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By C. A. Rowland

"Plant owners and operators, plant designers and grinding mill manufacturers are giving much attention to the design and manufacture of autogenous and semi-autogenous grinding mills, particularly the mills that have large diameters and draw power up to 10,000 hp and greater. Reliable designs giving long operating lives are required in today 's ore processing plants.This paper reviews bench-scale and pilot-plant testing to determine first if the ore is suitable .to be ground by these methods and then reviews the data obtained from pilot-plant testing that is used to select the mills and the grinding circuit. The paper then discusses the use of the pilot-plant results to design the mills. The most important pilot-plant data used for mill design are power and the amount of ball charge to be used. The mill size selected is a combination of these factors. Pilot-plant data not only establish power requirements, but can be used in the selection of the type of drive, variable speed or fixed speed, and the operating procedure to be followed. This leads into the mill control circuit to be used. The total charge in the mill, the type of drive and mill discharge arrangements are needed in the calculation of stresses and bearing loads. Conclusions reached from pilot-plant work are used to obtain data for process design, and autogenous and semiautogenous mill design should be part of any test program incorporating either or both of these grinding methods."

Jan 1, 1981

By Milton Williams

A comparison is made between the amount of interstitial water found by analysis in cores and that estimated from the resistivity curve of the electric log for the corresponding strata of producing reservoirs. It is shown that while the determined and the estimated water saturations are in good agreement in some cases, this agreement may be due to a fortuitous compensation of errors. Estimates of water saturations made from the electric 1og by use of existing relations should, therefore, be employed with caution. Also presented are data on the variation of salinity of interstitial waters in reservoir sands, and on the effect of variation of salinity and porosity on the validity of estimates of water content made from the electric log. INTRODUCTION Throughout the history of electric logging there have been recurrent cycles of optimism and pessimism as to the value of the electric log in the quantitative estimation of reservoir fluid content. The very early days of electric logging were an optimistic period, in which there was widespread faith in the ability of the resistivity curve to reflect fluid content, and in the ability of the potential curve to indicate textural characteristics. In time the accumulation of exceptions to this idealistic behavior brought about a general disillusionment, and caused the more pessimistic of those dealing with electric logs to believe that the sole importance of the log lay in stratigraphic correlation. Within the last several years optimism as to the quantitative use of the electric log has been revived, primarily as the result of the stimulating work of C. E. Archie' on the estimation of interstitial water in sands from resistivity data. Even though the general trend of thought on the quantitative value of the electric log reflects optimism, it is inevitable that there are some widely divergent opinions of the validity of quantitative estimates based on the electric log. A valid method of estimation of fluid content by means of the electric log and a general knowledge of the textural character of the reservoir rock would be of signal importance, not only in that it would save time and money in securing information on reservoirs now being drilled, but also because it would permit the evaluation of reserves in many fields drilled without adequate core data subsequent to the advent of electric logging. Because of this importance, Humble's Production Research Division, in cooperation with various other company divisions, initiated several years ago series of tests designed to evaluate the reliability of estimates of fluid content made from the electric log. The investigation was limited at the outset to sand reservoirs, since it was felt that the inclusion of limestone reservoirs would entail needless complications. In devising these tests it was immediately apparent that the chief difficulty in evaluating the worth of any method of estimation lay in establishing the true value of fluid content. The results of direct analyses of cores cut with ordinary mud were not sufficient, because of the probability of contamination of the fluids by filtrate from the drilling mud; the results of restored state tests on cores were deemed unsuitable because these results can hardly be said to furnish a primary standard. The method adopted was the direct analysis of cores cut with an oil-base drilling fluid. Such cores, when properly handled, are believed to afford the most precise determination of water content available at the present, and, in addition, lend themselves readily to the determination of various other properties which are pertinent to the estimation of fluid content from the electric log. Since it was desired to compare the fluid contents estimated from the electric log run in ordinary mud with cores cut in the same hole, the use of oil-base fluid necessitated the changing over, after all cores were cut, to a conventional mud. This procedure presented several advantages, one of which was that the use of oil-base fluid permitted

Jan 1, 1950

By J. S. Hegwer, P. M. Dunlap

An improved acid for the treatrrzent of sulfate-con-raining limestones and dolomites is described. The acid is designed to reduce he reprecipitation of dissolved calcium sulfate and the possibility of plugging permeable flow channels. In addition, this improved acid has a much lower reaction rate than that of regular acid; the advantages of a "retarded" acid are obtainable. Field testing of the acid has shown it suitable for use in sulfate-containing formations. Substantial improvements in productivity generally resulted. INTRODUCTION Acid treatments of limestones, dolomites and other formations bearing carbonate deposits are frequently unsuccessful when the calcareous formation contains sulfate, either as anhydrite (CaSO,) or gypsum (CaSO4. 2H2O). Preliminary dissolution in acid followed by redeposition of calcium sulfate appears to be a major factor contributing to poor well performance after acidizing. The precipitate is usually the gypsum form of calcium sulfate, but in higher temperature formations it may be anhydrite. The freshly precipitated crystals are nearly always very small and needle-like. They may occupy a gross volume many times that of the original anhydrite crystals and will obviously constitute an impediment to flow through newly enlarged flow channels. It is believed that the redeposition problem is most severe when anhydrite lines the fracture systems and large pores which supply the effective permeability of a formation. Microscopic inclusions of calcium sulfate also present large sulfate surface areas for dissolution in acid. In either case, great amounts of calcium sulfate may dissolve before the acid can be spent on formation carbonates. For regular spent acid (originally 15 per cent hydrochloric acid) the precipitate could be as much as 270 Ib gypsum/1000 gal acid. Two techniques have been applied by the industry for reducing sulfate plugging during acidizing. The method'.' commonly employed in the field is the attempted removal of a quantity of regular treating acid before it has reacted completely with the formation. This is practiced because the solubility of calcium sulfate is greater in a solution that is still acidic than in one which has been largely spent on the formation rock. The chance of precipitative plugging is therefore reduced if the withdrawal is successful. However, it is often impossible to get the acid out of the formation before precipitation occurs. A second possible method, which at first glance appears practical, involves addition to the acid of sequestering agents which form strong soluble complexes with calcium ions. These chemicals do increase the "solubility" of calcium sulfate in fresh acid, but to a lesser extent in spent acid. The sequestering agents have, therefore, proved unsatisfactory because the amount of sulfate eventually deposited from the spent acid may be greater than that from regular acid. Another logical approach to the problem of calcium sulfate reprecipitation is the prevention of the initial dissolution of calcium sulfate by the common ion effect. This may be accomplished by adding a soluble calcium salt to the fresh acid. The use of calcium salts in treating acids is not entirely new. An earlier suggested use of a soluble calcium salt in hydrochloric acid apparently failed to recognize the full extent to which the solubility of calcium sulfate could be suppressed. The present study extends this earlier work and adds certain improvements toward the development of a practical anti-anhydrite acid. LABORATORY DEVELOPMENT Calcium Sulfate Solubility Table 1 shows the results of a laboratory study performed to establish the effect of calcium chloride concentration on gypsum solubility. Because of the strong tendency of calcium sulfate to form supersaturated solutions, accurate solubilities are difficult to determine. These solubility data probably are reliable to within ± 15 per cent. The solubility of calcium sulfate in 15 weight per cent hydrochloric acid increases with increasing temperature. This trend is also followed in hydrochloric acid which cantains calcium chloride. This is contrary to the solubility behavior of calcium sulfate in water, wherein the solubility decreases with increasing temperature.

