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By K. C. Strebig, C. W. Schultz, A. A. Selim

The effect of some organic additives in diamond drilling of quartzite was investigated in the laboratory. The drill was designed to measure the rate of penetration, the thrust, and the torque and to record each as a function of the distance drilled. A statistical plan was followed throughout the investigation and an equation representing the bit performance was derived from the mathematical theory of reliability. The drilling torque was found to increase with the use of additives while the sliding coefficient of friction and the wear coefficient decreased. The energy per unit volume consumed was found to increase with the use of additives. A hypothesis explaining the effects achieved with the additives is given. INTRODUCTION For some time researchers have attempted to increase drilling efficiency by adding certain agents to the flushing medium. Much of this interest is the result of the observations of Rehbinder, Shreiner and Zhigach1 They postulated that "...in processes for the mechanical destruction of solids, a region of increased crack formation is created in the deformed layers adjoining that surface of destruction, forming the predestmction zone. The surrounding medium (for example, a liquid) which wets a given solid will penetrate the embryo microcracks of the predestruc-tion zone. Increasing the molecular affinity of this liquid for the surface of the solid considerably facilitates the deformation and destruction by softening the solid in the zone of increased crack formation. In this manner, the hardness or strength of the deformed body is decreased by the influence of the penetration of the liquid into the predestraction zone." This is known as the "Rehbinder effect". Rehbinder's work has prompted many investigators to examine the effect of additives on the mechanical destruction of rocks. Engelmann, Terichow and Selim reported that the maximum penetration of the rock by a diamond point in a solution environment was at the isoelectric point of the solution.* Robinson reported that his results did not appear to support the theory of Rehbinder.3 Joris and .McLaren suggested that additives with surface tension lower than water will be more efficient in cooling the diamonds.4 Their effectiveness in removing the fine cuttings from the face of the bit will also improve the efficiency of the system. They reported an improvement in impregnated bit life and penetration rates with the use of soluble oil additives. In contrast, Long and Agnew, drilling with surface set bits, reported that lubricating agents increase bit temperature and wear.5 A significant change was reported6 in the mechanical properties of rock with polar additives. It was concluded that this change in the mechanical properties of the rock in the presence of the additive is due to the rock hydrophilic properties. Ethylene glycol, glycerine and anionic detergent were selected for this investigation because their surface tension is lower than that of water. The surface tension of these additives for the concentrations studied was 42 to 75 percent of the surface tension of water. A low surface tension additive would wet the surface of the diamonds more easily and hence would be more effective in cooling the diamonds. Another characteristic of these low surface tension additives is their effectiveness in removing the cuttings and preventing the flocculation of the formed particles in the drilling process. This article summarizes the results of an investigation performed at the laboratories of USBM, Twin Cities Mining Research Center. The objective of the investigation was to study the over-all effects of some organic additives on the performance of diamond impregnated bits in atmospheric drilling conditions only and not in downhole pressured conditions.

Jan 1, 1970

By Matti J. Saarivirta

The relative machinabilities of the precipitation-hardenable Cu-0.9 pct Cr, Cu-0.25 pct Zr, and Cu-0.9 pct Cr-0.25 pct Zr alloys are improved from 18 to 80 pct by 0.75 to 1.25 pct Pb. The Lead also improves the tensile strength, hardness, ad resistance to softening of the Cu-Cr and Cu-Cr-Zr alloys. When the alloy containing 0.7 to 2.2 pct Cr, 0.10 to 0.25 pct Zr, 0.75 to 1.25 pct Pb, and balance copper is solution-annealed at 1000°C (1830°F) and then aged at 525°C (Y75°F), tensile strength of 65,000 psi, 16 pct elongation, 62Rb hardness, and 84 to 87pct IACS electrical conductivity are obtained. The copper base Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys have high electrical and thermal conductivities, high strength and resistance to softening at elevated temperatures, but their machinability is poor, i.e., close to that of the pure copper. In the manufacture of various components such as welding electrodes or electrical and thermal conductors it is ofter desirable that the alloy have good machinability for high production rates and long tool life. Thus, alloys that combine these properties may be used not only for existing applications, but for new ones where good machinability is a requirement. This investigation was undertaken to improve machinability without impairing other desirable characteristics of the Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys. These commercial alloys contain about 0.4 to 1.2 pct Cr, 0.10 to 0.25 pct Zr, and balance copper. Lead was selected as an element that should improve the machinability and possibly other characteristics of the alloy. WORK PROCEDURE This investigation began with a study of the effect of lead on the hardness, tensile strength, electrical conductivity, and machinability of the binary alloy containing 0.10 to 1.30 pct Cr and balance copper. This was followed by an investigation of the effect of lead on the Cu-0.1 to 0.4 pct Zr and Cu-Cr-Zr alloys. The alloys were made from initially oxygen-free copper and for comparison some castings were made from phosphorus-deoxidized Lake Copper. Commercially pure chromium, zirconium, and lead were used for alloying. In melting the chromium was added to molten copper at 1400°C (2550°F), the heat held for 15 min at temperature, and the temperature then lowered to 1350°C (2460°F) when the other elements were added. The alloys were held for 15 min at this temperature and cast into a cast-iron mold. One-kilogram, 3-in.-diam castings were made. An argon cover was maintained during melting and casting to prevent oxidation. The chemical compositions of the alloys are shown in Table I. The micro structure and properties of the alloys were studied in the cast and wrought conditions prior to and after various solution-annealing and heat-treating cycles. The relative machinability was determined as a function of the lead content and compared with the free-machining Cu-lpct Pb alloy. To determine the machinability, 13/16-in.-diam cast specimens were cut by a machine hack saw using a constant cutting speed of 50 fpm, a fixed feed force, and a new blade for each alloy specimen. Molybdenum highspeed steel saw blades, 0.032 in. thick with 14 teeth per in., were used in all tests. No cutting fluid was used. Five tests were made on each specimen and the average elapsed time per test was taken as a measure of the relative machinability for that alloy. The variation of cutting time for each alloy was less than 110 pct.

Jan 1, 1969

By D. G. Westlake

Resistance was measured as a function of temperature, 77° to 350°K,for niobium with hydrogen concentrations up to 3.76 at. pct. Cooling curves exhibited a discontinuity in slope that was attributed to the initiation of hydride formation. A thermal hysteresis was explained in terms of diffusion and the effects of mechanical constraint on nucleation and growth. The heat of solution of hydrogen in saturated Nb-H solid solution was 2. 737 * 0.045 kcal per g-atom, including an unknown stress contribution. The critical ternperatures for hydride formation during cooling and for embrittlement are correlated but not coincident. This, too, has been explained in terms of mechanical constraint and stress-itlduced tratzsfomtation. Nb-H alloys undergo a ductile-brittle transition with decreasing temperature.'-3 Similar behavior has been noted for v-H.1,5 For the latter system, there is evi-dence6 suggesting coincidence of the temperature of minimum ductility and the critical temperature T, for initiation of metal hydride precipitation during cooling. A decrease in ductility due to the presence of brittle hydride particles is readily explainable. The fact that ductility begins to decrease at some temperature higher than T,4,5 has led us6 to suggest that precipitation may be strain-induced locally during tensile testing. Wood and Daniels' have reported that a plot of temperatures for 10 pct reduction in ductility vs hydrogen concentration in niobium is not coincident with, but parallels, the solvus.7,8 They believe this indicates a correlation of precipitation and embrittlement. Unfortunately, the two reported solvuses 7,8 to which Wood and Daniels refer are not in agreement with each other. Furthermore, neither solvus was determined experimentally: each was a plot of calculated solubilities. Thus. neither is highly dependable for determining whether embrittlement coincides with initiation of hydride precipitation. Longson 9 studied phase relations in the Nb-H system between 77° and 473°K by dilatometry. Comparison with metallographic observations convinced him that discontinuities in the slopes of his dilatometric plots were coincident with the initiation of hydride precipitation. Plotting the logarithm of the hydrogen concentration vs the reciprocal of the temperature at which precipitation was initiated during cooling, he obtained a straight line shown in Fig. 1. Walter and chandler,'' using X-ray techniques to detect the for mation of a second phase? have obtained three experimental points in the temperature range 295° to 338°K which fall within Longson's experimental error for this plot. A similar plotg of temperatures at which dissolution was completed during heating was a parallel line shifted toward higher temperatures. A straight-line plot was obtained, also, for the temperatures of the ductile-brittle transitions,9 but it was shifted toward still higher temperatures. Longson calculated an activation energy of 2.980 * 0.300 kcal per mole for the hydrogen embrittlement mechanism, compared with 3.180 * 0.400 kcal per mole for hydride formation. Despite this agreement, he concluded, "It seems unlikely that embrittlement results from hydride formation..." because hydrogen embrittlement was observed at temperatures above the solvus. It is our contention that embrittlement is correlated with precipitation of the hydride.6 Because only Longson has investigated Nb-H phase relations at sub-ambient temperatures, we deemed it advisable to re-determine the temperature dependence of the solubility using the resistometric technique already proven successful for the V-H system.6 Coincidence of our solvus with temperatures for embrittlement would

Jan 1, 1970

By Y. Nakada, U. F. Kocks, B. Chalrners

THE orientation dependence of work hardening has previously been studied over the entire range, i.e., including special orientations of high symmetry, in aluminum1-3 and silver.* The differences between various orientations are substantial, and the trend is the same in all fcc crystals. However, there are quantitative differences in behavior between aluminum and silver at room temperature, particularly in the (100) orientation. While many experiments on gold have been reported,5'9 none included the special orientations. We therefore undertook tension tests on gold crystals of the axial orientations (100),(110), (Ill), (211), and, as a representative of single slip, one whose Schmid factor was 0.5 (hereafter referred to as m = 0.5). Single crystals of dimensions 1/4 by .1/4 by 6 in. were grown from the melt1' at a rate of 4 in. per hr, using gold of 99.99 pct purity obtained from Handy and Harman. A growth rate of 1/8 in. per hr, or a purity of 99.999 pct,ll produced no difference in results. The crystals were annealed at 1000°C in air for 24 hr and furnace-cooled down to room temperature, after which they were electro-polished in a solution of potassium cyanide (40 g), potassium ferrocyanide (10 g), soda (20 g), and enough distilled water to make 1 liter of solution, at a current density of 0.02 amp per sq mm. After 2 or 3 hr, a very smooth surface was obtained by this method. Nine m = 0.5, two (loo), one (110), three (Ill), and one (211; crystals were tested at room temperature in a floor-model Instron machine at a tensile strain rate of 0.5 pct per min. The accuracy of the stress measurement was k10 g per sq mm up to 500 g per sq mm, k2 pct for higher stresses. The strain measurement was accurate to t2 pct. The scatter of stress at a given strain among the crystals of the same orientation was small, *5 pct being the largest. The representative stress-strain curves for various orientations are shown in Fig. 1. Table I summarizes the work-hardening parameters as used by seeger.12 Results of other investigators are also included in this table for comparison. There are no previous data for the corner orientations. Values for m = 0.5 crystals agree fairly well with those of Berner. Tm is defined as the stress at which the stress-strain curve begins to deviate from linearity of Stage 11. However, in practice this is a very difficult value to estimate because each investigator has a different idea of linearity. Therefore, the comparison with the values of other investigators may not be valid. In the present experiment, (100) crystals had the highest 111, followed by (111) crystals. The work-hardening rate in Stage I1 was highest for the (111) crystal followed by the (100) crystals. Our value for 0x1 of m = 0.5 orientation agrees very well with those of other investigators. 1) Single-Slip orientation (m = 0.5). These crystals were oriented so that the primary-slip vector was contained in one side face. The dimension perpendicular to this side should then not change if single slip indeed takes place. Within the accuracy of measurement, this dimension did not change during the deformation. Since the accuracy is k0.2 pct, the amount of secondary slip is less than 0.7 pct of the slip on the primary-slip system at 30 pct tensile strain. This is in conformity with the results obtained by Kocks" for aluminum crystals. The tensile axis moved toward (211) during the deformation. Slip bands, Fig. 2(a), were very fine and closely spaced. Some deformation bands were observed. There were no clear-cut cross-slip traces such as the ones observed on aluminum m = 0.5 crystals. 2) (111) Crystals. The orientation of the tensile axis was stable during the deformation. From this observation, one can deduce that at least three slip systems must have operated, and probably all six because the remaining three all have cross-slip relation to one of the first three.' It was very difficult to observe the slip markings. Consequently, we could not confirm by this method that six systems were operative during the deformation. At high strains (above 50 pct shear strain), this orientation had the highest stress-strain curve. At 80

