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By E. S. Machlin

An extension of the thermodynamic theory has been made for the case of irreversible growth processes occurring by the motion of an interface. The theory is applicable to such diverse phenomena as diffusion, growth in recrystallization, continuous grain growth, growth of carbides, etc., growth of eutectoid products, growth in solidification, recovery, "slipless" flow, etc. THE publication of a recent book1 has served to focus attention on a very powerful means of treating certain irreversible processes. This method which has been formally described as the thermodynamic theory of irreversible processes is applicable to processes which involve an approach to equilibrium and for which the deviations from equilibrium are small. The irreversible processes can be classified into three groups: chemical reactions, transport processes (diffusion, heat and electrical flows), and relaxation phenomena involving a degradation of internal energy to more stable states. The limits of applicability of the theory can be precisely defined1,2 for each type of irreversible process. For example, in a chemical reaction at constant temperature and pressure, the Gibbs free energy released per mol in the process should be less than the thermal energy, RT. Another type of irreversible process, which sometimes involves a combination of the first two of the above-mentioned groups, is treated in this paper. This process is one characterized by the motion of an interface separating two regions having different values of free energy and may be briefly described as a growth process. Prigogine2 and Herring3 have treated special cases of this type of process. Previous conscious applications of the theory in metallurgy have been limited to the field of diffusion, one of the transport processes. Darken,4 Bardeen,5 Prigogine2 and others have made significant contributions in this respect. Some other applications of the theory are described in this paper. The Theory The thermodynamic theory of irreversible processes is based on the work of Onsager,6 DeDonder,7 Prigogine2 and others. A resume of the theory has been given by Prigogine2 and DeGroot.1 A brief description of the theory follows, although for a complete understanding the reader is urged to read the references. It is first assumed that the change in entropy, even for a system removed from equilibrium, is given by dS = [dU + pdV - Si µi, dn, - Sk Pk dxk]T-1 Using this expression, the irreversible entropy production in the system is calculated by subtracting the contribution to the change in entropy of the system by transfer of heat, work, or matter from the surroundings. Thus, for example, the irreversible entropy production of a system at constant temperature and pressure is given by dtS = — — dG (DeDonder7) Now it has been shown by Prigogine,2 DeDonder,7 and DeGroot1 that the rate of irreversible entropy production diS/dt, when calculated in the manner suggested, can be written as a sum of products of conjugate forces XK and fluxes Jk, i.e., d,s/ = Sk Jk Xk [I-1] dt The assumption is next made that a linear relation exists between a given flux and the forces, obtained from Eq. I-1, i.e., Ji = Sk Lik Xk (i = 1, 2, . . . n) [I-2] Generally, there is a degree of freedom in choice of the fluxes and forces. However, for all the choices consistent with Eq. I-1 the Onsager8 relations, based on the principle of microscopic reversibility, namely, Lik = Lki, are valid. The coefficients Lik, depending upon the choice of the conjugate fluxes and forces, may be more or less dependent upon the parameters defining the state of the system. In general, the proper choice of fluxes and forces utilizing Eq. I-1, makes the coefficients Lik independent of time. Also, because many of the three classes of irreversible phenomena have already been treated,1,2 a proper choice can be made by analogy. In any case, the validity of Eq. 1-2, from whatever choice made using Eq. I-1, must be tested by experimentation. The theory, thus, comprises the following steps: 1—The irreversible entropy production is calculated to yield Eq. I-1. 2—The terms in Eq. I-1 are grouped

Jan 1, 1954

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By J. J. Pfeiffer, A. A. Oming, J. W. Myers

The method used to process washery refuse for use as a building material aggregate is described. Results of studies made in investigating this process are summarized. The Bureau of Mines, in cooperation with two commercial coal producers, studied the feasibility of using coal washery refuse in manufacturing lightweight aggregate for building materials. Lightweight aggregate is used in making masonry products of lower bulk density than can be produced from conventional aggregate such as sand, gravel, and crushed rock. Among the advantages of lightweight masonry are reduced deadweight loads which reduce materials cost, lower cost of construction labor, and improved thermal and sound insulation. A process for making lightweight concrete aggregate from coal-washery refuse appeared attractive because of the availability of raw material which contained sufficient fuel to carry out the processing. Vast quantities of such refuse have accumulated throughout the coal-producing areas of the U.S. Generally it is stored in unsightly piles, creating a problem of air pollution and using space that could be devoted to other purposes. Conversion of the refuse to lightweight aggregate could remedy these conditions and effectively utilize a material normally considered waste. The first part of the program was conducted in cooperation with the Truax-Traer Coal Co. to determine the feasibility of utilizing refuse from the company&apos;s coal preparation plant at Ceredo, W. Va., in manufacturing lightweight aggregate. The aggregate was to be used in making cement blocks comparable to those known in the building trades as cinder blocks. This project was completed in 1954. Based on the results of this work, the cooperator began commercial development and formed the Trulite Corp. for this purpose. A plant capable of handling 120 tpd of refuse was constructed for approximately $120,000. It began operating on June 1, 1955.&apos; In 1959 a similar study was made, under a cooperative agreement with the Carbon Fuel Co. of Charleston, W. Va., to rrscertain the suitability of refuse from its plant for conversion to lightweight aggregate. Under this program various modifications of equipment were made, and the investigation of process variables begun in the previous project was extended. PROCESSING METHOD The formation of lightweight aggregate from coal-washery refuse js governed, in part, by the fusion characteristics of the mineral constituents of the refuse when heated above their softening temperatures. The heat required for this purpose is supplied by the combustihle matter in the refuse. Some of this combustible matter is coal with high ash content, but most of it is carbonaceous shale. Whereas the density of aggregate prepared from clay or shale depends largely on expansion, the density of aggregate made from refuse is reduced by burning out the combustible matter and, to a lesser extent, by expansion of the residue in the fuel bed. A chain-grate stoker with an updraft air system was chosen for the conversion process in preference to a downdraft sintering machine or a rotary kiln. In down-draft sintering, which operates on the overfeed burning principle, the volatile matter from the refuse would distill off without burning, resulting in inefficient combustion and interfering with proper operation of the equipment. The rotary kiln is designed primarily for processing material that lacks, or is low in, combustihle matter with the heat of reaction supplied from external sources. Washery refuse, which is relatively high in carbonaceous material, could burn at the wall of the kiln causing clinker formation with resultant decrease in throughput and increase in production cost. With an up-draft air stream on a chain or traveling-grate stoker, the volatile matter would be carried into the ignition and burning zones where the heat could be utilized more efficiently. The combustion procedure in this type of unit may be considered as consisting of four periods: 1) initial ignition of the top of the bed by furnace radiation, 2) ignition travel through the bed until the whole bed is ignited, 3) burnout of the combustible material with high air rates to fuse and expand the residue, 4) a cooling period. Investigation of the process required a study of the variables that affect both