By Michael W. Lewis

The latest downturn in the world’s metal prices has forced many mining companies to focus on cost reduction and productivity improvements to remain competitive. Maintenance represents a significant part of the overall operating costs in the mining industry. A structured, proactive maintenance approach, such as reliability-centered maintenance, can achieve cost reductions and productivity improvements. Remote condition-monitoring systems are becoming commonplace because they have the potential to identify problems before failure. Detection of equipment degradation before failure will enable repairs to be scheduled, thereby reducing costs and interruptions to production. The mining industry is in the midst of uncertain times. Decreasing commodity prices, demand, head grade and capital availability along with increasing environmental requirements have put pressure on mining companies to significantly reduce costs to maintain short- and long-term viability. Corporations are looking at expansion, merger/consolidation and financial/hedging programs to achieve these cost reductions. Mines are reducing costs by eliminating all but essential expenditures, increasing production levels, reducing overtime and investing in new technologies.

Jan 1, 2000

Jan 1, 1901

By F. Wald, A. J. Rosenberg

The general features of the constitution of the B-Pt system were determined using standard rnetal-lograph~c, thermoanalytic, and X-ray diffraction techniques. Three compound were found. Two of these, Pt3B and Pt,B, are formed by peritectic reactions at 523° and 890°C, respectively. The third, Pt3B,, is congruently melting with a flat maximum at 940°C but decomposes eutectoidally in to Pt,B ant1 boron nt - 600° to 650°C. THE low-temperature allomorph of boron (red, simple rhombohedra1 a boron) is of scientific and technological interest as an elemental semiconductor.' However, the studies of this material have been hampered by its reported instability above 1200"~ which precludes crystal growth from the melt (mp - 2200°C). Crystallization from platinum solutions has been suggested as an alternative crystal-growth technique, but has met with only limited success.' The technique depends upon the existence of a significant difference between the eutectic temperature and the transformation temperature of boron. In order to clarify the conditions for further crystal-growth experiments, we found it desirable to redetermine the main features of the B-Pt phase diagram since previous reports on the system1'5'6'7 are in marked disagreement. EXPERIMENTAL The experimental methods used were thermal analysis, metallography, X-ray analysis, and, to a lesser extent, measurements of microhardness. Most of the alloys were prepared from spectrograph-ically standardized boron obtained from Johnson-Matthey &Co., Ltd. (212 ppm impurities, exclusive of carbon and oxygen) and platinum powder obtained from F. Bishop & Co. (200 ppm impurities, mainly of other platinum group metals). Some alloys were also prepared with very high-purity, float-zone refined boron (99.9999 pct obtained from "Wacker Chemie" and extrahigh-purity platinum (99.999 pct) obtained from Johnson-Matthey & Co., Ltd. The reported results did not depend on the choices of these starting materials. Five-gram alloy specimens containing 10, 20, 25, 27.5, 30, 33.3, 34, 35, 37, 37.5, 38, 39, 40, 41, 42, 43, 45, 50, 55, 60, 70, and 80 at. pct B were made by melting the elements together in boron nitride crucibles using rf heating of a graphite susceptor, either in vacuum or under high-purity argon. All alloys were heated to at least 1800°C for -5 to 15 min. Most of the alloys did not wet the crucibles when the latter were outgassed by preheating under vacuum. In any event, no weight loss was detected after melting, and the nominal composition was assumed for all specimens. Thermal analysis on 2.5-g samples were carried out in boron-nitride crucibles under a vacuum of 5 x X torr. The apparatus was heated in a "Kan-thal A 1" wound furnace, which limited the maximum temperature to about 1100°C. The output of the indicator thermocouple was fed to a dc recorder with a 1-mv full-scale span and an adjustable zero. The apparatus was calibrated repeatedly, using the freezing points of high-purity aluminum, silver, and gold. The results justified the use of the NBS voltage vs temperature tables for Pt/Pt 10 pct Rh thermocouples. All thermal analyses were run at least twice and both the heating and cooling effects were recorded. Most of the alloys had a very strong tendency to supercool. However, the use of mechanical vibration permitted reproducibility within *5°C for all alloys, except in the region around 40 at. pct B. Only the cooling effects are plotted in Fig. 2, since they appear to be more reliable. For metallography, the alloys were cut with a diamond cutting wheel, cast in a polymethacrylate resin, ground and polished with diamond paste, and etched with dilute aqua regia, a common etch for platinum alloys. Both copper and molybdenum radiation were employed to obtain X-ray diffraction data using Debye-Scherrer cameras and a "Norelco" diffractometer Diffractometry with high scanning speeds (1 deg per min) using nickel filtered CuK, radiation was used to identify the main regions of the diagram. However, molybdenum radiation was used for the detection of boron, since the latter showed very strong absorption and fluorescence effects with CuK, radiation. RESULTS AND DISCUSSION Three intermediate compounds, corresponding to the compositions Pt3B, Pt2B, and Pt3B2, were found in the system. Fig. 1 reproduces their X-ray diffraction spectra, together with those of pure boron and pure platinum. As can be seen from the thermal-analysis data in Fig. 2, Pt3B and Pt2B are formed by