Jan 1, 1964

By J. R. Jargon, H. K. van Poollen

Non-Newtonian fluids may be injected into a reservoir during secondary recovery operations. The non-Newtonian fluid used in this work is a power-law type of fluid that is, the viscosity of the fluid decreases as the flow rate or rate of shear increases. This paper presents equations for steady-state linear and radial flow of such fluids, transient behavior results from a finite difference model of a radial system, and transient behavior results from a field test. The equations that describe the flow of a non-Newtonian fluid are non-linear and are solved numerically. Finite difference solutions are presented as curves of dimensionless pressure drop at the wellbore us dimensionless time for a constant injection rate. Solutions were obtained for 5-percent, 10-percent and 100-percent PV of a non-Newtonian fluid for injection rates of 1, 10, 100 and 1000 cc/sec and for a 5 percent PV of non-Newtonian fluid located at T = Tw' 3, 10, 20, 50 and 100 ft for a flow rate of 1 cc/sec. The buildup curves do not exhibit a stmight-line portion as is the case for Newtonian flow through porous media. Correlations also are shown for the productivity index vs rate for the computer model study and the field tests. INTRODUCTION During various secondary recovery operations non-Newtonian fluids are injected. Such fluids, in general, include thickened water and gelled fluids. The term "non-Newtonian" implies that the viscosity is not only dependent upon temperature and pressure, but also on the rate of shear that is applied to the fluid. For example, water, which is a Newtonian fluid, will have essentially the same viscosity no matter what rate of shear is applied. A pseudo-plastic fluid exhibits a decreasing viscosity when higher rates of shear are applied; a dilated fluid has an increasing viscosity with increasing rates of shear. The objective of studies performed and described in this report is to obtain relationships and mathematical and empirical descriptions of the flow of non-Newtonian fluids through porous media. Simple mathematical relationships, computer studies that include the unsteady-state behavior of such fluids, and field tests are used. PREVIOUS LABORATORY STUDIES Laboratory studies have been performed by several investigators. The fluids used in one investigationl were surfactant-stabilized dispersions of water in hydrocarbons. Its Fig. 6 is reproduced as our Fig. 1. This effective-viscosity vs frontal-velocity diagram shows that this fluid is of the power-law type over a fairly large range of frontal velocities. Gogartyl developed an equation for the effective viscosity as a function of shear rate that reduces to Eq. 2 for frontal velocities greater than about 2 ft/D. The fluid characteristics used in the present study are similar to those reported by Gogarty. Christopher and Middleman2 performed experiments with power-law fluids flowing through pipes packed with glass beads. They used a modified Blake-Koteny

Jan 1, 1970

By Sylvan Z. Beer

The factors that determine the yield and crystal size in the two-temperature synthesis of A lp were examined. Low yields and small crystals were associated with low temperatures and pressure. Attempts to grow large crystals in the critical and supercritical region of phosphorus were unsuccessful. Crystal size increases markedly at elevated temperatures. Crystals grown at temperatures as high as 1450° C fluo-resced, under uv excitation, at energies close to the estimated band gap of about 2.4 ev, while crystals grown at lower temperatures tended to fluoresce in the red region of the spectrum. Those grown in the supercritical region showed no ALP fluorescence. Heating the high-temperature-grown ALP under vacuum greatly increased its fluorescence efficiency and moved the emission peak to higher energies. I HE III-V compounds, with few exceptions, have been prepared by the two-temperature method. In its classic form this technique is applicable to closed systems where at least one of the components, in this case the column V element, is a liquid or a solid with a high vapor pressure. One advantage of this method over flow systems is in its simplicity. In addition, because it is a closed system, it can, under the circumstances to be described later, be run at higher pressures of the volatile species than in flow systems. In instances where the III-V compound is soluble in the parent III metal to about 1 mol pct or higher, solution growth can be made to take place by slow cooling. This, for instance, is one way in which single-crystal GaP1 and Inp2 have been grown. Initial attempts to synthesize and grow A1P by this technique were not too successful; the yield was low and the crystals obtained were exceedingly small. The conditions required for improving the yield and growth by this technique were, therefore, sought. Two obvious conditions which could be controlling were examined. These were the temperature of the aluminum and the pressure of the phosphorus. The range of temperatures studied extended from about the melting point of aluminum, 660° to about 1450°C. The latter is dictated by the vapor pressure of aluminum which reaches about 1 Torr at that temperature and the limitations of the materials of construction as described in the next section. The pressure range of interest covers from below 1 atm to above the critical pressure of phosphorus, 82.2 atm. EXPERIMENTAL The Temperature of Aluminum as a Variable. A series of experiments were run in the conventional two-temperature manner. All refractories and quartz were dried by heating at 800° to 900° for a minimum of 24 hr, and usually much longer, before use. The aluminum

Jan 1, 1969

By Leonard H. Goldman, Harold E. Marr

The PGT uranium assay probe is a borehole tool developed by Princeton Gamma-Tech over the last several years. It has the ability to do an in-situ assay of uranium in the presence of any amount of disequilibrium. It has some advantages over coring including cost, speed of analysis, and accuracy. In this paper we would like to give a brief description of the measurement and then show some sample logs from South Texas. Uranium exploration and development is carried out primarily by gamma logging since uranium daughters are prolific emitters of gamma rays. The conventional gross gamma tool for uranium logging is limited in value because of the inability of this tool to distinguish uranium from its daughters and other naturally occurring radioisotopes, such as potassium and thorium. This problem becomes severe in cases of disequilibrium. Disequilibrium, in a geological context, is defined as the condition when the gamma radiations from the daughter products are being emitted in a location different from that of the parent uranium. In the decay chain of uranium almost all the gamma radiation emitted in the entire chain comes from the daughter product, bismuth-214. Bismuth-214 is separated from uranium by several long-lived isotopes that are chemically active and have different physical properties, often resulting in shifts in the location of bismuth- 214 relative to the parent uranium. In the United States orebodies exhibiting disequilibrium are a common occurrence and the use of a gross gamma log to delineate uranium orebodies can lead to errors. At present the solution to the disequilibrium problem is extensive coring followed by chemical analyses of the cores. There are several drawbacks in using this technique. First is the high cost of coring, the second is the fact that no results are available for days, or typically, weeks after the drilling is done. Thus for development work, coring and drilling must be done on a grid basis and many additional holes are cored to ensure that the entire orebody is mapped. Another disadvantage to cores is the fact that a small volume is sampled, the volume of the core itself. This leads to problems in the mapping out of the orebody when the ore de- posit is not very homogeneous. The PGT probe described in this paper is a new solution to the disequilibrium problem. Basically, the probe measures radiations that come almost directly from uranium itself. The first daughter of uranium, which is protactinium-234 (Pa-234), is only separated from uranium by a 24-day half-life and no disequilibrium problems build up in such a short time. The PGT probe measures the intensity of a one MeV gamma line emitted by Pa-234 and, using this information, calculates the concentration of uranium. The PGT probe is 24" in diameter and 12 feet long. The probe contains a microprocessor which passes the information to a larger minicomputer in the truck. All data is analyzed on site, and the results from a high speed printer are presented to the geologist. Data is also available on 9- track IBM compatible tape for further processing. The PGT probe output is linear with uranium concentration. The only correction factor is for borehole size, and that only becomes important in boreholes bigger than seven inches in diameter. Dead time is compensated in the probe itself and no problems have been encountered in ore zones up to several percent UjO8. In addition to the uranium assay, a conventional gross gamma log is plotted alongside. Grade thicknesses for zones above cutoff are calculated as well as disequilibrium factors. COMPARISONS During its commercial operation PGT logged a series of 18 holes that had been cored and assayed. All of the holes in this series were logged in normal operation by regular field operators. The time to log each hole was generally under an hour, and in typical operation a PGT logging truck will do between 7 and 8 holes a day. The results of the comparison of the PGT and the core assays are presented in a series of figures showing plots of the PGT assay, core analysis and gross gamma measurements. The first three figures show individual holes with the gross gamma plotted along with the core and the PGT assays. All three logs were from holes on the reduced side of a rollfront deposit in South Texas. In Figure 1 we see the two wings of the roll- front at 143 ft and 150 ft separated by a barren zone. The wings are well defined both by the PGT assay and the core. There is approximately a one foot shift which can be attributed to drilling errors. The gross gamma is showing a rather severe discrepancy, being considerably lower and not showing the barren zone. The grade thickness calcula-