Jan 1, 1962

By Joseph C. Mead, Alan Stanley

The MacIntyre Development of the National Lead Co. is located at Tahawus, N. Y. The operations involve the mining and concentrating of a titaniferous iron ore to produce an ilmenite concentrate and a magnetite concentrate. Construction of the MacIntyre plant was commenced during the summer of 1941,when world conditions threatened to cut off the supply of Indian ilmenite. An open pit mining operation was developed and the crushing and milling equipment put in operation in July 1942. A general description of the operation was given in the Adirondack Issue of Mining and Metallurgy for November 1943. The metallurgy of the mill operation was described by Mr. Frank R. Milliken,* Plant Manager, National Lead Company, MacIntyre Development, and presented at the AIME New York Meeting, February 1948. The magnetite concentrate produced in the milling operation was too fine (minus 20 mesh) to be used directly in iron blast furnace operation, and most of the magnetite had to be stockpiled in 1942 and 1943. In 1943, the Defense Plant Corp. built a Greenawalt sintering plant at Tahawus, N. Y., to put the magnetite concentrate in a more suitable form for use in the iron blast furnace. The Greenawalt sintering plant consists of three 10 by 25 ft sintering pans designed to produce 1800 gross tons of sinter per 24 hr. The vacuum to each pan is produced by two Greenawalt fans in series, pulling approximately 30,000 cu ft of air per minute at 50 in. water gauge vacuum. The plant started operation in August 1944. The present plant production averages 25 tons per operating pan hour (approximately 224 lb per operating hour per square foot of grate area) of plus 1 in. sinter. Raw feed to the plant consists of 61 pct magnetite, 4 pct anthracite coal culm, and 35 pct minus 1 in. return fines which are conveyed to a pug mill where the materials are mixed thoroughly and water added to give the mixture 5.5 to 6 pct moisture. The mixed prepared feed is conveyed to two 4 by 10 ft vibrating screens where the minus 1 in. plus 5/8 in. return fines are screened out and discharged into a surge bin for use as a hearth layer. The minus 5/8 in. prepared feed is discharged into another surge bin for use as prepared feed. A charge car, electrically operated, having a capacity of one charge of prepared feed and several charges of hearth layer, lays a thin layer of plus 5/8 in. return fines and 9½ in. depth of prepared feed into the pans. A fluffing roll and a vibrator on the car fluffs and spreads the prepared feed into the pans. An ignition car, electrically operated, ignites the top of the bed with a 30 sec flash burn. The 9½ in. bed sin-ters in approximately 13 min. Dumping the pan, and recharging and igniting the bed requires 2 min. To improve the quality of the ilmenite concentrate produced in the mill and to reduce the amount of titanium dioxide lost in the mill tailings and in the magnetite product, extensive research work and pilot plant operations have been done on grinding the crude ore to minus 65 mesh size (rather than to minus 20 mesh) and concentrating it by a combination of magnetic separation (for magnetite recovery) and flotation (for ilmenite re-covery). These tests have proved successful in increasing ilmenite re-covery and grade. With the development of the ilmenite flotation process to a stage where a full scale flotation plant was in the design stage, the problem arose of handling the 65 mesh magnetite concentrate that would be produced. In order to study and solve the problems of handling and sintering the 65 mesh magnetite in the sinter plant, a pilot sinter plant was secured from John E. Greenawalt. The effect of using 65 mesh magnetite in the sintering operations was then studied on the 2.4 sq ft test pan, operating under conditions as similar to the large plant as could be set up in the laboratory. A series of tests were run in the test pan on present sinter plant feed that had been mixed in the plant pug mill. An average production and an average quality of sinter produced in this series

