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By R. D. Lee

A simplification of the method of Hurst and McCarty for conducting potentiometric model studies by the single probe method is presented along with experimentally determined invasion patterns for certain idealized flow problems. The analytical solution for one class of these problems is given. Finally, a general description is given of a newly developed instrument which permits direct mapping of flow lines and determination of transit times in potentiometric-model studies. Introduction The object of this paper is to present: I. A simplification of the method of Hurst and McCarty for conducting poten-tiometric-model studies of oil and gas reservoirs by the single probe method. 2. Results of a series of studies of certain idealized flow problems and the general conclusions to be drawn therefrom. 3. A description of a new instrument, the Chronocartograph, which greatly reduces the labor and time required for conducting potentiometric-model studies. Certain general conclusions may be drawn as results of the investigation of the idealized flow problems. They are: I. Injection and extraction areas should be separated by as great a distance as conditions permit since, in general, the recovery prior to first breakthrough tends to vary as the square of this distance. 2. Little advantage is to be gained by use of more than eight injection wells or groups of injection wells for the case of circular productive limits. 3. Elongated shapes of productive limits are best exploited by injection on the extended major axis only, with a line of extraction wells lying on the major axis. 4. The use of peripheral injection wells for elongated shapes is permissible, if necessary, but requires extension of the line of extraction wells. The exploitation of an oil or gas field is effected either by the expansion of the gas and oil, or by their displacement by another fluid. Both methods may be used simultaneously. When the displacement of the oil or gas is the controlling factor there arises the problem of mapping the progress of the boundary between the fluid in place and the displacing fluid. This problem is of particular interest in the operation of a cycling project in a gas-condensate field, where the wet gas is produced from one or more wells, commonly called "extraction wells.'' This wet gas is taken into a processing plant where the condensate is removed. The remaining "dry" gas is injected back into the field through one or more wells, called "injection wells," both to conserve the gas for future use and also to maintain the pressure in the field. In an operation of this type it is essential to anticipate the manner in which the dry gas will spread through the field, because the ultimate recovery of the wet gas depends

Jan 1, 1948

By A. Madrazo

The Standing-Katz method for predicting liquid densities of reservoir fluids has been tested using experimental data of 154 bottom-hole or recombined reservoir fluid samples. New pressure- and temperature-correction curves for the Standing-Katz type correlation are presented which improve the accuracy of prediction. INTRODUCTION The present study was undertaken to investigate the known methods of determining liquid densities and to select one of them which might yield a better correlation if additional data were employed. An appropriate correlation would incorporate the following characteristics: (1) ease of handling in the computations, (2) results within engineering accuracy and (3) data easily accessible. After careful investigation of the different methods, the Standing-Katz correlation1 appeared to have these characteristics. The Standing-Katz correlation for liquid densities of hydrocarbon systems is based upon limited data. The original work, which employs apparent densities for methane and ethane, was based on data of 15 saturated crude oils in equilibrium with natural gas. Therefore, a test of the correlation using additional experimental data would serve either to validate the Standing-Katz correlation or to form a basis for corrections if such were necessary. PROCEDURE AND GRAPHICAL SOLUTION The data of 154 bottom-hole or recombined reservoir fluid samples were employed to calculate the densities at 14.7 psia and 60°F by the method described in Table 1. Volume contributions for methane and ethane were assigned from the pseudo liquid density plot (Fig. I), but volume contributions for N2, CO2 and HzS were not considered. The densities computed at reference conditions of 14.7 psia and 60°F were then elevated to their respective temperatures and pressures by the use of the correction curves proposed by Standing.' The percentage differences between the experimental values and the calculated values were determined; these samples were grouped into temperature, pressure and density ranges to determine a possible trend. It appeared that, at temperatures above 160°F, the calculated density values were consistently larger than the experimental density values; however, no obvious trend was found for the density and pressure ranges. There is a relationship between the pressure-correction and temperature-correction curves. This relationship, embodied in the temperature-correction curve, can be expressed as follows. The experimental densities of 125 samples above their bubble points were known. From these isothermal data, it was possible to determine an experimental-density difference between two pressures; and (from Fig. 2*), a calculated density difference between the same two pressures was determined. The relative effect of temperature must be considered in the calculated-density values. The effect of temperature can be determined by entering Fig. 3* at the two densities in consideration and obtaining the change in density at constant temperature. This change, or delta density, must be added

