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By P. T. Carter, A. B. Murad, H. B. Bell

N. A. Gokcen (Michigan College of Mining and Technology, Houghton, Mich.)—The activities of silica, represented in Fig. 5 for the systems MnO-SiO2 and CaO-SiO2, are in disagreement with the established binary phase diagrams. At Ns102 = 0.50 in MnO-SiO2, and at Ns102, = 0.65 in CaO-SiO2, each binary system is saturated with respect to silica at 1550°C, and therefore as102, is unity in each case. The curves for as102 (FeO-SiO2) and as102, (MnO-SiO,) should nearly co-

Jan 1, 1953

By H. R. Spedden, A. M. Gaudin, M. P. Corriveau

A preliminary study of silver ion adsorption by sphalerite in ion exchange column with influent electrolyte marked with radiosilver is described. Rapid ion exchange occurs at first followed by slow reaction controlled perhaps by solid state diffusion. One experiment with radiocopper instead of radiosilver is reported briefly. IT has been known for many years that sphalerite is floated after it has been activated by a metallic cation, particularly copper.' The activation of sphalerite by copper is known to be an exchange of an atom of copper for an atom of zinc at the surface of the sphalerite.2,3 It has been estimated from various guesses of the available mineral surface that the depth of the copper-bearing coating is of the order of thickness of one atom. However, the exact mechanism of the activation process is unknown. A number of metals other than copper act in the same general manner."' " In particular, it has been known that silver replaces zinc at the surface of sphalerite. As copper is usually divalent, whereas silver is monovalent, it may well be assumed that there are differences, perhaps major differences, in the detailed scheme of activation by these two cations. Furthermore, since silver has unusual photoelectric properties and may be a contributor to the fluorescence of sphalerite, a study of its activating mechanism might open up some interesting avenues for exploring these other phenomena. The choice of silver as an activator of sphalerite was suggested also by the fact that its radioactive tracer, silver 110, is particularly convenient in that it has a long half-life and is energetic enough to permit counting through a counter window. The experimental technique selected, therefore, included the preparation of solutions of silver nitrate con- taining a proportion of active silver nitrate sufficient to give convenient counting data. In further considering the method to be used, a desirable choice seemed the use of batch experimentation in which a given solution was allowed to act on a certain lot of mineral for a given length of time at a given temperature, this period of mutual reaction being followed by analyses of the separated solid and solution. But an alternative method seemed more attractive. This is the method now so familiar to the users of ion-exchange resins, which was first made famous by the Russian chromatographer, Tswett.6-8 It consists in forming the mineral into a porous column through which the solution is allowed to flow at a constant rate. The usual method of allowing a batch of solid to react with solution is the equivalent of a single plate distillation operation while the chromatographic or ion-exchange column is a multiple-plate method—the multiplicity of the plates being represented by the reciprocal of the rate of flow of solution through the column. It seemed to us that the chromatographic method had such

Jan 1, 1952

By L. S. Darken

IT has been known for sometime that in an ionic lattice, such as that of Ag2S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulfide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulfide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall1 support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffusion proposed by several authors, most recently by Birchenall and Mehl.2 This theory has, however, also been questioned3.4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however, Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz,5 who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a similar mechanism, whatever it may be, at a greater or lesser rate, thus giving rise

Jan 1, 1948

By Thomas C. Wilder

The activities of both components and the partial and integral molar thermodynamic properties of mixing for the liquid Al-Ge system at 1200°K and for the gertnanium-rich Al-Ge liquidus have been determined from data for eighteen alloys of compositions in the range 0.0593 < 0.880 using the reuersible gal-vanic. cell in the temperature interval 9320 to 1258°K. The liqui-dus compositions above 93 2 °K loere also ve determined by observing the discontinuities in the C us T plots for the high-melting alloys. This system shows moderate negative deviation from ideality throughout, the values for y° being 0.212 and 0.189 for aluminum and germanium, respectively, at 1200°K. Pavtial molar Properties of aluminum on the germanium-rich solidus and at infinite dilution in Ge(s) oboue 932°K were estimated from the foregozng measurements and the equlibrium data of previous investzgators. RECENT compilations of data1" have shown an increasing demand for knowledge of the thermodynamic properties of mixing of metallic alloy systems. In the case of binary-liquid systems where one of the components is a semiconductor this information is useful because, primarily, properties of the second (dopant) component on the liquidus, solidus, and at infinite dilution may be determined more accurately than from calculations based on the phase diagram. In this investigation a reversible galvanic cell was used to determine the chemical potential of aluminum in the two-phase region, liquid + [Ge], on the germanium-rich side of the A1-Ge system in the temperature range 932" to 1193°K. In addition, similar measurements for homogeneous liquid A1-Ge alloys for the entire composition range were obtained for the temperature interval 932" to 1258°K. The cell used was: The experimental technique and the treatment of the data were essentially the same as described earlier394 and are elaborated upon only briefly here. Each cell consisted of a liquid aluminum anode and three A1-Ge alloy cathodes of different composition which were held in Morganite alumina crucibles. The alloys were made up from aluminum and germanium weighed to the nearest 0.1 mg to a total weight of 5 to 10 g. Aluminum was a gift of Aluminum Co. of America and had a purity of 99.995+ pct. Germanium of transistor grade was a gift of Bell Telephone Laboratories. The four electrodes were contained in a larger alumina crucible which also held the prepurified fused chloride electrolyte. Contact to the electrodes was made by tantalum wire leads sheathed in alumina. The tantalum leads were centered in the electrodes by suitable positioning of an alumina radiation shield which fitted on the top of the - alulnina crucible. Two chrome l-alumel thermocouples, sheathed in quartz wells, completed the internal cell arrangement. The entire assembly was enclosed in an alumina tube, fitted with a water-cooled copper head so the system could be evacuated and then flushed with purified argon. *