Jan 1, 1950

By R. F. Sheldon

The discovery of the Carlin deposit was the result of discriminating geologic research and prospecting devoted to the objective of finding a gold deposit that could be mined by open pit methods. By the late 1950s, Newmont Mining Corp. was becoming increasingly concerned about the trend of rapidly rising underground mining costs unless bulk mining methods could be applied. The desirability of finding an open-pittable gold deposit was apparent. The attention of Newmont geologists was directed to Nevada by the publication of two papers: "Paleozoic rocks in North-central Nevada" (1958) and "Alinements of Mining Districts in North-central Nevada" (1960), both authored or co-authored by Ralph J. Roberts of the United States Geological Survey. John Livermore, geologist of Newmont Exploration Ltd., attended a talk given by Roberts in Ely, Nevada in the summer of 1961. These papers and the address by Roberts gave details concerning the Roberts Mountain overthrust, a 483 km (300-mile) long, shallowdipping fault which pushed clastic and volcanic rocks of early and middle Paleozoic age eastward over younger marine formations. Subsequent uplift and doming with consequent erosion had locally removed the upper plate strata exposing windows of lower plate carbonate rocks. Roberts noted that the principal mineral deposits of the region, including gold, were associated with these windows which exhibited a preferred alinement. In the summer and fall of 1961 Newmont&apos;s exploration geologists John Livermore and J. Alan Coope began a systematic examination of gold occurrences associated with these windows, aided by further discussion with geologists of the US Geological Survey. Attention was directed to the Lynn and Carlin windows, particularly to those formations lying immediately above and below the Roberts Mountain fault. It was appreciated at the time that many of the gold occurrences in the region were unusual in that no colours were obtained even when panning high grade samples. A large number of rock samples were collected and analysed using fire assaying procedures, and background values for gold were established. This systematic rock sampling resulted in the identification of a distinct area of anomalous gold values, and a block of claims was staked in late October, 1961. These claims, plus an adjoining optioned 32.4 ha (80 acres) of ground, cover the main area of the present Carlin gold mine. Prior to snowfall that winter, one of the bulldozed assessment pits required to establish a claim&apos;s discovery exposed 24 m (80 ft) of mineralization assaying 0.007 kg/t (0.22 oz per st) gold. In the spring of 1962 a program of trenching, sampling, and geological mapping followed by rotary drilling was underway. Other properties in the area were acquired. The generally undistinguished nature of the dolomitic siltstones and silty dolomitic limestones hosting the micron-sized gold particles, coupled with the lack of visually associated guide minerals, made identification of the gold bearing areas very difficult. The entire drill column had to be assayed to ensure that values were not overlooked, as very often sections that might be assumed to be waste turned out to be high grade. On September 10, 1962 a high grade intersection of 24 m (80 ft) assaying over 0.03 kg/t (1 oz per st) gold was encountered in the third hole drilled. An expanded program of both rotary and diamond drilling led to the further delineation of the ore body. By December 1963, the exploration program had established an initial reserve of 10 Mt (11 million st) grading 0.01 kg/t (0.32 oz per st) gold. A 1.8 kt/d (2,000 stpd) processing plant was constructed and the first gold bullion was poured in May, 1965, just two years and eight months after the discovery hole was drilled. REFERENCES Roberts, R.J., Holz, P.E., Gilluly, J., and Ferguson, H.G., 1958, "Paleozoic Rocks in North-central Nevada," Bulletin American Association of Petroleum Geologists, Vol. 42, No. 12. Roberts, R.J., 1960, "Alinements of Mining Districts in North-central Nevada," Professional Paper 400-B, US Geological Survey, Article 9.

Jan 1, 1985

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.&apos; Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By J. B. Dorsey, T. W. Brinkley

Performance of a high-pressure, vaporizing gas-drive project in a volatile oil reservoir is discussed. The project has been in operation for over 8 years. Present recovery from the over-all displaced portion of the reservoir is 40 percent, and an ultimate recovery of 60 percent is indicated. Calculations reflect an over-all displacement volume of 50 percent for the entire reservoir; therefore, ultimate oil recovery will be 30 percent of the entire reservoir oil originally in place. Laboratory vaporization tests conducted prior to project initiation also are presented and discussed, along with an analytical method of determining stock-tank oil production and gar injection requirements related to over-all volumetric displacement efficiency from these data. Introduction The Shoats Creek field is located in Beauregard Parish, La., in the extreme western part of the state (Fig. 1). Discovered in 1956, the field is productive in three Cockfield sand zones, ranging in depth from 8,000 to 9.000 ft. The upper two zones, 1st and 2nd Cockfield, are condensate-bearing gas reservoirs. The lowest zone, the 5th Cockfield, is a volatile-oil reservoir. Laboratory work conducted on crude oil from the 5th Cockfield zone shortly after field discovery demonstrated that, when contacted with dry gas, signidcant volumes of the oil could be vaporized at reservoir temperature and at an appropriately high reservoir pressure. Further study led to the conclusion that early initiation of a crude vaporization project in the 5th Cockfield zone would be superior economically to other methods of reservoir depletion. Consequently, the zone was unitized and gas injection operations started late in 1958. This paper discusses laboratory work performed in conjunction with the project, and project performance to the present. History of Development The 5th Cockfield zone in Shoats Creek is composed of a thin, very shaly, low-permeability sandstone. Oil accumulation is controlled by a structural trap bounded by faults along the north and west and by a water contact on the southern boundary (Fig. 2). The zone covers a productive area of 1,550 acres at an average depth of 9,000 ft. The net sand section is thin, having a maximum thickness of 10 ft and an average thickness of 5.5 ft (Fig. 3). Average reservoir rock properties, as determined from core analysis are presented in Table 1. Shaliness of the zone is illustrated by the typical electric log of the 5th Cockfield section in Fig. 4. Because of the thinness and poor quality of the sand, the 5th Cockfield was developed on a wide spacing. Eleven completions were made in the zone between 1956 and 1961 for an average density of 140 productive acres per completion, with the majority of wells being dually completed in the 2nd and 5th Cockfield. Average initial potential for producers in the 5th Cockfield was 130 BOPD. Oil from the 5th Cockfield has a stock-tank gravity of 50.5" API; with a bubble-point pressure of 3,515 psia, the oil was highly undersaturated at the original reservoir pressure of 4,675 psia. Pertinent properties of the oil as determined in the laboratory are presented in Table 2. Because of the volatile nature of the crude, laboratory studies of its susceptibility to vaporization, as well as a vapor-liquid phase study, were conducted in addition to a standard PVT analysis. The vaporization study was conducted in a visual cell; a stepwise illustration of this work and laboratory measurements are presented in Fig. 5. Field

