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By J. C. Borland, J. H. Rogerson

Jan 1, 1963

By E. T. Turkdogan, L. S. Darken

Calcium ferrite melts were equilibrated with sulfur and oxygen-bearing gases at temperatures within the range 1290°C to 1620°C. The results show that at oxygen partial pressures below 10-4 atm the sulfide-reaction occurs and at higher oxygen pressures the sulfur dissolves in the melt principally as sulfate ion. It is also observed that when the product increases, sulfate ions are converted to pyrosulfate ions and the results permit the evaluation of the pyrosulfate/sulfate ratio. It is shown that the ratio y CaSO,/rCaO increases with decreasing concentration of calcium oxide in calcium ferrite, silicate and aluminate melts. Indications are that oxy-acids, e.g. silica, alumina and ferric oxide, increase yCaS0,. A few experiments were carried out within the sul-tide range and the results are in accord with those obtained by other investigators on aluminate and silicate melts. BECAUSE of the industrial importance and theoretical interest, many investigators have studied the reactions between molten oxides, silicates or alumi-nates, and gases containing oxygen and sulfur. The early work reviewed by Schenckl and studies made by Bardenheuer and Geller2 indicates that solution of gaseous sulfur in an oxide melt resulted in the replacement of the oxide ions by the sulfide ions. Measurements made by Grant and Chipman3 on the equilibrium partition of sulfur between molten iron and complex silicate melts also demonstrated that, for a given temperature and silicate composition, the distribution of sulfur between slag and metal increased with decreasing oxygen content of the metal. Fincham and Richardson4 studied the effects of temperature and partial pressures of sulfur and oxygen on the solubility of sulfur in simple silicate and alumino-silicate melts. They observed that at oxygen partial pressures below about 10-5 atm sulfur in the gas dissolved in the melt as sulfide ions, replacing an equal number of oxide ions of the melt. At oxygen partial pressures higher than 10-3 atm, sulfur entered the melt as sulfate ions. Similar studies were made by St. Pierre and Chipman5 using calcium ferrite and calcium silico-ferrite melts. The experimental data presented in this paper were obtained in this Laboratory about 10 years ago; this is the first formal presentation although a preliminary report was given previously.6 In each of these experiments, a pure synthetic CaO-Fe2O3 melt in a platinum crucible was equilibrated with a gas mixture (SO2-O2, SO,-air, SO2-CO, or SO2-CO2-CO) at a temperature ranging from 1296°to 1620°C. The experimental technique was essentially the same as that reported by Darken and Gurry,7 the main difference being that the atmosphere in the reaction chamber contained sulfur dioxide together with oxygen, or carbon dioxide-carbon monoxide

Jan 1, 1962

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates (or sodium-free compounds) are required for certain end uses, but in general, nonsodium borates are used only where borax is not avail- able. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of about a million tons of B2O3. Leadership in supplying borates has shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates. In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, Calif., is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, Calif., the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "lo-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7- lOH2O. In addition to ship- ping all major refined borate products from Boron, the company ships semiprocessed ore concentrates to treatment plants elsewhere.

Jan 1, 1975

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

By E. G. Woods, A. G. Comer

A mathematical model is presented and solved for determinution of the saturation distribution and pressure in a radial gas-storage reservoir. The model consists basically of two parts: (I) the growing gas-bubble core, and (2) the surrounding aquifer. Since the total pressure at the injection well is a function of the two-phase flow in the gas bubble and the unsteady single-phase flow in the aquifer, the resistance to flow in both zones was taken into consideration. The assumptions involved for both the radial equivalent of the Buckley-Leverett two-phase-flow equation and the injection-pressure equation are as follows: (I) the geometry is radial, (2) the gas bubble is free to expand or contract, (3) compression or expansion of the gas within the bubble may occur at the beginning of a time step, (4) the fluids are immiscible, (5) water is incompressible within the gas-storage region whereas it is compressible outside of this region, (6) a stable gas-water interface exists and (7) gas injection occurs at a constant rate or a series of constant rates. The mathematical model was solved numerically using an IBM 650 computer. A comparison is presented between the predicted results of the model, the results assuming steady-state flow and the actual initial injection-pressure history of an operating reservoir. Using the initial field pressure for a basis, the average deviation between the predicted pressure and the actual field pressure was less than 4.3 per cent. INTRODUCTION Underground storage of natural gas in abandoned oil fields, in abandoned coal mines, in caverns and in aquifers has had varying degrees of success. The lack of these first three facilities in the vicinity of most major gas marketing areas is leading more and more to storage in virgin aquifers. For the most part, this storage in aquifers has led to the study upon which this paper is based. Several excellent papers have been published discussing the problems involved in the underground storage of natural gas; however, to these writers' knowledge, none of them considered the two-phase flow of fluids in the gas bubble and the fact that the gas bubble will grow or shrink in size depending upon the injection and withdrawal history of the reservoir. Not only will both of these factors influence the required injection pressure, but also they will have a definite bearing upon the amount of water production occurring upon withdrawal from the storage area. To solve this problem on an IBM 650 computer, several simplifying assumptions were made. Only the drainage portion of the relative-permeability curve was considered, thereby neglecting any hysteresis effects introduced during an imbibition cycle. The quantity of gas withdrawn during the period of the field study was only a small percentage of the total gas in place; therefore, this assumption is justified. For the problem studied in this case, the combined effects of capillarity and gravity were assumed to be negligible. This assumption becomes less valid as the formation thickness or the average pore diameter increases markedly. The justification of these assumptions should be studied in each case. THEORY This mathematical model for the prediction of saturation distribution and pressure for a radial gas-storage aquifer is based upon the equations for radial two-phase fluid flow'.' and for radial, unsteady-state, single-phase fluid flow.' The two-phase flow is considered to take place in a "core" whose radius is equal to the maximum radius that the gas zone will attain, as indicated in Fig. 1. The injection-withdrawal history is approximated by a series of constant flow rates. Within the "core", gas is assumed to behave as a semi-compressible fluid; that is, the gas is assumed to have a constant density based on the average gas-zone pressure for the flow period. Between each constant-rate time increment, the gas density is allowed to change. This involves an iterative solution of the pressure equation. The liquid phase in this zone is considered to be incompressible, whereas it behaves as a compressible liquid outside of this region. The equations of incompressible flow in the "core" may be written for the gas phase

By G. R. Smithson, John E. Hanway

This paper, the first of two papers covering the development of a metallurgical process for the treatment of a complex ore, describes the bench-scale experimental Program undertaken as a basis for initial process design. The results of using various potentially applicable process steps are detailed and the basis for selecting certain of these steps for Pilot-plant development is outlined. A process consisting of the steps of sulfate roasting, leaching, copper recovery, solution purification, zinc electrolysis, and brine leaching for lead recovery was recommended for further study. THIS paper describes the bench-scale development of a sulfate roasting process designed to recover copper, lead, and zinc from a complex ore. The extrapolation of the bench-scale results to pilot-plant design and the results of pilot-plant operation will be described by Lund, et al.' in a subsequent paper. Several years ago, the research divisions of the St. Joseph Lead Co. became responsible for the development of a metallurgical procedure to treat a complex sulfide ore containing copper, zinc, and lead sulfides. The primary objective was to devise a procedure which would permit economic recovery of the nonferrous values. As could logically be expected, the study of conventional flotation procedures was undertaken; in addition, however, because the physical nature of the mineral association in the complex ore indicated that physical methods of ore beneficiation might not prove to be entirely satisfactory, a program also was established to investigate alternative methods of direct metallurgical treatment for recovery of the metal values. Exploratory test work by the St. Joseph Lead staff led to the conclusion that a sulfate roasting technique represented the most attractive approach for a direct metallurgical process. Sulfate roasting would provide for the selective conversion of the nonferrous values to forms soluble in conventiona1.1 leaching agents and would permit their efficient separation from the insoluble iron and other gangue materials. It should allow efficient utilization of the thermal energy available from oxidation of the sulfide raw material, and might provide an opportunity for recovering byproducts such as iron and sulfur. The decision to evaluate a selective sulfation procedure as a basic processing step also was influenced by the excellent results obtained by the St. Joseph Lead Co. in using this procedure for the recovery of cadmium from zinc sulfide concentrates. The choice of selective sulfation as a major processing step served as a basis for an extended experimental investigation of the process with bench- and pilot-scale equipment to prove its feasibility. St Joseph Lead Co., aware that Battelle Memorial 1nstitute had participated in the development of several fluidized-bed sulfate roasting procedures, asked Battelle to undertake the bench-scale development of a suitable sulfation process. This paper describes the procedure used and the results obtained at Battelle in the treatment of the complex sulfide ore. EXPERIMENTAL WORK Nature of the Raw Material. The sulfide ore deposits of interest are essentially a massive sulfide, with the indivudual ore minerals being extremely fine grained and intimately intergrown with each other and with the associated gangue. The zinc in the ore is present mainly as sphalerite (ZnS), the lead as galena (PbS), and the iron either as pyrite (Fes2) or as pyrrhotite (FeS). Table I shows the chemical analysis of various individual samples of the ore. These analyses illustrate the variability of the ore body and impose a rather severe requirement on any type of metallurgical process—that of being able to tolerate probable wide variations in the assay of the head ore. The tentative flowsheet designed to serve as a guide for the initial experimental investigation of

Jan 1, 1962

By S. G. Epstein

Electromigration has been measured in dilute liquid alloys of lead in antimony and antimony in lead. In these alloys antimony migrates with the electron current; lead migrates in the opposite direction. These results, which contradict the mass criterion, were predicted by the electron drag model for electromigration in liquid alloys. The existing experimental data are shown to correlate with the difference in electrical resistivities of the alloy components. FOR many years investigators have attempted to relate observed electromigration phenomena in liquid alloys to the physical properties of the alloy components. The most successful correlation was found by Angus et' al.,1 who in 1959 proposed an empirical criterion for predicting the relative direction of motion of the components of a liquid alloy in an electric field: the component with the smallest atomic mass concentrates at the cathode. While this criterion is obeyed in nearly all the alloy systems which had been investigated, the physical basis for such an effect was not understood. It was also disturbing that the mass criterion predicted the wrong sign for the Haeffner effect; observations with pure liquid metals revealed that in every instance the lighter isotope was transported to the anode.2 Klemm3 explained these isotopic separations by suggesting that the lighter isotopes were more mobile and more easily carried to the anode with the electron stream. Additionally, several deviations from the mass criterion have been found in liquid alloys, notably involving transition metals such as chromium, nickel, palladium, and zirconium, which migrate to the anode in liquid bismuth.4'5 Recently, a model has been proposed6 in which electromigration in liquid alloys is attributed primarily to the interaction between the electron stream and the metal ions. In essence, this model predicts that the component with the greater electron-ion scattering cross section will be preferentially transported to the anode, displacing the other component to the cathode. The electrical resistivity of each pure component at its melting point is taken as the measure of its scattering cross section. This model was developed from the results of systematic studies with various solutes in liquid mercury,7'8 bismuth,9 and sodium.10 In every alloy, the component with the greater resistivity has centrates at the anode. Coincidentally, in every instance the component with the greater resistivity has also the greater mass, apparently satisfying the mass criterion. In order to differentiate between electron-ion coupling and atomic mass as the relevant physical prop- erty influencing electromigration, measurements were made with Pb-Sb alloys. Lead has an atomic mass nearly twice that of antimony, but lead has an electrical resistivity of 91 microhm-cm while antimony has a value of 113.5 microhm-cm at their respective melting points. The mass criterion predicts that in an alloy of the two antimony will concentrate at the cathode; the electron drag model predicts that antimony will concentrate at the anode. EXPERIMENTAL To conclusively determine the relative motion of lead and antimony in each other, solute electromigration was measured in dilute liquid alloys of antimony in lead and lead in antimony. Both starting materials were 99.999+ pct pure. The measurements were made with the same capillary-reservoir technique previously used for measuring electromigration in liquid bismuth alloys.11 Several changes in the experimental apparatus were necessary, however, to accommodate liquid antimony, which has a higher melting point than bismuth. The modified apparatus is depicted in Fig. 1. In each experiment four quartz capillaries were filled with the molten alloy. A direct current was passed through two of the capillaries; the electrode in one of these capillaries was made the cathode, and the electrode in the other was made the anode. The remaining two capillaries sampled the alloy in the reser-

Jan 1, 1969

By Henry J. Welge

The approximate methods which are now in use for calculating oil displacement from reservoirs by gas-cycling or gravity-drainage at constant gas pressure, or by water flooding, make use of fundamental relationships derived by Leverett' and Buckley and Leverett.2 The mathematical equations needed are derived by applying Darcy's law to the flowing phases, and by material balance considerations. ln general, any treatment of this type gives. for any particular exploitation time considered, a plot of oil saturation against distance in the reser-voir. The oil recovery must then be obtained by integrating in some manner the area under the plot. A useful analytical method has been derived for computing the average saturation, and hence the oil recovery. Use of this method simplifies the calculations because it makes unnecessary any numerical integrations. and even the saturation distribution plots are not needed. A further advantage of the method is that knowledge of the relative permeabilities is required only for a limited and intermediate saturation range. In both the Buckley and Leverett method and the method discussed here, a linear sand section is assumed, and in the case of gas drive the gas pressure is assumed sufficiently constant both with respect to reservoir position and time so that changes in gas density. solubility, or reservoir volume factor are negligiklle. Thus, the exploitation contemplates oil displacement as by an immiscible phase. Examples are given to illustrate how the new method can be used. INTRODUCTION AND THEORETICAL BACKGROUND This paper treats a simplified method for computing oil recovery when the oil is displaced, from the reservoir sand by a fluid which, within the limits of accuracy desired, can be assumed to be incompressible and immiscible with the oil. The method makes use of two basic relations originally developed for the case of water displacing oil. However, the case of gas displacing oil saturated with gas at a constant (or nearly constant) pressure may also be considered a displacement by an immiscible fluid. This is possible for the reason that the concentration of the gas in the oil never changes if tile pressure is fixed. consequently, any additional free gas must remain undissolved in the oil, and so must act essentially as an immiscible phase. For convenience, the cape of gas drive will be considered first. Both of the two basic relations needed refer to a linear reservoir, or one which may be somewhat idealized so that a constant cross-section is exposed to fluid flow. Further, the displacing phase is injected at one end, or face; of the reservoir, while the produced fluids are understood to emerge at one point only. which is the opposite face of the reservoir. As indicated in Fig. 1, the reservoir may he inclined by some angle 8. The first of the required equations may be derived by applying Darcy's law to both displacing and displaced phases, and subtracting the two equations. The result for water drive has been given previously, as Equation (13) of the reference by

Jan 1, 1952

By D. V. Carter, D. C. Williams

Four oil discoveries were made in east and east central Texas during 1940, three of which represented new fields. In the Chapel Hill field, Smith County, oil was found where formerly only gas and distillate were produced. The three oil fields discovered are: Hawkins, Wood County; Pittsburg, Camp County; and Tehuacana, Limestone County. Important extensions were made to the following fields: Bazette, Navarro County; Long Lake, Anderson and Leon Counties; Cayuga, Anderson, Freestone and Henderson Counties; Opelika, Henderson County; and Talco, Titus and Franklin Counties. At the close of the year 54 oil and gas fields were producing in the district. There were 13 other fields, 11 oil and 2 gas, which have been abandoned. The East Texas field led the district in the number of completions for the year. During the year about 622 wells (oil and distillate wells included) were completed and 80 wildcats were drilled. Production and Proration During the year 170,424,685 bbl. of oil (distillate production included) were produced in the district—a decrease of 2.6 per cent from the 175,053,729 bbl. (distillate production included) during the preceding year. The district's production for the year 1938 was 182,369,484 bhl. As usual, most of the district's annual production was in the East Texas field, which produced 139,095,694 bbl. (distillate production in- cluded) during 1940, or 81.6 per cent of the total oil produced as compared with 141,333,317 bbl. (80.7 per cent) for 1939. The December estimated daily average production in the district was 424,565 bbl. The district accounted for 34.9 per cent of the state's annual production, compared to 36.7 pcr cent of the state's 1939 production. The decrease in production for 1940 may be attributed to changes made in proration schedules. Any material changes in the district's annual production may be considered for the most part as a reflection of proration-schedule changes affecting the East Texas field, since it is by far the most important field in the area. The entire state was subject to 71 shutdown days for the year; the East Texas field to 131; and the Rodessa field (Cass County, Texas, portion) to 5 days. No important changes were made in field rules and regulations during the year regarding the allocation of oil in individual fields in this district. Discoveries The Hawkins field is in southeastern Wood County in and principally north of the town of Hawkins. Development to date indicates that the field is somewhat of an elongated anticline trending slightly east of north and the proved oil area appears at this time to cover approximately 4000 acres. The oil production has been secured from the Woodbine sand, Upper Cretaceous; a considerable quantity of gas has been encountered in the Sub-Clarksville formation (Eagleford shale) in the higher part of the structure. It appears that a free gas

Jan 1, 1941

By D. C. Williams, D. V. Carter

Four oil discoveries were made in east and east central Texas during 1940, three of which represented new fields. In the Chapel Hill field, Smith County, oil was found where formerly only gas and distillate were produced. The three oil fields discovered are: Hawkins, Wood County; Pittsburg, Camp County; and Tehuacana, Limestone County. Important extensions were made to the following fields: Bazette, Navarro County; Long Lake, Anderson and Leon Counties; Cayuga, Anderson, Freestone and Henderson Counties; Opelika, Henderson County; and Talco, