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By C. E. Birchenall, G. Derge

IN studying the kinetics of slag-metal reactions, it has become increasingly apparent that a complete knowledge of all aspects of interface phenomena will be required to clarify these processes adequately. A part of the data required for all oxidizing slags used in the refining of impure iron to steel is the rate of exchange of iron between the slag and metal phases. The simplest equilibrium of this type is that between liquid iron and iron silicate slag when both phases are equilibrated with the silica crucible containing them. In this study, the exchange of iron between the two liquid phases has been measured by using radioactive Fe as tracer. The observed high exchange rate indicates the ease with which such interfaces may be crossed in refining processes. The experiments required for this study involved relatively minor and normal modifications of well established techniques. Melting was accomplished by induction heating in heavy walled, fused silica, rotating crucibles." Rotation was used to minimize dilution of the slag by crucible erosion. The melting stock was ingot iron. Slags were prefused in iron crucibles using chemically pure grade oxide reagents. The special conditions applying to the active iron additions will be described for individual experiments. Suitable precautions were observed with regard to protection against radiation hazards.' Identification of Activity This particular study was initiated several years ago, but held in abeyance because the radioactive iron available at that time contained a foreign activity which concentrated in the slag so as to mask the iron activity and render the results unin-terpretable. With the benefit of experiences from other studies, radioiron of suitable purity can now be prepared. As received from the Isotope Div. of A.E.C., the unit appears to contain Fe + Fe50 and a high activity cobalt. The cobalt and iron are separated by repeated ether extractions, and the purified iron stored for sufficient time for the Fe'7 44 day half-life) to decay to negligible activity, leaving only Fe as the active isotope. This was confirmed by the absorption curves for slag and metal samples from heat No. 1. In Fig. 1 the experimentally measured points for the absorption curves of slag and metal are fitted by the calculated slope of 5.8 mg per sq cm in aluminum, which corresponds to the Mn K doublet emission resulting from the capture of an orbital electron of Fe" by the nucleus. This shows that the radioactive species are the same in both slag and metal and identifies it as Fe55 Description of Individual Heats For the first heat, the radioactive iron was contained in the prefused slag. The active Fe55 had been precipitated with carrier and was added as Fe2O3 during fusion in the iron crucible. The charge of 500 grams of ingot iron was melted, the protective iron sleeve added, rotation started, and a prefused, inactive slag was added to allow the system to approach equilibrium. After about 5 min at temperature, the wash slag was skimmed and the active slag added. Initial slag and metal samples were taken as soon as the slag was molten. Additional samples were taken at indicated intervals thereafter. Slag samples were dipped with a small iron spoon and metal samples were sucked into 1/4 in. ID silica tubes. The slag and metal samples were pulverized and mounted for radioactive counting. The slag samples were analyzed chemically for FeO. Temperature was read after the last slag sample by immersion of a Pt-Pt-Rh thermocouple protected by a fused silica sheath. Since no significant variation of rate with temperature was observed

Jan 1, 1954

By O. J. C. Runnals

The intermetallic compounds NpAl2, NpAl3, and NpAl have been prepared, and examined by X-ray diffraction methods. The compounds are isostructural with the corresponding U-Al compounds. NpAl3 is face-centered cubic with a = 7.785A and has the MgCu2 structure. NpAl is simple cubic with a = 4.2624 and has the AuCU3 structure. NpAl4 is body-centered orthorhombic with a = 4.428, b = 6.268, and c = 13.71A. The published description for the atomic positions in UAl, applies also to NpAl4 THE U-Al system has been examined by Gordon and Kaufmann.1 They identified the following intermetallic compounds: UAI2, UAl3, and a third, tentatively identified as UAl5. A structure analysis of the latter compound by Borie2 proved that the formula UAl4 was more consistent with the X-ray data. The crystal structures of UAl2 and UA have been reported by Rundle and Wilson.3 UAl2 was found to be isostructural with MgCu. The atomic positions in the simple cubic UA1, cell were found similar to those in the AuCu3 structure. Three analogous compounds exist in the binary system Np-Al. X-ray data for the compounds NpAl2, NpAl3, and NpAl4 are reported below. The neptunium used in the investigation was supplied through the courtesy of the Argonne National Laboratory as neptunium (V) nitrate. It was stated to have a radioactive content of 99.25 pct Np237. The impurity limits had been established by a spectrographic analysis given in Table I. Any titanium, boron, or bismuth impurity should be effectively removed during the fluorination of NpO2 to NpF4, and sodium, lithium, magnesium or strontium during the alloying procedure. The oxalate ignition technique, described by Westrum for the preparation of finely-divided reactive PuO2, was used.The neptunium (V) nitrate solution, containing 100 mg Np, was evaporated to dryness on oxalic acid crystals. The resulting oxalate was calcined to NpO, by heating in platinum at 650°C for 2 hr. An equimolar mixture of anhydrous hydrogen fluoride and purified hydrogen was passed over the NpO2 for 2 hr at 500°C. According to Fried and Davidson" the above fluorination conditions should produce the purple-black fluoride, NpF3 However, the light-green product showed only NpF4 lines on an X-ray diffraction pattern and contained only an estimated 5 pct of finely dispersed black NpF3 particles on microscopic examination. NpAl3: An intimate mixture of 50 mg of neptunium fluoride and aluminum powder (99.99 pct pure, —28 to $60 mesh) was heated to 900°C in a BeO crucible in vacuum by a tungsten coil for 2 hr, to allow the following reaction to proceed: NPF4 + 7Al + NpAl, + 4AlF. [1] The formation and sublimation of aluminum mono-fluoride in this system was verified from an X-ray diffraction analysis of the sublimate. The diffraction pattern was similar to one obtained in the aluminum reduction of UF4 to UF3,6 showing both Al and AlF3 lines. The resulting alloy was sintered at 1100°C for 1 hr. A powdered specimen of the crystalline product was sealed in a thin-walled quartz capillary for X-ray examination. The photograph was taken on a 14.32 cm General Electric powder diffraction camera, using filtered copper radiation. The films were calibrated in terms of a NaCl standard pattern. The wavelengths used in the calculations were 1.5418A for Cu K and 1.5405A for Cu K The powder diffraction pattern showed that NpAl is simple cubic with a = 4.262 % 0.005A, and is isostructural with UA13 where a = 4.27A1 or a =

Jan 1, 1954

By W. D. Haentjens, A. P. Pipilen, M. Weintraub, A. A. Orning

W. D. Haentjens (Barrett, Haentjens and Co., Hazleton, Pa.) — The authors are to be complimented on undertaking a project which has little available experimental data. There are so many variables in the hydraulic transport of solid materials that it is difficult to correlate the experimental information from one series of tests into usable data involving other materials or even similar materials but of different size consists. The friction data is of particular interest to those involved in pipeline design. Most such pipelines, however, involve portions which are not level and the effect of sloping or vertical lines might also be considered in extensions of this test work. Pump manufacturers are concerned about criticism resulting from the stated amount of degradation occurring in a pump. The amount of degradation is affected somewhat by pump design and this should be taken into consideration. The pump which was loaned for this work was a modification of a standard medium duty slurry pump. This modification was for maximum particle size, however if minimum degradation is the object, then other design changes would be indicated. Although there is a tendency to be less concerned with degradation in industrial applications, it is nevertheless an important factor in many uses and further studies should be made. In particular, the amount of degradation could possibly be segregated into more classifications, rather than charge some losses to the pump which apparently are occurring in other handling. It seems difficult to evaluate the degradation which occurs in handling the coal into the pump sump and in removing it from the line into the tank. Each handling, of course, contributes some degradation, as does the screening operation itself. These are all charged to the pump, or to the pipe line and pump together; and, although they may be small, they could possibly be evaluated. It is interesting to note the verification of the old rule of thumb of maximum particle size equal to approximately one-third of the pipe size. Our experience has shown size distribution to have an effect on the flow characteristics and if this data is available for the tests which were run, it would be interesting supplementary information. A. P. Pipilen, M. Weintraub and A. A. Orning (Authors' Reply) — In this paper the authors have attempted to outline some of the major factors affecting a rational design for a solids-liquid transport system. They are grateful to Mr. Haentjens for pointing out several other equally important considerations. Pump manufacturers, in general, should be complimented on the strides that have been made in decreasing particle degradation within the pump. Considerable research and a great deal of mathematical analysis is required before pump design in this field can become a science rather than an art, for each system requires a different set of compromises. As Mr. Haentjens indicates, maximum-particle-size handling capability may be inconsistent with minimum degradation; even more important, the rotor profile for the most efficient transfer of energy to the fluid may have to be compromised to reduce particle breakage, for, whenever particle density differs from fluid density, the two phases will have different trajectories. Some evidence of this geometric factor is provided by a cursoy analysis in the Bureau of Mines Report of Investigations now in preparation, where it is indicated that, for the pump used, degradation decreased when the tangential velocity was decreased and when the radial velocity was increased. This relation, itself, is probably a function of particle size and concentration. Some data on particle size distribution, as requested by Mr. Haentjens, will be provided in the Report of Investigations referred to above in addition to that already presented in Table II of the original paper. However, in the limited number of tests it is difficult to distinguish between cause and effect, for not only did the particle size distribution alter the flow characteristics, but, through the medium of degradation, the operating conditions rapidly altered the particle size distribution.

Jan 1, 1965

By M. J. Hordon

Measurements of the 103 yield stress of ordered and disordered poly crystalline Cu ,Au were related to the ordered antiphase domain size determined by resistivity measurements. For undeformed material, a yield stress maximum wa obtained at a critical domain diameter of about 40A. Plastic deformation resulted in a marked increase in the yield stress and electrical resistivity of the ordered alloy compared to the disordered, the strain hardening rate increasing regularly with initial antiphase domain size. Order hardening was accompanied by a sharp reduction in size of the initially large domains. It has been observed that the yield stress of ordered and partially ordered Cu3Au alloy varies sensitively with antiphase domain size aid degree of order.ly2 In addition, ordering of the lattice leads to a marked increase in the strain hardening rate (order hardening) as compared to the rate for the disordered alloy. In the present investigation, changes in the electrical resistivity and yield stress of ordered polycrystalline Cudu with varying initial domain diameters were measured after tensile plastic deformation in order to examine the effect of cold work on the antiphase domain size. EXPERIMENTAL PROCEDURE Au-Cu alloy of 99.99 pct purity analyzing 50.85 wt pct Au-balance copper was obtained from the Handy-Harmon Co., N. Y., in the form of 0.061 in. diam drawn wire. Wire specimens 3 in. in length were given the following annealing treatment in nitrogen: 500" for 72 hr, 820" for 15 hr, and 450" for 5 hr, followed by a water quench. The annealing sequence resulted in a completely disordered structure with a grain size of about 0.2 mm. The disordered specimens were then reannealed at 360' in nitrogen for periods varying from 10 min to 150 hr followed by quenching to produce ordered structures with varying domain sizes. The degree of ordering and variation of domain size was followed by electrical resistivity measurements made at room temperature using a low resistance precision Kelvin double bridge apparatus. The specimen resistance was determined over a length of 4.0 cm between two brass knife-edge contacts while the specimen was immersed in an oil bath to minimize temperature variations. In addition, the current flow in the circuit was minimized by a current pulse technique in balancing the bridge in order to avoid heating the specimen. Using a sensitive galvanometer to detect the bridge null, the accuracy of the resistance measurement Wire specimens were plastically strained in tension with an Instron tensile unit at strain rates in the range 5 x 10"5 sec-' to 2 x 10"4 sec-'. Stress and extension data were fed into the Instron chart drive amplifier to obtain the actual stress-elongation curve from which the yield stress at 10"3 strain was determined. The maximum resolution of the apparatus was approximately 50 psi stress and 3 x 104 strain. At various plastic strain levels, deformation was interrupted and the electrical resistivity determined after removing the stress. RESULTS AND DISCUSSION 1) Yield Strength of Ordered Cudu. In order to determine the effect of the ordered antiphase domains on the initial yield stress, specimens were prepared with varying domain sizes ranging from zero for 5 completely disordered structure to about lo5A for a completely ordered structure by suitable annealing treatment. Domain sizes were estimated by comparing room temperature electrical resistivity data with the original data of Jones and sykes3 as modified by rdle.' In agreement with previous work, the resistivity varied sensitively with domain diameter and degree of order, decreasing from approximately 11.6 x l0- ohm-cm for the disordered structure to about 5.9 x l0- ohm-cm for ordered domains above 10"3 cm in diameter. Fig. 1 shows the change of the 103 yield stress with ordered domain size. It is evident that the maximum