Jan 1, 1969

By T. C. Poulter, B. M. Caldwell, D. E. Brink

The flash X-ray has been used more than a decade to study the configuration of the jet from a shaped charge. The high-speed, rotating-mirror smear camera has provided time-distance graphs of detonations and shock fronts in transparent materials, and the high-speed framing camera has given pictorial representations of the progress of explosive phenomena. Adequate means for measuring the paths and velocities of all parts of the shaped-charge cavity Iiner during the collapse phase have not existed heretofore. A technique enabling the single-lens framing camera to make stereoscopic photographs of the cavity liner while it is collapsing has been developed. Analysis of this photographic record gives the directions and velocities of various parts of the Iiner surface, permitting direct quantitative measurement where this has previously been impossible. Significant improvements in shnped-clrarge design are expected to result. INTRODUCTION The familiar oilwell jet perforating charge, generally referred to as a "shaped charge", is related to the Mun-roe charge first described by C. E. Munroe in 1888 and later by Neumann in 1910. It differs in construction from the Munroe charge in that its cavity is lined with some inert material (usually metal)&apos;, and it differs in performance by projecting a fast jet of dense liner material against the target instead of a stream of expanding detonation products. Fig. 1 represents a typical shaped charge in axial cross section. The charge is circularly symmetrical about its longitudinal axis. The cavity at the right is lined with metal, usually copper; and, with the exception of air, the liner is otherwise completely empty. High-explosive material is intimately in contact with the convex surface of the liner and extends in the other direction to the booster. This is a pellet of high explosive having somewhat different characteristics and serves to couple the detonator to the main charge. When the detonator is fired, a small hemispherical reaction zone of very high temperature and pressure occurs at its output end. The booster responds, adding its own latent energy to the reaction, thereby initiating the main charge. The reaction progresses throughout the main charge at a velocity of 7 to 8 mm/microsecond until all the explosive material has reacted. With a reaction pressure of about 160,000 atm, the surrounding material is moved rapidly away from the high-pressure zone. As the detonation proceeds along the cavity liner, moving from apex to edge, the liner is collapsed toward the axis of the cavity, where liner material from all parts of the concave surface converges. A zone of extraordinarily high pressure results. with only one escape path—outward along the axis. The particles from the liner, thus, become a jet of very high velocity, with a density characteristic of the material from which the liner was made. The kinetic energy of the jet, concentrated in a small area of the target, has great penetrating power. It overcomes the strength of any target, and the target material crumbles or deforms plastically to escape from the path of the jet. An unlined cavity charge, on the other hand, projects a turbulent body of hot gaseous material against a target and erodes the exposed surface. With equal quantities of explosive, the penetration effectiveness of an unlined charge is a small fraction of that of a lined charge. Given an explosive charge with a detonator at one end and an axially symmetrical metal-lined cavity at the other, one has a perforator of considerable potency. To maximize the penetrating and other desirable effects,

By R. H. Pemberton

The principle of airborne electroniagnetic prospecting is well-known. &apos;The basic geonhysicai texts in inost cases discuss the main elements involved in electromagnetic prospecting. However. there is ceriainlv iittle information available to the public concerning he present types of airborne eiectromagnerlc systenis being flown today by both contracting companies and some of the mining companies which have their own instruments. This is unfortunate since it is difficuit for those people not conducting such operations to understand thoroughly the iarge variation in the electromagnetic instrunlents available. Basically, the aeriai electromagnetic induction method utilizes a primary or transmitting coil through which is generated an alternating magnetic field at a frequents: generally of the range of 100 to 2000 cycies per sec. This primary field links with buried conductors and generates eddy currents within them. These eddy currents in themselves generate a secondary magnetic field of the same frequencv, but generally nut-of-phase with respect to the prinlarv field. This secondarv field is detected above the ground in the pick-up or receiver coil which is tuned to the frequency of the current applied to the primary transmitter coil. One of the main problems in the development of an airborne electromagnetic system is that of maintaining constant coupling between the cransmitting and receiving coil systems. Any variations in the coupling due to relative motion between the two coils will result in an in-phase signal being induced in the receiver coil. [However, any variation in the coupling does not result in an out-of-phase signal change in the receiver coil. The first airborne eiectromagnetic svsteins which were developed utilized a large prlniarv coil set up on the aircraft with the receiving coil being towed behind in a bird, generally at the end of a cable of about 500 ft. in length. It is possible with such a system to record the out-of-phase or quadrature responses more readily than the in-phase re-sponse. One system utilizes a dual frequency method, wnereby the out-of-phase responses at two frequencies are recorded. Another system used today records a single-frequency olrt-of-phase response. Recentlv home companies have succeeded in measuring from ne air both the out-of-phase and the in-phase components. The usefulness of recording in-phase is weil-known, but unfortunately this is difficult to obtain in any towed-bird system. In order to measure the true in-phase signal, the most straightforward system is that in which both the transmitter and receiver coils .Ire affixed in space so that there is little or no relarive motion between the two coils. THE FLIGHT SYSTEM The particular system which Canadian Aero Service is using at present is mounted on a Sikorsky S-55 helicopter (Fig. 1). A record of both the in-phase and out-of-phase responses is made at a frequency of 390 cycles per sec. The transmitter coil is set on a boom mounted in the front of the helicopter; the receiver is set on a tail boom extending back from the helicopter. Separation between these coils is about 65 ft. The two coils are mounted in a vertical co-axial relationship. Having the transmitting coil in a vertical plane ensures that maximurn coupling will occur with vertical conductors rather than flat-lying conductors. Having them mounted as they are in a co-axial relationship on the helicopter ensures that maximum response will occur when the flight direction is orthogonal to the strike direction of a given conductor. The present sensitivity of the Em system is 20

