which does not fit the hypothesis put forward by Liu. It is much more likely that thermal activation of cross slip is important in determining which texture develops, as proposed by Dillamore and tors. These workers have proposed an explanation for the differences in observed texture among the fcc metals and the pole figures predicted consist of an orientation spread which is in better agreement with observation than the limited number of discrete orientations suggested by Liu. The theory of Dillamore and Roberts is also able to account for the differences between aluminum and copper which Liu still leaves unexplained. Y. C. Liu (author&apos;s veply)—The writer appreciates the interest of Dr. Dillamore, but must discuss some of his comments in order to avoid cross purposes. The phrase, "forty-eight slip systems," which appeared twice in the text—in the caption of Fig. 1 and the first paragraph in the Discussion—might unfortunately have led Dr. Dillamore to disagree

Jan 1, 1965

By R. T. Hukki

John F. Myers (Consulting Engineer, Greenwich, Corm.)—Since the art of comminution has lain practically dormant for many years, it is very interesting that R. T. Hukki approaches the subject with a new concept. One is reminded of the research carried on by A. W. Fahrenwald of Moscow, Idaho, a few years ago. Fahrenwald mounted a steel bowl on a vertical shaft. The balls and ore placed in the bowl were rotated at fast speeds, thus simulating the supercritical speeds used by Hukki. The rolling action of the balls against the smooth shell liner has pretty much the same effect. The action is horizontal in one case and vertical in the other. Both researchers report good grinding activity. It is also constructive that such able investigators give to the students of comminution their interpretation of their laboratory results in terms of large-scale operation. History shows that it takes a lot of time for such radically new ideas to be absorbed by the industry. Typical of this is the present-day activity of cyclone classification in primary grinding circuits. The idea of cyclone classification has been kicking around for 30 or 40 years. Certainly we all suspect that the ponderous grinding mills of today, and their accessory apparatus, large buildings, etc., will ultimately give way to small fast units, just as this has occurred in other industries over the past 50 years. At the moment there is no evidence that ball and liner wear is prohibitively high. In fact, at the time Fahrenwald was demonstrating his high-speed horizontal machine at the meeting of the American Mining Congress, several years ago, he assured this writer that the balls retained their shape much longer than they do in conventional tumbling mills. Rods and balls that slide (as some operators in uranium plants are experiencing) get flat. Apparently the balls have a rolling action. Mr. Hukki&apos;s references to the processing capacity of the Tennessee Copper Co. mills is adequate. Those studying this subject will be greatly interested in the paper presented by Richard Smith of the Cleveland-Cliffs Iron Co. at the annual meeting of the Canadian Institute of Mining and Metallurgy in Vancouver April 24, 1958. This paper will be published during the latter part of 1958 in the Canadian Institute of Mining and Metallurgy Bulletin. Hukki&apos;s pioneering spirit is to be commended. R. T. Hukki (author&apos;s reply)—It has been heartening to read the objective discussion by J. F. Myers. The sincerity of his opinions is further strengthened by the fact that the article he has discussed contradicts in a major way the parallel achievements of his life work. Myers is right in his opinion that in general it takes a long time before new ideas are accepted by the industry. On the other hand, revolutions usually take place at supercritical speeds. There are many indications at present that both the unit operation of grinding and the related subject of size control are now just about ripe for a revolution. In grinding, brute force must ultimately give way to science. Rapid progress can be anticipated in the following fields: 1) Autogenous fine grinding at supercritical speeds will be the first advance and the one that will gain recognition most easily on industrial scale. At this moment, little Finland appears to be leading the world. Crocker recently made a statement that in nine cases out of ten, your own ore can be used as grinding medium more effectively and far more economically than steel balls. This is true. The present author would like to introduce a supplementary idea: In eight cases out of the nine cited above, it can be done at the highest overall efficiency in the supercritical speed range. Fine grinding must be based on attrition, not impact. The path of attrition may be vertical, horizontal, even inclined. 2) In coarse grinding, the conventional use of rods is sound practice. However, even the rods can be replaced by autogenous chunks large enough to offer the same impact momentum as the rods. To obtain the momentum, the chunks must be provided with a free fall through a sufficient height in horizontal mills operated at supercritical speeds. Coarse grinding must be based on impact. Detailed analysis of the subject may be found in a paper entitled "All-autogenous Grinding at Supercritical Speeds" in Mine and Quarry Engineering, July 1958. 3) All conventional methods of classification, including wet and dry cyclones, are inefficient in sharpness of separation. Continuous return of huge tonnages of finished material to the grinding unit with the circulating load is senseless practice. In the near future the present methods will be either replaced or supplemented by precision sizing. These three fields are also the ones to which J. F. Myers has so admirably contributed in the past. Fine Grinding at Supercritical Speeds. By R. T. Hukki (Mining EnGineERInG, May 1958). Eq. 9, page 588, should be as follows: T , c, (a — 6&apos;) n D Ltph On page 584 of the article the captions for Figs. 4 and 5 have been placed under the wrong illustrations and should be interchanged.