Jan 1, 1963

By Dennis Peterson

INTRODUCTION The business arena has dramatically changed for most producers and consumers of commodities. International debt, currency shortages, political upheavals, etc., require corporations today to be sophisticated and flexible enough to change their purchasing and sales techniques in order to maximize returns. Many external factors, such as interest rates, trading partners, currency changes, and government edicts, can have an adverse effect on a company's bottom line. Totally out of a company's ability to control or predict, these. factors force the commodities based corporation to constantly re-evaluate its operating scope and domain. The principle of back-yard only operations and the laissez-faire with blinders style of management is no longer a viable way to run a business. The industrial world has been operating for the past 10 to 15 years as though there were no commodity nor raw material crisis. For developed countries the primary products sector has become marginal, whereas it was central in the first half of the century. A radical change in the method of doing business is necessary to offset a depression in the industrial economy. The risk of collapse may be heightened by a banking crisis caused by massive defaults on the part of commodity producing debtors, whether in the third world or in our own farm producing sector. The raw materials economy has become divergent with the industrial economy. This is a major change in the world economy with tremendous implications in both developed and developing countries for economic and social policies and economic theories. Basic competition issues, such as low labor costs, are likely to become less of an advantage in international trade. In developed countries these costs are going to account for a smaller portion of total costs. The total costs of automated processes are lower than those of traditional plants with low labor costs. Automation in the commodities sector eliminates the hidden but high cost of not processing at capacity created by poor quality, rejects and maintenance for product change-overs. The cost of capital will become increasingly important in international competition. Over the last ten years the U.S. has become the highest cost country in this area. Reversing the U.S. policy of high interest rates and costly equity capital should be a priority for management decision makers. In the rapid industrialization of this century, Japan developed by exporting raw materials, (principally, silk and tea), at steadily increasing prices. Germany developed by leap frogging into the high-tech industries, mainly in electricity, chemicals and optics. The United States did both. Both avenues are blocked for today's rapidly industrializing countries because (a) the deterioration of the terms of trade for primary products, and (b) it requires an infrastructure of knowledge and education far beyond the scope of a poor country. Many explanations exist for the explosion of international money flows. The shift from fixed to floating exchange rates in 1971 may have given initial impetus by inviting currency speculation. The surge in liquid funds flowing to petroleum producers after the oil shocks of 1973 and 1979 was definitely a major cause. There can be little doubt that the U.S. government deficit also played a big role. The American budget deficit has become a massive void, sucking in liquid funds from all over the world and making the U.S. the world's major debtor country. In reality, a trade and payments deficit is actually a loan from the seller of goods and services to the buyer, that is, to the U.S. From now on, the global ramifications of business will have to be treated in economic theory and business policy alike. Economic theory teaches that the comparative advantage factors of a real economy determines operative and financial policy. These comparisons -- labor costs, productivity, raw materials cost, energy costs,

Jan 1, 1990

INTRODUCTION The meaning of cash flow has already been defined as after-tax earnings available for use by the corporation or business. It is therefore apparent that a significant part of mineral economic evaluation is concerned with correct and accurate computation of taxable income under existing tax laws, and the proper treatment of tax allowances and deductions. The various methods of depreciation, depletion, and amortization are all means whereby the investor can earn back or recover, before taxes are imposed, the investments made for purposes of doing business or for the production of income. Each of these three types of tax deduction are applied to different investment items such as property, equipment, buildings, research, etc. The cost of buildings, equipment, machinery, and transportation equipment are representative of capitalized business costs that must be recovered by depreciation over the life of the asset. The property investment costs of acquiring natural resources such as minerals, oil and gas, and standing timber are examples of investment costs that may be recovered by depletion. Several other capitalized business costs, such as research expenses and trademark expenses, may be recovered by amortization. The term "capitalized" means that the in- vestment cost is not deducted as an operating expense in the year that it is incurred, but is spread out over a period of years through depreciation, depletion, or amortization deductions according to lawful schedules. Of course, any capitalized cost can only be deducted once. The other costs of doing business which are not capitalized, such as labor and operating costs, are said to be "expensed," i.e., they are written off for tax purposes in the year they occur. DEPRECIATION Depreciation, according to US tax law, is a deduction from taxable income permitted as a "reasonable allowance for the exhaustion, wear and tear of property out of its use or employment in a business." The original cost of the property is the usual basis for determining depreciation. Since depreciation write-off is applied over the useful life of the asset, the first step is to determine the estimated useful life or its allowable depreciable life. These two lives may or may not be the same. No average life is applicable to all types of depreciable assets under different conditions or in different types of business. It is the taxpayer's responsibility to determine the useful life of the asset according to his own operating conditions and experience, within the guidelines set by the US Internal Revenue Service (IRS). The Class Life Depreciation Range (ADR) System permits the taxpayer to choose from a range of depreciable lives at 20% below or above the present guideline life. The second step required in calculating depreciation is to determine an estimated salvage value for the asset. The salvage value is an estimate, made at the time of acquisition, of the amount of money which can be realized by the sale of the asset at the end of its useful life. The four depreciation methods most widely used in the US are: (1) the straight-line method, (2) the declining balance method (double declining balance), (3) sum of the years - digits method, and (4) units of production method. Straight-Line Depreciation Method The straight-line depreciation method is the simplest for calculating depreciation. The depreciation for each year is determined by subtracting the estimated salvage value from the first cost of the asset and dividing the result by the years of life. The method gives equal annual deduction over the depreciable life. Salvage value equal to or less than 10% of the first cost may be ignored. [first cost - salvage Straight line = years of life ] Declining Balance Depreciation Method Declining balance depreciation, or double declining balance (DDB) as most frequently applied, is used for accelerating depreciation in the early years of the asset and is the fastest depreciation method allowed by the US Internal Revenue Service. The declining balance