Jan 1, 1965

By Voyle R. McFarland, Robert A. Burmeister, David A. Stevenson

The distribution of lead between phases in the Ag-Sb-Te system was studied using microautoradio -graphy. Two compositions were investigated, both containing an intermediate phase Known as silver antimony telluride as the major phase, and one containing AgzTe and the other SbzTes as the minor phase. For both compositions, two thermal treatments were used: nonequilibrium solidification from the melt and long equilibration anneals of the as-solidified structure. For each composition, lead was segregated in the minor phase of the as-solidified structure, but was distributed in the matrix after anneal. The electrical resistivity and carrier type were insensitive to the distribution of lead in the two-phase structure. ThERE has been considerable interest in the Ag-Sb-Te system because of its thermoelectric properties. The major interest has been in compositions on the vertical section between AgzTe and SbzTes, particularly the 50 mole pct SbzTes composition AgSbTez (compositions are conveniently expressed as mole percent SbzTes along the AgzTe-SbzTes section). One of the major problems in the proper evaluation and utilization of this material is the inability to control the electrical properties through impurity additions: all alloys prepared to date have been p-type, even with the addition of large amounts of impurities. It has been shown Wit all the compositions previously studied contain an intermediate phase of the NaCl st'ructure as a major phase (denoted by b) and a second phase, either AgzTe or SbzTe3, as a minor phase.'-3 One explanation for the unusual electrical behavior of this material is that the impurity additions have a higher solubility in the second phase than in the matrix; the impurity would segregate to the second phase, leaving the bulk matrix essentially free of impurity.4 In order to investigate this mechanism with a specific impurity element, the distribution of lead between the two phases was determined using autoradiography. Lead 210 was chosen because of the suitability of its 0.029 mev 0 particle for autoradiography and also because of the interest in lead as an impurity in this system.5'6 EXPERIMENTAL PROCEDURE Two compositions were taken from the vertical section between AgzTe and SbzTes, 50 mole pet SbzTes (Viz. AgSbTez) and 75 mole pct SbzTes, in which AgzTe and SbzTes appear, respectively, as the minor phase. Lead containing radioactive lead (pb210) was added to the above compositions to provide a concentration of 0.1 wt pct Pb. The material was placed in a graphite crucible in a quartz tube which was then evacuated and sealed. The samples were melted and solidified by cooling at a rate of 8°C per min and then removed and prepared for microa~toradiography. After autoradiographic examination of these samples, they were again encapsulated and annealed in an isothermal bath at 300°C for a number of days and prepared for examination. An alternate method of preparation employed a zone-melting furnace; the molten zone traversed the sample at a rate of 1.2 cm per hr and the solid was maintained at a temperature of 500°C both before and after solidification. This treatment had the same effect as solidification at a slow rate followed by an anneal for several hours at 500°C. In order to obtain the best resolution, thin sections of the alloy were prepared by hand lapping to a thickness of approximately 20 p. Other samples were prepared for examination by lapping a flat surface on the bulk sample. The resolution, although somewhat better in the former procedure, was adequate in both instances and the majority of the samples were treated in the latter fashion. A piece of autoradiographic film (Kodak Experimental SP 764 Autoradiographic Permeable Base Safety Stripping Film) was stripped from its backing, care being taken to avoid fogging due to static-electrical discharge. A small amount of water was placed on the sample, the film applied emulsion side down on the surface of the sample, and the sample and the film dipped into water in order to assure smooth contact. After drying, the film was exposed for 2 to 5 days, the period of time selected to give the best resolution. The film was developed on the specimen and fixed and washed in place. Two major factors must be considered in establishing the reliability of an autoradiograph: the in-

Jan 1, 1964

Crushing and grinding The Crushing and Grinding Technical Committee There was substantial activity in the area of crushing and grinding with the improved outlook in the industry. The Crushing and Grinding Committee's theme of 1987's Annual Meeting in Denver was Fundamentals of Mechanical Design for Crushing and Grinding Mills. At the meeting, the concept of gearless sag mill variable speed drives was taken out of the closet, dusted off, and a wraparound motor was put on hard copy with the ordering of a 9.7- x 4.5-m, 8.2-MW (32- x 15-ft, 11,000-) sag mill. Additionally, comparisons were provided to the mill design of the gearless drive sag mill and the twin 4.5 MW (6000 hp) do variable speed drives placed on the drawing board for the Kennecott UCD Expansions. This involved a 10- x 4.5m, 8.9 MW (34- x 15 ft, 12,000 hp) sag mill. Differing opinions were also expressed in technical presentations pertaining to the need for quality mill specifications in design and manufacturing. J. Berney-Ficklin of Bechtel presented a paper outlining the need for quality design and manufacturing specifications in large scale grinding mills, and the overall cost reduction in capital and operating costs. Others presented differing specific views, but all emphasized a central theme. Quality and reliable designs in large mills should not be compromised. In-pit crushing applications continue to increase, overseas and in the US, in both mining and quarrying. Different in-pit crushing units have been classified as mobile, with integral transport systems; semi-mobile, typically modular systems that use separate transporters for repositioning; semi-stationary plants that must be dismantled before transporting and typically require earthwork and concrete foundation work; and stationary in-pit crushing plants, which remain in place for the life of the pit. The majority of equipment sales of conventional crushing and grinding circuits in 1987 were to gold mining operations. There have been two areas of end use: • conventional jaw/gyratory or impact crushing circuits preparing low grade ores for heap leaching; and • small scale sag/ball mill circuits preparing higher grade ores for classical cyanide leach/ recovery circuits. There was also continued interest in ABC and SABC circuits for both base and precious metals plants. High pressure roll crushers continue to attract considerable interest in the cement industry. There, they are used to prepare raw materials or clinker for subsequent ball/tube milling. However, they have apparently been less successful in the mineral industry where the energy savings/ capacity gains have been much less dramatic. Several papers covering the theory and application of these machines were presented in an industrial minerals session on cement at the SME Annual Meeting. The Third International Conference on Hydrocylones, held in England in October produced several papers of interest on classification and screening to the mining industry. In particular, a new cyclone apex, developed by Mt. Newman Mining, shows promise of reducing water flow to the cyclone underflow stream and, therefore, increased underflow pulp densities and reduced fines recycle in grinding circuits. A twin vortex hydrocyclone was also described and shown to give a sharper split than conventional units. Similar double cyclones were introduced in the 1950's, but failed to achieve widespread acceptance. This was due mainly to a proneness to blockage in the transitional zone. It will be interesting to see whether this latest variant can overcome this problem in the typical operation. A number of North American iron ore plants installed the capability to produce fluxed iron ore pellets. Most chose to grind the stone on site with circuits designed to grind taconite ore. Methods employed to grind this material included single-stage ball mills closed with fine screens, rod and ball mill circuits - both open and closed with cyclones - and semiautogenous mills, followed by ball mills closed with screens or cyclones. Dewatering and tailings disposal B.M. Moudgil and D.L. Sober, University of Florida Due to tightened environmental regulations and the need for more efficient land use, a greater interest in dewatering and waste disposal has developed. As a result, research efforts in flocculation, surface chemistry, and polymers science have focused on the problems related to the dewatering of solid mineral wastes. A few studies have been conducted to examine the flocculation process. Hogg et al., (1987) discussed the formation and growth of flocs. They determined the size and density of flocs was controlled by the physical conditions of the system (e.g. agitation,

Jan 5, 1988

By B. G. Matson, M. A. Whitfield, G. R. Dysart

This paper describes the development of u computer program to calculate changes that occur in the length of tubular goods due to temperature and pressure changes during stimulation operations. Due to the numerous variables involved and the uncertainty of all static and dynamic conditions that could exist, it becomes a staggering task for individuals charged with completions to perform the necessary mathematical calculations. The computer program permits advance calculations for several sets of conditions. INTRODUCTION In the Delaware basin of West Texas alone, 50 wells were contracted or drilled to 15,000 ft or deeper in 1965. Deep well activity is continuing in this and other areas on an expanding scale. Many of these deep wells require extensive stimulation for successful commercial production, and during these operations, pressures and temperatures are encountered that have a pronounced effect on the length of tubular goods. This length change during a large-volume, high-pressure stimulation treatment utilizing fluids considerably cooler than bottom-hole temperature can be of such a magnitude that permanent damage to casing and tubing will result unless mechanical design, pressures and fluid temperatures are evaluated and controlled. These pressure and temperature effects can be calculated. However, the process lends itself well to computer solutions because of the mathematical nature of the problem and the calculating hours involved in arriving at an answer. The engineering-hour demand becomes more severe as tapered strings are involved. On initial treatments on a given well, surface pressure and injection rate conditions are unknown, and offset well conditions have not proven to be a reliable method for making predictions. For these reasons, it has become rather standard procedure for operators to compensate for these uncertainties by placing unnecessary pressure and fluid temperature restrictions on stimulation design. On a number of occasions treating fluids have been preheated to as much as 160F as a means of compensating for thermal contmction resulting from pumping cool fluids. The maintenance of packer seals has been treated by Lubinski, Althouse and Logan',' and the problem of therma1 effects on pipe has been explored by Ramey." These works were expanded and the results made applicable to everyday oilfield terminology before submitting them to computer programming. The pressure and temperature effects on tubing movement previously mentioned occur simultaneously as fluid moves through the pipe. The pressure changes, for purposes of explanation, are categorized here as to the various effects these pressures have on a tubing string. These divisions are (1) the piston-like results of forces acting on horizontal surfaces exposed to pressure, (2) swelling or ballooning of the tubing along its entire length due to the forces of pressure acting against the tubing walls, (3) the elongation of tubing due to frictional drag and (4) corkscrewing of the pipe due to internal pressure. Thermal changes are also of great importance, as their results may be more significant than any of the pressure effects. Steel is an excellent conductor of heat and the earth is a relatively poor conductor. It has been calculated that pipe temperatures at depths of more than 20,000 ft approach within as little as 25" the temperfature of the surface fluid after pumping for 2 hours, or a drop in temperature in some treatments of more than 220F. The equations presented in this paper were developed for computer programming and simplicity of input information; therefore, numerical constants such as Young's modulus for steel (28 X 10\ si), the coefficient of thermal expansion of steel (6.9 X 10."IF) and Poisson's ratio for steel (0.3) are included with unit conversion factors. The moment of inertia of tubing cross-sectional area with respect to its diameter was changed to a constant times (D' — d') where D is outer diameter and d is inner diameter. Units in the equations are length in feet, diameter in inches, density in pounds per gallon, pressure in psi, rate in barrels per minute and time in hours. PISTON-LIKE REACTIONS A change in tubing internal dimensions and the exposure of other horizontal surfaces to different pressures on the inside and outside of the tubing result in a reaction much like a piston under pressure. Such is the case when the internal diameter changes in a combination string of pipe, when seals of a slick joint assembly are subject to pressure and in the end effects of a tubing string. The change in tubing length due to the piston effects of a slick joint packer is affected by the various diameters involved, the tubing pressure Ap,, the casing pressure ,Ap,, length of pipe L, densities of fluid in the tubing before and during pump-