Jan 1, 1961

By I. A. Lesk

The various materials utilized in the construction of integrated circuits, and the resultant materials interfaces, are discussed with emphasis on a materials system that is compatible with all types of integrated circuits and minimizes the number of different interfaces. Problems with interfaces may originate in the silicon, on its surface, and between other materials within the integrated-circuit package independent of the silicon. ThE difference between integrated-circuit theory and practice may generally be spelled out in terms of the difficulties in fabricating a desired structure. There are, of course, problems in forming the requisite materials, of the necessary composition and geometry, where needed. A distinct class of problem, however, is associated with interfaces— generally between different materials, but occasionally between regions of the same material. We require that each interfacial system perform its proper electrical, mechanical, and thermal function, and do so in an unchanging manner with time under the most severe operating conditions. In a practical sense, we deal in nonideal systems, such that it is generally not possible to form an interface exactly the way it was intended, even if we allow for a knowledge of the practical limitations of the fabrication system. Another way of looking at this situation is to realize that, when we form a group of interfaces under apparently the same experimental conditions, there are often differences of important consequence between them. Very high-magnification pictures, such as are obtained by an electron microscope, reveal fine structure that often differs over the area of a given sample, as well as from sample to sample. Low-magnification pictures look better, but don&apos;t eliminate the problem. The trend towards integrated circuits, and away from circuits fabricated utilizing separate components, is very strong in many areas of electronics. A typical silicon monolithic integrated circuit, still in place in the wafer on which it was fabricated, is shown in Fig. 1. The increased reliability which is being experienced through the use of integrated circuits can, to a large extent, be credited to the reduced complexity of the interface system that is present in the electronic system. A glance at Fig. 1, however, with all of its epitaxial and diffused p-n junctions, and interconnect system, shows that interfaces have been far from eliminated. Fig. 2, depicting a schematic cross-sectional view of a (partial) typical integrated circuit, illustrates in detail the numerous interfaces that occur in this type of structure. Besides the individual circuit elements, there are interfaces for isolation, and, Fig. 3, even a crossover requires a series of interfaces. What has been accomplished, however, irrespective of whether or not the total number of interfaces in the circuit is increased or decreased, is that the variety of interfaces is very much reduced. This is because there are fewer materials involved. Since the expense incurred in an R & D program to improve reliability is pretty much directly proportional to the variety of interfaces involved, it is economically advisable to work with integrated circuits for highest reliability. That is not to say that circuits built using standard components could not be made as reliable as integrated circuits, but that the expense involved because of the more complex over-all interface system would be much greater. Although electronic performance utilizing integrated circuits with all silicon elements (i.e., transistors, diodes, resistors, capacitors) is adequate for many applications, there are numerous instances where thin-film passive elements must

Jan 1, 1965

By J. T. Dewan

An experimental setup is described whereby the responses of Neutron logging instruments have been determined opposite formations of different porosities and under various borehole conditions. The results of these tests are presented in several charts which show how the Neutron log is affected by the following factors: hole diameter, casing, cement, salinity and weight of drilling mud, and position of logging tool with respect to the wall of the hole. The responses in the case of empty holes are also shown. A chart is furthermore presented which shows the shapes of the Neutron log, as a function of logging speed and time constant, at the boundaries between two formations with different porosities. These were derived mathematically using as a basis laboratory determination of the shape of the curve under static conditions, i.e. at very low logging speed. Corrections for the readings made opposite thin beds are given by these computations. The correction is found negligible under usual logging conditions for beds thicker than about 4 ft. INTRODUCTION The Neutron log is used in borehole surveys both for the delineation of porous formations and for the quantitative estimation of their porosities.1,2,3,4,5 It is common practice to calibrate the response of the Neutron log in terms of porosity values for each given geological unit by means of empirical comparisons between the deflections of the neutron curve and the porosity values given by the core analysis in a sufficient number of wells. Usually, the plots of the porosity values vs Neutron log deflections show a definite trend. It is therefore possible to trace an average line across the plotted points. This average line constitutes a calibration curve which can be used to evaluate the porosities from the Neutron logs in the other wells drilled in the same region. Futhermore, when the porosity values are plotted on a logarithmic scale and the Neutron log deflections on a linear scale, the calibration curve is practically a straight line. Accordingly the calibration curves are often determined by simply tracing a straight line between two points corresponding to two widely different porosities. Different choices are made for these two points, depending on local conditions. For example, one point will be defined by plotting the deflection of the Neutron curve opposite a formation known to be very tight, for which an average porosity value of 1 or 2 per cent is assumed. The other point may correspond to shale sections, to which a porosity of around 40 per cent is ascribed. The information provided by the eletrical logs — in particular the Laterolog, Limestone log or Micro-Latero-log — is also very often a help in the calibration of the Neutron logs. Empirical approaches such as these make possible the derivation of fairly reliable porosity values from the Neutron logs in many cases, at least in open holes and in essentially clean formations. There are, however, several causes of uncertainty which may sometimes entail appreciable errors. On the one hand, the Neutron log readings are influenced by the borehole conditions: hole diameter, presence or absence of casing and cement, presence or absence of drilling mud, characteristics of the mud, and position of the logging instrument with respect to the wall of the hole. The amplitudes of the curves opposite thin beds are furthermore atfected by the bed thickness,

Jan 1, 1957

By W. S. McCain, B. A. Wilcox, A. H. Clauer

The creep and creep-fracture behavior of a Ni-200-2Th0, alloy has been studied over the temperature range 816° to 1038°C and stress range 4000 to 19,000 psi Specimens having their axes either parallel or transverse to the final sheet-rolling direction were tested in air, and the apparent activation energy for creep was found to be 92 kcal per mole, regardless of specinien orientation. The stress dependence 01- the steady-state creep rate, was satisfied by where n depended on orientation; n = 9.7 for rrzaterial transverse to the rolling direction and n = 24.3 for material parallel to the rolling direction. In the latter case, the relation was also valid. The rupture strength of material parallel to the rolling direction was -1.5 times gveater than the transverse rupture strength. Several tests in vacuum revealed that here the creep rate was higher and rupture life lower than for comparable tests in air. THERE is an increased interest today in producing improved dispersion-hardened alloys for high-temperature structural applications. This had led various materials designers to modify existing alloys, such as thoriated nickel. One system that has received considerable attention is based on chromium additions to Ni-ThO2, with the obvious motive of improving the oxidation resistance. Another effect of chromium is that of lowering the stacking-fault energy, y, of nickel. For example, the addition of 30 wt pct Cr decreases y from -225 erg per sq cm for pure nickel1 to -70 erg per sq cm.&apos; This decrease in y could have several effects on the deformation behavior. There is some evidence that cross slip of dislocations around Tho2 particles is a mechanism of tensile3 and creep4 deformation in TD Nickel (Ni + 2 vol pct ThO2) at temperatures below 0.5 the absolute melting point of nickel, T,. A decrease in ? by chromium additions should increase the difficulty of cross slip. Also it has been suggested that the high-temperature (T > 0.5Tm) rate-controlling creep process in "recrystallized" Ni-Tho2 alloys is the climb of edge dislocations over Tho2 particles.5 According to weertman6 a decrease in the stacking-fault energy should decrease the dislocation climb velocity resulting in a decreased steady-state creep rate. Thus, chromium additions to recrystallized Ni-Tho2 alloys would be expected to decrease the creep rate, all other conditions being constant. However, a difficulty arises when the stacking-fault concept is applied to high-temperature creep of dispersion-strengthened metals which are produced on a commercial or semicommercial scale. This occurs because the materials are processed so that they have a high-stored energy of cold work, and the other substructural effects could obscure any influence of stacking-fault energy per se. An example of an alloy with a high stored energy of cold work is TD Nickel bar. This material has a fibrous grain structure (1 I diam by 10 to 15 p long), and the structure is stabilized by the ThO2 particles. Annealing at high temperatures, e.g., 3 hr at 1300°C, causes no recrystallization or grain growth.4 Previous work by the authors4 showed that the high -temperature creep behavior of TD Nickel could not be related to any simple dislocation theory of creep, and this probably was associated with the complex initial structure of the material.

