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By Charles H. Grant

Some of the limiting factors relative to explosive crushing of rock and ways to overcome a few of these problems are presented. Relationships between borehole diameters, bench heights, and spacings, along with a review of the influence geometry has on energy as these are changed, are discussed. Efficiency in use of explosives and the decay of energy as it moves through rock and is absorbed and dissipated, is described, along with fragmentation as a function of spacings and energy zoning, etc. Communications are one of the major problems encountered. In an effort to provide a better understanding of the use of explosives, it is necessary to take a little different view of what explosives are, how to look at them as tools to fragment rock, and some of the problems encountered in doing so. First, take the explosive: although there are many factors involved, consider these as being reduced to only two — shock-strain imparted to the rock by the high early development of energy, and the gas effect which is a combination of heat, moles of gas formed, rate of formation of these gases which develop pressures, etc. First, consider shock energy by itself and assume there is no gas effect in the reaction. Fig. 1 illustrates a block or cube of rock, in the center of which is detonated an explosive charge which is 100% shock energy. Tensile slabbing would be seen on the surface and probably the cube of rock would generally hang together even though microcracks were formed. If the situation is reversed and an explosive whch has no shock energy and only gas effect (Fig. 2) is considered, the cube of rock would act as a pressure vessel and contain the pressure from the gas effect until it exceeded the rock-vessel strength; then the rock would break in a few large pieces. If these two kinds of energy are put together and the area of shock-strain around the explosive (Fig. 3) is considered, the two energies will be seen working together to furnish broken rock. The gas effect applies pressure to the microcracks formed from the shock energy to weaken the rock-pressure vessel and propagate these cracks to break the rock apart. It not only will be broken more finely, but will break apart at a lower pressure than the gaseffect case, since the shock energy has first weakened the rock vessel. Although tensile spalling from the shock-strain imparts momentum to the rock, the main source of displacement comes from the gas effect. The term "rock" is being used to mean any material to be blasted. These energies are absorbed by the rock in different ways. First, classify rock into two main categories: "elastic" and "plastic-acting." Elastic rock should be thought of as rock which can transmit a shock wave and is high in compressive strength, such as granite or quartzite. Since this elastic rock transmits a shock wave well, it makes good use of the shock energy from the explosive-forming cracks, etc., for the gas effect to work on. Plastic-acting rocks are rock masses which are relatively low in compressive strength and absorb shock energy at a much faster rate, thereby making poor use of the shock energy by not developing as extensive a cracked zone for the gas effect to work on. Rocks of this type are generally softer materials such as some limestones, sandstones, and porphyries. For the most part, the shockenergy part of the explosive reaction is wasted in plastic-acting rock, leaving most of the work to the gas effect. Since the ratio of gas effect to shock energy is different in different explosives, it is easy to understand why some explosives perform well in elastic rock and poorly in plastic-acting rock, and vice versa. Some of the most difficult blasting situations arise when mixtures of plastic-acting and elastic rock are encountered (Fig. 4). Fig. 4 shows an example of granite boulders cemented together with something like a decomposed quartz monzonite which is plastic-acting. The elastic granite boulders will transmit the shock-strain within itself, but when this shock tries to move through the monzonite to the next boulder, its intensity is absorbed by the monzonite and little shock-strain is placed on the adjoining boulder. In addition to this loss by absorbtion, shock reflection at the surface of the boulder will effect tensile spalling. The net effect is poor breakage of the boulders which do not have drillholes in them as they simply will be popped out with the muck. The same is true (Fig. 5) when layers and joints make