Jan 1, 1980

By G. K. Manning, W. E. Few

T has been known for some time that both'inter-granular carbide and intergranular oxide phases cause brittleness in molybdenum. Parke and Ham' indicated that 0.0025 pct 0 present in molybdenum after solidification from the melt was sufficient to induce intergranular brittleness during forging. However, material containing 0.06 pct C could still be forged. However, adding this amount of carbon to insure deoxidation causes the formation of carbides on freezing. These carbides are precipitated at grain boundaries, and Rengstorff and Fischer' have shown they have an unfavorable effect on the room-temperature ductility of molybdenum. Take? in 1928 proposed that the solubility of carbon was a constant value of 0.30 pct from room temperature up to 1800°C. In 1935, Sykes, Van Horn, and Tucker' obtained X-ray data suggesting that the solid solubility of carbon in molybdenum was between 0.07 and 0.09 pct at temperatures from 1500" to 2100°C. The a-solubility line for carbon was included in the Mo-C diagram given in the Metals Handbook as a tentative line based on the data of Sykes, Van Horn, and Tucker. In order to determine the partial phase diagrams for these systems, it was necessary to construct a high-temperature furnace suitable for heat treating molybdenum at temperatures up to 4000°F. A molybdenum resistance furnace was built for this purpose in which samples could be heat treated in a purified atmosphere and quenched from any desired temperature.' Experimental Work Solubility of Carbon: Arc-cast molybdenum supplied by the Climax Molybdenum Co. and 18-gage molybdenum wire samples produced by powder metallurgy at the Fansteel Metallurgical Co. were used in determining the a-solubility line for the MO-C system. The cast molybdenum contained 0.032 pct C initially. Two lots of 18-gage wire were used, one containing 0.011 pct C and the other 0.005 pct C initially. All material contained a carbide phase as received. Fig. 1 illustrates the carbides found in the untreated material. Heat treatment in a purified hydrogen atmosphere was found to reduce the carbon content in the as-cast molybdenum. Purified argonT also decarburized molybdenum samples at temperatures above 3500°F; however, the carbon content remained constant during heat treatment in purified argon at lower tem- peratures. The argon was purified by passing it over titanium at 750 °C and then through a magnesium perchlorate drying tower. The hydrogen was purified by passing it through a commercial hydrogen deoxidizer, followed by a drying tower. Specimens having different initial carbon contents were heat treated in argon at 3500°F for periods ranging from 5 min to 5 hr and were analyzed for carbon. Samples of the same final carbon content had the same microstructures regardless of time at temperature. Furthermore, a gradient between center and surface in the amount of undissolved carbide particles present was never observed. It was concluded that at these low carbon levels, and at the high temperatures involved, diffusion proceeds so rapidly that the specimen is always substantially homogeneous in carbon content, in spite of the gradual loss in carbon. Based on the above findings, the following procedure was used to determine the carbon-solubility limit at 3000°, 3500°, and 4000°F. At each of these temperatures, a number of samples were heat treated, as shown in Table I, and rapidly cooled to room temperature. Since the samples lost carbon in proportion to the length of time heated, a series of samples were obtained of varying carbon contents. By use of a rapid cooling rate, the phases present at the high temperature were retained at room temperature. All samples were examined microscopically. Those found to contain either no excess carbide phase or only a very small amount were then analyzed for carbon. The samples actually analyzed for carbon

Jan 1, 1953

By F. R. Scauzillo

Equilibrium data which should be useful in the design and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and the correlation of these data by the use of the thermo-dynamic equilibrium ratio. The equilibrium ratios of water are used to solve the glycol absorber problem; such solutions are necessary to define the number of trays and the glycol circulation rate needed to meet drying requirements. Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the water-TEG-natural gas system. These activity coefficients have been used to calculate the equilibrium dew points for aqueous TEG concentrations of 60 to 99.9 weight per cent for the temperature range of 40° to 120° F. They also provide a means of calculating equilibrium ratios for water in the water-TEG-natural gas system; this applies to any desired TEG concentration and to the temperature range from 40° to 120°F. INTRODUCTION During the last several years, the drying of natural gas with aqueous triethylene-glycol (TEG) solutions has become very prominent. Most users of TEG as a drying agent have been satisfied with the performance of TEG solutions at the conditions used; however, there always has been some discussion of the drying ability of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60°F, but more particularly temperatures above 100°F, and pressures above 1,000 psia. Today, when higher wellhead temperatures such as 120°F are more commonly encountered many are skeptical of TEG's ability to dry sufficiently well to provide dew points around 32°F, which is generally the maximum tolerable when attempting to dry a gas to contract specifications of 7 Ib/MMscf. These views probably have evolved to some extent from the days when suppliers would not guarantee dew-point depressions in excess of 65° to 75 °OF. Also, the feelings about TEG drying may have arisen from the lack of information about the equilibrium relation of water in the drying operations. Porter and Reid' have reported equilibrium data for a 95 per cent TEG solution, while Townsend2 reported equilibrium data for 95, 98 and 100 per cent TEG solutions. Townsend also presented a calculational method which obtains activity coefficients in the liquid phase and, subsequently, the equilibrium water content of a saturated gas over glycol from published3 atmospheric dew points. Wise, Puck and Failey' presented activity data for the water-TEG system at atmospheric pressure. In the past, the equilibrium ratios published for water in a 95 per cent by weight aqueous TEG solution have been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations. Since essentially all such gas operations require the use of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for aqueous TEG and gas systems and to provide some means of calculating the equilibrium ratio of water in the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented herein consider only the equilibrium drying ability of the TEG solutions and do not consider the effect of temperature and pressure on the tray eficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the water in the lean TEG entering the top tray of the absorber. BASIC EQUILIBRIUM RELATIONS A relationship which relates the K value of water in the natural gas-water-TEG system to the vapor pressure of water at the system temperature, the total pressure of the system and the activities of the liquid and gas phases has been evaluated. It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid phase,

By W. Mckewan, W. M. Fassell

The oxidation rates of copper have been determined at temperatures from 600" to 900°C in oxygen from 14.7 to 400 psi total oxygen pressure. The oxidation rate of copper is unchanged by oxygen pressures within the range studied. The observed data extend Feit-knecht's conclusion concerning the pressure independence of copper from atmospheric pressure to 400 psi. All samples studied in the above-mentioned temperature and pressure range have both Cu2O and CuO present in the oxide film. NUMEROUS papers have been published on the oxidation of copper, some of which have noted the effect of oxygen pressure on the oxidation rate of copper. It must be noted, however, that no data on the oxidation rates of copper at pressure in excess of 1 atm have been reported in the literature. (Le Chatelier¹ reported that a black oxide of silver was formed at 300°C and 15 atm pressure.) This is likewise true for the other metals. This investigation was initiated to obtain experimental oxidation rate constants for pure metals at elevated temperatures and high oxygen pressure. Copper was selected as the first metal since probably more reliable data are available on its oxidation rates and related physical and chemical properties than for any other metal or alloy. As a general summary, the following conclusions appear well established for the oxidation of copper: 1—The oxide coating consists of Cu2O with a superficial coating of CuO providing the ambient oxygen pressure exceeds the equilibrium pressure for the coexistence of Cu2O and CuO.² The following sequence of phases is then Cu/Cu2O/CuO/O2 (gas). The Cu2O consists of large crystals that have no relation to the orientation of the metal crystals, except for a very thin layer adjacent to the metal." The CuO consists of very fine crystals randomly oriented. If the oxygen pressure is below the equilibrium pressure for the coexistence of Cu2O and CuO, the coating consists of Cu,O only. 2—The rate-determining factor in the parabolic oxidation of copper is the diffusion of Cu+ ions through the Cu,O layer.4,6,7 The Cu+ ions are accompanied by electrons to maintain electrical neutrality. The mechanism of the reaction at the Cu2O/CuO interface and the method of growth of the CuO is in some doubt. 3—On copper, there are three reported pressure effects: (a) At pressures below 0.3 mm Hg oxygen pressure, the oxidation rate increases directly with pressure.', ' .Vxygen starvation at the surface may account for this effect. (b) At oxygen pressures from 0.3 to 63 mm, the oxidation rate increases as the 7th root of the oxygen pressure providing the temperature is such that only Cu2O is present in the film. (c) At pressures from above the equilibrium pressure for the coexistence of Cu2O and CuO (varies with temperature) to atmospheric pressure, the oxidation rate is independent of the oxygen pressure.' Equipment In order to determine the oxidation rates of metals in an oxidizing atmosphere at pressures up to 400 psi, the equipment is somewhat different than for low pressure work as is shown in Figs. 1 and 2. A Leeds and Northrup Micromax recording controller (A) is used to control the temperature of the Ni-chrome furnace winding in conjunction with a Micromax electric drive unit. The drive unit adjusts a 20 amp Variac (variable transformer) to control the power input into the Nichrome furnace winding. Due to the "self heating" of the sample by oxidation, frequently encountered in oxidation rate studies, it is essential that the sample temperature be measured independently. This is done by means of a series of six chromel-alumel calibrated thermocouples located spirally around the oxidizing metal sample. Each thermocouple is partially shielded from the direct radiation of the furnace wall by