Jan 1, 1968

By R. V. Ramani, C. J. Bise

INTRODUCTION Classification of coal seams as thin, medium, and thick is both subjective and relative and is more a reflection of the statistical mode of the thicknesses en- countered in a mining region. A geological factor more precisely understood as defined than thickness is the inclination of the seams to the horizontal, commonly referred to as the pitch or the dip of the seam. Thick and steeply pitching seams present far more challenges to the ingenuity of the mining men to devise methods for their extraction than the thick and less steeply inclined ones. In a marginal case, where a thick coal seam may be minable by surface or underground methods, the decision bears a close relationship to the technological developments in the mining scene. Near surface thick coal seams are a special gift of nature and are not as wide- spread as the ones that call for the application of under- ground methods. Recent advancements in surface mining equipment have made it possible to surface mine to great depths. Stripping ratios of 30: 1 (cu yd of over- burden removed per ton of coal) have been achieved. The extraction of thick seams which preclude the use of surface methods is the concern of this chapter. Specifically, the objective here is to outline the special technological factors in underground mining of thick coal seams and to illustrate through several case histories the methods that are practiced in the North American continent. For the purposes of this chapter, a thick seam is defined as one which is not readily minable with currently available equipment without modifications to the extraction method or the equipment. At the present time, a thickness of 4.8 m (16 ft) can be considered as the lower limit, although developments in equipment and methods can be expected to push this limit upwards. The data for the case histories were collected from two extended mine visits in 1975 and 1978, and from other published accounts of the mines visited. Reference is drawn particularly to reports by Bise, Ramani, and Stefanko (1976) and Rarnani and Kenzy (1979). THICK SEAM MINING METHODS The various methods of mining thick seams can generally be grouped into three major categories: full face methods, where the entire thickness of the seam is re- covered in a single pass; slicing methods, where the seam is extracted to its full thickness by horizontal or inclined slices either in an ascending or descending order; and caving methods, where the seam is undercut and the en- tire coal seam is recovered by caving the top coal into the excavated cut, or some variations of the basic sub- level caving method. As shown in Table 1, in each of these methods, the coal is removed by either room-and-pillar or longwall methods. Hydraulic mining and transport of the coal in open flumes or in pipelines are also practiced. Addition- ally, the void created by the removal of coal may be filled with a packing material (stowing) except in the caving methods. The pitch (dip) of the seam, particularly when it is greater than 0.26 rad (150), imposes severe operational limitations on mobile equipment. A more detailed general discussion of the methods can be found in Bise et al. (1976) and Vorobjev and Deshmukh (1964). Specific discussion on the many variations of the three basic methods can be found in the papers presented at the international symposia that were held in

Jan 1, 1982

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

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By J Vann, C Seymour

Geology is generally treated as a æfront endÆ step in mine development. After infill drilling, the majority of resource estimation, mine-planning, development, mineral processing strategies and operational procedures are planned and implemented with little geological input, particularly in open pit operations. However, significant benefits in overall costs, cash flow, and technical risk reduction can be realised when sound geology is utilised more rigorously throughout the mining process. This under-utilisation of geology in the mining process has arisen due to a combination of factors:A lack of interest in, or knowledge of the full mining process by geologists. Few geologists fully understand where their inputs make critical impacts on downstream users. As a result of this, geologists generally do not focus their inputs towards areas of greatest value added, ie addressing issues critical for other members of the mining team. Most importantly, few geologists effectively communicate their results to the downstream users of their geology models. The results are that the potential benefits of geology, and the appropriate status of geology in the mining industry, are not fully realised. It is fundamental to realise exactly what geologists do. Geologists constrain geological processes and geometry. All geoscientific tools at the geologistsÆ disposal are geared towards one of these goals. An emphasis on geological processes is present throughout the exploration process, whereas in the resource estimation and mine development process an emphasis on geometry is required. The mining process is a web of disciplines that are attempting to optimise development of a resource to provide value to shareholders. Yet few people within these disciplines have a full appreciation of this web, and where sound geology inputs can add value through various feedback loops. Geology inputs do not end at the resource estimation stage, nor are they relegated to grade control implementation. If geologists have an appreciation of the mining process and close liaison with the other disciplines such as geostatistics, geotechnical engineering, hydrogeology, and mining engineering, they can significantly benefit project costs, timelines, and constrain technical risk by addressing their issues at the earliest possible stage. Furthermore, the mining process is not a single pass timeline, but an iterative process where the exploration, resource definition, mine planning and mining loop is continually repeated over the life of a project. Therefore, the potential inputs of geology are critical throughout the mining process. Effective communication of the impacts of geology inputs on downstream users is often lacking on mining projects. The most effective way to communicate geological results is through where it impacts most û project risk. Focussing all geology inputs and communication in terms of potential material risk allows the geologist to be more effective in contributing value to the mining process, and allows the downstream users of geology inputs to better constrain the risks associated with their aspects of the mining project. Through a program of geologists:taking an interest in the entire mining process and identifying critical areas for geology inputs to downstream users (the geologistsÆ clients); focussing geology inputs to address the potentially material issues on mining projects; and communicating their inputs to the æclientsÆ in terms of technical risk, geology will be much better integrated into the mining process. As a result, the potential benefits of geology throughout the mining process will be realised, and the status of geologists within the mining process will be elevated to a more pivotal position.