By C. Widham

Introduction It is generally accepted as dogma that sampling contributes most of the error in gold fire assays. Differences in assay results on pulps from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" of relatively coarse gold particles. It is true that coarse gold particles can contribute to substantial sampling fluctuations. But, while the process of sampling is probably the major source of error, the analytical process cannot be completely ignored as a possible contributor to erratic assay results. To maintain a stable assay process, the analytic part of the system must also be kept in control. One method of monitoring the performance of the analytic system is to systematically assay standard materials, whose sampling characteristics are carefully controlled. Gold assay standards are not prepared, nor can they be prepared, to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for both preparation (i.e., comminution and splitting) and fire assaying and then come to conclusions only about the fire-assay process. Because most gold ores are very heterogeneous, sampling errors would, in most cases, completely mask the contribution of the analytical errors. Assay-standard material is prepared only to assess the accuracy and variability in the fire assay process. Because the objective of the assay standard is to provide information about the fire assaying, it is necessary to control the sampling error of the standard material, so that it is only a minor constituent of the discrepancies observed in any assay results. To do this requires that the particle size of the standard material be reduced to a point where the relative standard deviation of the sampling error (i.e... the standard deviation of the errors divided by the average gold content of the material) is 2% or less. For all but very homogeneous mineralization, this means that the material must be reduced to 100% -150 mesh before the sampling errors are adequately controlled. However, even reducing the particle size can contribute to sampling problems. The liberation of gold may cause segregation that can cause large sampling fluctuations that are not easily controlled while maintaining the desired grade. Because, in most cases, the standard material would already be in the "pulp" state when it is submitted to a lab for assay, it is not possible to entirely conceal the nature of the sample from the lab. This is a problem inherent in using assay standard material. Because of the contribution of sampling to error generation in the assay process, the use of "coarse" material does not solve the problem of submitting a totally "blind" standard to the lab. In the sections that follow, the selection, preparation, testing and use of gold fire assay standard material is discussed. While some may dismiss the production of standard material as folly, it is possible to produce and utilize standard material to stabilize and improve the fire-assay process to produce more reliable assay results. Material selection It is desirable to use material that has as nearly the same metallurgical characteristics as the samples with which the standards will be included. However, this is usually difficult. For many reasons, including the particle size at which a significant amount of the gold mineral is liberated, the sampling characteristics of even -150-mesh material may preclude the use of geologically and metallurgically similar ore as a standard. It is usually easier to get material having desirable grade characteristics with the necessary sampling properties than it is to find geologically and metallurgically similar material with the required sampling characteristics. High-grade standards are especially difficult to find and prepare. This is because, as grade increases, the size of the gold particles usually increases. Larger gold particles are liberated and tend to segregate during comminution, and the homogeneity of the material cannot be maintained. For grades much above 3 g/t (0.088 oz/ton), it is very difficult to find material that has the proper sampling properties. Old mill tailings are likely candidates for assay standards. Some of these have sufficiently homogeneous mineral contents, so that the sampling errors can be effectively controlled. Where mill tailings are either not available or are not acceptable, mineralization that has exhibited homogeneous results in reassays of the pulp material is also a good candidate for the standard. Finally, the mineralized rock being sampled may (and should) be used if adequate homogeneity in the -150mesh material exists. "Adequate" ("acceptable") homogeneity is defined below.) It is important to use standards having a wide range of grades. This alone may preclude the material being

Jan 1, 1997

By Robert L. Slobod

In much of the work reported in the literature on long cores. true connate water value, probably have not been obtained because of insufficient flow of 011 to attain equilibrium. A -.satisfactory method for establishing connate water in long cores has been developed in which oil flow is maintained until no additiona1 water is displaced. INTRODUCTION Long cores have been used by sev-erals investigators in an effort to evaluate the efficiency of oil recovery for various producing schemes. The effects of many variables such as rate of displacement. pressure drop, volume of displacing medium, gas-oil ratio, inter-facial tension, and others have been investigated, and the merits of gas drive have been compared with water drive. In the older experiments no connate water was used. but in the more recent stndies the philosophy of the experiment calls for a core containing oil and connate water (irreducible water) as the starting point of the experiment. The method generally used to establish this condition in long cores involves dynamic' displacement wherein one or more phases are forced through the core. flow being maintained at a constant rate or at a constant pressure until a steady state is reached wherein there is no change of saturation with time. It is one purpose of this paper to point out that in much of the work reported in the literature true connate water values probably have not been obtained. The reason for this failure is pointed out. and a method for obtaining more reliable connate water values on long cores is presented. It is impossible at this time to completely evaluate the effect on the conclusions in the earlier papers resulting from the failure to obtain true connate water in the long cores, but some data are presented which indicate that serious errors may he present in many cases. MATERIALS AND APPARATUS Cores cut front outcrop sandstones (Strawn. Torpedo, and Elgin sandstones) with permeabilities of the order of 300 md were used. The major experiments were made with a core 18-in. long and 2-in. in diameter. Cores of the same diameter but only 12-in. long were used in a few tests? and in some work a core I-in. in diameter and 11-in. long was used. These materials were all somewhat bentonitic. 'To reduce the effect of such constituents, one of the cores (Torpedo No. 10) on which the most work was performed was acid extracted at the start of the experiment. Brine containing 50,000 ppm chloride and naphtha (Stoddard's Solvent) were used as the water and oil phases, respectively. The core was mounted in a rubber sleeve which forms the inner lining of a brass cylinder. In this arrangement2 the rubber sleeve is forced against the core by applying pressure to water in the annular space between the rubber sleeve and the brass cylinder wall. The core is therefore sealed in rubber so that all fluids introduced at the input end of the core flow through the core. With this equipment the core may be easily removed for inspection and analysis. Also, other cores may be introduced for study with no extra time for preparation such as is required when plastic mounting is used. When pressure or conductivity measurements are desired at intermediate points along tile length of the core, the brass cylinder comprising the outer jacket of the core holder is cut into section, of the desired length. Each section is then made up as an individual unit with its own rubber sleeve (see Fig. 1). The individual units are then butted up against a ring of plastic or other insulating material which carries an electrical contact for resistivity measurements and an opening which can be used for the measurements of fluid pressures. The individual units are forced tightly against the plastic ring separators and held in place with several tie rods. Inlet and outlet end butts of the same diameter as the core and several inches in length are provided to control the introduction and withdrawal of fluids and to complete the arrangement for sealing the core within the rubber sleeve. Fluid flow is maintained either by applying pressure to the liquid confined in a reservoir or by the use of a gear pump. The latter is preferable where continuous flow at a moderate rate over a long time interval is desired since a small volume of liquid can be readily recirculated using filters to prevent plugging of the core. EXPERIMENTAL The oven-dried core is weighed and is then completely saturated with brine