Jan 1, 1967

By G. Pizzi, G. M. Ciucci, G. L. Chierici

The use of the material balance equation to estimate the volume of hydrocarbons originally present in a reservoir, whose producing mechanism is partly due to water drive, has been discussed in the literature by several authors. There is no general agreement upon the possibility of obtaining reliable results by this method. Gas reservoirs in contact with an active aquifer are considered in this paper. Theoretical considerations based on the cybernetic principle of uncertainty (which states that the internal structure of a system cannot be uniquely determined from its observed external behavior) lead to the conclusion that the volume of gas originally present in a reservoir of this type cannot be uniquely determined from its past history. The range of values which encompasses the actual value of the reserves varies from case to case and must be determined by either numerical or analogical methods. Results obtained for six gas fields are reported. All these fields were produced with small fluctuations in their production rates, as is common practice for gas reservoirs; no gas storage fields were considered. Results obtained show that reserves values in a range of 1 to 2, associated with appropriate aquifers, allow the matching of the reservoir past history with mean-square deviations less than the experimental errors involved in pressure and produclion measurements. Similar results have been found in several other partial water drive gas reservoirs. From these results it is concluded that gas reserves cannot be uniquely determined from the past performance of partial water drive reservoirs, at least in cases where the reservoir has been submitted to small fluctuations in the production rates, and pressure data of normal accuracy are available. INTRODUCTION A number of authors have analyzed the problem of estimating the reserves originally present in a partial water drive reservoir from its past pressure-production performance. Literature which deals with this subject can be grouped, according to their conclusions, as follows. 1. A reliable value for the reserves can be obtained even if reservoir data (pressure and cumulative production) are affected by errors within the normal range.&apos;-&apos; 2. A reliable value for the reserves can be obtained only if reservoir data are very accurate&apos;- or if past production performance has been subjected to abrupt variations in the production rate."&apos; 3. No unique value for the reserves can be obtained from reservoir past production performance. This conclusion has been based upon theoretical considerations" and verified in several field cases. The purpose of this paper, which deals only with partial water drive gas reservoirs, is to test the above conclusions against actual field cases. Some theoretical considerations on this problem are also presented. THEORETICAL CONSIDERATIONS As the behavior of a gas reservoir communicating with an aquifer depends on both the aquifer and the reservoir characteristics, the physical system to be studied is the combined gas reservoir plus aquifer. The information which is available for studying the performance of such a system is the well production rates and bottom-hole pressures, all given as functions of time. The external behavior of the reservoir-aquifer system is therefore described by 2n input variables (Gp, Wp,) and n output variables (p,), n being the number of wells in the reservoir. In reservoir engineering it is common practice to consider the reservoir as a whole, disregarding the internal distribution of pressures and of producing wells. This practice is equivalent to substituting the above multi-variable system with a single-variable system, where the average reservoir pressure is the only output variable and the cumulative production G,(t) and W,(t) are the input variables. The internal structure of such a system, defined by initial gas reserves G, aquifer shape and dimensions, boundary conditions and petrophysical parameters distribution throughout the aquifer, is unknown. Therefore, from a cybernetic point of view the system is a "black-box It has been demonstrated" that for a blackbox the indetermination principle holds. Accordingly, the number of different internal structures (or set of parameters) which can account for the observed external behavior is infinite. As a consequence, the initial reserves cannot be uniquely determined from the reservoir past performance. When W,(t) is known, the determination of G from