Jan 1, 2000

By L. B. Gittinger

Sulfur is a nonmetallic element widely distributed in nature. It constitutes 0.06% of the earth&apos;s crust but only a very small portion occurs in sufficiently concentrated amounts to justify mining. Sulfur occurs in practically all animal and plant life. It constitutes approximately 0.09% of the elements in the oceans; it has been found in meteorites. Sulfur was known and used by man before recorded history. The American Chemical Society approved spelling for the element is sulfur. The English spelling sulphur is used commercially in the United States. In ancient times, sulfur was called brimstone, literally "burning stone." Today the term brimstone is used interchangeably with the term elemental sulfur. Sulfur is found naturally in the elemental form in subsurface deposits associated with gypsum and anhydrite in salt domes and sedimentary formations in evaporite basins and in solfatara-type deposits associated with volcanoes and mineral springs. Sulfur occurs also in molecular combination in ferrous sulfides (pyrites and pyrrhotite) and nonferrous sulfides (copper, lead, zinc, and nickel), and in mineral sulfates (gypsum and anhydrite); as hydrogen sulfide contaminant in natural gas; as organic compounds in crude oil and tar sands; and as pyrite and organic compounds in coal and oil shales. Sulfur resources are abundant and exist throughout the world but the extent to which they can be classified as reserves is greatly circumscribed by prevailing prices and technology. Estimates of world sulfur reserves are compiled by the U.S. Bureau of Mines. A compilation of reserves by area and source of sulfur published in 1970 and presented here as [Table 1] totaled 2.47 billion tons (Lewis, 1970). The effect of the decline in prices which has occurred since the earlier estimate is dramatically illustrated by the 1972 estimate of the U.S. Dept. of the Interior which shows world sulfur reserves of only 1.2 billion tons (Anon., 1972d). Sulfur is produced commercially from one or more sources in nearly 70 countries of the world. World production of sulfur in all forms totaled 41.6 million tons in 1971. (Sulfur statistics given in this chapter are long tons.) Native deposits, sulfides and oil and gas contributed, respectively, 31, 41, and 25% of world production (Table 2). Of the sulfur produced from native deposits, salt domes accounted for 54% and evaporite basin deposits, 44%. Volcanic deposits are of little significance except for local consumption. The past two decades have seen important shifts in the world&apos;s sulfur sources. In 1950, native deposits and sulfides each supplied about one-half of the world&apos;s production. During the 1950s, sulfur recovered from oil and natural gas grew rapidly, representing about 10% of the total by 1960. Since then, the petroleum industry has continued to increase its relative importance as a source of sulfur, representing more than 30% at 1972 year-end. Sulfur is generally classified as elemental or nonelemental for statistical purposes. Elemental sulfur is sulfur produced in the pure, uncombined form. It includes production from native deposits, as well as that recovered in the elemental form from oil and natural gas or other sulfur-bearing materials. When produced from other than native deposits, it is generally referred to as recovered elemental sulfur. Nonelemental sulfur is that which is utilized commercially in molecular combination with other elements, such as sulfides or sulfates. Elemental sulfur is being produced from salt dome deposits in the Gulf Coast region of the United States and the Isthmus of Tehuantepec in Mexico, and from evaporite basin deposits in west Texas, Poland, Sicily,

Jan 1, 1975

By A. E. Worthington, R. F. Meldau

An analog computer study was made of the reduction of the magnitude of the SP by formation geometry and resistivity effects. Practical field .situations were studied. The analog data were converted to the form of departure charts. These charts may he used to determine the reduction in the SP due to the above eflects pith good precision Quantitative interpretation of the SP log in terms of formation water resistivity is presently based on the premise that the observed SP is equal to the electrochemical potential developed across a shale between the mud filtrate and the formation water. This procedure inherently assumes that, first, no electro kinetic (streaming) potential is present, and, second, that the SP is not reduced by resistivity or geometry effects in the formation. When, however, such a reduction of the observed SP does occur, one may write, SP = b,E, b, E, (1) where SP is the observed self-potential opposite the center of the bed under consideration. In this case, E, is the electrochemical potential, E, is the electrokinetic potential, b, is the electrochemical reduction factor, and h, is the electrokinetic reduction factor. The first assumption above is equivalent to assuming E, = O in Eq. 1 and the second assumption is equivalent to h, = b, = 1. Examination of electric logs shows that for many formations of interest the observed SP is reduced below its maximum value. The object of this work is to aid quantitative SP interpretation in at least some of these situations by obtaining values for b, and b, in Eq. 1 as functions of realistic combinations of bed thickness, depth of invasion, and formation resistivity. The only previously published work in this field known to the authors is by H. G. Doll&apos; in 1948. He evaluated b, under conditions permitting exact analytical solution. His work clearly established the importance and qualitative nature of formation geometry and resistivity effects upon the SP, but the necessity of obtaining analytical solutions restricted his study to situations of limited practical interest. In order to extend such studies to practical combinations of formation parameters which do not lend themselves to feasible analytical solutions, the results reported in this paper were obtained by use of a special analog computer. THE ANALOG MODEL The analog model used for this study was the Guyed Analog Computer which originally was designed and built for resistivity log departure curve studies. It consists of a two-dimensional mesh of resistors, with the vertical mesh corresponding linearly to vertical distance along the borehole, and the horizontal mesh corresponding to radial distance from the borehole axis. By proper choice of horizontal resistor values, a three-dimensional, axially symmetric, borehole-formation problem can be modeled with this two-dimensional array. These and other details of the model are contained in a paper by H. Guyod&apos;. The geometry used for the SP studies with the analog is depicted in Fig. 1. This configuration has a horizontal plane of symmetry, and, hence, the model, and the following discussion, need only to be concerned with one quadrant such as shown in Fig. 2. A further simplification arises by considering that both the natural potential sources and those used in the model have fixed internal impedance. Therefore, the current flows produced by these sources can be separated and studied independently ( i.e., the superposition theorem can be applied). SP = SP, i SP, = h,E, + b,E, ,(7)