Jan 1, 1980

By J. W. Hickman

INTRODUCTION RECENT work by the authors1 on the oxide films formed on alloys of titanium and zirconium with nickel and copper indicated that an investigation of the oxides which form on alloys of copper and nickel might permit the relative rates of formation and diffusion of the ions of. these metals to be determined. This binary system is of further interest since the alloys which form are of the solid solution-type over-the entire range. In addition nickel is much more oxidation resistant than copper. A comparison of the free energies of formation of the simple oxides which may occur on these alloys indicates that nickel oxide should be observed over the entire time and temperature ranges of oxidation for all alloy compositions.1 In. order for nickel oxide to predominate on the surface, it is necessary that nickel ions form and diffuse to the surface. Two factors which may influence the formation of nickel oxide may be the ionic sizes, where Cu+ is 0.96Å and Ni-++ is 0.70Å, and the charges on the ions. On the basis of size, Ni++ should diffuse more readily than Cu+ while on the basis of charge, Cu+ should form more readily than Ni++. According to Uhlig2 passivity to corrosion in an alloy appears at a critical composition which for copper-nickel alloys is related to the tendency of the d band of electronic energy states to fill with electrons. This composition in the copper-nickel alloys corresponds to 40 at. Pct nickel at which composition Uhlig2 (quoting La Que's data) states that the alloy system becomes passive. Magnetic and specific heat data indicate that the d band of copper-nickel alloys is filled at 6o at. pct copper or 4o at. pct nickel. Mott and Jones3 have shown that if, on alloying nickel with copper, one considers a copper atom to be identical with a nickel atom except for an extra electron (nickel -has the-configuration: 3d8 4s2 and copper: 3 d10 4s) then at 60 at. pct copper or 4o at. pct nickel enough electrons are contributed by copper to fill the d band of the alloy. At this composition the magnetic susceptibility approximates zero according to Grew.4 Although the electron diffraction data will not determine the rates of the several reactions which may occur during oxidation, yet a determination of the structures of the surface oxides may yield information concerning the relationships, if any, which may' exist between the oxide structures which form and that composition where the magnetic susceptibility approximates zero. It is quite possible, of course, that the mechanisms of the oxidation and corrosion reactions may be so widely different that no correlations between them may be possible. SURVEY OF LITERATURE The metals, copper and nickel, which are face-centered cubic, form solid solution alloys which are face-centered cubic with no superstructure for all compositions. Three oxides of nickel have been investigated structurally by X ray diffraction. Of

Jan 1, 1948

By C. R. Fast, George C. Howard

Laboratory and field testing of various squeeze cementing techniques and materials revealed that many improvements could be made in squeeze cementing operations. The use of a slow-pumping squeeze cementing procedure permitted the control of the quantity of cement displaced into a formation and aided in obtaining a high final squeeze pressure. Field testing indicated the desirability of obtaining high final squeeze pressures, the need for improved formation breakdown fluids, and the necessity of controlling the pressure differential during testing after a squeeze job. INTRODUCTION During the past few years, squeeze cementing operations have been investigated, both from the theoretical as well as the practical point of view, in an effort to arrive at some solution to the many and varied problems that arise with this type of operation. A review of well files indicated that in many instances, wells were being squeeze cemented four and five times before a satisfactory pressure buildup was obtained. There seemed to be considerable variation in opinion as to the proper method of squeeze cementing, as well as disagreement as to the proper breakdown agent, the quantity of cement that should be used, type retainer and length of WOC* time that was necessary. Consequently, it was deemed advisable to approach this problem theoretically, field testing each idea developed in hopes of eventually arriving at a squeeze cementing procedure that would give reasonable assurance of a successful job after one squeeze cementing operation. This investigation was. therefore, divided into two broad headings: (1) Preliminary studies, which include both theoretical and laboratory studies, and (2) Field investigations to determine the proper squeeze cementing methods. PRELIMINARY STUDIES Overburden Pressure Studies Squeeze cementing problems are so intimately related to the earth's overburden pressure that solutions to them are very difficult, if not impossible, without an understanding of the nature and magnitude of the overburden pressures encountered at the depths of producing wells. It was thus felt that the first approach to research on squeeze cementing should be made through a study of these pressures. Since there has been rather loose usage of a number of the terms related to overburden preasure by different writers, the terms to be subsequently used are defined here. Theoretical overburden pressure is the calculated pressure at any given depth exerted by the theoretical weight of overlying formations as calculated from the average rock density. Fluid displacement pressure is that pressure at which fluid can be injected into a formation after it has been broken down. It may be more or less than the theoretical overburden pressure. Formation breakdown pressure is that pressure at which a formation parts or breaks and is usually thought of as fluid displacement pressure plus rock strength. Breakdown agent is that fluid with which the formation is fractured. The first step in the study of the earth's overburden pressures involved a review of pertinent technical literature. The general opinion expressed was that the overburden pressure gradient of the earth's formations is roughly 1.0 psi per foot of depth, and that application of sufficient pressure to stratified formations. will cause them to part at or parallel to the bedding planes. The second step in the study of overburden pressures involved a study of available well data in an effort to obtain some definite information as to the actual values experienced in the field for the above mentioned terms. Data from 115 cement squeeze jobs in the Gulf Coast area and 46 cement squeeze jobs and acid jobs in the West Texas-New Mexico area were closely analyzed. The analysis of these data showed that the average formation breakdown