Jan 1, 1970

By L. Valentik

Many attempts have been made during the last 40 years to evaluate the performance of gravity separation equipement, that is, the effectiveness with which light and heavy particles are separated. The most comprehensive treatment of the subject was made by Cerchar at the 1st International Conference on Coal Preparation held in Paris in 1950. The methods suggested by the Conference were accepted and very widely used in the last two decades. This paper discusses an improved method of evaluation in the light of the now-accepted standard presentation. The float-and-sink analysis of the product is presented on a Gaussian distribution curve, resulting in an easier visualization of the inherent difficulties of separation. The ogives of the distribution curve me then plotted, giving a quantitative measure of the deviation from perfect separation as an error distance instead of an error area. Illustrations of the new method are given both for gravel and for coal preparation, but the content is valid and applicable to other types of minerals which are separated by gravity methods. Many attempts had been made during the last forty years to evaluate the performance of heavy-media separation (HMS) equipment, that is, the effectiveness with which floats and sinks are separated.'-' The most comprehensive treatment of the subject was made by Cerchar at the 1st International Conference on Coal Preparation held in Paris. 6 The primary aim was the thorough understanding of the mechanism of separation and the unified presentation of data on gravity separation so that the evaluation and comparison of washery performance could be made from all over the world. No strict overall standardization has been achieved, but after the conference a more or less uniform presentation of performance was accepted, which, during the last two decades, has been very widely used. In this paper, illustration of the old methods and an improved method of evaluation will be given. HEAVY-MEDIA SEPARATION (HMS) PERFORMANCE CRITERIA In the ideal HMS process, all material lower in density than the specific gravity of separation (SGS) would be recovered as floats and all material of higher density would appear as sinks. In order to evaluate the misplaced material, the washery products are tested at the density at which the washing unit is operated. The original type of plot1,7, 8 is shown in Fig 1; this was developed primarily for coal cleaning units. The curve for raw coal represents the cumulative percentages of sink material. The refuse curve is also plotted as a cumulative sink, the percentages being expressed in terms of raw coal. This diagrammatic representation of the results of washing units has the merit of easy visual observance of the degree of separation obtained. The error areas (cross-hatched) are a measure of the amount of misplaced material and therefore they can be used to characterize the quality of separation. The ideal and actual separating performance between floats and sinks can be best seen from the partition curve developed by Tromp,2 where the ordinate is the percentage recovery of the sinks, and the abscissa is the specific gravity (Fig. 2). It can be seen from the shape of the curve that as the SGS is approached, the proportion of material reporting to the improper product increases rapidly. In fact, the SGS can be defined as the density of the material in the feed that is distributed equally between float-and-sink products. When the upper half of the curve is inverted, a shape similar to that of a Gaussian error distribution curve is obtained and therefore the analysis of gravity separation may be carried out by using the law of probability. The shape of the curve in Fig. 2 is determined partly by the density composition of the feed, and partly by the sharpness with which the unit separates floats from the sinks.9, l0

Jan 1, 1970

By H. R. Babitzke

As part of a continuing project to develop refractory metal alloys for high-temperature structural applications, the Bureau of Mines applied solid solution and precipitation strengthening techniques to improve the properties of columbium alloys. The purpose was to investigate the effects of hafnium, tungsten, and boron on the formability, strength, and oxidation resistance of columbium. The experiment was of factorial design with two replications which called for 72 ingots of 36 basic compositions, weighing 150 grams each. Hafnium, tungsten, and boron were evaluated at 3, 3, and 4 levels, respectively. Values of alloy content are all in atomic percent. The highest strength observed was 29,000 psi at 1,200° C for alloys Cb-15Hf (No. 3), Cb-7.5Hf-5W-2B (No. 14), and Cb-15Hf-5W-2B (No. 15). At 1,200° C, the ternary alloy Cb-15Hf-5W (No. 6) which has shown good properties in previous Bureau of Mines investigations was the most resistant to oxidation For boron additions, the alloys oxidized more readily with increasing amounts of this element. The fabricability of the alloys high in boron became increasingly difficult, resulting in an inadequate number of alloys required for a complete statistical analysis for all the tests. As a result of the decrease in ductility, an insufficient quantity of tensile samples were available for a proper analysis for the high-temperature strength data.

Jan 1, 1970

By J. E. Terry

This paper outlines the steps that are being taken to close the gap between training and industry and indicates areas in which more work needs to be done. Although based on experience in the Maritime Provinces, it is applicable to industrial and educational studies across the length and breadth of Canada.