Jan 1, 1959

DeLamar, the largest silver mine in the United States outside the Coeur d’Alene District in Idaho, came into production in April 1977. It is a joint venture of Earth Resources Company and Canadian Superior Oil Co., with Earth Resources being the operator. The property is a consolidation of several old operations dating back to the 1800s; the better known of these are the DeLamar and Sommer-camp mines. DeLamar is situated in southwestern Idaho near the Oregon border in the Owyhee Mountains, 88 km (55 miles) southwest of Boise, Idaho. Heavy snowfalls and very low temperatures are common in the wintertime. Planned production was 77,500 kg (2.5, million oz) of silver and 5 13 kg (16,500 oz) of gold per year. Expected life at a milling rate of 1,540 mtpd (1,700 stpd) was 20 years, with an ore grade of 144 g Ag and 1.58 g Au per mt (4.2 oz Ag and 0.046 oz Au per st). Present production is at the rate of 1,900 mtpd (2,100 .stpd). The total cost to bring the mine into production was reported to be approximately $22 million, and the mill was reported to have cost about $10,000 per daily ton of design capacity. At DeLamar, naurnanite (Ag2Se) is the principal silver .mineral occurring with acanthite (Ag2S) disseminated through quartz veins and a silicified rhyolitic ash-flow tuff of Miocene age. The mineralization is relatively iron and manganese free and is readily amenable to cyanidation giving recoveries of 85% silver and 92% gold, which occurs free. When the plant was started, considerable difficulties were encountered in handling the wet sticky ore because of the high clay content. Following primary crushing, the ore is stockpiled. Due to the sticky nature of the ore, the vibrating feeders initially installed under the stockpile were replaced by a reclaim hopper and an apron feeder which was fed 24 hours a day by a front-end loader. The minus 200 mm (8 in.) ore is fed to a 5.5 m by 2.75 m (18 ft by 9 ft) autogenous mill followed by a 2.75 m by 4.57 m (9 ft by 15 ft) ball mill and cyclones. The mills are equipped with 750 kw and 520 kw (1,000 hp and 700 hp) motors. Both mills discharge to the same cyclone feed sump and a portion of the cyclone underflow is returned to the autogenous mill. Cyclone overflow, which is 20% plus 74 microns (200 mesh), is leached in four agitators in series for 72 hours (45 hours at the 2,100

Jan 1, 1981

By E. R. Brownscombe, Francis Collins

The pressure distribution in a reservoir producing an incompressible fluid by radial flow in a horizontal structure is a simple logarithmic function&apos; used daily by reservoir engineers. The assumption of an incompressible liquid is equivalent to assuming that pressure is maintained constant at the well radius and at some external "radius of drainage," or, in other words, that the entire flow into the well passes across the external radius. In most cases a well is surrounded by other wells draining adjoining areas so that the "radius of drainage" is not a line of constant pressure with flow equal to the flow into the well but rather a contour of zero pressure gradient across which no flow occurs, production being due to the expansion of the liquid within the area. The radial flow steady state pressure distribution for this case does not seem to be extensively used despite the fact that the mathematical analysis has been given in detail&apos; and the results are simple and generally applicable. &apos;The object of this discussion is to develop this result from a physical rather than a mathematical viewpoint, thereby aiding intuition in judging circumstances to which it may be applicable. If the production rate at a well in an unsaturated reservoir is maintained constant while no flow occurs across the outer radius a steady state will soon be reached in which the flow rate or pressure gradient is constant with time at all points in the reservoir. To preserve such a condition it is necessary that the pressure decline at the same rate at all points in the reservoir, that is, the curves of pressure versus radial distance at successive times are all parallel. Then each unit volume of oil is expanding at the same rate and contributing an equal share to the production. The rate of flow q across any circle r is thus proportional to the volume of the reservoir between r and the external radius re, or q = qw (I-r2/r2e) ......(1) where q, is the production from the well and it is assumed that rw is very small compared with re. This equation can be combined with the differential form of Darcy&apos;s law for radial flow, 2phkr dp q =—— ........(2) aµß dr ( where q is not a constant as in the incompressible flow case but is a function of r given by Equation (1). If Equation (1) is substituted in Equation (2) the variables p and r can be separated and the result integrated to obtain the pressure distribution p = pw +--------In------------- 2pkh[ rw 2re2] ......(3) This equation differs from the incompressible case only in the addition of the term proportional to the square of the radius