By P. R. Gage, R. W. Bartlett

At high temperatues and reduced oxygen pressuves, molybdenum silicicles oxidize to form SiO(g) vathev than a passivating SiO2 film. This is a sevious problem for low-pressure applications of sili-cide-coated rejvactory tnetals. As oxiclalion pvoceeds, the higher oxidntion potential of silicon initially suppresses oxidation of molybdenum and silicon is depleted near the surface. Eventually, silicon depletion causes secondary passivation (SiO2) mid an active to passiue transition in oxidntion behavior at moderately low pressures. At very low pressures, silicon depletion continues until steady-state oxidation of both silicon and rnolyhdenum can proceed at rates propovtional to their initial stoicliiorrzetvies. Ohsel-vations of &apos;oxidatiou-rate belzcriliov at temperatures from 1101° to 1700°C and oxygen pressures from 10-7 to 1 at in were made using thermogravimetn&apos;c, X-ray diffraction, and elect?*on-rtric?ro/,vobe techniqrres. The experimental results are in good agreement with calculated lirnits for the various types of behavior that were based on tlievtnochernicnl atzd dffusion rate data for the Mo-Si system. A protective oxide film normally forms during the oxidation of elemental silicon. However, at elevated temperatures and reduced pressures this film is not present and oxidation is rapid. wagnerl has shown that this behavior occurs because SiO(g) is more stable than SiO2. The behavior of the silicides at high temperatures is similar but more complicated. Molybdenum and several silicide compounds are involved and the chemical activity of silicon, or the equivalent silicon vapor pressure, can vary considerably in these phases. Also, diffusion in the silicides resulting from reactions in which a higher silicide is reduced to a lower silicide, or molybdenum containing dissolved silicon, must be considered. EXPERIMENTAL AND ANALYTICAL METHODS Isothermal oxidation experiments were conducted using hot-pressed MoSi2 and Mo5Si3 wafers. Each experiment was conducted at a fixed oxygen pressure by controlling the flow of oxygen in and out of the furnace chamber. Most of the experiments were conducted in a molybdenum-wound tube furnace. Special construction features, including use of a high-purity dense A12O3 refractory tube, permitted operation in high vacuum to 1500°C. Higher temperatures could be obtained at higher working pressures and with a sacrifice of tube lifetime. Temperature was measured with three Pt 6 pct Rh/Pt 30 pct Rh thermocouples and controlled with a proportional controller. Weight changes were monitored with a quartz spring balance. The few experiments, at higher temperatures and low pressures, were conducted in a cold wall vacuum chamber using induction heating with direct susceptance of the sample. Because of the variable levitation effect of the induction coil on the sample, weight changes could not be monitored continuously in these experiments. All samples representing both experimental methods were weighed before and after oxidiation and examined with a microscope and analyzed by X-ray diffraction. The analytical treatment assumes equilibrium at interfaces and uses existing thermodynamic data. For convenience, equilibria are expressed as chemical potentials or as vapor pressures of the gases involved. The resulting differences in equilibrium vapor pressure between adjacent interfaces and between the surface and external atmosphere drive diffusion processes in the solid and gas boundary film, respectively. These diffusion processes govern the rate of oxidation. A bibliography of the sources of thermochemical data for the reactions pertinent to the Mo-Si-O system is given in Table I. Reactions are listed with the sources of free-energy data referenced. Since all of these reactions involve one or more gas species, usually oxygen, a plot of the product-gas chemical potential, -RT In Pg, vs absolute temperature for each reaction is given in Fig. 1. These curves can be used to determine equilibrium vapor pressures or to compare the stability of different compounds in the various gases: O2, Si, SiO, and Moo3,. The data of Table I and Fig. 1 were used to determine the analytical results presented in this paper. EXPERIMENTAL RESULTS The weight changes for three MoSi, samples oxidized at 1500°C are plotted against time in Fig. 2. The treatments were identical except for the indicated variance of oxygen pressure and each curve represents one of three characteristic types of behavior that were observed. The upper curve is an example of passive oxidation, which is defined as