By Jack A. Crichton, Henry J. Gruy

This paper discusses methods used in the estimation of natural gas reserves and the general conditions under which the various methods are applicable. The factors used in estimating natural gas reserves are reviewed. Errors which have been found to occur frequently are listed. Introduction The estimation of natural gas reserves has become of paramount interest because of the increasing importance of gas in the nation's economy. Gas is a most desirable fuel, a fact substantiated by the continued rise in the market demand. In addition, new uses for gas are being developed by the chemical, plastic, and associated industries, and plants are being built to make gasoline from natural gas. These are a few of the factors contributing to the importance of the nation's natural gas reserves. With the increased importance of gas there is an increase in the need for reliable estimates of the magnitude and availability of natural gas reserves. These estimates are being used currently: (I) to determine which fields contain sufficient available reserves to justify the construction of pipe-line outlets to serve particular markets; (2) to design pipe lines necessary to serve those fields adequately;] (3) to determine the location of industrial and chemical plants; (4) to finance the development of gas properties, and the construction of gas pipe lines; (5) to determine fair and adequate depletion allowances and depreciation rates; (6) to justify applications for gas pipe lines before various regulatory bodies; (7) to determine the number of wells required to exploit the reserves most economically; (8) to aid in establishing values for the purchase or sale of gas properties, and for purposes of inheritance taxes; (9) to determine equities under unitized operations; (10) to provide a basis for calculating the economics of gas-cycling operations. History or Estimation of Natural Gas Reserves The natural gas industry in the United States had its beginning during 1826 when natural gas was used for lighting the city of Fredonia, N. Y. The first natural gas pipe line was a 25-mi]le wooden line constructed from hollowed logs, connecting West Bloomfield and Rochester, N. Y. There is no record of an attempt to estimate the gas reserve at West Bloomfield but an attempt was made to determine the capacity of the well by measuring the time required to 611 a large balloon. One of the earlier publications concerning estimation of natural gas reserves is the "Manual for the Oil and Gas Industry," published by the Treasury Department, United States Internal Revenue, in i9i9. The following methods of computing "gas depletion" are listed: (I) production decline of the gas well or property; (2) decline in open-flow capacity; (3) comparison with the life history of similar wells or properties, particularly those exhausted Art

Jan 1, 1949

By J. W. Rutter, K. T. Aust

THE object of the experiments to be described in this report was to determine, first, which grains, out of a large number introduced into a sample in which their growth could proceed, were able to grow most successfully; and, second, the factors which control their growth selection. In an earlier study of grain boundary migration in high-purity lead,' it was found that, under some conditions, the most successful grain in an experiment of this type bears a special orientation relationship to the grain into which it is growing. The present work represents an extension of the previous study, directed at the determination of the orientation relationships which appear under a wider variety of conditions. Experiments of this general type have been done using commercial aluminum2 with somewhat conflicting results. In the present experiments, in contrast to the above,' the sample composition was a principal controlled variable, resulting in a considerable clarification of the phenomena observed. EXPERIMENTAL TECHNIQUE The experimental technique used in this investigation was essentially that employed previously in studies of grain boundary migration kinetics.1'3 The material used was zone-refined lead with various small amounts of tin or silver added to study the effect of varying the sample composition. The specimens were in the form of single crystals, about 1/4 in. 1/4 in cross section by 3 to 4 in. in length, grown from the melt in a horizontal graphite boat. A crystal grown in this way generally contained a lineage or "striation" substructure of the type shown in Fig. 1 of Ref. 1. This substructure consists of an array of low-angle boundaries which partition the crystal into regions misoriented from each other by a few degrees. The substructure constitutes a source of driving energy, estimated to be about 4000 ergs per cc, for the migration of a large-angle grain boundary into the striated crystal. New grains were introduced by plastic deformation in compression of a localized reglon at one end of the sample. Re-crystallization occurs at room temperature in the deformed region, introducing a large number of new, striation-free grains into the specimen. These grains are able to grow into the melt-grown crystal on annealing at a suitable temperature. The stria-tions are removed by passage of the grain boundary, as the substructure energy is utilized to produce the boundary migration. Usually, only one or two of the recrystallized grains persist after growth has occurred for about 1 cm out of the deformed region. Laue back-reflection X-ray photographs were obtained to determine the orientation relationship between the melt-grown crystal and the recrystallized grain or grains which grew most successfully in each specimen. EXPERIMENTAL OBSERVATIONS Fig. 1 shows the results obtained for a series of specimens to which had been added tin in the range from 0 to 5 ppm by weight. In this figure is plotted, in the standard stereographic triangle, the single axis about which the most successful recrystallized grain or grains are related to the starting, melt-grown crystal by the smallest rotation. The range of angular rotations observed about such axes is indicated beside each stereographic triangle. The results shown in the stereographic triangle on the left, Fig. l(a), were obtained by localized deformation at one end of each specimen at room temperature, followed by annealing in a furnace which had been preheated to 300°C. The furnace atmosphere was argon. It will be seen that the orientation relationships observed between the melt-grown and recrystallized grains are quite random. On the right, Fig. l(b), are shown results for samples in which the de-

Jan 1, 1961

By B. H. Caudle, A. B. Dyes, R. A. Erickson

The study of the influence of fluid mobilities on the sweepout pattern resulting from the injection of gas or water has been extended to cover the production period which follows breakthrough of the injected material. Mobility ratios over the range common in field operations (0.1 to 17) were studied for several pattern floods (five-spot, staggered, and direct line drive). The experimental data required for these studies were obtained by the use of the x-ray shadowgraph technique using miscible oil phases of different viscosities in porous plate mode1s of a reservoir element. From the shadowgraph pictures obtained before and after breakthrough of the injected fluid, flowing ratios at the producing well and cumulative volumes injected were calculated. The method for applying such data in predicting field behavior is illustrated for a water flood of a five-spot. For this case a range of mobility ratios of 0.5 to 5.0 results in: (I) nearly complete (95 to 100 per cent) sweepout pattern efficiencies at abandonment conditions, (2) production after breakthrough being responsible for as much as one-third of the total recovery at the lower mobility ratios, and (3) a twofold variation in the operating life of the reservoir. In determining the merits of a secondary recovery operation, the fraction of the reservoir which is ultimately to be swept by the injected fluid is of major importance. Because of its significance a large amount of research has been applied to the study of areal sweepout efficiency. Muskat, Wyckoff and Botset1,2 have presented the classic analysis of the pattern efficiency at breakthrough for several injection patterns in which the mobility of the fluids ahead of the injected phase front was equal to the mobility of the fluids behind the front. Aronofsky3 as extended this analysis of recovery at breakthrough through numerical computations and by the stepwise use of the potentiometric model to include the effect of different fluid mobilities ahead of and behind the invasion front on the line drive performance. Fay and Prats' have also employed numerical computations to show the influence of one other condition of fluid mobilities on the five spot flood. In a previous paper' a new method of attack on this problem which employed x-ray and porous plates was described. At that time experimental results were also presented which described the effect of fluid mobilities on the reservoir area contacted by the injected fluid at breakthrough for the five spot and direct line drive patterns. Most of the literature pertaining to sweepout pattern efficiency has emphasized the pattern which is obtained at breakthrough of the injected phase. The increase in the sweepout pattern which occurs after breakthrough

Jan 1, 1955

By B. D. Cullity, J. T. Norton, M. Telkes

M. Balicki—As one who some years ago spent much time searching for an alloy with high thermoelectric power that would be suitable for heat energy-electric energy converter based on the principle of a thermoelectric pile, I would like to make a few comments touching upon that aspect of this excellent paper. The specifications which one of the authors has formulated so aptly do not appear to me as complete, and I would like to add to them the following two demands: (1) Melting point not less than 500°C and (2) elongation on 2 in. at least 5 pct. Condition 1 would insure good thermodynamic efficiency of the pile by permitting a reasonably high temperature of the hot junction and at the same time making it suitable for such application as salvage of vast amounts of energy which is lost in the form of sensible heat of waste gas leaving industrial and other furnaces. Condition 2 is also a very important one; particularly, because of the fact that all elements and alloys which exhibit attractive thermoelectric properties seem to be as a rule very brittle. The design, erection, and maintenance of a pile incorporating a brittle material in one of the most crucial parts of the converter would be a very difficult and costly affair indeed. To illustrate this point I may mention great difficulties I encountered when trying to make thermocouples of silicon. Casting of 1/4-in. rods in iron or graphite mould yielded only broken pieces which had to be welded into a bar. Such a bar had to be handled very carefully during the determinations. Raising the molten silicon by vacuum into a silica tube and solidifying it there solved the problem of stability as well as that of electrical insulation of a bar. On tests this bar (98.5 pct Si) showed dE/dT = — 275.5 microvolts per degree C vs. copper. Thermocouples made of this grade of silicon and pure nickel developed 0.39 v when temperature of the hot junction was approximately 1000°C. The possibility Dr. Gonser has mentioned of trying to impart to metals good thermoelectric properties by alloying them with silicon, has been considered. The preliminary survey which I have made was, however, disappointing. Perhaps, it will be advisable to record the results obtained (table VI), as this might save repetition of search in fields already covered.

Jan 1, 1951

By J. D. Wood, J. T. Smith

ALLOYS with a dispersed second phase in a metallic matrix are generally much stronger than the matrix itself. Plastic deformation in dispersion-strengthened alloys is usually confined to the matrix phase when recovery processes are active, while in the absence of recovery both phases may yield.' The alloy system studied in the present research was WC-12 wt pct Co and consisted of noncoherent WC particles dispersed in the cobalt matrix. Some particle-to-particle contact existed but not enough to produce a continuous WC skeleton. The microstruc-ture of the WC particles was characterized by very straight edges, forming a trapezoidal shape in any plane of polish. Previous investigations with WC-Co alloys at room temperature have shown that fracture of the WC particles occurs in transverse rupture testing.' Room-temperature slip was reported for WC particles after indentation for hardness measurements.3 Elevated-temperature deformation of WC particles in a WC-12 pct Co alloy was suggested by recent electron microscope studies of specimens deformed at 900' to 1000°C.4 In highly deformed alloys, the WC edges were serrated in contrast to the usual straight or smooth appearance. WC-12 pct Co and WC-15 pct Co alloys have been previously studied under elevated-temperature com-pressive-creep conditions by the present authors. Electron microscope studies of two-stage replicas from deformed specimens showed no evidence of slip or fracture of the WC particles. These specimens were brought to temperature and allowed to equilibrate prior to the application of the creep load. It was believed that the load-application rate, a crosshead speed of 0.005 in. per min on an Instron universal testing machine, was sufficiently low that recovery within the cobalt matrix was sufficient to limit the deformation to this matrix. A series of experiments was performed to evaluate the influence of loading rate on the deformation of WC-Co alloys. A WC-12 pct Co alloy was selected for these determinations. The average WC particle size was 4.45 p with an average linear separation between particles of 0.59 p. The selected temperature was 800°C and was monitored with a Chromel-Alumel thermocouple attached to the specimen. Testing was conducted in an argon-atmosphere chamber to prevent oxidation of the WC-Co specimens. This chamber was mounted on an Instron universal testing machine equipped to apply the load at a fixed rate. Each specimen was loaded to 110,000 psi compression stress at 0.05 and 0.5 in. per min. The loading rate was monitored prior to insertion of the test chamber and was found to be almost precisely the nominal rate selected. The specimens were raised to temperature and held to equilibrate with the surroundings, and then the load was applied and held for 4 hr to duplicate the exposure time utilized for the creep specimens. The time to reach full load at a crosshead speed of 0.005 in. per min was some 500 sec and was reduced to 50 and 5 sec as the loading rate was increased to 0.05 and 0.5 in, per min, respectively. The model developed by Ansell,' when recovery processes do not occur, considers that fracture or deformation of the dispersed particles is necessary to relieve back stresses on dislocation sources and allow dislocations piled up against particles to sweep out in the matrix to cause plastic deformation; he further states that, even at elevated temperatures, the dispersed-particle deformation is necessary for yielding in the absence of recovery. For the case of straight dislocation segments piled up against a straight barrier, such as the straight-sided WC particles, the shear stress, 7 exerted on a particle is: where h is the spacing between particles (0.59 p), a is the applied stress (110,000 psi), p, is the shear modulus of the matrix (6.7 X lo6 psi at 80O°C), and b is the Burgers vector of the matrix dislocation. From Eq. [I], the shear stress, 7, exerted on the WC particles when no recovery occurs is of the order of 6 X lo6 psi at 800°C. The limiting stress, F, that will

Jan 1, 1969

By Allan B. Tanner

The effects of radon in drillholes on gamma-ray logs have been described by L. S. Hilpert and C. M. Bunker1 Since these effects may cause drastic error in the evaluation of uranium deposits, it is useful to know the conditions under which significant amounts of radon tend to accumulate in drill- holes. In the studies described here, atmospheric conditions were found to dominate in the control of the behavior of radon in drillholes in the vicinity of a uranium orebody. The site of the investigation was in McKinley County, New Mexico, about 12 miles north of Grants. Drillholes of 4 ¼ -in. diam, on 25-ft and 100- ft centers, penetrate ore in dry rock at a depth of about 100 ft. A geologic log of the drillhole of primary interest is shown in Fig. 1. Gamma-ray logs revealed three zones of ore-grade mineralization in the Todilto limestone. A 6-ft zone, the lowest of the three, assayed 0.20 pct U3O8 by chemical analysis. The limestone ores in this area contain disseminated uraninite and some yellow and orange secondary minerals.

Jan 7, 1959

By R. S. French, W. R. Hibbard

M. Balicki—As one who some years ago spent much time searching for an alloy with high thermoelectric power that would be suitable for heat energy-electric energy converter based on the principle of a thermoelectric pile, I would like to make a few comments touching upon that aspect of this excellent paper. The specifications which one of the authors has formulated so aptly do not appear to me as complete, and I would like to add to them the following two demands: (1) Melting point not less than 500°C and (2) elongation on 2 in. at least 5 pct. Condition 1 would insure good thermodynamic efficiency of the pile by permitting a reasonably high temperature of the hot junction and at the same time making it suitable for such application as salvage of vast amounts of energy which is lost in the form of sensible heat of waste gas leaving industrial and other furnaces. Condition 2 is also a very important one; particularly, because of the fact that all elements and alloys which exhibit attractive thermoelectric properties seem to be as a rule very brittle. The design, erection, and maintenance of a pile incorporating a brittle material in one of the most crucial parts of the converter would be a very difficult and costly affair indeed. To illustrate this point I may mention great difficulties I encountered when trying to make thermocouples of silicon. Casting of 1/4-in. rods in iron or graphite mould yielded only broken pieces which had to be welded into a bar. Such a bar had to be handled very carefully during the determinations. Raising the molten silicon by vacuum into a silica tube and solidifying it there solved the problem of stability as well as that of electrical insulation of a bar. On tests this bar (98.5 pct Si) showed dE/dT = — 275.5 microvolts per degree C vs. copper. Thermocouples made of this grade of silicon and pure nickel developed 0.39 v when temperature of the hot junction was approximately 1000°C. The possibility Dr. Gonser has mentioned of trying to impart to metals good thermoelectric properties by alloying them with silicon, has been considered. The preliminary survey which I have made was, however, disappointing. Perhaps, it will be advisable to record the results obtained (table VI), as this might save repetition of search in fields already covered.

Jan 1, 1951

By Alfred H. Bell

The year 1937 has been outstanding in the history of the Illinois oil industry. During the course of the year the state's daily production has been trebled, increasing from 12,000 bbl. per day at the beginning to 37,000 bbl. per day at the end, and the year's total, 7,426,000 bbl. is 66 per cent above the previous year's production of 4,475,000 bbl. The production in January was 368,000 bbl.; in December it was 1,085,000. Production from the old fields increased slightly. Most of the new production is from fields in the central part of the Illinois Basin, an area that for many years was considered unfavorable to the occurrence of oil and gas. The principal producing horizon of the new fields is the McClosky "sand," an oolitic limestone in the Ste. Genevieve formation of lower Mississippian age. Although development has not yet gone far enough to permit accurate estimates of oil reserves in the new fields, it is believed that they are of the order of 100,000,000 barrels. The following are the oil fields discovered in 1937 listed in order of amount of daily production at the end of the year; Noble (Richland County), Clay City, including Southeast Clay City (Clay and Wayne counties), Patoka (Marion County), New Centralia (Clinton County), Olney (Richland County), Cisne (Wayne County),.Beecher City (Fayette County), and Rinard (Wayne County). One gas field, the Russellville, in Lawrence County, was discovered in 1937. For locations of the new fields see Fig. 1. A generalized geologic column for Illinois, showing producing horizons in the new fields, is given in Fig. 2. The total productive area of the new fields at the end of 1937 was 1712 acres, in which 230 wells were producing. Thisrty-five dry holes were drilled within 1/4 mile of producing wells. At the end of the year there were 19 drilling wells, 28 rigs standing, 18 rigging up and 4 new locations in these fields. In the whole state 447 wells were completed, of which 284 were oil producers and three gas producers. Total initial daily production of

Jan 1, 1938

By N. J. Grant, B. C. Giessen, U. Wolff

With the aid of the splat-cooling technique of rapid quenching, metastable alloy phases based on antimony ad bismuth have been prepared. At room temperature, simple cubic phases were found in the Sb + Au, 56 + Yd, and Sb + Ni systems. Another phase was retained in the Au-Bi system at -190°C; in this systent, a microcrystalline phase and a rhombohedrally distorted phase were also observed. The crystal chemistry of these phases is discussed in terms of their valence electron concentration range. A remarkable five-step Phase sequence was found upon heating and equilibration of certain metastable Au-Bi alloys. USING the splat- cooling technique of rapid quenching from the liquid,' a large number of metastable intermediate alloy phases have been prepared in recent years. Thus, Hume-Rothery phases of the hexagonal type based on the valence electron concentration have been produced in systems where they are missing in equilibrium, e.g., Ag-Ge 1 or AU-Sb. 3 In a comprehensive study of metastable alloys based on tin, simple hexagonal metastable y phases were found, raising the total of stable and metastable y phases from 3 to 13. 4 In the In-Bi system, five new metastable intermediate phases were retained.' In most cases, the new metastable phases have some crystal chemical characteristics in common: a) They have rather simple, elementlike structures with few atoms per unit cell, e.g., y phase,4'5 or the metastable primitive cubic phases in the Ag-Te and and Au-Te systems.= b) Their structures are often related to those of the terminal phases, or to elements that are straddled in their position in the periodic table by the constituent elements; this is the case for metastable ß (In-Bi) with the structure of white ß Sn,' or metastable a (Cd-sn). 4 c) They seem to represent the crystal structures appropriate to certain average group number (AGN) ranges in which no or few single-phase structures exist in equilibrium. These average group number ranges can probably be equated in the case of many elements of the Ba(Zn)-Bs(As) groups with the averaged valence electron concentration. In the present work, the splat-cooling technique has been applied to the alloys of antimony and bismuth. In equilibrium, neither element forms intermediate alloy phases with other B elements from groups Bl(Cu) to B4(Si) that contain more than 66.7 at. pct of Sb or Bi, respectively, e.g., AUSb 2. 7 Thus, antimony- or bismuth-rich phases, which might be closely related to antimony or bismuth, and which would reflect struc- tural changes occurring on alloying with small amounts of addition elements, do not exist. Also, the terminal solubility of antimony and bismuth for all B metals is very small. It was therefore of interest to investigate the influence of enforced, nonequilibrium solid solution of addition elements in antimony and bismuth on their crystal structures. It was found that additions of group B 2-B4 metals act distinctly differently than additions of group T 10 and B1 metals. The latter set of additives will be treated here. EXPERIMENTAL TECHNIQUES Alloy preparation and splat-quenching followed closely the procedures described in Refs. 1, 4, and 5; they consisted of the preparation of master alloys from high-purity starting materials (99.99+ pct) and blast-atomizing of 20-mg quantities onto copper sheets. The resulting approximately 1 to 5 u thick foils were investigated by X-ray diffraction. The cooling rates obtained are of the order of 107 to 10 8 C per set,'" causing solidification to proceed at a rat; of approximately 100 cm per sec.' Powder patterns of the resulting fine-crystalline materials were taken with filtered CuK, radiation. For antimony alloys the substrates were held at room temperature and for bismuth alloys at -190°C both during splat foil deposition and X-ray investigation. Annealing treatments at several

Jan 1, 1969

By R. J. Charles

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

Jan 1, 1958

By Philip W. Simmons

THE Colorado Plateau uranium province is in a mining boom rivaling the most colorful days of the early West. The application of scientific skills and the use of modern and novel mechanical equipment, however, is unique. No metal has ever received such concentrated effort from geologists and mining engineers. Moreover, no other metal has had the variety of tools available for finding and mining ores. Radiation detection equipment, bull- dozers, truck-mounted wagon and core drills, jeeps, airplanes, helicopters, tractor loaders, self -propelled 3-wheeled dump cars, front-end loaders and fleets of modern trucks are some of the present-day tools of the uranium prospector and miner. Because uranium is so vital to our national defense, the Atomic Energy Commission has offered many incentives for its mining. Through a series of circulars, the AEC has established base price schedules and various incentive payments. The incentive payments for acceptable ores from domestic mines are: (1) a guaranteed base price of $3.50 per Ib for ores assaying 0.20 pct U3O8 and more; (2) premiums based on grades above 0.20 pct U3O8 as for example, ores assaying above 0.50 pct U3O8 receive $1.00 per lb premium; (3) a development allowance of 506 per Ib of U3O8 contained in ores assaying over 0.10 pct U3O8 (4) an ore haulage allowance of 64 a ton mile for a maximum of 100 miles; and (5) an initial production bonus which may amount to as much as $35,000 in addition to all other payments. The producers have been guaranteed this policy until Feb. 28, 1957. The other four will continue until April 1962.

Jan 4, 1954

By Arnold H. Kackman

At the Kaiser Cement and Gypsum plant near San Jose, Calif., one rod-ball mill has taken over the entire raw grinding function for the largest single cement operation in the West. Installed as part of a major overhaul performed on the plant by Kaiser Engineers, the new mill does the work of seven previous mills in feeding the plant&apos;s six kilns and keeping pace with its annual capacity of 8.5 million bbl of cement. Installation of the mill, which is the largest in the world, was started in December of 1966 and completed in April of 1967. The over-all modernization program surrounding the new mill has included the modification of existing crushing facilities; the building of new raw materials handling and blending facilities, new raw milling facilities, and new slurry handling facilities; and the installation of a digital-analog control system.

Jan 7, 1967

By H. P. Leighly, F. C. Perkins

THERE have been several statements in the literature about the difficulty of producing single crystals of high-purity (99.99pct) by the strain-anneal method. Consequently, investigators tend to employ low-purity aluminum for their single-crystal experiments, or else resort to the Bridgman or other techniques which depend on solidification for the production of single crystals. The following paragraphs describe a solid-state method for the manufacture of single crystals of high-purity aluminum which should provide crystals with greater perfection than those formed by solidification. The starting material for this method of producing single crystals was secured from the Aluminum Corp. of America and has a purity of 99.99 pct, the balance being trace amounts of impurities. Specimens approximately 1 by 4 in. are sheared from sheet having a nominal 0.050 in. thickness. The specimens are given a preliminary anneal at 640°C for approximately 3 hr in order to remove fabrication strains and to produce an average grain size of about 1/4-in. diam. The specimens are then etched in Tucker&apos;s etchant (45 pct HC1, 15 pct HNO3, 15 pct HF and 25 pct H2O) to remove the oxide film. Critical strain is applied by wrapping each specimen about a 1 3/4 in. round and subsequently straightening it against a flat surface. The high-purity aluminum sheet is sufficiently soft that this operation can be accomplished by ordinary finger pressure. The specimens are immediately annealed again at 640°C for 3 hr and reetched for examination. Ordinarily, considerable growth of certain of the grains will have occurred, and occasionally a single crystal will be produced on the first attempt. The procedure of alternately straining, annealing and etching is repeated until the majority of a batch of specimens contains usable crystal sizes. Typical examples are illustrated in Fig. 1. The greatest changes in crystal sizes are produced in the initial treatments. As the average crystal sizes get coarser in the later treatments, the sever- ity of the strain must be increased in order to produce grain boundary- migration. This increase in severity is effected by decreasing the diameter of the round used for straining (to 1 1/2 in., for example) and/or wrapping the specimens about the round twice, with opposite faces in contact with the round, before flattening. Usually the strain treatments described are not severe enough to produce nucleation in coarse grain high-purity aluminum. The growth of grains occurs by strain-induced grain-boundary migration. It has been observed that the grain boundaries move most readily during the first hour or so of each annealing treatment and that the rate of movement decreases with extended holding times at temperature. Prolonged annealing treatments are therefore not usually beneficial. Similarly, the rate of growth of each crystal appears to depend upon the orientation of the crystal with relation to those of its neighbors. Frequently island grains are formed after the initial heat treatment as the result of slow grain-boundary migration. These sometime become stationary during later heat treatments. Twin orientation interfaces are frequently developed during annealing. These imperfections can usually be removed by increasing the severity of strain to produce actual nucleation of new grains of more favorable orientation at the imperfection interfaces. The largest single crystals produced in our laboratory by the above method measured 4 by 1 by 0.050 in. Examination of Laue back-reflection patterns from a limited area of the specimens, gave no evidence of polygonization. Probably there is some indication of polygonization in the original grain area provided a more sensitive technique is used for detection. Experiments to produce wider specimens were less successful, possibly because wider sheets increase the complexity of the strains induced by deformation and promote widespread nucleation. Grain boundary migration occurs preferentially in a direction parallel to the longitudinal axis of the specimen. The choice of specimen geometry with respect to the rolling direction of the sheet appears to be immaterial in regard to the production of single crystals.

Jan 1, 1961

By J. Washburn, R. Drouard, E. R. Parker

Temperature dependence of the rate of recovery in zinc single crystals after a simple shear deformation at low temperature was investigated. Some tentative suggestions regarding the annealed and strain-hardened states of a crystal are discussed. RECOVERY may be defined as the gradual return of the mechanical and physical properties of strain-hardened metal to those characteristic of the annealed material; an increase in temperature increases the rate of recovery. The annealing process in strain-hardened polycrystalline metals is complicated by the inhomogeneity of strain which always exists in aggregates. Polygonization in bent regions of the crystals and growth of new almost strain-free grains starting at points of severe local distortion1-:&apos; make it almost impossible to isolate and study the recovery process. Homogeneously strained single crystals, however, do not polygonize or re-crystallize and hence they can be used advantageously to study recovery. In such crystals strain hardening is completely removed by recovery alone. Since recovery is a process whereby certain lattice disturbances introduced by plastic flow are gradually reduced, a knowledge of the rate and temperature dependence of this process for various conditions of prestrain might be helpful in formulating a model of the strain-hardened state. For simplicity it seemed desirable to limit the type of prestrain to the simplest obtainable, i.e., simple shear strain. In the experiments to be described, recovery was studied by observing changes in the stress-strain curve of prestrained zinc single crystals held for various times at temperatures above that employed for straining. Single crystals were grown from the melt by a modified Bridgeman technique from Horse Head Special zinc 99.99 pct pure, and from spectrographically pure zinc 99.999 pct pure. They were grown as 1 in. diameter spheres and acid-machined&apos; to the final specimen contour. The test section was a cylinder about 1/8 in. high and 3/4 in. in diameter. The conical sections adjacent to the test section were cemented into the grips so the load could be transmitted to the crystal as uniformly as possible. The specimens were oriented so that in testing the maximum shear stress was applied along one of the slip directions, [2110], in the (0001) plane. Details of the production and testing of such specimens have been presented.&apos; Each test was carried out according to the following schedule: 1—The crystal was strained at — 50°C until it reached a maximum shear stress, ,,,. The strain rate was approximately 5 pct per min in all cases. 2—After straining, the crystal was unloaded before the temperature was changed. Unloading required about 3 min. 3—The temperature of the specimen was then increased from — 50°C to the temperature, T, of recovery. This change in temperature was completed in a time of less than 2 min. The specimen remained at temperature, T, for a time, t, which differed for the various specimens. 4—Thereafter the temperature was again reduced to — 50 °C in approximately 3 min. 5—While at —50°C, the stress-strain curve after recovery was obtained. 6—The specimen was then unloaded and annealed for 1 hr at 375 °C in a helium atmosphere to bring about complete recovery. Cooling to room temperature after anneal required 90 min. 7—The same crystal could be re-used for another test because the plastic properties after annealing closely duplicated those of the original crystal. The specimen was immersed during the test in a bath of methyl alcohol which, through a system of tubes, could be pumped through either of two heat exchangers to regulate the temperature; this was accomplished by circulating the liquid through coils immersed in a bath of acetone and dry ice for cooling or in a bath of warm water for heating. Test temperatures were thus maintained constant within ±1°C. The — 50°C temperature was low enough so that no measurable recovery occurred during unloading and reloading. The stress-strain curve continued after recovery along a path below, but approximately parallel to, the path of a curve obtained in an uninterrupted test. Fig. 1 shows some of the results from a specimen of 99.999 pct Zn. The amount of downward displacement of the curve due to recovery was a

Jan 1, 1954

By R. W. Fountain, W. D. Forgeng, G. M. Faulring

Precipitation of the phase Co3Ti (Cu3Au type) from a Co-5 pct Ti a11oy has been investigated using single-crystal X-ray diffraction techniques. Oscillation and transmission Laue patterns of specimens aged for short-time periods at 600" C indicate the formation of titanium-rich and titanium-poor zones coherent with the {100} matrix planes. Longer aging times at 600° C establish that the equilibrium phase also forms on the {100} matrix planes as platelets. These observations are corroborated by electron metallography; electron diffraction studies show the phase Co3Ti to be ordered. A probable sequence of the precipitation reaction is discussed. A previous publication by two of the present authors reported on the phase relations and precipitation in Co-Ti alloys containing up to 30 pct Ti.1 The results of this investigation established the existence of a new face-centered cubic inter metallic phase, ranging in composition from about 17.0 to 21.7 pct Ti at temperatures below 1000° C The decomposition of the fcc supersaturated solid solution was studied employing hardness and electrical resistivity measurements. The changes in hardness upon precipitation in alloys containing 3, 6, and 9 pct* Ti were found to be associated with an initial increase in hardness followed by a plateau and then a second, more pronounced hardness increase. Investigation of this behavior by electrical resistivity measurements suggested that two different kinetic processes were involved, which, when interpreted in terms of the kinetic relation,2-4 indicated that initial precipitation was in the form of thin plates. On continued aging, the plates impinged during the growth process. The general features of these findings have been confirmed by Bibring and Manenc,5 while, in addition, they report the phase to be ordered. The present investigation was undertaken to provide more definite information on the structural relationships between the precipitate and the matrix. EXPERIMENTAL PROCEDURE Single crystals of a (20-5 pct Ti alloy were prepared from the melt employing the Bridgman technique. Poly crystalline rod, 1/2 in. in diam, prepared from vacuum-melted material, was machined to 3/8- in. diam to remove any surface contamination that may have resulted from hot-working. The crystals were grown under a purified hydrogen atmosphere in high-purity alumina crucibles heated by induction. Considerable difficulty was encountered in attempting to grow monocrystals because of the high melting point of the alloy and the high solute concentration. However, one crystal about 6 in. long was obtained which was essentially a single crystal except for one or two very small grains around the periphery. The as-grown crystal was solution heat-treated for 24 hr at 1200°Cin a purified argon atmosphere and water-quenched. One-quarter-in. slices were taken from each end of the solution heat-treated crystal for chemical analyses, and the remainder of the crystal was mounted and oriented by the back reflection Laue Method. The chemical analysis of the crystal was as follows: Pct Ti Pct 0 Pct C Pct N Pct H Pet CO 5.29 0.08 0.004 0.002 0.0003 Balance By proper tilting of the crystal, it was possible to obtain slices 1/32 in. thick of [loo] and [110] orientation. The solution heat-treated crystal slices were sealed in silica capsules for the aging treatments, with titanium sponge placed at one end of the capsule to act as a getter. All slices were water-quenched from the aging temperatures, the capsules being broken under the water to ensure a rapid quench. Thinning of the slices for transmission X-ray studies was accomplished by a combination of mechanical and electrolytic techniques, the final thickness being about 0.1 mm. Laue patterns of the solution heat-treated crystal indicated that no strain was introduced by the thinning technique. ELECTRON METALLOGRAPHY After X-ray examination, the structural changes attending the precipitation were followed by examination of direct carbon replicas of polished and etched surfaces of the single-crystal slices and extracted phases. The earliest indication of significant structural change was observed after aging at 600°C The structure of a heavily etched, solution-treated crystal is shown in Fig. l(a). Aside from the etch pit pattern, no regularity of background structure is observed. On the other hand, in the background of the specimen heated for 500 hr at 600°C, the etching pattern shows a directionality indicating the influence of minute precipitate particles, Fig. l(b). On electrolytic dissolution of this specimen in 10 pct HC1 in alcohol, a large volume of very small, flattened cubes

Jan 1, 1962

A professional and special section of the United States Employment Service, Department of Labor, has been created for the purpose of aiding officers and men who have been discharged from military service, but who, for various reasons, cannot resume their former positions, to place themselves in industry without loss of time. Its work is carried out in conjunction with the Engineering Societies Employment Bureau. The machinery of this new professional section is being set up as rapidly as possible, and an office is already in operation at 16 East 42c1 St., New York. The work in the New York State district is under the direction of Mr. Henry Bruere, formerly City Chamberlain of New York City. Dr. Thomas T. Read, Chairman of the A. I. M. E. Committee on Industrial Organization, has charge of the clearance between the State offices of the Eastern States. This service is designed for the purpose of placing not only men in the engineering professions, but for all other kinds of professional and highly trained, skilled men. Full details regarding the qualifications desired in a man should be given, so that employers may be put in touch only with such available men as will fully qualify for the positions.

Jan 2, 1919

Agnico-Eagle Mines Ltd. comprises a Gold Division at Joutel, Quebec, and a Silver Division at Cobalt, Ontario. In 1979 the Silver Division milled 41,700 mt (46,000 st) of ore at a recovered grade of 139 g per mt (4.06 oz per st) for a production of 5,816 kg (187,000 oz) of silver. The 100 -year -old mining, camp of Cobalt has long been noted for its high-grade silver ores, and now seems to be on the threshold of being revived with several companies operating in the area. In 1979, the Gold Division milled at the rate of 27,200 mt per month (30,000 st) and processed 333,000 mt (367,000 st) at a grade of 6.58 g per mt (0.192 oz per st) with a mill recovery of 91.670 to produce 2,013 kg (64,700 oz) of gold. The average total cost per ton milled was $22.10 per mt ($20.05 per st) which was $3.66 per g ($1 13.90 per 0s). These figures make Agnico-Eagle one of the lowest cost producers in North America. Gold occurrence in the Joutel ore is fine-grained and contained within sulfide facies composed mainly of pyrite with minor pyrrhotite. Two underground mining methods are employed with long hole stoping accounting for about 75% of the ore mined and shrinkage stoping the remainder. Ore from underground is hoisted into a 545 mt (600 st) coarse ore bin from where it is conveyed to a 45 mt (50 st) surge bin ahead of the 10-51 Hydrocone crusher. Crushed ore is then screened to make a 13 mm (112 in.) product with the oversize being recrushed in a 7-60 Hydrocone. Mill feed is conveyed to two 900 mt (1,000 st) fine ore bins. The Hydrocones were installed as part of a new crushing plant in March of 1980 and have contributed substantially to an increase in mill capacity. Space has been left to install a third crusher in the future. The fine ore bins discharge to a 2.75 m by 3.66 m (9 ft by 12 ft) rod mill, followed by a 3. 7 m by 5.5 m (12 ft by 18 ft) ball mill in closed circuit with a Krebs 380 mm (15 in.) cyclone to produce a 7070 minus 37 micron (400 mesh) .flotation feed. This pulp is first treated in a 34 cu m (1, 200 cu ft) Maxwell flotation cell and then in an additional twelve 2.8 cu m (100 cu ft) cells. Combined flotation concentrates are reground to 9070 minus 37 microns (400 mesh) in a 1.8 m by 4.9 m (6 ft by 16 ft) ball mill in closed circuit with a single Krebs 254 mrn (10 in.) cyclone. Flotation tailings are sent to the tailings dam. Reground concentrates are then aerated with lime to a single Pachuca and thickened in a 16.75 m (55 ft) diameter thickener with the addition of diesel fuel to render any activated graphite inert to adsorption of

Jan 1, 1981

By J. J. B. Rutherford

IT is now well known that troublesome intercrystalline corrosion may occur in austenitic stainless steels following exposure of the metal to a temperature within the range 1000° to 1500° F. (540° to 815° C.). The present paper describes a satisfactory method of estimating the extent of such corrosion, based on the measurement of the electrical resistance of a specimen before and after attack. This new method enabled us to study quantitatively the effect of several factors upon intergranular corrosion in the 18 Cr, 8 Ni type of alloy. The results show that susceptibility to this attack increases with increasing carbon content and grain size and appears to pass through a maximum for certain combinations of temperature of sensitization and period during which the alloy was maintained at that temperature; and are in complete accord with our interpretation of the mechanism of this phenomenon. The method is probably applicable to other metals or alloys subject to intercrystalline attack, such as the aluminum alloys of the duralumin type. The methods hitherto in use for estimating the degree of intergranular attack fall into three types: (1) microscopic examination,1 (2) macroscopic examination of fractures, and (3) determination of the time required for complete failure or disintegration .2 None of these lends itself very well to a measurement of the extent of corrosion. The first two are qualitative in nature and the third provides an arbitrary value largely dependent on individual judgment, since failure is a progressive phenomenon and not a sudden event. Our experience is that weight-loss determinations, although valuable in some types of corrosion investigations, bear no simple relation to intercrystalline corrosion in this type of alloy, as is to be expected since the phenomenon probably involves only the thinnest films between adjacent metallic grains.

Jan 1, 1932