Jan 1, 1950

By A. J. Shaler

The subject of the mechanism of sintering has received much attention in the past few years, particularly since the beginning of the series of AIME seminars in powder metallurgy of which this paper introduces the fourth. In the first of these, F. N. Rhines1 brought together and discussed the available experimental data on the sintering of pure metallic powder, and succeeded in bringing to a sharp focus the attention of workers in this field on the established observations which a satisfactory theory must explain. Several other authors3,5,6 have, in the last few years, studied the phenomena that occur when cold metallic powders, loose or in the form of compacts, are first brought to elevated temperatures. Some workers&apos; in the field of friction have recently studied the adhesion of solid metal surfaces when they are brought into close contact. These researches have indicated that several separate mechanisms operate simultaneously, at least during the first part of the sintering process. Some of them have been called transient mechanisms4 because they are in general not absolutely necessary to sintering. Powders may be so prepared and so treated that these transient phenomena do not take place during subsequent sintering. This does not mean, of course, that their industrial and scientific importance is any less than that of the steady-state phenomena. The latter are changes that go on during sintering no matter how the powders are made or treated; they cannot be divorced from sintering. One way to analyze the process of sintering into its component parts is perhaps to distinguish between these transient and steady-state phenomena. Some of the transient phenomena have been studied in the past few years. Huttig3 has shown that, when the temperature of metallic powder is slowly raised, the following events generally occur in order: (1) physically adsorbed gases are desorbed; (2) there is an atomic rearrangement of the surface, a sort of two-dimensional "surface-reciystallization"; (3) there is a breakdown of chemically adsorbed surface compounds; (4) there is a recrystalliza-tion in the volume of the metal. All these changes are shown by Huttig and his coworkers to be completed fairly rapidly at lower temperatures than those generally used in sintering and are therefore not a part of the mechanism whereby the density of a mass of powder continues to change after long heating at an elevated temperature. But the first and third of these changes release gases in quantities which may or may not help to control the steady-state mechanisms, depending on when the voids become isolated from the outside of the compact. Among the phenomena studied by Steinberg and Wulff,8 there is the effect on sintering of residual stresses arising from the pressing operation. They found that the lateral surfaces of a green compact of iron are under a longitudinal residual tension-stress of the order of magnitude of half the yield-point for solid iron. If the outside surface is in tension, the core must be under longitudinal compression. When the compact is heated, the surface residual stress is thermally relieved first, and the compact therefore initially expands in the direction of its axis. This is a transient phenomenon, if for no other reason than the possibility of sintering unpressed powders, as demonstrated by Delisle,9 Libsch, Volterra and Wulff10 and others.1 The subject of recrystallization is dealt with further in a separate section, in view of its prominent place in sintering literature. It, too. is one of these transient phenomena. Among the steady-state parts there may be distinguished the attraction between particles and its consequences, the spheroidization of voids in the compacts, and the densification or swelling of the compact. There is considerable evidence4,7 showing that cold metallic surfaces, when brought to within a few interatomic distances of one another, are attracted to each other by forces of the order of many thousands of pounds per square inch. A calculation, discussed in greater detail in another section, shows that this force changes but slightly when the temperature of the surfaces approaches the melting point. Actual measurements of forces of adhesion of this magnitude have been made by Bradley12 on some nonmetals, but none has yet been made on cold or hot metals. This force is of sufficient magnitude to cause some plastic deformation in powder compacts, as will be shown below. A second force of steady-state nature is due to the surface tension, which probably has the same origin as the force of attraction between surfaces.164 A paper by Udin, Shaler, and Wulff1,3 gives the results of precise direct measurements of its value for solid copper. The demonstration of the tendency for the surface tension to shrink a pore was long ago given by Gibbs.17 He showed that its effect on a curved surface between two phases is equivalent to a pressure perpendicular to that