Jan 1, 1970

By F. C. Appleyard

As one of the more important Industrials Minerals, gypsum occupies a significant place in the economy of the United States, particularly in that segment which can be loosely called the Construction Industry. For many years, products made from gypsum have been a major building material, and the usefulness and versatility of these products is such that their widespread use is expected to continue. In 1968, according to U.S. Bureau of Mines statistics, the value of all gypsum products sold in the United States was 405,000,000 - and although this value has dipped from the 1964 high of $ 432,000,000, it is expected to trend upward in the next few years to equal and surpass this figure as the construction industry recovers from its current squeeze of "tight money" and high interest rates. There are many factors to be measured in determining the potential value of any mineral deposit, and how it might fit within its particular industry. What, then, are the qualities which a gypsum deposit must have in order to profitably participate in the four hundred million dollar plus business which is the gypsum industry? First let's consider the geology of gypsum, the geographic distribution of deposits, and the more important factors such as size, grade, capital requirements, and operating cost. Then, an understanding of the uses of gypsum, various types of products, and location of markets would be helpful, along with such other factors as the structure of the industry, price trends, etc.

Jan 1, 1970

Some of the problems associated with drill core evaluation of alluvial tin deposits and correlation with plant-scale recovery are discussed. Panning churn-drill cores on site tends to undervalue such deposits because of failure to recover completely all the available liberated cassiterite, and secondary gravity processing may also fail to give an accurate determination of potentially recoverable tin. However, by using a combination of heavy liquid separations, x-ray fluorescence analysis for Sn, and normal methods of reflected and transmitted polarized light microscopy, a quantitative assessment of alluvial material can be carried- out. The information obtained may include the liberation characteristics and distribution with size of the cassiterite, the nature and quantities of the various gangue minerals, and the amount of potentially recoverable cassiterite in the material as compared with the amount locked with light gangue minerals and hence difficult or impossible to recover. In addition, an analysis of the efficiencies of the various gravity processes, such as panning, jigging, and tabling, used to determine "recoverable tin" in the alluvial material, can be carried out. A detailed example is given of this type of investigation, in which an assessment was made of a churn-drill core from Uncia, Bolivia.

Jan 1, 1970

By D. E. Kirby

The electrochemical reduction of AlC13 was investigated as a process for the production of aluminum. An externally heated, single-compartment cell with a rammed refractory lining was used with molten KCl-NaCl-AlC13 electrolyte. Aluminum was deposited qt 700° to 760° C with a current of 100 to 200 amperes on a molten aluminum cathode. Chlorine was evolved at a graphite anode and collected and measured to provide a quantitative evaluation of the AlC13 reduction. Aluminum was removed from the cell by siphoning or ladling. Granular AlC13 was added periodically to replenish that depleted from the electrolyte. Concentrations of 7.5 to 17.5 percent AlC13 in the electrolyte were optimum for operation. Anode current efficiencies of 83 to 85 percent were attained, using anode current densities of 5.9 amperes per square inch and an anode-cathode distance of 4 inches. The chemically bonded, alumina liner was resistant to attack by aluminum and chlorine but susceptible to erosion at the surface of the electrolyte. Titanium diboride proved suitable for the electrical connection to the molten aluminum cathode. Aluminum of a purity equal to or better than 1100 series metal was electrowon continuously from commercial AlC13 for a period of 4-1/2 months.

Jan 1, 1970

By C. J. Havard, G. C. Taylor, D. G. Cook, N. C. Ollerenshaw, D. K. Norris

"The area encompassed by this report is the eastern and northern Cordillera, shown on the composite map accompanying these background papers. It extends from the 49th pm•allel to the Arctic Ocean and from the Rocky Mountain and Tintina trenches to the Interior Plains. The Mackenzie delta is included in the discussions because of the implications of the bedrock geology of the Arctic Plateau and Coastal Plain on the hydrocarbon and mineral potential beneath it.The eastern and northern Cordillera forms the back-bone of the Western Canada sedimentary basin and from it most of the principles of orogenesis and epeirogenesis relating to the understanding of the structural, depositional and fossil record of the basin have been derived. It may be divided roughly into two parts, reflecting basic differences not only in structural style but also in mineral potential. The more easterly and younger rocks generally contain hydro-carbons, coal and non-metallic minerals; the more westerly and older rocks contain metallic and industrial minerals."