Jan 1, 1954

By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969

By E. C. W. Perryman

IN spite of the large amount of work which has been carried out on the recrystallization of aluminum and its alloys, there has been no complete investigation of the recrystallization characteristics of A1-Mg alloys. The most complete investigation is that reported by Bungardt and Osswald' who, working with commercial-purity materials, found that the temperature both of beginning and of complete recrystallization increased with magnesium content up to about 2 pct Mg, then decreased with a further increase in magnesium up to 5.0 pct, and thereafter increased again. Michaud and Segolz working with 99.93 pct A1 also found the temperature of beginning of recrystallization to decrease as the magnesium content increased from 2.13 pct to about 4.5 pct. Chossat3 using aluminum of 99.99 pct purity found that 0.12 pct Mg had no effect but that 0.4 pct Mg increased the recrystallization temperature by about 30°C. That no effect was found for 0.12 pct Mg does not agree with the later results reported by Demer and Beck4 who found that 0.025 pct Mg in 99.99 pct A1 increased the time for complete recrystallization and furthermore increased the activation energy for the recrystallization process. Kratz" using 99.997 pct A1 found that 0.5 pct Mg increased both the temperature of beginning and of complete recrystallization by 100°C. Chadwick and Hooper" working with commercial-purity material found that 1 pct Mg increased the temperature of complete recrystallization by about 40 °C for cold reductions in the range 17 to 72 pct. With smaller amounts of cold work produced by stretching (10 pct strain), they found no significant effect of magnesium. The latter result agrees with that obtained by Williams and Eborall' who found no effect of 2 pct Mg on the recrystallization temperature of commercial-purity aluminum strained 10 pct or less by stretching. Experimental Procedure Material Used: The chemical analyses of the materials used throughout this investigation are given in Table I. Fabrication: The alloys were cast in iron molds which had been washed thoroughly with alumina. After scalping, the ingots were annealed for 16 hr at 450°C, pressed, annealed at 450°C for 16 hr and hot rolled to 0.25 in. After hot rolling, the slabs were alternately annealed and cold rolled to 0.036 in. Cold-rolling reductions between intermediate anneals were kept at about 30 pct and a high intermediate annealing temperature of 450°C was used so as to obtain, as nearly as possible, similar starting grain sizes for the different materials. All intermediate anneals were done in a salt bath and were followed by cold-water quenching so as to retain all the magnesium in solid solution. The final cold reductions investigated were 20, 30, 40, 50, 60, and 80 pct. The initial grain sizes, that is, the grain size before the final cold reduction, were all very similar. Annealing Procedure: Specimens, 1 in. sq, were cut from the 0.036 in. sheet and annealed in a salt bath, the temperature of which was controlled to k2"C. Separate specimens were annealed for different times at 350°, 375", 400°, and in one or two cases at 415°C and after annealing were quenched in cold water. The time taken for a specimen to reach temperature was approximately 5 sec. Metal-lographic examination after annealing showed that no precipitation of Mg+413 occurred during cooling. Procedures Used for Determining Recrystallization Characteristics: All specimens were electrolyti-cally polished and etched by the method described previously1° and polishing was continued until about 0.002 in. had been removed from each side of the specimen. Using this technique, the smallest recrys-tallized grain which could be observed with cer-

Jan 1, 1956

By Thomas E. Garnar

Zirconium and hafnium are curious elements because they are almost always found together in nature. Zirconium was discovered by Klaproth in 1789 and isolated 35 years later by Berzelius. Because hafnium's chemical properties are so close to those of zirconium, it was not discovered until 1923 when Coster and Von-Heresey detected it using x-ray spectrographic analysis. These elements occur most commonly in nature as the mineral zircon (ZrSiO4) and less commonly as the oxide baddeleyite (ZrO2). They also are found as a variety of other silicates. Zircon was identified as a component in alluvial and beach sands in 1895, but it was not produced in any quantity until 20 years later. Zircon is always a coproduct from TiO2 mining and processing. During World War I it was produced as a coproduct of beach sand mining for titanium minerals just south of Jacksonville Beach, FL, and was patented as a refractory. It was not until the 1930s when Zircon Rutile, Ltd. began mining at Byron Bay on the east coast of Australia that zircon was first used as a foundry sand. Later in the 1940s, NL Industries, Humphreys Gold Corp., and E. I. du Pont de Nemours & Co., Inc. began production of zircon sands from fossil beaches in northeast and northcentral Florida. Baddeleyite first became available as a commercial product in 1916, but never in the quantity of zircon. Zircon holds a unique position as an industrial mineral because it is used for both its physical and chemical properties as well as an ore of zirconium and hafnium metals. Australia is the major zircon producer followed by South Africa and the US. Zircon is also produced in India, Sierra Leone, Sri Lanka, Malaysia, China, Thailand, and Brazil. Undeveloped heavy mineral beach sand reserves containing zircon are known to occur in Egypt, Malawi, Senegal, and Tanzania. Locations are shown in Fig. 1. Mineralogy Zirconium and hafnium are always present together in naturally occurring compounds. Most commonly they form as the silicate sometimes containing iron, calcium, sodium, manganese, and other elements. Less commonly they are found as oxides in combination with titanium, thorium, calcium, and iron. Zircon is the most common form. It is extremely resistant to weathering, therefore, often it is present in ancient beach sands and placer deposits. Although resistant to alteration from external sources, it is vulnerable to internal alteration as the result of thorium and uranium substituting for zirconium either in the zircon lattice or in solid solution. Alteration to the metamict state takes place as radioactive emanations from these elements disorder the crystal lattice, accompanied by hydration, reduction in specific gravity, and changes in color. The mineralogy of zircon and baddeleyite and variation of physical and chemical properties are shown in Table 1. The effects of zircon's internal alteration and darkened color can be corrected by heating to 1000°C for 30 min or so. A certain time-temperature relationship makes it possible for decolorization and reordering of the crystal lattice to take place when heating at higher temperatures for shorter periods or at lower temperatures for longer periods. After heating, x-ray diffraction patterns are sharper, the grains may be harder, and except for particles of malacon, the grains will be white or colorless in the absence of grain surface coatings. The color change is only temporary and the particles slowly darken with time. Zircon fluoresces light yellow in shortwave ultraviolet light. If exposed to ultraviolet light for extended periods of time, white (calcined) zircon turns purple. With time the induced color begins to fade and eventually disappears (e.g., calcined Florida zircon exposed to ultraviolet light for 24 hr still retains faint, but discernible, purple color after six months).