Jan 1, 1950

By P. G. Shewmon

A novel technique for determining the surface energy (?) and its derivative with respect to orientation, (?') is described. Essentially it involves the 'floating" of a wedge on the substrate, said wedge being made of a material which is not wet or only slightly wet by the substrate, i. e., as a greased needle "floats" on water. A thermodynamic analysis of a system in which the wedge is supported entirely by surface energy is given. If the original suyface is not at a cusp orientation, the surface tension is directly measurable from the groove angle formed. If the original surface is at a cusp orientation, there may or may not be a groove depending on the relative value of ?' and the weight of the wedge. Experiments primarily on copper and silver showed that sapphire, quartz and refractory metal wedges were wet while graphite wedges were not. The technique was demonstrated to work using graphite wedges, but the results obtained were not as eccurate as those obtained by other workers using the wire-creep experiments. It is concluded that the technique might prove most useful with non-metals where ?' is large and filament creep experiments would be quite difficult. If an absolute value of the surface free energy (?) of a metal is to be determined, the most reliable methods used to date measure an average over the various orientations exposed on a polycrystalline sample. For example, ? for silver, gold, and copper have been measured by determining the force required to just keep a thin wire,' or foil,' specimen from contracting under the influence of ?. Herring 3 has predicted and experiment confirms, that the sensitivity of this method is inversely proportional to the grain size.' Thus it cannot be used to measure ? for a particular orientation by using a foil single crystal or a very coarse-grained specimen. An accurate value if ? for tungsten averaged over a range of orientations has been determined using a field emission technique. The same techniques cannot or have not been used to measure ? for non-metallic solids, and as a result the values available are much less accurate.4 This Paper resents a means of making an absolute determination of ? for a particular surface orientation on any solid, as long as the given surface orientation does not break up into other orientations during an anneal. Experimentally ? is found to vary with orientation and at a few low index orientations it is found to have a cusped minimum, i.e., the derivative of ? with respect to the orientation of the surface changes discontinuously at the low index orientation, see Fig. 1. The slope of a plot of ? vs orientation (herein designated ?') is called the torque on the surface, since it tends to rotate the exposed surface toward the low index orientation, or if the surface is at the cusp orientation it opposes any force tending to rotate the surface out of the low index orientation. The ratio ?'/? has been determined for a few metals, but in cases where this ratio is high there is presently no means of determining either ?'/? or the absolute value of ?' for the orientations present on an annealed surface. The technique discussed herein also provides a means of determining an absolute value of ?' for those orientations which deviate only infinitesimally from a cusp orientation. It should work best on surfaces where ?'/? is large; that is, for cases where no other technique is available for measuring ?'. Aside from trying to learn more about surfaces through measuring ? and ?', the primary reason for wanting values of ? or ?' is to study adsorption. From measurements of the variation of ? for a particular orientation with the concentration of an impurity, one can obtain the number of impurity atoms adsorbed per unit area (Ti) on that orientation using the Gibbs adsorption equation.' where µi is the chemical potential of the adsorbed impurity. Thus, if absolute values of ? could be obtained for the free surface of a given surface orientation as a function of µi, ri could be determined for the given orientation. Furthermore, by equilibrating a grain boundary with the given surface at various values of ki, one could also determine ri for the grain boundary. Similarly Robertson 6 has pointed out that if y is taken to be a continuous function of and µi, then a2 ?/a @a µ2 = a2 ?/a pi a +. Thus, at all orientations away from cusps the following equation holds From a measurement of ?' vs ki, it is thus possible

Jan 1, 1963

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' 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 ED. E. Furman, R. H. Atkinson

HITHERTO the practical creep testing of precious metals has received little or no attention. The only previous creep tests of precious metals have been made with wires under conditions such as to yield much more rapid rates of creep than in engineering tests.', ' Up to the present time the value of creep bars of adequate size, in the absence of real need for engineering data, has deterred investigators. However, the increasing use of platinum at high temperatures has demonstrated the need for reliable creep data for the guidance of engineers, especially those engaged in designing certain specialized chemical plant equipment. In order to supply this need, creep tests were conducted at 1382°F (750°C) on 0.290 in. diam specimens of platinum, 90 pct Pt, 10 pct Rh and palladium. The platinum was high purity, nominally 99.95 pct Pt. The 90 pct Pt, 10 pct Rh was of the same high quality as is used for making gauzes for the catalytic oxidation of ammonia. The palladium was also of high purity; two batches of palladium bars were tested, one deoxidized with calcium boride and the other with aluminum. Spectrographic examination of the palladium confirmed its good quality; the only significant impurities apart from the residual deoxidizers were traces of silicon and lead. Procedure The creep bars, which were furnished by Baker and Co. to our specification, were 6 ¾ in. in overall length with a 4½ in. (4 in. gage length) reduced section 0.290 in. in diam and had the ends threaded (?-NC16). It may be of interest that the bars were valued at up to $600 each. The specimens were supplied in a 50 pct cold-worked condition to facilitate attachment of the creep extensometer, which was of the push rod type. Because of the softness of the platinum and palladium, the extensometer rings were secured to the test section by means of circular knife edges instead of the usual pointed set screws. The extensometer rods extended through the bottom of the furnace and readings were taken with a 0.0001 in. "Last Word" dial gage fastened to the rods for the duration of the test. The bars were directly loaded by hanging weights from the lower specimen grip. All tests were conducted at 1382°F ± 2°F, and an effort was made to maintain the temperature gradient over the test section within 2°F. The ends of the furnace tube were packed with asbestos wool, which allowed a very slow circulation of air through the tube. Annealing was accomplished in the creep furnace before the load was applied. The platinum and palladium specimens were annealed at the test tem- perature for about 17 and 24 hr respectively; in the case of the rhodioplatinum it was found expedient to anneal for 1 hr at 1922°F (1050°C). Pilot samples cut from the same stock as the bars were used to check annealing procedures. Pertinent measurements of grain size and hardness were recorded. Results and Discussion The creep data obtained are given in Table I and the creep curves are plotted in Figs. 1, 2, and 3. Two platinum specimens, tested under a stress of 250 psi, had almost identical creep rates at 2000 hr, namely 0.000008 and 0.000009 pct per hr. A third platinum specimen, stressed at 400 psi, had a creep rate at 2000 hr of 0.000026 pct per hr; the reason for a rather sharp decrease in creep rate during the period from 1200 to 1600 hr is unknown. As it was thought that 90 pct Pt, 10 pct Rh would have a lower creep rate than platinum, the first sample was tested at 400 psi; however, the creep rate was approximately 50 pct greater. Microex-amination revealed that differences in grain size might be responsible for the unexpected result, as annealing at 1382°F developed an average grain diameter of 0.0021 in. in the rhodioplatinum specimen compared with 0.004 in. in the platinum bar. Annealing the alloy for 1 hr at 1922°F (1050°C) increased the average grain diameter to 0.0032 in. and materially improved the creep resistance, making it much better than platinum. A second specimen annealed at 1922°F (1050°C) and tested under a stress of 550 psi had a creep rate of 0.000022 pct per hr at 2000 hr, which was still substantially lower than that shown by the specimen annealed at 1382°F (750°C) and stressed at only 400 psi. In contrast to the creep behavior of the platinum and rhodioplatinum specimens, the palladium bars, whether deoxidized with calcium boride or aluminum, were characterized by high first stages of creep. However, after about 1200 hr of test, the creep