Jan 1, 1950

By John E. Young

U.S. Steel Corp.'s Winifrede mine is operated by Lynch District in the mountainous region of eastern Kentucky. This region is characterized by narrow finger ridges and precipitous slopes, which present both an opportunity and challenge in the design and selection of coal-handling facilities for the movement of coal from the section belts to the railrod cars. Lynch District selected diesel-powered locomo¬tives and 100-ton articulated cars capable of negotiating sharp curves. The drop¬bottom mine cars are equipped with longitudinally hinged doors that are auto¬matically opened and closed. Lynch District selected a large-diameter steel-lined borehole for lowering the coal approximately 1000 ft from the seam level to the valley floor railroad load-out point. Taking advantage of gravity, the presized coal is "lowered" vertically approximately 720 ft to existing entries of a previously abandoned mine. The coal is then conveyed horizontally into storage. The coal¬handling facility from the mine-car dump to the railroad load-out point is fully automatic through use of tone control. TV cameras are installed along the facility to continuously monitor the strategic points. The diesel locomotives are either directly operated or remotely radio-controlled, depending on the functions Per¬formed. U.S. Steel Corp.'s Winifrede mine is operated by Lynch District in the mountainous region of eastern Kentucky. This region is characterized by narrow mountain ridges and precipitous slopes which present both an opportunity and challenge in the design and selection of coal-handling facilities for the movement of coal from the section belts to the railroad cars. The narrow finger ridges precluded use of under¬ground haulage and, thereby, presented the opportunity to use high-capacity equipment on the outside bench. The precipitous mountain slopes, steepest at the Wini¬frede seam horizon, presented a challenge to select a solution for lowering the coal approximately 1000 ft from the seam level to the valley floor railroad load-out point. It was evident from the start of planning that these two factors predominated; namely, rail haulage and coal lowering, and solutions to these would determine the final design of the Winifrede mine coal-handling facilities. The Winifrede mine derives its name from the Wini¬frede Seam which comprises the total reserve recov¬erable from this facility. The seam is 5 ft high with a good siltstone bottom and competent shale or sandstone roof. The seam is at an elevation of 2700 ft where the mountain ridges are long and narrow. This configuration of the reserve was ideal for conveyor belt installation to transport the coal from the working face to the outside bench. The preclusion of underground rail haul¬age permitted an opportunity to review the type of locomotive power and to select high-capacity equipment without the limitations associated with underground systems. Since the basic electrical design of the mine was al¬ternating current, with rectification to direct current for shuttle cars required only in the face areas, there was no point in bearing the burden of additional cost of dc trolley installation. And, since the haulage would re¬quire only a few tunnels to negotiate sharp points and to reach the back side of the reserves, diesel power was selected for the haulage locomotives. To provide stability on the almost continuously curv¬ing track and to provide the maximum width of haul¬age equipment, both locomotives and mine cars, stan¬dard railroad gage was chosen to offer the largest choice of equipment. The decision was made to select a standard 45-ton railroad diesel locomotive but to lower the cab height to reduce tunnel excavation requirements. The mine car was the next challenge. Past experience in Lynch operations indicated that drop-bottom cars would be a successful application with the free-flowing coal. The search was for a drop-bottom car within the dimensions of the locomotive to discharge the coal in the shortest time. Numerous types were considered and visits made to various sites to observe cars in operation.

Jan 1, 1972

By G. A. Moore

A brief review is given of methods designed to produce metallic iron of high purity, and typical results are listed. A recent method, utilized at the National Bureau of Standards, consists of the extraction of ferric chloride by ether, reduction of this ferric chloride to ferrous chloride, further purification of this chloride, and the subsequent electrolytic deposition of metallic iron. iron produced by this procedure apparently is softer than, and otherwise different in properties from, any iron previously prepared and contains appreciably smaller amounts of impurities. THE history of attempts to produce "pure" iron reaches to antiquity and it may be presumed that each ancient armorer who succeeded in making a better steel concluded, correctly, that he had done a better job of removing the "base metals," and incorrectly, that he now at last had a "pure" metal. Early metallurgical papers mentioned use of "pure iron" in making alloys—this "pure" iron in most cases being inferior to some commercial stocks of the present time. Improvement has been continuous, and usually at a sufficient rate to convince each succeeding group of workers that they, at last, were using the really pure metal (until the analysts also improved their techniques to again discover the impurities). These adventures were reviewed in some detail by Cleaves and Thompson.' Although the ores of a metal may be abundant, difficulties in extracting it may make the pure metal very rare. When impurities are restricted to a total of a few parts per million, nearly all pure metals become rarities. Lead, copper, gold, mercury, silver, zinc, aluminum, bismuth, and the six platinum metals are claimed to be available with total impurities ranging from 2 to 50 ppm. The present small and scattered world supply of so-called "pure" iron holds an unimpressive place in another group of 16 metals having approximately 100 ppm of foreign material. Of about 20 less rare metals, only the platinum metals are more costly to prepare. While the production of such rare varieties of iron may appear insignificant in the presence of thousand-ton operations with 95 to 99 pct metal, it must be emphasized that all researches on commercially interesting irons and steels are in fact studies of the modifications of the properties of iron by additional materials. Until the properties of high purity iron are directly measured, all ferrous research must operate without known base values. Traces of impurities may affect the properties of a metal in many ways. Infinitesimal traces of solutes, by disturbing the electronic configuration, greatly change the electrical properties of transistors and semiconductors2-3 and slightly larger traces might alter these quantities in iron. Soluble impurities which disturb the perfection of lattice arrangement not only may alter the magnetic constants and electric properties, but by their close association with dislocation phenomena probably control the very existence of the "yield point"; determine the value of yield stress; and perhaps control the selection of slip and cleavage planes. It has been speculated that impurities might even cause the allotropic transformation in iron, but in any case their rearrangement must contribute to the unreliability of heat capacity and other thermodynamic measurements. Impurities which do not remain in solution may cause even greater effects on the properties. Microscopically visible amounts of phases other than ferrite can be found in all high purity irons which have come to my attention. It can be calculated that from 50 to as little as 2 ppm of an insoluble material might be sufficient to completely film all grain boundaries in irons having grain sizes from ASTM Nos. 10 to 1. Should this occur, such films, even though invisible, may be very important in fracture problems, especially at extremes of temperature:' Studies of grain growth and diffusion normally imply consideration of a single-phase system, hence, in the presence of insoluble impurities they can be expected to give ambiguous data." High purity iron is also in demand for use as chemical and spectro-chemical standards; for work in classifying the lines of the iron spectrum; for biological work in nutrition; and for work in nuclear physics. where the presence of some sensitive

Jan 1, 1954

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By R. A. Greenkorn

This project originated in a practical problem—we needed five tracers that could be used together to locate flow paths in a pilot flood. While tracers for subsurface liquids have been used since the turn of the century,1-15 none of those reported in the literature appeared to be either consistent or quantitative enough for our purposes. Most were used in field systems without controlled experiments to determine the accuracy and precision of analysis, and many were tracers that could not be used collectively. The ideal tracer, of course, would follow the fiuid of interest exactly, traveling at the same velocity as the fluid front. But the ideal is impractical to attain because adsorption-desorption effects cause the tracer to lag behind the front; these effects, plus diffusion-dispersion effects, cause the tracer front to spread more than the fluid front. Thus, our objective was not to locate a tracer that would be ideal for all circumstances but rather, to find one that would approximately follow the fluid, or one that under controlled conditions could be corrected to calculate the movement of the fluid front. We considered tracers satisfactory—(1) if they were easy to analyze; (2) if their breakthrough-elution curves were not too different from those for the chloride ion, a tracer believed to follow the fluid front closely; and (3) if we could calculate from the curves a material balance, at 1.25-PV (pore volume) injected, within 5 per cent of that calculated from chloride curves. Of a possible 35 materials, we selected 13 tracers that could be quickly and easily identified and whose analysis was claimed to be accurate within 5 per cent. Only one of these, tritiated water, was a radioactive tracer. Radioactive tracers are easy to detect even in small quantities, but they require special handling and special equipment. Also, those that can be used together are limited because special equipment is required to separate emissions from the various tracers. Two of the original 13 tracers were eliminated in static tests to determine how accurately and precisely they could be analyzed, and to check on gross adsorption. The remaining 11 were flowed through a 9-ft linear sandstone model, and breakthrough-elution curves were obtained. Finally, three tracers were field-tested as breakthrough tracers. These tests are described in the following sections. The 13 tracers considered in these experiments were EDTA (ethylene diamine tetra acetic acid), fluo-rescein, picric acid, salicylic acid and ammonium, boron (as borate), bromide, dichromate, iodide, nitrate and thiocyanate ions, plus chloride ion and tritiated water. All but the chloride ion and tritiated water were subjected to static sand tests to eliminate the tracers that could not be analyzed quickly and accurately and to eliminate those that showed excessive adsorption. All but two of the tracers, EDTA and salicylic acid, qualified for flow tests on this basis. The procedures used in the static tests (see Appendix A for analytical details) were as follows. Each tracer (in the amount shown in Table 1) was dissolved in 1,000 ml of water. Then, 800 ml of this solution was added to 500 gm of sand, and the remaining 200 ml was reserved as a control standard. The sand-tracer mixture was agitated once a day over a 10-week period, and during this period we analyzed five duplicate samples from this mixture, along with five duplicate samples from the control solution. From the control-sample analyses, we constructed a control chart on which the sand-tracer analysis results were plotted. The control chart, and its use to determine accuracy and precision of analytical results, as well as the amount of adsorption, is described in Appendix B. The results of the static tests are summarized in Table 1, which lists the concentration c (concentration at time t) divided by c, (initial concentration). If there was no adsorption, c/c, = 1. The acceptable deviation from this value varied from tracer to tracer, depending upon the limits of analytical precision established for the different tracers. The best results were obtained with boron, bromide and dichromate, with all values falling within limits of accuracy and precision. Ammonium, iodide, nitrate and picric acid also were satisfactory, although the ammonium results were erratic. Flourescein and thiocyanate were unsatisfactory ini-

By Irving B. Cadoff, Stojan M. Zalar

AgInTe2, CuInTe2, and all Proportions of CuxAg1-xInTe, forMed homogeneous single phase alloys after direct solidification from the nielt. X-ray analysis indicated a zinc-blel~de strzccture typical of the chalcopyrite compounds, and the electrical resistivity and Sccbeck coefficient values were in the semiconducting range. AuInTe, and AuxA4g,-, InTe, formed by what appeared to be a peritectic reaction (the thermal analysis curves showing more than one arrest) and were conseyue~ztly polyphase. Substitution of copper into AgIrzTe, resulted in a continuous transition in the room tenzperature Seebeck coefficient from the negative AgIzTe, to the positive CuInTe,. A zero coefficient was obtained at about Cuo.55 Ago.45 InTe, . The temperatzire variation was similar to that observed for the stoichiometric compounds, that zs, tendency towards "p" concEuction at elevated temperatures. The thernzoelectric figure of merit for the compo~uzds, as determined by the Putley -Harmnn method were in the range 10- to 10-7 "K-l; the thermal conductivities in the order of 0.15 cal per sec-cm-oK. INCREASED interest in semiconducting intermetallic substances is expanding much of recent research from simple binary compounds into polyatomic systems and solid solutions. Ternary compounds A' represent a covalent extension of the binary semiconductors Within the a tin isoelec-tronic series, Ag-Cd-In-Sn-Sb-Te-I, divalent cadmium atoms in CdTe are being substituted for by monovalent silver and trivalent indium atoms to form the compound AgInTe, . By cross-substitution with elements of other isoelectronic series, a great number of ternary compounds A 'B"'c? is possible. In all of them, however, a necessary though not sufficient condition for the covalent, semiconducting bond—that there be four sharing orbital electrons per atom—must be fulfilled. In AgInTe,, each silver or indium atom is tetrahedrally surrounded by four tellurium atoms, while each tellurium atom is co-valently bound to two silver and two indium atoms. Synthetic chalcopyrites A'B"'c~ were first recognized as potential semiconduct&rs by Goodman and Douglas.' Austin, Goodman, and Pengelly discuss preparation difficulties and some electronic measurements on AgInS, , AgInSe, CuInSe, , AgInTe, , and CuInTe,. Chalcopyrites A B c2v are mentioned in papers attempting to classify and predict semiconducting behavior of intermetallic compounds; on the basis of saturated tetrahedral sp3 bonds,3 by specific selection criteria,' and by crystallographic considerations."

Jan 1, 1962

By Alan J. Strauss

The Group IV elements germanium, tin, and lead form nine 1:1 compounds with the Group VI elements sulfur, selenium, and tellurium. This paper reviews the properties of the pseudobinary solid solutions formed by these compounds, including the extent of mutual solid solubility, temperature-composition phase diagrams, transport properties, deviations from stoichiometry, optical properties, and energy band structure. Particular emphasis is placed on the Pbl-xSnxTe and Pb1-xSn,Se alloys with rocksalt structure, because of current interest in these malerials for generating and detecting infrared ,radiation. ThE Group IV elements germanium, tin, and lead form nine 1:1 compounds with the Group VI elements sulfur, selenium, and tellurium. Some of the physical and electronic properties of these compounds, including their melting points1-8 and energy gaps,4'9-12 are listed in Table I. Four compounds (SnTe, PbS, PbSe, and PbTe) have the cubic rocksalt (Bl) structure. At room temperature GeTe has a rhombohedra1 structure closely related to the B1 structure, into which it is transformed at about 400°C. Four compounds (GeS, GeSe, SnS, and SnSe) have the orthorhombic B29 structure. In samples which have not been intentionally doped with impurities, the electrical conductivity is due primarily to electrons or holes produced by the ionization of donor or acceptor lattice defects associated with deviations from stoichiometry. Undoped samples of PbS, PbSe, and PbTe may be either n type or p type, depending on whether they contain excess lead or an excess of the Group VI element, respectively, but only p-type samples of the other compounds have been reported. This paper will review the properties of the pseudo-binary solid solutions formed by the nine 1:l compounds. The topics to be considered include the extent of mutual solid solubility, temperature-composition phase diagrams, transport properties, deviations from stoichiometry, optical properties, and band structure. Particular emphasis will be placed on the Pb]-xSnxTe and Pbl-xSnxSe alloys with B1 structure, which are promising materials for generating and detecting infrared radiation in the 8 to 14 µm atmospheric window and beyond. MUTUAL SOLID SOLUBILITY The extent of mutual solid solubility in the pseudo-binary systems has been investigated for fourteen of the eighteen ternary systems (in which the two terminal compounds have a common element) and for nine of the eighteen quaternary systems. In most cases, X-ray diffraction measurements made at room temperature were used to determine the structure and lattice parameter(s) of the phase(s) present in samples of various compositions prepared by freezing from the melt. In many investigations, including the extensive studies of Krebs and co-workers,13'14 the samples were annealed at elevated temperatures before X-ray measurements were made. In some cases, metallographic examination and thermal analysis have also been employed. The results for the ternary and quaternary systems are summarized in Tables II and III, respectively. (The original references should be consulted for the annealing temperatures.) The solubility of one compound in the other is at least 5 mol pct in all cases, and is often much larger. Complete solid solubility has been observed in all systems so far investigated in which the terminal compounds have the same structure, although in the PbS-PbTe system complete solubility is limited to elevated temperatures. Thus complete solid solubility occurs in five systems where both compounds have the B1 structure (SnTe-PbTe, PbS-PbSe, PbS-PbTe at temperatures above 805°C, PbSe-PbTe, and SnTe-PbSe) and in three where both compounds have the B29 structure (GeS-SnS. GeSe-~n~e-, and SnS-SnSe), as well as in two involving GeTe and a compound with B1 structure (GeTe-SnTe and GeTe-PbTe). On the basis of thermal analysis data, complete solid solubility at sufficiently high temperatures has also been reported for the GeSe-GeTe2 and SnS- pbS22 systems. This seems unlikely, however,

Jan 1, 1969

By G. H. Anderson

H. R. HANLEY*—I have been asked to discuss briefly the development of rotating cathodes for the electrolytic deposition of cadmium. The earliest recorded use of rotating cathodes was by Hoepfner at Frufurt, Germany about sixty years ago. He elec-trolized zinc chloride solution using diaphragms to separate electrodes. In the early experimental work of the Bully Hill Copper Mining and Smelting Co., Shasta County, Calif., rotating aluminum cathodes 4 ft in diam were used in the electrolysis of an acid zinc sulphate solution. Finished cathodes weighing up to 400 lb were produced. Because of mechanical difficulties, this type of cathode was abandoned for zinc, but was later used for cadmium because of the relative smoothness of deposit in comparison with stationary plates with comparable current densities. Cadmium sponge which forms on the cathode at moderate current densities (without special treatment) is entirely eliminated by a slow rotation. The rate of rotation of the cathode has an effect on the mechanical nature of the deposit. A high rate of rotation concentrates the adhering electrolyte on the shaft; a moderate rate appears to concentrate on the cathode a short distance out from the shaft tending to corrode the deposit in the form of a ring. At a very slow rotation (2 to 3 rpm) the adhering electrolyte gravitates nearly vertically, thus avoiding the cutting ring referred to above. The true explanation for the smoother deposits obtained on rotating cathodes may not be given definitely as the numerous factors involved are not thoroughly understood. Smooth deposits are obtained when the orderly growth of the metal crystals in the cathode lattice are disorganized. Thus the crystals form and grow for a very short interval when they are arrested and a new crystal forms. The continued growth of the original crystals provides large crystals and a rough deposit. Also if the acidity of the electrolyte is low, hydrogen gas bubbles adhere to the deposit. As the cathode is rotated the gas surface is brought into the atmosphere where they burst; thus the deposit is made on a surface relatively gas-free. An aluminum hub distance piece was riveted to each aluminum disk 4 ft in diam, slipped on a 4 1/2 in. steel shaft and pressed tight to prevent acid electrolyte seeping through to the shaft. The 9-cathode assembly was supported on insulated bearings. Electrical contact to the shaft was made through what was equivalent to a copper pulley. Sufficiently high conductivity brushes were placed on the face of the pulley to lead the current to the cathode bus bar. The assembly was driven by a link belt contacting a sprocket insulated from the shaft. The lead anodes were semicircular and supported on porcelain insulators placed on the bottom of the cell. Two anodes were provided for each cathode to permit an 8-in. space between them without increasing the ohmic resistance. This ample spacing permitted easy stripping of deposit with the assembly in place. Cathode cadmium was melted under 650 W cylinder oil. After casting, the primary slabs were remelted under molten caustic soda and cast into pencils 1 1/32 in. in diam. Rotating cathodes for deposition of cadmium are used at Risdon, Tasmania, and at Magdeburg, Germany. W. G. WOOLF*—This paper is very-interesting to me because in our work at the Electrolytic Zinc Plant of the Sullivan Mining Co. we had an exactly similar problem—that is, a method of producing cadmium from our purification residue, the recovery of the contained copper as a copper precipitate which could be sent to a copper smelter and the production of merchantable cadmium. It is interesting to me, not knowing of the work of the Risdon people, how closely we approximate them in their main metallurgy, diverging at several interesting steps which I would like to discuss for just a moment. For example, at Risdon they oxidize their purification residue. In our practice we take the current residue as it is produced in the purification department of the zinc plant and process it in the cadmium plant. The only oxidation that it obtains is the oxidation in the presses, the dumping of the presses and the collection and transportation of the residue to the cadmium plant. We find that the leaching of that residue does not necessarily require the oxidation step that the Risdon people evidently find necessary. The discussion of oxidation comes in again in the matter of the treatment of the precipitated cadmium sponge with zinc dust which again at Risdon is oxidized but which we do not attempt to oxidize except as it oxidizes itself in the storage. There is a partial oxidation which cannot be avoided, as Mr. David-sou pointed out, but we make no attempt to attain a complete oxidation and we dissolve the cadmium sponge in the sul-

Jan 1, 1950

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By T. D. Tiemann

The chemical and mineralogical composition of Caribbean bauxite ores are described. Extraction of alumina by several processes from both Haiti and Jamaica bauxites is discussed and data presented. IMMENSE deposits of bauxite occur in the Caribbean islands of Hispaniola and Jamaica in the high plateau lands and have been excellently described by 0. C. Schmedeman.' The bauxite occurs as deposits in catchments or etched depressions in Tertiary limestone believed to have been deposited in the Eocene and Oligocene periods.' In appearance both the Haiti and Jamaica bauxites resemble a relatively high iron clay and have indeed been mistaken for such.' They are very soft and friable and disperse readily on vigorous agitation in water. The color range in general is light brown to red. Chemically, the outstanding characteristic of the bauxites is the low silica and high ferric oxide content. The extremely low silica makes them particularly valuable for the production of alumina in the Bayer plant since silica is responsible for the loss of both alumina and soda chemically combined as XNa,OYSiO2,ZAl2O2. The ferric oxide, only traces of ferrous iron are present, offers no interference in the production of high grade alumina. Typical oxide analyses of three types of ore are given in Table I2 and a list of the elements occurring in spectrographic quantities in Table 11." The size of the individual particles in the ore makes successful petrographic examination extremely difficult. The ores contain some relatively coarse grains of heavy minerals such as ilmenite, magnetite, and rutile, but other than occasional crystals of a few microns, the greater portion of the minerals are submicroscopic in size and approach colloidal dimensions. The mineralogic composition of the ores has been investigated by X-ray and differential thermal analysis.' These investigations indicate that the predominant mineral phases present are gibbsite (A1203.3H2O), boehmite (Al2O3.H2O), hematite (Fe2O3), and goethite (Fe2O3-H2O). There is no evidence of the occurrence of diaspore (Al2O3.H2O) in either the Haiti or Jamaica ores, but some type of "amorphous" alumina may be present in some of the bauxites of Jamaica." The temperature stability regions in the alumina-water system have been investigated and are given in recent literature. In the temperature range where the hydrated forms are stable, as determined by hydrothermal bomb methods," ibbsite is the stable phase to 155°C (311°F), boehmite from 155°C (311°F) to 280°C (536oF), and diaspore from 280°C (536°F) to 450°C (842°F). Although quite similar in many characteristics, the Haiti and Jamaica ore show a divergence in mineralogic composition that is reflected in the extractability of the alumina described in later paragraphs. Two principal differences occur in mineralogic composition. The iron-bearing mineral in the Haiti ores is predominantly hematite, while in the Jamaica ores goethite is predominant.4 Directly related to the extraction of alumina are the two minerals, gibbsite and boehmite. Boehmite is relatively high in the Haiti ores and in some of the less soluble Jamaica ores, while gibbsite predominates in the ores in Jamaica amenable to the American Bayer process of extraction. Pedersen and Related Processes In general, all processes for the extraction of alumina involving sintering or fusion of bauxite ores with limestone, soda ash, or a combination of limestone and soda ash followed by leaching, are based on the formation of alumina compounds that. yield alumina soluble in the subsequent leach. The principal idealized reactions in respect to alumina and silica for the three types of processes are as follows: Soda Ash Sinter: A12O3 + Na2CO3 = Na2O-Al2O, + CO2 SiO2 + Na2CO3 = Na2O . SiO2 + CO2 A12O2 + SiO2 + Na2CO3 = Na2O.Al2O8. SiO2 + CO2 Leach (with excess water): H2O + Na2O-A12O3 = 2 NaOH + A12O3 (insolution) H2O + Na2O-SiO2 = 2 NaOH + SiO2 (in solution) Soda Ash— Limestone Sinter: Na2CO2 + A12O3 = Na2O.A1203 + CO2 2CaCO3 + SiO2 = 2CaO . SiO2 + 2CO2 Leach (with excess water): Na2O' A1208 + H2O = 2NaOH + A13O3 (in solution) These latter reactions are the basis of the sinter process currently used for the recovery of soda and

Jan 1, 1952

By Bruce Chalmers, D. C. Larson

Aluminum crystals with longitudinal-axis orientations of (111) . (110), and (100) were deforined in tension and annealed. The conditions of deformation were controlled so that the re crystallization nuclei originated in either the heavily deformed regions at saw cuts {artificial nucleation) or in the lightly deformed matrix (spontaneous nucleation). The artificial-nucleatioln experiments showed that in lightly deformed (110) and (100) crystals low-angle twist boundaries are most mobile, while in (111> crystals and heavily deformed (110) and (100) crystals high-angle tilt boundaries with near (111) rotations are favored. The spontaneous-nucleation experiments showed the existence of preferred orientations in the (111) crystals. The nonrandomness of the grain orientations is quantitatively determined through a comparison with the results which would he obtained from a randowl set of grain ovientations. PREVIOUS recrystallization studies have been performed on single crystals deformed in tension.1 7 The crystals used in these studies usually had random tensile-axis orientations and the extent of deformation was not a primary consideration. The present study concerns the recrystallization of single crystals with tensile-axis orientations of (Ill), (110), and (100). The emphasis of this work is on the influence of the tensile-axis orientation and the degree of deformation on both the nucleation and growth processes. The multiple-slip orientations were chosen because secondary slip or slip intersection promotes nucleation.1,5,8 These crystals recrystallize at lower strains than the crystals which are oriented for single slip. Also, the greatest variation in deformation behavior is exhibited by the multiple-slip orientations. The stress-strain curves for crystals with tensile-axis orientations of (111) are higher than the stress-strain curves for poly-crystals, and the stress-strain curves for crystals with tensile-axis orientations of (100) are lower (at large strains) than the stress-strain curves for the crystals which deform initially in single slip.g The recrystallization nuclei originated in either 1) the homogeneously* deformed matrix of the crys- tals or 2) the heavily and inhomogeneously deformed regions at saw cuts. The nuclei will be referred to hereafter as spontaneous and artificial nuclei, respectively. The two terms do not imply a difference in the nature of the nuclei; they imply simply a difference in the mode of introduction of the nuclei. During spontaneous nucleation very few (always less than ten) grains nucleate, while during artificial nucleation large numbers of grains nucleate. Only a fraction of the artificially nucleated grains penetrate very far into the deformed matrix during annealing. The grains that penetrate the farthest into the deformed matrix will be referred to as the dominant grains. EXPERIMENTAL PROCEDURE The thirty-five crystals used in this investigation were grown from the melt in milled graphite boats at a rate of 1.6 cm per hr. The crystals had dimensions of approximately 6 by 12 by 80 or 6 by 6 by 80 mm and the aluminum was of 99.992 pet purity. The as-grown crystals were annealed at 610°C for 24 hr and furnace-cooled. They were then heavily etched and electropolished in a solution of five parts methanol to one part perchloric acid. The crystal orientations were obtained by back-reflection Laue photographs and were accurate to ±2 deg. The tensile-axis orientations were (loo), (110), and (111). Two of the side faces of the (111) crystals were (110) lanes. The (110) crystals had both {100) and {110) side faces and the (100) crystals had (100) side faces. The crystals were deformed at a strain rate of 0.003 per min. Shear stress and shear strain were obtained by multiplying and dividing the tensile stress and strain, respectively, by the Schmid factor, m. For the (111) crystals m = 0.272 and for the (110) and the (100) crystals m = 0.408. The Schmid factor is effectively constant during deformation for all orientations. The deformed crystals were sawed into 1-in.-long specimens while the crystals were totally enclosed in a graphite boat. The sawing was performed very carefully in order to limit the plastic deformation to the sawed regions. The specimens were electropolished in the solution mentioned above to remove the sawed-end deformation as well as controlled amounts of surface material. A special stainless-steel grip was used to hold the specimens during the electropolishing treatment. The gripping faces were flat, with no teeth, to prevent the introduction of extraneous de-

Jan 1, 1964