Jan 1, 1983

By J. S. Levine, M. Prats

Several methods are available for calculating the performance of solution-gas-drive reservoirs from the PVT properties of the oil and from the relative permeability and other properties of the formation. These methods require a number of simplifying assumptions. The present method of computation has made use of a high-speed computer to solve simultaneously the nonlinear partial differential equations that describe two-phase flow by solution-gas drive in order to calculate the performance of a reservoir. Some of the results obtained by the nonlinear partial differential equation solution are compared with those obtained with an approximate method, which has been called the semisteady-state solution. The pressure and saturation profiles from the wellbore to outer boundary calculated by the two methods are compared for one constant-terminal-rate case and two constant-teminal-pressure cases. The agreement in these profiles, as well as in the values of average reservoir pressure and cumulative recovery, leads to the conclusion that, for most engineering calculations, the semisteady-state method will give a reasonable approximation to the numerical solution of the differential equations describing solution-gas drive. An unfavorable (as regards ultimate oil production) set of relative permeability curves was used in the calculations in the belief that the effect of the parameters which were studied would be emphasized to a greater degree. Furthermore, the reservoir was assumed to be completely homogeneous, and these results should not be considered applicable to any other type of reservoir. Gravity effects are not considered. The absolute permeability was varied from 25 to 0.5 md. At an economic limit of 2 B/D, the recovery for a 25-md reservoir is about 1.8 times as great as that for a 0.5-md reservoir. The effect of permeability on the producing gas-oil ratio is minor. Once PVT properties of the oil and the relative penneability properties of the reservoir are fixed, the pro- during gas-oil ratio is found to be a function of the fraction of oil recovered. Well spacings of 10, 40 and 80 acres were considered. For the assumed homogeneous-reservoir properties, the effect of spacing on recovery at an economic limit of 2 B/D was very slight. Certain dimensionless groups can be used to extend the results to other fields having different penneabilities, spacings, reservoir thicknesses, well radii and porosities, so long as the PVT and relative permeability properties are similar to those used in this paper. INTRODUCTION An important aspect of reservoir engineering is the prediction of the performance of the reservoir based on the limited information normally available early in the life of a field. Usually, soon after a field has been discovered, it is necessary to decide upon the spacing to be employed and the production program to be used for most efficient utilization of reservoir energy. Where these decisions have not been dictated by legal or political considerations, they have frequently been based on experience factors which indicate that two fields with similar characteristics will probably have similar performances. To the extent that the industry has been successful in economically exploiting oil reservoirs, this rule-of-thumb method has been found to have merit. A large amount of theory has been developed with which it is possible to predict the performance of a reservoir by using certain known properties of the oil and the formation. Because of the difficulties of the mathematics involved for a drainage area having square or rectangular boundaries, the problem usually has been simplified and idealized by assuming each drainage area to have radial symmetry and the field to be represented by a number of these drainage areas. Muskatl was one of the first to formulate the theory for two-phase flow and to solve the equations for a few cases by numerical integration, using the relatively slow means of computing available at that time. His equations describing

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By L. A. Weitzenkamp, N. M. Bashara

A study of the electrical conductivity of gold films less than 200 in thickness indicates a negative temperature coefficient of resistance and a thermal actiuatlon energy of less than 0.25 ev. The films consist of discrete metal islands of linear dimensions from a few angstroms to 1000A. Films were able to withstand applied fields up to 60,000 v per cm before breakdown occurred. A model for the conduction mechanism is proposed which involtes a Potential barrier due to work junction, irriage forces , and an electrostatic potential arising from separating an electron from a neutral island leaving behind a positively charged metal island. Activation energies of less than 0.25 ev ave consistent with this model, which includes a tunneling andor Thermal mechanism for conduction between the separate metal islands. An apparent satuvation effect in conductivity at high fields is observed experimentally. The saturation effect may be explained by the influence of the electrostatic contribution to the potential barriers for the transition through several islands adjacent to the original island which was activated to give up an electron. The proposed model gives Poor quantitative agyeement for the intermal electrical field between islands. ThIS paper will relate the structure of discontinuous metal films to the electrical properties and will emphasize the following topics: 1) the relation of the conduction mechanism to particle size and a comparison of particle size from electrical measurements with electron-microscope studies; 2) the saturation of the conductivity at high electric fields; and finally, 3) a comparison between the external field applied and the apparent field between particles. che- latter comparison points to a need for a modification in the model for the conduction mechanism first proposed by orter' and expanded by Neugebauer and webb2 which will be dealt with in the discussion. The paper is based on results on gold films on glass microscope slides. The clms were vacuum-evaporated and were about lOOA thick, thickness being measured by interferometry. It has been observed that metal films of this thickness do not exhibit bulk metallic conduction. Films thinner than some critical thiclmess, depending upon substrate temperature and other factors, have conductivities which increase with increasing temperature with thermal activation energies of less than 0.25 ev. Electron-microscope studies3 have shown that these films consist of discrete metal islands having linear dimnsions from a few angstroms to approximately 1000A. When the metal is being vacuum-deposited on the substrate, islands on the order of a few angstroms appear first. As the deposition continues the islands may tend to agglomerate into larger particles and may eventually grow together into a continuous film,3''' In our tests the conductivity of the gold films was found to be about ten orders of magnitude less than the bulk conductivity of gold. When oxygen was introduced into the test chamber the conductivity decreased by a factor of about one-third. This can be related to an increase in work function for gold caused by adsorption of oxygen, as reported by Oullet and Rideal.s Exposure to an atmosphere of water vapor caused an increase in conductivity by a factor of 2 or 3 when a low field was applied. When the films were exposed to water vapor under a high field the conductivity increased by as much as two orders of magnitude. The activation energies measured were much less than the work function for gold, 0.25 ev or less, with the smaller activation energies observed for thicker films. It will be shown that the activation energy is a function of particle size and spacing. In general the model for the potential between metal islands would include the effective work function, the image force, the applied field, and an electrostatic term. The electrostatic contribution arises from the potential required to separate an electron from a conducting sphere. According to Neugebauer and webb2 the maximum potential due to the field and the electrostatic term only is