Jan 1, 1970

By Neil C. Hario

The purpose of this paper is to explore the various designs and design alternates available for large fine crushing plants, and to discuss objectives and criteria upon which these designs are founded. Common practice for size reduction of run-of-mine or run-of-pit ore in preparation for subsequent treatment utilizes a three-stage system. First stage, or primary breaking is generally carried out with jaw or gyratory crushers. The usual output from this stage provides a feed for fine crushing in the size range of 6 to 10 inches. This discussion is limited to the process of fine crushing, and we will further limit it to what is commonly called secondary and tertiary crushing. We define a large crushing plant as one with a minimum capacity of 2,000 tons per hour. Generally, these plants utilize cone type crushers to reduce ore for rod, ball, or pebble mill feed.

Jan 1, 1970

By Keros Cartwright

Sanitary landfilling has become one of the most widely used methods of disposing of solid refuse. A principal concern of regulatory agencies and the public itself is that landfill operations do not degrade the physical environment, including water resources, and the ground-water reservoir in particular. Ground-water and engineering geology can guide landfill operations into suitable terranes or develop measures to compensate for any natural limitations at a particular site Experience and research in Illinois suggest four activities relating to landfill disposal that warrant attention by geologists and engineers: (1) Regional delineation of favorable and unfavorable hydrogeologic conditions to facilitate planning and preliminary screening of potential landfill sites. (2) Site evaluations, with considerations of geologic materials, topography, water levels, flow systems, and local occurrence and use of water resources. (3) Re- search on aspects of the hydrogeologic environment that control effects of, or are modified by, landfills. (4) Formulation of practices in the siting, construction, and operation of landfills that prevent, mitigate, or isolate deleterious effects. The first two activities are basically in the domain of earth science, requiring the application of fundamental concepts of geology and hydrology and conventional site-exploration methods. The third activity, research, requires contributions from geology as well as other disciplines, including soil physics, sanitary engineering, and chemistry. The fourth calls for policy decisions by regulatory agencies and elected officials, using the contributions of scientists and engineers.

Jan 1, 1970

By David R. Maneval

In 1956 the Legislature of the Commonwealth of Pennsylvania created a "Coal Research Board" in the Department of Mines and Mineral Industries. Over the years through amendments to the original legislation, the scope of authority for research has been expanded from the narrow area of improving and increasing the utilization of coal to covering all aspects of coal technology and any other area of interest which would be of value to the coal industry. In January of 1964, the Board commenced a vigorous program using appropriated funds and funds donated by the coal industry to finance a research program devoted to seeking solutions to the mine drainage problem. A review of published literature on the treatment of mine drainage indicated that much work done up to that point in time concerned only the mechanism of mine drainage formation and theoretical chemistry. Very few applied, developmental, or engineering studies had been devoted to finding practical solutions to the problem of polluted waters being discharged from active or abandoned mines. Projects were therefore undertaken on a wide variety of more utilitarian approaches. This paper will discuss briefly some of the pollution abatement approaches which have been funded by the Coal Research Board of this State, and will describe in some detail a multistage flash evaporator treatment plant now under construction.

Jan 1, 1970

By William Wargo

The basic reason for lining underground cavities is to keep the cavity open during its useful life by providing adequately for the support of the surrounding rock and for the necessary degree of water tightness. This covers the entire field of support methods from the simpliest timber support to reinforced concrete in all its variations as applied to tunnels, galleries or shafts. The problem involved in the design of more efficient and economical lining systems for even bigger cavities has been magnified by increased speed of advance made possible by better blasting tecniques, improved tunneling machines and more efficient material handling. Tunnel lining today requires a disproportionate amount of time and money compared to other operations mostly due to the manuel labor involved in its installation. One solution to this problem is the developement of an entirely new concept in tunnel lining designed notoonly to overcome this bottleneck but also to open up the field for further increases in speed of advance. This new lining system acts first as a fast protective armour then becomes the concrete metal form and ends up as reinforcement sheet inside the concrete lining. This system developed and manufactured by Bernold A. G. of Switzerland since October 1968 has been installed in 25 applications in Europe under all ground conditions from stable rock to unconsolidated ground.

Jan 1, 1970

By Thirumalai, K.