By S. H. Moll, R. E. Ogilvie

The investigation of solid-state diffusion phenomena may lead to much information concerning binary alloys. In particular, a study of the concentration gradients present in multiphase diffusion couples can lead to the determination of the solubility limits of the single-phase fields in the phase diagram. The specific concentration gradient which results from the heat treatment of a diffusion couple depends not only upon the time and temperature of diffusion, but also upon the number of phases existing in equilibrium at the diffusion temperature. Such concentration gradients possess sharp discontinuities whose terminal points correspond to the solubilities existing at the limits of the two-phase field in the phase diagram at the diffusion temperature. In general, there will be a discontinuity in the concentration curve for each two-phase field which exists in the phase diagram between the concentration limits of the couple. A number of investigators have analyzed the gradients present in multiphase diffusion couples. 1-8 The iron-titanium phase diagram exhibits a y loop in the temperature range from 900" to 1400°C, and the limit of the a + y field lies at some composition which is less than 1 wt pct Ti for any temperature. It was felt that a diffusion study could yield values not only for the diffusion coefficients involved, but also for the chemical solubilities in the phase diagram. The concentration gradients were analyzed by an X-ray absorption technique developed by Ogilvie.6 The absorption of a monochromatic X-ray beam is measured in steps parallel to the diffusion direction and the resulting intensity gradients are transformed into concentration gradients by applying the laws of X-ray absorption in a binary system. This technique has been applied by ogilvie6 to the systems Ni-Au, Cu-Au, Fe-Cr, and Ni-Cr; by Gelles7 to the systems Be-Fe, and Be-Ni and by Hilliarde to the system Al-Zn. Linear X-Ray Absorption Analysis—The use of X-ray absorption analysis as a tool for determining concentration gradients arises from the fact that the beam is absorbed according to the quantity and species of elements present in the sample and not according to their state of aggregation. This method is more advantageous than the chemical analysis of machined layers since it is less time consuming and less expensive and can analyze a very small area. IF a homogeneous binary alloy (A + B) is analyzed with two different monochromatic X-ray beams I0(2) and lo(2) the following relation between the transmitted intensities, the intrinsic absorption coefficients of A and B for the two different radiations and the weight fraction of each element may be derived.&apos; In (I/Io) (a+b) xa(u/p)a(2) + xb(u/p)8(2) Eq. [1] is independent of specimen thickness and density, but requires that either element A or B possess an absorption edge between the wavelength limits of the two monochromatic beams. I, is evaluated for each radiation by measuring the transmitted intensity through a varying number of foils of a suitable absorber. A plot of the natural logarithm of the transmitted intensity as a function of the number of foils, when extrapolated to zero foils, yields the value of I,. If a plot of the ratio in Eq. [ I] is calculated as a function of xA, then a master curve results. From

Jan 1, 1960

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.&apos; Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By P. Datta, L. L. Handy

For a wetting phase displacing a nonwetting phase from a porous medium the distribution of the residual fluid may depend on displacement conditions. Although this subject has been debated in the literature, only a few experiments have been cited to support the various conclusions. Experimental results presented in this paper show that fluid distributions are dependent on imbibition pmcedures. Results agree qualitatively with predictions from the pore doublet model. If the rate of water imbibition is restricted, the nonwetting phase is trapped preferentially in .the larger pores as expected. But if the rate of water imbibition is unrestricted, trapping occurs somewhat more in the smaller pores. These conclusions were deduced primarily from relative permeability measurements. INTRODUCTION Relative permeabilities are known to depend on the saturation history of the porous medium. For either continuously increasing or continuously decreasing wetting phase saturations, however, they have normally been assumed to be single-valued functions of saturation. Severat investigators have compared relative permeabilities measured by different methods and have reported acceptable agreement.1-5 Studies of simple models of the displacement process suggest that the distribution of residual fluids can be influenced by the displacement method. If this is so, relative permeabilities also should depend on the method of displacement. These predictions have not been supported by experimental data. The object of this paper is to investigate experimentally some of the predictions of these model studies. The particular question of importance is whether steady-state and unsteady-state methods should be expected to give the same values of relative permeability. Much of the reported data showing agreement between steady-state and unsteady-state methods have been obtained on un consolidated sand. Johnson, Bossler and Naumann, however, compared steady-state and unsteady-state results for Weiler sandstone and found no significant differences.5 Levine made a detailed study of pressure and saturation distributions for a laboratory waterflood in a consolidated system but made no attempt to calculate performance from steady-state relative permeability data Bail and Marsden in a somewhat similar set of experiments did attempt a comparison of observations with predictions but the results were inconclusive.7 Excluding gravity, two forces affect the distribution of wetting and nonwetting phases during an unsteady-state, immiscible displacement: viscous and capillary forces. If relative permeabilities are indeed the same when measured by steady- or unsteady-state methods, the fluid distributions at the same fluid saturations must be similar for both methods. Furthermore, the implication is that the relation between capillary and viscous forces is the same for both methods insofar as the effect on microscopic fluid distributions is concerned. Unsteady-state displacements are normally run at high rates to maximize the ratio of the viscous to capillary forces. The objective is to reduce the effect of capillary forces on macroscopic fluid distributions. For floods in which the phase which wets the porous medium displaces the nonwetting phase, capillary forces compete with viscous forces in determining fluid distributions.8 The residual nonwetting phase is discontinuous. Competitive aspects of viscous and capillary forces and the resulting effect on water-oil distribution in porous media have been illustrated in an elementary way using a pore doublet model. This model and predictions from it have been discussed at considerable length by Rose and Witherspoon, Rose and Cleary and by Moore and Slobod.9-13 Rose and Witherspoon show that so long as water invades the model at a rate equal to or greater than the free imbibition rate, the water will move through the larger capillary of a doublet first and trap oil in the smaller capillary. On the other hand, if a negative pressure is applied to the water

Jan 1, 1967