Jan 1, 1967

By Kenneth E. Gray

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton's equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?' lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.' It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By F. P. Bullen

Empirical relationships between fracture stress, orientation angle, and diameter of crystal have been determined at 77°K. Orientation ranges of markedly different behavior were found—a law of constant normal stress&apos; of value a (diameter)-1/2 for the fracture of ductile crystals, and a condition of shear stress (or strain) for more brittle crystals. The observations are not consistent with current theories. An interpretation is advanced which is also applicable to observations on the effect of prestrain at room temperature on the subsequent fracture stress at 77°K and to the effect of cyclic stressing on the cleavage strength.&apos;&apos; The law of constunt normal stress&apos; and the brittle ductile transition are also explained. The interpretation is more consistent with the initiation of cracks by intersecting dislocations than with theories based on stress -concentration by dislocation arrays. ZINC single crystals are particularly suited to the study of cleavage because fracture occurs on the basal plane over a wide range of crystal orientations. Analysis of the conditions of stress and strain at fracture in crystals of different orientations should indicate which parameters control the cleavage process. Unfortunately, controversy has arisen over the correct empirical relationship between tensile fracture stress and orientation. Schmid&apos;s observations1,2 favored a &apos;law of constant normal stress&apos;, as observed in other materials.2 For zinc, however, the observed values are far below the theoretical strength and cannot represent the true limit of cohesion between neighboring atomic planes. Hence, the interpretation of such a &apos;law&apos; is not straightforward. Deruyttere and Greenough3,4 found a complex variation between tensile fracture stress and orientation; this variation did not agree with a &apos;law of constant normal stress&apos;. Two theories have been advanced to account for their observations: a) the propagation of cracks from low-angle boundaries,5 and b) the release of energy from piled-up dislocations during crack-propagation.4 The present work resolves the apparent discrepancy between the observations and shows that neither of the above theories are applicable to the tensile fracture of zinc single crystals. A phenomenological explanation, along the lines suggested by Gilman,&apos; is advanced and successfully applied to previously unexplained effects. EXPERIMENTAL DETAILS &apos;Crown Special&apos; redistilled zinc was used, except for one comparison series op tests using &apos;Tadanac&apos; electrolytic zinc. Crystals of 1 mm diam, subsequently called &apos;1 mm crystals&apos;, were grown from the melt in vacuo in precision-bore Pyrex tubes internally coated with graphite. Several specimens 1 in. long were cut from each crystal and chemically polished. Jigs were used to minimize handling strains, and crystals were mounted in the Polanyi machine the day prior to testing to allow recovery from any such strains. One-mm crystals were chemically polished for long periods to obtain 0.1 mm (approx) crystals. One-mm crystals were cemented into miniature gimbals by &apos;Araldite&apos; casting resin. The Appendix gives the reasons for using gimbals and the results obtained by other methods. More complete details of all techniques are given elsewhere.7 The symbols and terminology used are as follows: X = orientation angle (angle between tensile axis and line of greatest slope in the basal plane). T = tensile stress (on true cross-section) S,N = shear and normal stress (components of T with respect to the basal plane) ? = shear strain D = crystal diameter. The subscript &apos;f&apos; will be used to denote values at fracture. PART I-ANNEALED CRYSTALS EXPERIMENTAL OBSERVATIONS One-mm crystals were used to establish the variation of fracture stress at 77°K with orientation at fracture (Xf), Fig. 1. For 18 deg = Xf = 55 deg, a &apos;law of constant normal stress&apos; was observed. For Xf > 55 deg, the fracture condition approximated to a constant shear stress. At Xf< 18 deg, twinning occurred before fracture so that the results were not typical of homogeneous single crystals,4,8— such specimens will not be considered herein. The dependences of fracture stress upon Xf were of similar type for 6 mm,* 1 mm, and 0.1 mm crystals,

Jan 1, 1963

By J. J. Taber

The turbulent flow drag coefficients, or friction factors, have been experimentally determined for the cut-tings normally encountered in drilling operations. The gas law and average drag coefficients for characteristically flat particles (limestones and Shales) and for angular to sub-rounded particles (sandstones) were used to extend Newton&apos;s equation to a more useful form. The resulting equations are expressions for the slip velocity of a particle as a function of the particle size and shape, the bottom-hole injection Pressure, and the Bottom-hole temperature. The velocities necessary to lift actual rock cuttings as observed in the laboratory were compared with velocities predicted from the derived equations. Results indicate that there is no single correct circulating velocity and that the commonly used 3,000 ft/min linear velocity may he sufficient to lift only very mall particles. The advantage, in terms of horsepower requirements, of cycling high pressure air to obtain lower compression ratios was shown. INTRODUCTION A promising departure from standard rotary hydraulic drilling is air or gas drilling. In many instances the rate of penetration and bit life increases resulting from this method have been very substantial. Further the application of air drilling in areas of lost circulation or water sensitive pay zones has been highly successful. Purpose For the drilling contractor, the practical question remains, "How much air pressure and volume should I have?&apos; lt is necessary to have a reasonable knowledge of the air velocities and pressures required in air drilling operations for the proper design and most advantageous use of surface equipment and for adequate removal of cuttings from the borehole. Eased on experience, most operators agree that at least 3,000 ft/min linear velocity is necessary for satisfactory hole cleaning.&apos; It was the purpose of this investigation to evaluate the drag coefficients, or friction factors, for the cuttings normally encountered in drilling operations, i.e., sandstones, limestones and shales, and to utilize the values obtained to develop an expression for the minimum velocities and pressures (hence the volumes) necessary to lift these cuttings. THEORY Several investigators have done extensive work on the ability of drilling mud to lift bit cuttings. They conclude that the ability of a drilling mud to lift cuttings is dependent on the density difference between the rock being drilled and the drilling mud, the cutting size and shape, the mud flow constants, and the flow state (laminar, transitional or turbulent) of the mud. However, drilling muds are not true fluids but have a variation of viscosity with velocity in laminar flow and a constant apparent viscosity in turbulent flow. A survey of the literature revealed that no experimental work had been done to determine the velocities necessary to lift actual rock cuttings using a compressible fluid such as air or gas. In 1953, Nicolson6 stated that in air drilling fluid mechanics the particles could be assumed spherical in shape and that ; constant drag coefficient of 0.5 could be used due to the highly turbulent flow of the circulating air. By equating the turbulent resistance on the particle to the gravitational force on the particle, he obtained the expression, ^ = 2.67^y ,.......(1) where V, is slip velocity of spherical particle, ft/sec; D is particle diameter, in.; p, is particle density, 1b/ft8; and p, is fluid density, lb/ft3. However, as stated earlier, most operators seem to agree that adequate hole cleaning can be obtained by circulating a sufficient volume of air to give a linear velocity of 3,000 ft/rnin in the annular space. Basic Equation The velocity with which a solid particle freely falls through a fluid will increase until the accelerating force, gravity, is equal to the resisting forces, buoyancy due to the fluid displaced by the particle and friction due to the relative motion of the particle through the fluid. When the accelerating and resisting forces become equal,

By R. P. Alger, C. A. Doh, M. P. Tixier

The principle, the equipment and field operation of sonic logging are described. The tfio-receiver system produces logs independent of hole size and mud. Field experience is given and forms the basis for the interpretation of the log. The derivaiion of porosity values from measured velocities is discussed, according to the type of formations (hard formations, compacted sands, and unconsolidated formations). The time-average equation proposed by M. R. J. Wyllie, A. R. Gregory and L. W. Gardner is uscd as a basis for the computation of porosity in limestones, cemented sandstones and compacted sands. Variations in the lithologic character of limestones do not seem to change the porosity calibration markedly. The compaction of sands is related to the compaction of shale adjacent to them; and, thus, the shale velocity is used for the establishtnent of empirical relations for the computation of porosity in un-consolidated formations. Various forrnu.las are tentatively presented to account for shale and fluid content. Field experience demonstrates that considerable attenuation of sonic energy takes place in unconsolidated formations, particularly when gas bearing, and in fractrured formations. Unusually large attenuation produces skipped cycles, a feature easily recognized. The application of sonic logging to structura1 studies is featured, showing its possible integration with the dipmeter. Correlation and its application to the irrterpretation of seisrmic surveys are reviewed. The paper is illustrated with field examples. Sonic logging is the recording of the time required for a sound wave to traverse a definite length of formation. Sonic travel-times are inversely proportional to the speed of sound in the various formations. The speed of sound in subsurface formations depends upon the elastic properties of the rock matrix, the porosity of the formations and their fluid content and pressure. Below the "weathered" or low-velocity layer extending from 50 to 100 ft or so below the surface, sound velocities may range from about 6,000 ft/sec in shallow shales to as much as 34,000 ft/sec in dolomites. In hard formations (well cemented and/or compacted), the sonic log reflects the amount of fluid in the formations; hence, it correlates well with their porosity. In unconsolidated formations, which are usually of fairly high porosity, the sonic log gives an approach to porosity determination, when its readings are corrected for lack of compaction, shaliness, and fluid content. In such formations the sonic log may also indicate the presence of gas and may distinguish between oil- and water-bearing beds. Field experience with the sonic log in soft formations is more limited than that in hard formations. As a result, interpretation in soft formations is not as well developed at the present time. In all types of formations the sonic log is of considerable value for correlation and for the more detailed and accurate interpretation of seismic data. EQUIPMENT AND PRINCIPLE FIELD OPERATION The basic features of the sonic log" are a two-receiver system and two available short spacings. The log is recorded on film using a standard field unit. An SP curve is run along with the sonic curve to give a more interpretable log and to establish absclute depth control for comparison with other logs run in the same well. If desired, a gamma-ray curve may be recorded simultaneously with the sonic curve. Fig. 1 shows the sonic-gamma ray combination sonde. The sonic portion consists of a sound transmitter and three receivers mounted 3, 4 and 6 ft from the transmitter. When the first and second receivers are used, a sonic log of I -ft spacing (distance between receivers) is obtainea. Use of the first and third receivers provides a 3-ft spacing. The transmitter emits pulses at the rate of l0/sec. After the transmission of a pulse the first arrival of sound energy at each receiver triggers its response system. The differ-

By J. A. Herbst, D. W. Fuerstenau

This paper examines the zero order production phenomenon in the context of the size discretized batch grinding model. A restrictive interrelationship between the selection and breakage parameters of the model, which is mathematically sufficient to ensure zero order behavior, is delineated. Based on this interrelationship, a scheme is developed for predicting the values of the selection and breakage parameters for all size fractions from a minimum of experimental data. To test this scheme, dolomite was ground in a laboratory batch ball mill. Successful simulation of the comminution behavior of this system was achieved using the batch grinding model with the parameter values obtained from the proposed scheme. Historically, a preponderance of comminution research has centered on attempts to relate breakage energy to the performance of comminution machines. Concomitantly, grinding data were interpreted almost exclusively in terms of inherently empirical energy-size reduction relationships1-3 or "laws of comminution"4- 6 which were based on highly oversimplified descriptions of the fracture process. In some instances, these relationships provide a crude basis for the correlation of experimental data, but, invariably, this approach is inadequate for meaningful process simulation. The control and optimum design of comminution circuits require a mathematical model capable of depicting the size reduction behavior of every size fraction for grinding conditions of technological importance. Energy-size relationships do not provide this detailed information. For example, an energy-size analysis for batch ball-milled dolomite has recently been completed in the authors&apos; laboratories.7 This analysis provided a satisfactory correlation between the hypothetical size modulus, which characterizes only the finer portion of the size distribution, and the input energy. However, this relation did not constitute an adequate description of the complete system. In general, one of two distinct viewpoints toward simulation has been adopted in recent comminution research. The first approach focuses on the fracture of single mineral specimens, with the essential aim of representing the over-all process in terms of the breakage characteristics of individual particles and the characteristics of the stress field which the particles experience within the particular size reduction device. As illustrated by Harris&apos;s review,&apos; the actual incorporation of single-specimen fracture information into a description of the behavior of a multiparticle comminution system has seldom been attempted. The only model to accomplish this incorporation was the one developed by Schönert.8 The Schonert model treats single-passage grinding machines in terms of a distribution of effective loads acting on a particle, a distribution of required particle breakage energies, and the breakage product distribution. However, the use of single-particle fracture behavior to derive models of the size reduction process is at present limited to machines in which the particle residence time is approximately equal to the time required to apply stress. As a result, Schönert&apos;s analysis cannot be used to advantage to simulate the complex environment which prevails within a tumbling mill. For multiple-passage systems a second approach to the description of comminution processes has been more fruitful. This approach entails the formulation of a mathematical model which is phenomenological in nature in that it lumps together the entire spectrum of stress-application events which prevail in a system under a given set of operating conditions. The appropriately defined average of these individual events is then considered to characterize the over-all breakage properties of the device. Thus, to analyze the performance of a tumbling mill, the manner in which the particles of a particular size (or size fraction) are stressed need not be distinguished. Instead, a single parameter is assumed to represent the resistance of that size to fracture, given the average grinding environment which exists in the mill. The isolation of such a parameter and a related set of quantities, which constitute the breakage product size distribution for the average event in this size fraction, allows the formulation of physically meaningful descriptive equations capable of yielding precise and detailed information for simulation.

Jan 1, 1969