Although the term "spalling" has long been known, Norton l first referred to its usage for the fracture or disintegration of materials subjected to rapid temperature changes. Spalling of ceramic materials at high temperatures has received attention in the past. Removal of the char formed during ablation in re-entry of space vehicles has been referred to as mechanical spalling. The first experiments to evaluate the process of rock fragmentation by thermal spalling were conducted by Stoces using a series of gasoline burners on the quartz veins of the Zinnwald deep mines in Germany. After the development of rocket-jet burners, the principles of 'thermal spalling combined with high fluid momentum found wide practical application in rocks. The well-known jet piercing process for drilling blastholes in taconite and for jet channeling in the quarrying of granite are among the more notable of these application^.

Jan 1, 1970

By K. P. Gupta, P. C. Panigrahy

The stabilization of the R, a-Mn, and 0-Mn phases have been studied in the Mn-Ti-Fe and Mn-Ti-Co systems. Iron and cobalt both appear to stabilize the (Mn-Ti) R phase to almost the sarne extent. The R-phase region was found to extend from the lowest e/a to slightly beyond the maximunz e/a limit known for this phase. But, while iron appears to stabilize the a-Mn phase, cobalt tends to stabilize the p-Mn phase. In the two systems manganese appears to get replaced by iron and cobalt in each of the mentioned phases. The instability of the a-Mn phase in the Mn-Ti-Co system and the /3 -Mn phase in the Mn-Ti-Fe system cannot be explained on the basis of adverse size effects because atomic diameters for both iron and cobalt (C.N. 12 at. diam) are ziery similnr and not much different from manganese which they replace. Qualitatively, the reason for the stability of the a-Mn and the p-Mn phases can be traced to the more favorable e/a ratio prevailing in the respective systems and to a competing tendency between the two phases. In transition metal alloy systems the o, p,P, R, a- Mn,' and p-Mn2 phases have been claimed as electron compounds. A large volume of work has been done to establish the criterion for the formation of the o phase but until very recently practically no systematic work was done on the a-Mn and the /3-Mn phases. A recent investigation on the P-Mn phase3 indicates the e/a criterion for p-Mn phase stabilization. Since the R phase was first known to appear only in certain ternary systems1 no detailed work was then possible for this phase. The R phase has been recently discovered as a binary intermetallic compound in the Mn-Ti~ and Mn-si~-' binary systems. The existence of binary R phases opens up the possibilities of studying the effect of alloying elements on the stabilization of the R phase. Of the two binary systems possessing an R phase, the Mn-Ti system appears to be more interesting because at a suitable high temperature it is possible to find the three electron compounds, the a-Mn, p-Mn, and R phases, side by side and it is possible to study the effect of a third transition element on these three electron compounds. For the present investigation iron and cobalt, so called B elements for the formation of electron compounds, have been used as the third element to study the stabilization of the a-Mn, P-Mn, and R phases. EXPERIMENTAL PROCEDURE The alloys were prepared by using 99.9 pct pure electrolytic Fe and Mn, 99.5 pct Co, and crystal bar titanium, supplied by Semi Elements Inc., New York and Gallard Schelsinger Mfg. Co., New York. Weighed amounts of the components were melted in recrystal-lized alumina crucibles in an inert atmosphere (argon) high-frequency induction melting unit. Titanium was made into fine chips for easy dissolution and a special charging procedure was adopted to avoid contacts of titanium chips with the alumina crucibles. Up to 20 at. pct Ti, the maximum titanium content in the investigated alloys, there was no visible sign of reaction of titanium with the alumina crucibles. With a careful control of melting time and temperature the losses were minimized and were always found to be below 0.1 pct. Because of such small and almost constant weight losses, the alloys were not finally analyzed. The alloys were wrapped in molybdenum foil and annealed in evacuated and sealed silica capsules at 1000" * 2°C for 72 hr and subsequently quenched in cold tap water. Annealed samples were examined metallographically and by X-ray diffraction. For all high manganese alloys oxalic acid solutions of various concentrations and 1.0 pct HN03 solution were found suitable as etching reagents. Best contrast between the a-Mn and the R phases could be obtained by using freshly prepared 60 pct glycerine + 20 pct HN03 + 20 pct HF solution. For high iron and cobalt containing alloys, especially for alloys containing the a-Fe, y-Fe, and P-Co phases, 15 cc HNOJ + 60 cc HC1 + 15 cc acetic acid + 15 cc water solution was found to be the best etching reagent. All X-ray diffraction work was carried out (using specimens prepared from annealed powders) with a 114.6 mm diam Debye-Scherrer camera using unfiltered FeK radiation at 25 kv and 10 ma. All calculations for X-ray diffraction work were carried out using an IBM 7044 digital computer RESULTS AND DISCUSSION The two ternary systems, MnTiFe and MnTiCo, were investigated near the manganese rich end, Figs. 1 and 2, and show some common features. In both alloy systems large extensions of narrow R phase regions occur at almost constant titanium contents. At titanium contents higher than that of the single phase R-phase alloys, the same unidentified X phase was found in both ternary systems. The extensions of the X phase close to the Mn-Ti binary indicate that this phase could be the TiMns phase. Too few X phase diffraction lines were present in the diffraction patterns to make positive identification of the X phase. In contrast to this similarity the two systems show opposite behavior in the extensions of the a-Mn and 8-Mn phase regions; while iron tends to stabilize the a-Mn phase, cobalt

Jan 1, 1970

By C. D. Williams, C. E. Ells

The susceptibility of quenched and aged Zr-2.5 wt pct Nb alloy to embritt2ement during irradiation has been examined for a number of solution temperatures and aging times. Material quenched from temperatures approximately 40°C below the transus has high tensile ductility, and this ductility is insensitive to aging at 500°C or to irradiation. If, however, the material is quenched from temperatures above the transus it becomes highly susceptible to loss of ductility either from aging at 500 or from irradiation. Inter granular failure is characteristic of the materials having low ductility. The distribution of the equilibrium phase is found to control the susceptibility to embrittlement by restricting 6 grain growth during heat treatment and thus influencing crack propagation. IN zirconium, as in titanium, -stabilizing alloy additions are used to obtain high strengths via quench and age heat treatments, and the Zr-2.5 pct Nb alloy has been developed1 because of its strength advantage over the Zircaloys. Early in the development of the Zr-2.5 pct Nb alloy the problem of 13 embrittlement was appreciated, and for this reason the solution temperature was chosen below the p transus.' In the course of irradiation studies on quenched and aged Zr-2.5 wt pct Nb alloy it was found' that irradiation introduced an important aspect of p embrittlement, riz., material quenched from the phase and aged 24 hr at 500°C was severely embrittled by moderate doses of neutron irradiation. This effect had not been studied in titanium alloys. In titanium the metallurgical features leading to 0 ernbrittlement were found to be structures with: a) coarse a platelets at the grain bondaries, b) finely dispersed a uniformly distributed throughout the (0) matrix,6 c) Widmanstatten a-13 with more than 50 pct P, d) the presence of some metastable p transformation products,3 and e) large prior -phase grain size.5 Alternatively, the presence of a uniform distribution of coarse a was conducive to high ductility and a structure largely of equiaxed a was very dctile. The detailed mechanisms of the embrittlement have not been worked out for all of these conditions, although weakness at either a-matrix boundaries or prior p grain boundaries have been prominent in the eculation. It was proposed that acicular a might act as a mild notch, and low ductility has been associated with easy fracture along its boundary.' There have been two opposing suggestions for the source of the high ductility associated with equiaxed a phase. JaffeeB proposed that this a would accept a large por- tion of the oxygen, thus increasing the ductility of the matrix, whereas after study of a Zr-Nb-Cu alloy Weinstein and oltz proposed that the a phase, softer than the martensitic matrix, acted to blunt cracks formed in the matrix. In the present work we have studied the effect of neutron irradiation on the ductility, particularly the P embrittlement, of the Zr-2.5 wt pct Nb alloy. By a variation of solution temperature and aging time a variety of metallurgical conditions have been examined, and a range of resultant ductilities obtained. The ductility has been related to the material microstructure and mode of fracture. EXPERIMENTAL The alloy used in the present work came from two separate ingots fabricated into rod of 3/8 or i in. diam, Table I. For both batches the P transus temperature was approximately 890° C. Most of the heat treatments were done directly on lengths of the j} in. diam rod, after which the tensile test specimens were machined. Quenching was achieved by dropping rods from a dynamic vacuum into water, the cooling rate estimated to be 2 100°C per sec. For aging the rods were encapsulated in evacuated silica tubes. Round tensile test specimens, with gage diam and length 0.160 and 1.0 in., respectively, were used throughout and pulled at room temperature or 300°C on Instron tensile machines, at a crosshead speed of 0.05 ipm. Specimens were irradiated in the NRX and NRU reactors, in facilities described in previous publications.'0 The metallurgical conditions examined have been: All tensile test specimens were machined with axes in the axial direction of the swaged rod. Although the specimen had a degree of preferred crystallo-graphic orientation with basal plane normals both parallel with and perpendicular to the tensile axis, the material was comparatively isotropic." The techniques of thin foil examination in the electron micro-

Jan 1, 1970

By W. A. Zingg

Impervious zones in copper waste heaps create a problem in contacting the rock with leaching solutions. These zones are normally associated with compacted layers .formed on the surface of each lift by dump truck traffic and by disintegration of the rock exposed to atmospheric conditions. These layers are usually only a few feet in depth--but, nevertheless, act as barriers to vertical flow causing the leach solution to perch in the heap, Consequently, much of the rock remains untouched and the leach solution breaks out the side of the heap instead of continuing downward to bedrock. One solution to this problem is breaking the hard pans with explosive charges. However, to use explosives means adopting new explosive materials and methods. To use this process successfully requires finding answers to operating conditions inherent to waste heaps. Foremost among these are: (1) type and size of casing that can be used because of limitations brought about by drilling problems, caving and, corrosive conditions; (2) perforating the casing at required levels; (3) an explosive capable of being pumped; (4) obtaining detonation of the, main charges through, the wail of the casing; (5) an explosive with the ability to propagate through the voids of the rubble and one which is not affected by water, acidic solutions, or back pressure conditions from hydrostatic heads; (6) to heave and rupture the compacted zones without chambering or recompressing the waste material.

Jan 1, 1970

By G. H. K. Schenck

Weather changes of a daily, weekly, or seasonal period affect mineral production and cause significant losses that are considered unavoidable. Private weather forecasting services are available on a contract basis that can significantly reduce the uncertainty associated with weather-induced changes in the production of and demand for minerals. This paper provides examples of current practice and reviews the opportunities that await those producers who incorporate weather services as an integral part of their operating, scheduling, and planning procedures. Private weather forecasts can be highly accurate because atmospheric trends such as conditions and movement tend to persist and are related to previous meteorological events. Commercial meteorological services are prepared to deal specifically with a mineral producer's special problems (Table 1). Tactical use of private forecasts is a major advance over the severely restricted value of public forecasts which, of necessity, are general in nature and cover a dispersed geographic territory. Private weather services provided on a consulting fee basis offer the mineral producer the opportunity for tactical and strategic response to weather conditions at an acceptable cost. This contrasts with the too-frequent current tendency to view weather as a random variable the costs of which are unknown and about which nothing can be done.

Jan 1, 1970

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.' and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By Jacques B. Wertz

Recurring movements remotely connected with the Murray fracture zone and the San Andreas fault complex, together with the slow northwestward drift affecting the Baja California peninsula, could progressively have accentuated the tensional situation already connected with the anticlinorium in southern Arizona. From the fragmentary data gathered on the Texas lineament, it appears that a very mild curvature, concave to the northeast, may be present along this belt throughout Arizona. Those localities where the successive changes in direc¬tion of the strands of the lineament belt seem to occur do generally coincide with intersections of both north-northwestern and northeastern breaks. It is along the outward, southern fringe of the belt (at such structural centers like Bisbee, Baboquivari, Ajo) that the greatest impact of regional movements could be expected to have occurred through tangential-torsional stresses. Although it si accepted that the north-northwestern and more particu¬larly the northeastern fractures in Southeast Arizona are propitious to or partially responsible for mineralization, it seems undeniable that the Texas lineament belt must have greatly increased the potentialities for ore throughout the Arizona copper province. While intrusive bodies occur near major intersections, with the Texas lineament belt as a common denominator, it seems, the ore deposits are to be found close to one of the intrusive stocks, varying in distance from contiguity (Bisbee) to one or two miles away (Silver Bell orebodies).

Jan 1, 1970