Jan 1, 1950

By A. Aly Selim

A computer model was developed to calculate the fragmentation cost for in situ leaching operations as a function of the blast design and deposit parameters. The model is based on blasting an ore zone only or an ore zone plus overburden by either a coyote blast or a vertical blasthole system. The model calculates the blast design parameters and the fragmentation cost based either on a user input powder factor value or on a powder factor calculated by the model as a function of the overburden height and the ore zone thickness. Examples of blast design parameters calculated by the model are the number and spacing of blastholes for a vertical blasthole system and the number and spacing of crosscuts for a coyote system. The model also calculates the total amount of explosives, the detonating cord length, and the number of primers. The cost of blasthole drilling can be calculated by the model based either on purchasing and operating a drill or on a user input value of the contracted cost of drilling. Application of the model to an example ore deposit showed that the vertical blasthole systems were more economical than the coyote system when there was no overburden and the deposit had an average ore thickness less than 45 meters. With no overburden and ore thickness greater than 45 meters, the vertical blasthole system was either more or less expensive than the coyote system depending on the number of levels used in the coyote system. With overburden, the coyote system was less expensive than the vertical blasthole system for blasting either the ore only or the ore plus the overburden. A coyote blast will usually produce larger particle sizes than a vertical blasthole system. Larger particle sizes can result in lower copper recoveries so that a less expensive coyote blast may not improve the overall economics of an in situ leaching operation. Blasting the ore zone only was generally less expensive than blasting the ore plus the overburden by either blasting system. Also, for the example considered, the coyote system costs were less sensitive to changes in overburden thickness and powder factor while the vertical blasthole system costs were less sensitive to changes in ore thickness.

Jan 1, 1977

By Willard Jillson

WITHIN the last ten years Kentucky has become celebrated for its low-sulfur bituminous coals. Prior to this time, many investigators had discovered the abundance of this coal but the fact was unknown to the general public until the last extension of Kentucky&apos;s mountain railroads was completed. The coals of Kentucky are, broadly, separated into two geographic units-the eastern and the western coal fields. On a basis of their sulfur content these coal fields fall into three units, which are indicated on the accompanying map, by numbers, 1, 2, and 3. The area marked 1, the very southeastern part of the State, shows the lowest sulfur, all coals being averaged. In this field the maximum is 1.04 per cent. and the minimum as low as 0.68 per cent.-both averages and not individual analyses, which would of course show much greater variation. Included in this group are the following counties: Lawrence, 0.87 per cent.; Martin, 0.75 per cent.; Johnson, 0.73 per cent.; Magoffin, 0.S7 per cent.; Floyd, 0.88 per cent.; Pike, 0.68 per cent.; Knott, 1.04 per cent.; Perry, 0.77 per cent.; Letcher, 0.80 per cent.; Leslie, 0.70 per cent.; Harlan, 0.79 per cent.; Knox, 0.86 per cent.; and Bell, 0.92 per cent. The total average sulfur content for these thirteen counties is 0.82 per cent. Bordering the restricted low-sulfur field of eastern Kentucky is the No. 2 belt (slightly darker), which is commonly known as the western border of the eastern coal field. Here the maximum sulfur is 2.91 per cent. and the minimum 1.05 per cent. Again these are averages and not individual analyses. The counties in this group are: Greenup, 2.60 per cent.; Boyd, 1.67 per cent.; Carter, 1.07 per cent.; Morgan, 1.40 per cent.; Wolfe, 1.83 per cent.; Lee, 2.93 per cent.; Breathitt, 1.85. per cent.; Owsley, 1.09 per cent.; Jackson, 1.06 per cent.; Rockcastle, 2.30 per cent.; Clay, 1.09 per cent.; Laurel, 1.08 per cent.; Pulaski, 2.24 per cent.; Whitley, 1.05 per cent.; McCreary, 1.50 per cent.; and Wayne. The sulfur percentage average for this area including fifteen important counties is 1.65 per cent.