Jan 1, 1965

By H. J. Gluiskoter

The chlorine content of the coals in the Illinois Basin ranges from 0.00% to more than 0.60%. The chlorine content of the Herrin (No. 6) Coal has been mapped on a regional scale and, in general, increases with the depth of the coal. The depth-chlorine correlation exists because the coal is in apparent equilibrium with the composition of the ground water associated with it, and the salinity of the ground water generally increases with depth. At least part of the chlorine can be easily removed from the coal in the laboratory. In a natural weathering experiment, chlorine values decreased markedly during an 8-week period. Results to date indicate that none of the coals studied has a sufficiently high chlorine content to make it unusable in high-temperature steam boilers, although special steps may be necessary in the preparation or utilization of some of the highest chlorine coals. Investigations into the occurrence and distribution of chlorine in Illinois coals have been in progress at the Illinois State Geological Survey for over 35 years. Since 1948, chlorine analyses of face channel samples and of drill core samples of coal have been made routinely. The increased interest in chlorine and alkalies in coal in the U.S. followed that in Europe, where power plants during World War II were called upon to produce at higher levels than previously and with less down time for maintenance. Higher steam temperatures were reached, resulting in increases in the amount of fouling of external heating surfaces and in corrosion of boiler tubes when high chlorine coals were used. Early studies of the problem showed that coals with high chlorine content were more likely than those low in chlorine to cause difficulties in installations fired with powdered fuel. Crossleyl reported that the first rule of thumb developed for British coals was that coals considered to be high in chlorine (more than 0.30%) caused the most trouble, those intermediate in chlorine content (0.15% to 0.30%) were less likely to cause difficulties and those low in chlorine (less than 0.15%) generally were not associated with alkali bonded deposits and corrosion. However, this relatively simple picture was not adequate to characterize the difficulties that could be expected during the utilization of a large number of coals and Crossley1 developed another scheme for assessing the chances of superheater corrosion. This scheme took into consideration the observation that coals high in sulfur as well as chlorine are more likely to cause corrosion and fouling than coals low in sulfur and high in chlorine. Crossley also considered the ash content. When two coals had the same chlorine and sulfur contents, the one with the greater amount of ash would be the less likely to cause difficulties. Knowing only the amount of chlorine in a coal obviously will not give all the answers. Indeed, the significance of the chlorine content has been much discussed and it has been suggested that perhaps the total alkalies are a better indicator of possible troubles. The observation that the deposits that form

Jan 1, 1968

By M. C. Chang, J. Dasher

The Crucible mine in Pennsylvania, operating on Pittsburgh seam coal, is rated at 5000 tpd. The washing plant, built in 1943, is rated at about 400 tph, using hydroseparator boxes to wash the coarse coal (4 x 5/16 in.) and hydrotator units for the fine coal (5/16 x 0). It is generally acknowledged that gravity concentration equipment cannot be used efficiently to bene-ficiate coal finer than about 65 mesh. Before the present flotation circuit was installed, Crucible recovered its fine coal slurry, predominantly —24 mesh material, by passing it through a battery of five 14-in. and one hundred and ten 3-in. Hey1 & Patterson cyclones in parallel with a 75-ft Dorr thickener. About two thirds went to the cyclones and one third to the thickener. Underflows from cyclones and thickener were filtered, respectively, in one 12-disk Eimco and two 4-disk Oliver filters fitted with stainless steel cloth. The resulting cakes were added to the coarse metallurgical coal. The filtrates, overflow from the 3-in. cyclones, and thickener overflow were recycled to the coarse coal plant. The three major problems encountered in this system became acute when the mine switched from track-mounted machinery to the more economical off-track equipment. The quality and uniformity of product declined, too much slime accumulated in the circuit, and waste pond disposal became highly impracticable. Lowering of Quality and Uniformity: Since the filter cake was not beneficiated in any way, addition of this material, which contained about 18 pct ash. would certainly lower the quality of metallurgical coal. Difficulties of handling the high-ash, high-moisture cake were compounded by the lack of adequate blending facilities at the mine, making it impossible to maintain uniform feed for the coke ovens. For a two-month test period, to verify the source of trouble, all filter cake was excluded from the metallurgical coal. The excluded filter cake was stocked in the yard. Slime Buildup: The moisture retained in the coarse coal products and the filter cake provided daily the only means of slime bleed from the circuit. As this bleed was not enough to offset the incoming fines in the raw coal feed, there was excessive buildup of slimes. To operate at all, it was necessary to purge the system each weekend by pumping all the solids from the thickener to a waste pond. The slimes built up during the week progressively increased the apparent viscosity and density of the circulating plant water, so that hydroseparators and hydrotator units had to be constantly adjusted. Uniformity, yield, and quality of the metallurgical coal suffered in consequence, and the filter cake ash and moisture contents increased from Monday to Friday. Limited Waste Disposal: Location of the plant does not permit unlimited waste pond area. Maintenance of a waste pond for the purpose of emptying the thickener during weekends became a costly burden that could not be tolerated. HOW THE PROBLEMS WERE SOLVED The flowsheet (Fig. 1) chosen to overcome these difficulties is considered the one most economical to install and operate. In a preliminary change made before the flotation circuit was installed, the cyclones and thickener were first operated in series, the overflow from the 3-in. cyclones, after flocculation, being discharged into the thickener and the thick-

Jan 1, 1960

By T. M. Geffen, R. E. Gladfelter

Lipson1 has recently presented a technical note wherein theoretical considerations were used to demonstrate. that the adsorption us saturation relation for a linear absorption method is not necessarily a single valued function of saturation.1 It was concluded that the absorption us saturation relationship is subject to the same hysteretic effect as is the flow behavior between the drainage and imbibition systems. It is the purpose of this note to show, by experimental results, that for the manner in which fluids are distributed in porous materials during fluid flow, the relative X-ray absorption us saturation relationship is single-valued regardless of the saturation history. The design of the apparatus used to measure relative X-ray absorption of cores undergoing fluid flow tests is similar to that described by Morgan, McDowell and Doty. A few modifications have been incorporated in the design to increase sensitivity and simplicity of measurement. The sensitivity is such that for usual types of cores a recording pen movement of approximately 12 linear in. is occasioned between the recording of the core dry and when it is completely full of an absorbing liquid, a solution of approximately five per cent by volume of iodo-benzene in a close-cut hydrocarbon fraction, or a solution of 50,000 ppm sodium iodide in water. Two types of experiments were conducted, one in which the liquid was inside the core, and the other with the liquid outside the core. Tests with the liquid inside the core were run to cover the saturation range encountered in both the drainage (gas drive) and imbibition (liquid flood) flow systems. It is pointed out that the same core was used, but the tests were conducted at different times with the recording mechanism balanced at a different position. Therefore, the absolute values of relative X-ray intensity at any saturation are not the same in each test. In the second type of test the same core was used, but this time its pore space cmtained only gas, and various thicknesses of oil contained in plastic cells were placed in front of the dry core. As before. the relative X-ray ah- sorption was measured and compared to the quantity of oil in front of the core. The arrangement of the fluids with respect to the path of X-rays in these two types of tests represent fluid distributions of a wider difference than can be expected between that established in a core just due to imbibition and drainage saturation flow histories. Thus any deviation from a straight line relationship of the log of the relative X-ray intensity us saturation calibration should be readily apparent. Results of the laboratory tests are given in Fig. 1. A schematic diagram showing the position of the fluids with respect to the path of the X-ray beam is given for the two cases investigated. In the case where the oil existed outside the core (Case B), the log of the X-ray intensity (log, I/I,) is related directly to the cell thickness (amount of oil in X-ray beam path). This correlation is in full agreement with X-ray theory. In the case where the oil or water existed inside the core (Case A) which covers both drainage and imbibition types of flow processes, again the relationship between absorption and saturation (amount of oil in X-ray beam path

Jan 1, 1952

By J. Campbell

Various models are discussed for the evaluation of the negative pressures which may occur in solidifying materials which exhibit various deformation modes: elastic-plastic, Bingham, viscous, or creep flow. The inadequacy of the previously proposed elastic-plastic solution for solidifying metals is revealed by comparison with the more reliable creep results which are given graphically for aluminum, copper, nickel, and iron. The maximum tensions experienced in the liquid phase of solidifying spheres ranging in size from large castings to submicron powders are in the range from —10&apos; to —105 atm for these metals. THERE has been much recent interest in the negative pressures associated with the volume change on solidification and in the possibility of the occurrence of cavitation. Considering the freezing of a highly supercooled liquid, an attempt to evaluate the stresses in the liquid ahead of the rapidly moving solidification front has been made by Horvay1 on a microscale and by Glicksman2 on a macroscale. In a casting of a wide freezing range alloy, the pressure differential due to viscous flow of residual liquid through the pasty zone has been discussed by Piwonka and Flemings,3 In a previous publication4 the author has attempted to estimate the negative pressure occurring in the residual liquid of a spherical casting, employing an elastic-plastic model to describe the collapse of the solidified shell under the internal tension. An earlier model assuming a rigid shell was shown to be inaccurate by many orders of magnitude. The elastic-plastic model is critically reviewed here, and other models are developed which are thought to be more closely related to metals and other materials near their melting points. The spherical geometry (Fig. 1) is chosen because the highest shrinkage pressures would be developed, although the analyses are readily adaptable to cylindrical geometry. A parallel sided casting experiences little internal tension because of the relatively easy dishing inward of the sides. (This commonly observed phenomenon has previously been attributed solely to atmospheric pressure.) Furthermore, small regions of confined liquid in a large solidified volume of a casting approximate reasonably well to spherical geometry. ELASTIC-PLASTIC MODEL The author has shown4 that as solidification proceeds the internal hydrostatic tension builds up until the elastic limit of the shell is exceeded. At this point the internal pressure is closely -2Y/3. Subsequently a plastic zone spreads from the inner surface toward the outer surface of the shell. When the whole casting is deforming plastically a rather more generalized analysis taking account of the externally applied pressure PA + 2y/b gives the internal pressure as: P = Pa + 2y/a + 2ys/b - 2 Y In(b/a) [1] The 2y/a and 2ys/b terms result from the tendency of the liquid-solid and solid-vapor interfaces to shrink, reducing their energy, and thereby helping to collapse the solid phase and compress the liquid phase. The 2y/b term would be important only for powders. The last term arises because of the plastic restraint of the solid, resisting collapse and so effectively expanding the residual liquid. From Eq. [I] it is easily shown that there is a minimum in the pressure at the radius amia= y/Y [2] which is of the order of 103K for the metals aluminum, copper, and iron, and corresponds to the minimum pressure Pmin = 2 Y[l-ln(bY/y [3] The results of a fully worked out elastic-plastic solution are given in a previous reporL4 The main criticism which may be leveled at this analysis when applied to metals at their melting points is the strong dependence of the yield stress on the strain rate. The strain rate varies with both solidification conditions (e.g., whether chill-cast or slowly cooled) and during solidification, as is indicated in the following section. Thus an appropriate choice of Y is very arbitrary. Before proceeding to a discussion of models which are strain-rate-dependent, it is necessary to evaluate the strain rate as a function of the rate of solidification. SOLIDIFICATION RATE Various empirical relations have been deduced5 for the rate of thickening of the solid shell by pour- out tests on partially solidified spheres. These, however, are unsatisfactory for our purposes since they become very inaccurate when the liquid core is very small. A theoretical approach is therefore necessary, and some solutions are set out below. Making the assumptions of constant surface temperature of the casting during freezing, no superheat, and a material freezing at a single temperature, Adams8 deduces the approximate solution: which becomes when b » a: Employing a semiempirical approach vallet6 finds:

Jan 1, 1969

By J. K. Brooke, F. A. Renninger

During 1966, crushed stone production in the United States totaled just over 811 million tons valued at almost $1.2 billion. This represented in- creases of 4 % in tonnage and 5 % in value over that for 1965. Excluding the crushed stone used for agricultural and certain industrial purposes (cement, lime and flux), crushed stone mineral aggregate production totaled 616.3 million tons valued at almost $910 million, also up roughly 4% in tonnage and 5% in value over the 1965 figures. Limestone was by far the most widely used rock variety, followed by basalt, granite and sandstone in that order. Concrete aggregate and roadstone continued as the main uses for stone, accounting for 63% of all tonnage produced in 1966 and 60% of total stone value. Sand and gravel production in 1966 increased 3% over that for 1965. Total 1966 output was just in excess of 934 million tons valued at almost $985 million as compared with 908 million tons at $957 million for the previous year. Excluding the higher valued industrial sands, 903.2 million tons of sand and gravel valued at $891.6 million were used directly as mineral aggregates, representing a 2.9% increase in tonnage and a 2.4% increase in value over 1965.

Jan 2, 1968

By E. P. Pfleider

DIAMOND drill research work was initiated at the School of Mines, University of Minnesota, in late 1949. The Drilling Symposium held in Duluth that spring highlighted the problem of high cost and core recovery and the need for controlled testing. An advisory committee made up of informed representatives of both mining companies and drilling companies was formed to suggest and advise on a program of drill research. A Hy-Mac hydraulic drill unit, see Fig. 1, especially designed for experimental testing, was obtained for this work by the School of Mines through the courtesy of the Carboloy Co. It is an extremely flexible unit, capable of exerting a forward thrust of about 1750 lb and turning at speeds from 650 to 2200 rpm. The feed arrangement is so designed that the advance can be set either at a constant rate or permitted to vary at a fixed pressure, see Fig. 2. The

Jan 1, 1952

By R. W. Smith, K. H. Lee

Bond type simulated closed-circuit grindability tests and batch grindability tests were run on six pure minerals plus a limestone and a taconite ore. The simulated closed-circuit tests were made at five different meshes of grind. The minerals tested varied widely in hardness and breakage pattern. For all simulated closed-circuit tests both Bond and Holmes work indices were calculated and compared. The Bond grindability testlm6 has been widely and quite successfully used for predictions of such items as ball mill power requirements and as an aid in plant comminution equipment selection. The test is interesting in that although run as a series of batch tests it is over-all a simulated closed-circuit test with a circulating load of 250%. The simulated closed-circuit feature is probably the primary reason for the notable success of the test. Perhaps the major criticism that can be brought against the test is that it is time consuming, since it normally takes a trained technician about an eight-hour shift to perform it.4 For many purposes this is an acceptable time requirement. However, if a grindability test is to be used for mill control purposes it should be performed in as short a time interval as possible, preferably under an hour. Sometimes in industry strictly batch tumbling mill tests are run and an attempt is made to correlate such batch tests with plant mill operation. Then an attempt is made to adjust operating tumbling mills based on data from the tests. The tests, however, frequently do not correlate well with operating data. The purpose of the present work was to explore some of the similarities and differences between a simulated closed-circui.t grindability test and a batch type test. Six different minerals plus a limestone and a taconite ore were tested in the experimentation. These materials varied widely in hardness, breakage characteristics, etc. Standard dry Bond grindability tests were mn on all materials at 48, 65, 100, 150 and 200 meshes of grind. Feed material was prepared by stage cmshing to -6 mesh. Initial feed volume was 700 cc. Care was taken to maintain the standard constant weight (about 20125 gm) and number of balls (283) during all the tests. Rotational speed was 70 rpm. Table I lists the materials studied along with pertinent data regarding the materials and Bond grindabilities obtained. In addition, dry batch tests were performed on all materials. These tests were made in the same mill as was used for the Bond tests. An identical ball charge and an identical feed volume were used. After rotating the mill for a predetermined number of revolutions at the same rotational speed as for the Bond test, the material was removed and separated from the ball charge. A screen analysis was performed on this product. Knowing the original size distribution of the feed and the size distribution of the product, it was possible to calculate the grindability or grams of a particular mesh produced per revolution of the mill. After the screen analysis of the product, the various fractions were recombined and placed back in the mill for further grinding. After grinding for additional revolutions of the mill the procedure was repeated. Thus, it was possible to obtain grindabilities for each material at a number of meshes of grind and for various revolutions of the mill. Grind-abilities obtained from batch tests are shown in Table 11. COMPARISON OF BOND AND BATCH GRINDABILITIES Figs. 1A through 1D show relationships between batch and Bond grindabilities. Figs. lA, lB, 1C and 1D show respectively graphs indicating the relationships for batch tests run for 100, 300, 500 and 700 revolutions of the mill. For a particular material on each graph, points are shown for 200, 150, 100, 65, and 48 meshes of grind except for several missing coarse meshes of grind for galena which did not fall conveniently on the figures. For each material and graph the point nearest the origin is for 200 mesh, the next for 150 mesh, the next for 100 mesh, etc. Considering Fig. lA, it is interesting to note that all relationships shown are essentially straight lines. There are, however, considerable differences

Jan 1, 1969

By David M. Hopstock

The performance of the most common type of low-intensity dry magnetic separator is analyzed on the basis of fundamental physical principles. Expressions are developed for estimating the optimal choice of design and operating parameters for beneficiation of magnetite ores. By proper choice of these parameters either a high-grade concentrate or a low-grade tailing can be produced from an incompletely liberated feed.

Jan 1, 1976

By R. E. Old

THROUGH the use of pressure and production records, formation properties and bottom-hole sample data, the performance of an oil reservoir may be studied analytically to define and evaluate the natural forces acting on and within the reservoir. Use is made of material-balance methods and the equations for natural water encroachment to estimate reserves. Methods for calculation of pressures are given. A study of the Jones sand, Schuler field, Arkansas, has been made and is given here to illustrate the value of the methods discussed.

Jan 1, 1942

By V. H. Gottschalk

THE solubility of gases in metals has been of interest since Graham&apos;s time in 1866, but, although the subject was actively studied by iron and steel metallurgists during the eighties, the era of painstaking laboratory investigation begins in 1907 with the publication of Sieverts&apos;1 thesis on the occlusion and diffusion of gases in metals. Since then, Sieverts has worked almost continuously in this field, and his views on the subject are the prevailing ones at the present time.2 Probably the most important result obtained by Sieverts, and frequently verified since by other observers, is the discovery that at a constant temperature the solubility of almost all gases in both the liquid and solid state of most of the metals is proportional to the square root of the pressure (for pressure above 100 mm.). The obvious explanation of this fact is that the gas dissolves as atoms and not as molecules, although it has been pointed out a number of times, first by Donnan and Shawl in connection with their work on the solubility of oxygen in silver at 1075° C., that the formation and solution of a compound of the metal and gas would also be indicated by a variation of the solubility with the square or higher root of the pressure. Sieverts4 himself raised the question whether the usual explanation (i. e., that the gas dissolves as atoms) may not be wrong, when he found that the square root law held also for the solubility of sulfur dioxide in molten copper; in which case dissociation into simpler molecules or atoms does not take place. Stubbs5 subsequently showed that Sieverts and Krumbhaar&apos;s "constant" for sulfur

Jan 1, 1932

By Joseph W. Roe

MaNY questions arising in the work of the mining engineer may be solved quickly and with suffcient accuracy by the methods of descriptive geometry; but, unfortunately, this subject is more often considered from a mathematical view-point than as an effective tool for solving practical problems. Some of the principles involved are merged into the ordinary operations of mechanical drawing, and are used unconsciously by the engineer in his every-day work. The rest are stowed away on the book-shelf with his forgotten or rarely-used college text-books. One reason for this condition of " innocuous desuctude " may lie in the uifortunate and often cumbersome notation which it has been found necessary to introduce. If some of these principles can be recalled to the engineer&apos;s attenti011 in terms of&apos; every-day use they may prove of practical hearing. Recently, in talking with several mining engineers, I used some of the drawing-room methods of a machine-designer, to the evident surprise of those around me. These men were perfectly familiar with the methods, but their application to mining-work had not occurred to them. At their suggestion the present paper is offered, not in ally way as a treatise, but merely to suggest a certain point of view, in hope that it may lead others far more familiar with mining-problems to pursue the subject further. I. To Find the Strike. As the simplest and most fundamental problem, let it be required to find the strike of a vein when the location and elevation of three points on the outcrop are known. It mill be assumed for the present that the rein is a plane.

Jan 1, 1911

By S. J. Green, R. D. Perkins

Little data exists on the high strain rate behavior of geologic materials. Uniaxial stress tests by Kumar1 and by Serdengecti and Boozer2 present some results to strain rates in the range 10 to 103 per sec. The two references cited are the only ones the authors found for high strain rates. Techniques for experiments at high strain rates are not well developed and, in general, leave questions with respect to interpretation of data when the material behaves in a brittle manner. The most reliable data at very high strain rates (104 to 106 per sec) are found in some recent flat-plate work3-5 where experimenters have impacted one plate into another, thereby creating a uniaxial strain loading. The standard uniaxial stress-strain curves cannot be obtained directly from these tests; however, yield (or fracture) may be studied by measuring the "elastic" wave magnitude. These data then may be compared to uniaxial stress data by resorting to some preassumed yield/fracture criteria. Even with the most liberal interpretation of existing data, little can be said of the effects of high strain rate on stiffness, yield/fracture, and post-fracture behavior of geologic materials. It is the purpose of this work to begin to add to the understanding. The data presented here are intended to provide material information for use in calculating the response of geologic materials to high rate deformations. These data can be applied directly to determine parameters such as the elastic modulus and Poisson ratio as a function of stress. Furthermore, these data can be used to derive an understanding of yield/fracture and the effect of rate on the yield/fracture surface. The work presented is a first step, and is

Jan 1, 1972

By Harold M. Mooney

WHEN apparent resistivity data are taken with the symmetrical Wenner 4-electrode spread, a fixed center position is used and readings are taken for values of electrode separation. Basic data consist of apparent resistivity plotted against separation of adjacent electrodes. The interpreter attempts to infer geologic structure, such as the depth to discontinuities and the nature of subsurface earth materials. An earlier paper1 described methods for interpreting resistivity data. All of these involve a severe assumption, namely that the earth in the region of interest consists of horizontal layers, electrically homogeneous and isotropic. The actual earth never satisfies this assumption exactly and may deviate from it so much that none of the above methods can be applied. Attempts in three directions have been made to modify the assumption so that it approaches known geologic complexity more closely.

Jan 12, 1954

By I. Lowthian Bell

THERE has been probably no improvement introduced into the manufacture of iron which created more surprise in the minds of practical smelters and of scientific men than Neilson&apos;s discovery of the hot blast. In 1829, Messrs. Dunlop & Co. consumed at the Clyde Works, near Glasgow, nearly 7 3/4 tons of coal to make a ton of pig iron, of which about 20 cwts. was employed under the boilers of the blowing engines, leaving nearly 7 tons for the consumption of the furnace itself. In the year 1833, by heating the air to 612° F. (322° C.), they reduced the 7 3/4 tons to 3 tons by the mere burning of 8 cwts. of coal in the apparatus for raising the blast to this temperature. The statement just given is strictly true in a commercial sense, but when we come to consider the question as one of physical science, it is necessary to eliminate some of the conditions which conduced to so extraordinary a result. Anterior to Neilson&apos;s time the fuel employed in smelting iron was coke, and it was supposed at that period, erroneously, however, that coal in its raw state, when burned with cold air, was totally unfit for the purpose in question. This mineral, as it was obtained from the Lanarkshire coal-field, contained about 35 per cent. of volatile matter, but the process of charring it was performed in so unskilful a manner that instead of receiving 88 cwts. of coke from 135 cwts. of coal, 60 cwts. only was the product of the operation. Again, the reduced consumption of carbon in the furnace itself was accompanied by a corresponding diminution of blast, and this was followed by an economy of half a ton in engine coal. After making a proper allowance, however, for all these collateral circumstances, we are within the mark when we admit that in actual coke, which is really the form the fuel has to assume before it is burnt in the blast-furnace, not less than 30 cwts. was saved by heating the blast to 615° F. (322° C.). This unexpected economy, be it remembered, was obtained by the combustion of the 8 cwts. of coal, somewhat wastefully applied in the hot-air apparatus. Numerous have been the opinions advanced by different authorities in the scientific world to account for the apparent anomaly, but none,

Jan 1, 1877