Jan 1, 1952

By H. R. Froning, R. O. Leach

In wertability alteration flooding, a chemical agent is rnoved through a reservoir by the flood water to increase oil recovery by decreasing the degree of wetting of the rock by the oil. Substantial amounts of the chemical may be lost during movement through the reservoir. The extent of the loss, and therefore the economics of the process, depends in some cases on factors which are difficult to reproduce in the laboratory. Therefore, a short-duration, low-cost field test method is needed to permit evaluation of chemical requirements under actual field conditions. This paper describes a small scale rest conducted at a single well for measuring chemical requirements, thereby giving a more reliable evaluation of this important factor in the applicability and economics of the process. In the rest a small wafer slug containing the chemical agent and a nonadsorbed tracer is displaced into the reservoir by a known volume of wafer. The well is then placed on producrion. Chemical loss per barrel of pore volume contacted is calculated from [he fractional recoveries of the agent tested and the nonadsorbed tracer. The method has been used to determine within the actual reservoirs the chemical requirements for both a sandstone and a dolomite reservoir. Several chemical agents are potentially available for wettability alteration flooding, although none is universally applicable. For some applications of the method, chemical costs per barrel of additional oil recovered can be substantially less than one dollar. INTRODUCTION Wettability alteration flooding provides a means of increasing oil recovery from reservoirs by decreasing the degree of wetting of the rock by the oil and increasing the displacement efficiency of the flood water. Earlier studies demonstrated a relationship between oil recovery during waterflooding and the degree of wetting of a rock surface by an oil. The application of wettability alteration flooding to the Harrisburg field of Nebraska provided a field test' of this recovery process. Subsequently, additional laboratory and field tests have developed additional procedures for evaluating wettability alteration flooding, and have indicated where the process may be applicable. Applicability of this process to specific reservoirs is determined by a progression of tests to determine sus- ceptibility of the reservoir to alteration of its wettability, to indicate the degree of recovery improvement and to estimate the amount of chemical required to process the reservoir. The economics of applying improved oil recovery processes depends not only upon the degree of improvement in oil recovery achievable by the process but also upon the process costs and the timing of the income and the investment. Emphasis in this paper is on the expenditure aspects of the process. The work reported in this paper indicates that the chemical investments required for wettability alteration flooding are substantial. For evaluating the economics of a potential flooding application it is imperative that a sound estimate of the chemical requirements be made for the reservoir. Generally, true reservoir conditions are not adequately simulated in laboratory chemical propagation tests. Because of wide well spacings, many years might be required to obtain chemical propagation data from conventional pilots or inter-well tests. Consequently, n short-duration, low-cost method is needed to determine chemical requirements in the field. The potential applicability of wettability alteration flooding is discussed, as well as the economics of wettability alteration with respect to the inherent and imposed restrictions on the timing of income and investments. DETERMINATION OF CHEMICAL REQUIREMENTS In the process of moving a chemical bank through reservoir rock, some of the chemical agent lags too far behind the flood front to be effective or is otherwise lost to the reservoir system. The extent to which these losses occur overshadows the reductions in chemical concentration due to diffusion and to mixing with the reservoir fluids. Experience indicates that almost without exception, chemicals which induce a wetting change undergo either sorption reactions or chemical reactions with mineral constituents of the pore surfaces. Other reactions may occur between the added chemical and the reservoir oil and water. Even in limiting consideration to reactions of the relatively inexpensive inorganic salts, bases and acids, the reactions may be exceedingly complex. Reservoir pore surfaces consist of more than silica in sandstone reservoirs, and more than calcite or dolomite in carbonate reservoirs. Many mineral species are present, each exhibiting specific tendencies to react with an injected chemical. The reactions which occur can consume enough of the agent to have an important effect on economics. These reactions can cause a change in pH of the chemical bank, or may remove some of the active chemical by precipitation, adsorption or reaction to form a new chemical which may or may not be effective in

By H. Tudeshki

A great amount of aggregate is utilized in civil engineering applications such as road construction, railway infrastructure, concrete production, etc. Igneous rocks are the preferred raw material due to their high strength and abrasion resistance. Rock quality assurance is a key factor and has great influence on the quality of constructions in civil engineering. One of the major problems encountered by both the producers and users of igneous aggregate rock is the fact that, with the passage of time, some specific rocks lose their strength, up to a complete loss of structure, i.e. disintegrate and degrade. This phenomenon has a great influence on the quality, strength and durability of aggregates. In the last decades, different methods and procedures such as the glycol test, the methylene blue dye test, as well as the Los Angeles test, have been introduced to distinguish rock properties, and to identify these problems. However, as these wet-chemical methods are time consuming, hard to perform, only to be applied to hand-piece samples, requiring special laboratory equipments, and are only possible to be accomplished under laboratory conditions, their application has always been severely limited. To address this widespread quality management problem of the quarry industry, a relatively quick, easy and user-friendly approach is necessary. It calls for a systematic solution with a device that can simply be used in the day-to-day routine of a mine for quality control of the quarry´s daily production. Our research is concentrated on developing a systematic method for early recognition and diagnosis of rock quality, in order to control and manage the quality of the quarry production in advance. Our new approach is based on two rock parameters: magnetic susceptibility and loss on ignition. The measurement of these parameters provides reliable information on the quality of the rock and allows the quality control process to be accomplished and performed at the borehole location. Our new approach has been assessed through extensive field and laboratory studies and has been implemented on the drill-cuttings of a basaltic andesite quarry. The results of the experiments are discussed in detail, including their impact on increasing resources and environmental protection.

Aug 1, 2013

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By J. T. Dewan

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

Jan 1, 1957

By L. S. Darken

A quadratic formalism is developed lor the representation of the excess free energy, and of the activity coefficients of each component of a ternary system in the vicinity of a single component selected as solvent. This formalism, in contrast to the e formalism, is thermodynamically consistent at .finite concentrations. Numerous specific systems are used as illustrations, with cross checks where possible; these systems are Fe-C-X systems in the vicinity of 1600°C and include practically all those for which reliable data are available. It is shown that this formalism is usually quite adequate to rebresent available data up to a solute concentration of 20 to 30 at. pet. It is hoped that the formalism here presented may prove useful for the treatment and tabulation of data on ternary and multi-component solutions. SINCE, as discussed in a prior paper,' we do not as yet have an adequate basic understanding of the nature of binary metallic solutions, we cannot hope to be in better position for ternary and multicomponent systems. However, the accumulation of thermodynamic data on ternary and multicomponent metallic solutions has led to an urgent need for a rational formalism for the presentation and use of such data. Notable attempts to represent the isothermal isobaric thermodynamics of ternary solutions were made by Benedict et 01.' and by Wohl.3 These attempts were directed toward developing an analytic expression adequate to encompass the entire ternary triangle, primarily for organic systems; they generally involve the power-series approach, which has been shown' to be inappropriate, in general, even for binary metallic systems. On the other hand, interest in the thermodynamics of ternary and multicomponent metallic solutions has tended to focus either on general thermodynamic relations4-10 over wide compositional ranges, or on cases where one or more components have been at rather low concentration. This latter approach has been followed by Wagner,= by chipman,11 and by Alcock and Richardson,12 and more recently in many publications by the same and other authors. It has already been shown' that the thermodynamic behavior of binary metallic systems is, in general, relatively simple only in the terminal regions. Hence, it would appear that any approach, at this time, to a simple formalism for ternary and multicomponent systems must, a fortiori, be limited to the vicinity of the major component or solvent. The present treatment is aimed to be useful for a given solvent with moderate solute concentrations ranging up to 20 or 25 at. pet and in exceptional cases to considerably higher concentrations. In order to achieve even this modest objective, it is necessary that any appropriate formalism have built into it 1) a thermodynamic consistency (at least within the desired degree of approximation), and 2) an approach at infinite dilution to Raoult's law for the solvent and to Henry's law for each solute. Let us first formulate the condition of thermodynamic consistency for a ternary system. Under isothermal isobaric conditions, we may write for the molal value G of any extensive function dG - C1 dN1 + G2 dN2 + G3 dN3 [l] where the G's are the corresponding partial molal quantities and the N's are the atom fractions. Taking component 1 as the solvent, this relation may be rewritten in terms of the independent variables N2 and N3

Jan 1, 1968

By F. E. Jaumot, R. L. Smith

Self-diffusion in zinc has been used as an instrument for comparison of the absorption and sectioning techniques as a means of studying diffusion. Single crystal as well as poly-crystal samples were used asanda the temperature range of diffusion extended from 200° to 415°C. For temperatures above 200°C, the data indicate that the results obtained from the absorption technique agree with those obtained from the sectioning technique. The effect on the values of the diffusion coefficient of electroplating vs evaporation as a means of applying the tracer was investigated and no significant difference observed. It was found that an excess or deficiency of tracer did not materially affect the results obtained from the sectioning technique, but invariably caused errors with the absorption technique. NEARLY all self-diffusion experiments and many alloy diffusion experiments have employed radioisotopes as the instrument for following the diffusion. Of the various techniques in which radioisotopes are applicable, the two most widely used are the sectioning and absorption techniques. In the former, the diffusion coefficient is obtained from a curve of log concentration vs the square of the mean penetration depth. In the latter, the diffusion coefficient is calculated from a knowledge of the decrease in activity at the surface after diffusion. In spite of the importance of knowing the reliability of the diffusion data and the widespread use of these two techniques, they had not been directly compared experimentally on the same samples. Thus, such a comparison was worthwhile. The specific system chosen for this comparison was the self-diffusion of zinc, since the metal was readily obtainable in high purity, single crystals were easily grown, and the anisotropic features of the diffusion added an additional factor of interest to the comparison. Self-diffusion in both single and polycrystals was investigated, since the possibility existed that grain boundaries and grain boundary diffusion might produce different effects for the different techniques. Also, the effects of electroplating vs evaporation as a means of applying the radioactive tracer, and the effects of applying an excess or deficiency of tracer material were studied. The general experimental procedures and the mathematical analyses of both techniques have been described previously in some detail, and only those points essential to an understanding of the present work will be discussed here. The mathematical analysis of the sectioning data requires only a knowledge of the solution of Fick's equation. where C,, is the initial concentration, C is the concentration at depth x, D is the diffusion coefficient, and p is the absorption coefficient of the solvent metal for the radiation from the solute. Having obtained F from the experiment, the value of z can be read from a plot of F vs In z, and D can then be calculated if is known. The necessity of knowing the absorption coefficient causes most of the criticism of the absorption technique. It is very difficult to measure accurately under the conditions existing in the diffusion experiment, but it is absolutely necessary, as will be indicated briefly later. Portions of this problem have been discussed in detail elsewhere." The difficulties involved in the measurement of the absorption coefficient arise from three principle factors: the physical characteristics of the absorber, the geometry, and complex radiation spectra. The first two are heavily dependent upon the third. If

Jan 1, 1957