Jan 9, 1919

By Edward Hart

Having occasion several years since to make ferrous sulphide, I attempted to do so by fusing a mixture of coal-brasses (FeS2) and dried ferrous sulphate. A very nice-looking sulphide was obtained; but on attempting to use it, I found that it was insoluble in dilute hydrochloric and sulphuric acids. The subject was laid aside at the time, but has since been taken up; and some curious results have been obtained, which I believe are new. I have made the material by all of the following methods and the product seems to be pretty much the same, however obtained : (a) FeS2 heated to fusion. (b) FeS2, and FeSO4 heated to fusion. (c) FeS2, and Fe2O3 heated to fusion. (d) FeS2, and FeCO3, heated to fusion. (e) FeSO4, and S heated to fusion. (f) Fe2O3 and S heated to fusion. Obtained in this way the mass after cooling breaks easily and is very nearly black in color. On the upper surface of the fused cake the color is generally reddish or brownish black. When this is treated with dilute sulphuric or hydrochloric acid, it refuses to dissolve; but if touched with the point of a file or any piece of wrought-iron, solution of the sulphide takes place with the evolution of sulphuretted hydrogen. If the iron is removed the evolution of gas ceases, and only begins again when the iron is again brought into contact with the fused sulphide. The same thing happens if the iron is connected with the sulphide by means of a platinum wire. But in all the samples of fused sulphide I have obtained, if the iron is allowed to remain in contact with the sulphide for a certain time (which varies with different samples of the fused sulphide) and is then removed, solution of the sulphide continues. Zinc, tin, and magnesium have the same effect as iron. In hydrochloric acid aluminium acts more rapidly even than iron. In sulphuric acid it has little if any effect. Copper in HCl, when brought in contact with the fused sulphide, dissolves quietly without evolution of gas. The solution of copper chloride formed becomes,as it flows down over the sulphide, converted into copper sulphide.

Jan 1, 1887

By M. E. Wadsworth, R. L. Pearson

THE dissolution of UO, in carbonate solutions can occur only il the tetravalent uranium is oxidized to the hexavalent state. The carbonate system is of particular interest because it provides a means whereby the oxidized uranium may be dissolved by forming the complex ion UO,(CO3)3-1. In the presence of oxygen the over-all reaction may be written UO+1/2O,4CO3T+2HCO2UO,(CO4)11+H2O [1] UO, was used in this study because it could be obtained in high purity and also because it is representative of the most refractory of the primary uranium minerals. The mineral ulrichite is the natural counterpart of the synthetic UO, used. The kinetics of the leaching of UO, should be similar for any of the uraninite type minerals. A pressurized system was used not with the hope it could be extended to commercial systems as a primary purpose but simply to provide the means whereby important temperature and pressure parameters could be varied for the evaluation of the kinetic processes. The importance of such pres-

Jan 1, 1959

By David Mitchell

THE production of fluorspar is one of the smaller nonmetallic indus-tries in the United States with a capital investment-about $10,000,000. Shipments from United States mines&apos; in 1936 totaled 176,231 short tons valued at $3,111,268, an average price of $17.65 per ton. The United States produces about 40 per cent of the world&apos;s fluorspar, of which about 90 per cent comes from the Illinois and Kentucky deposits along the Ohio River.2 Further detailed information on the fluorspar industry in the United States is given by Hatmaker and Davis.28 Fluorspar is marketed according to the following relative quantities and specifications: Consump- Specifications, Per Cent Use Form tion in 1936, Per Cent CaF2 SiO2 Fe2O3 Metallurgical Gravel 79 +85 -5 or lump Ceramic,. Ground 10 +95 -3 -0,1 Acid Ground 11 +98 -1 The concentration of the coarser sizes presents relatively little diffi-culty, good recoveries being obtained with jigs and tables. However, sizes smaller than about 10 mesh cannot be successfully treated by ordinary gravity separation methods and so have been accumulating as

Jan 1, 1938

By Garth M. Crosby, F. McIntosh Galbraith, Bronson Stringham

THE Hercules mine is located in the northeastern section of the Coeur d&apos;Alene district, approximately 1 1/2 miles north of the town of Burke, Idaho. Surface indications of the ore deposit were first discovered in 1886, but regular mine production was not started until 1902 and was continuous until April 1925, when the known ore had been extracted. Incomplete records show that from 1912 until operations were suspended the mine produced 2 1/2 million tons of ore containing 9.4 pct lead and 7.7 oz of silver per ton, together with an estimated 2 pct zinc, 0.3 pct copper, and 20 pct iron. This operation was the first in a series of mining enterprises culminating in October 1947 with the consolidation of Day Mines, Inc. In the same year it was decided to unwater the levels below the collar of the Hercules shaft in the hope of finding some indication of a recurrence of ore. The unwatering operation has been described in a previous paper.1 The initial exploration, following recapture of the workings, showed sufficient promise to warrant a detailed study of the mineralogy with modern techniques.

Jan 12, 1953

By M. B. Bever, A. K. Jena

In the investigation reported here, calorimetric measurements have been made to determine the heat of formation of the compound AuSb2 and the partial gram-atomic enthalpies of antimony and gold in dilute solution in liquid tin and their enthalpy interaction coefficients. In order to interpret the behavior of antimony and gold in dilute solution in tin, nonzero values are assigned to the energies of bonds between like solute atoms relative to the pure solute state. Sa.mples of the compound AuSb2 were prepared by melting stoichiometric amounts of antimony and gold (99.999 pct pure) in evacuated and sealed Vycor tubes, which were shaken vigorously and quenched in water. The ingots were annealed in evacuated and sealed tubes at approximately 700°K for 2 weeks. Metallo-graphic and X-ray examinations gave no indication of second phases or microsegregation. The samples were added from 273°K to tin-rich solutions in a solution calorimeter1 maintained at 623°K. The calorimeter was calibrated with tin; the heat content of tin, H623°K- H273°K, was taken as 4.08 kcal per g-atom.2 In each calorimetric run at least four additions were made. The total concentration of solutes in the bath at the end of any run did not exceed 1 at. pct. The measured heat effect of an addition was plotted against the average of the atom fractions x of Sb + Au in solution before and after that addition. From this plot the heat effect at infinite dilution h,,, and the composition dependence of the heat effect dh/dx in the composition range 0 < x < 0.01 were obtained. The results for the additions of antimony, mixtures of antimony and gold, and the compound AuSb2 are listed in Table I. The heat effect h on addition of a sample of the compound AuSb2 or a mechanical mixture of antimony and gold at 273°K to a tin-rich solution at 623°K can be expressed as:

Jan 1, 1969

By David Mitchell

THE production of fluorspar is one of the smaller nonmetallic indus-tries in the United, States with a capital investment-about $10,000,000. Shipments from United States mines1 in 1936 totaled 176,231 short tons valued at $3,111,268, an average price of $17.65 per ton. The United States produces about 40 per cent of the world&apos;s fluorspar, of which about 90 per cent comes from the Illinois and Kentucky deposits along the Ohio River.2 Further detailed information on the fluorspar industry in the United States is given by Hatmaker and Davis.28 Fluorspar is marketed according to the following relative quantities and specifications: Consump- Specifications, Per Cent Use Form tion in 1936, Per Cent CaF2 SiO2 Fe2O3 Metallurgical Gravel 79 +85 -5 or lump Ceramic.. Ground 10 +95 -3 -0.1 Acid Ground 11 +98 -1 The concentration of the coarser sizes presents relatively little diffi-culty, good recoveries being obtained with jigs and tables. However, sizes smaller than about 10 mesh cannot be successfully treated by ordinary gravity separation methods and so have been accumulating as

Jan 1, 1938

By D. W. Fuerstenau

THE object of this article is to point out the experimental relationship which exists among contact angle, adsorption density, zeta potential, and flotation rate data. In each of the experiments discussed in this article, the surface properties of quartz, as a function of pH, were measured in solutions to which constant quantities of dodecylam-monium acetate were added. Morrow1 and deBruyn2 worked with solutions containing 4.08x10-5 moles per liter, whereas Fuerstenau3 and Seele worked with solutions containing exactly 4x105 moles per liter, but this difference is not significant. The pH of the solutions was regulated with HCI or NaOH in all cases. In each case, the addition of collector was constant, but the concentration of dodecylammonium ions decreased because of the formation of dodecylamine at higher pH values.2 Contact Angles: Gaudin and Morrow1 presented data for the contact angle of quartz in solutions containing 4.08x10-5 moles of dodecylammonium acetate per liter between pH 2 and pH 10.15. Using the same captive bubble techniques, the writer measured contact angles on quartz in solutions containing 4x105 moles of dodecylammonium acetate per liter at pH values ranging from 9.9 to 13.2. Both sets of data are presented in Fig. 1, in which the contact angle in degrees is plotted as a function of the pH of the solution. From pH 2 to about 8, the contact angle

Jan 1, 1958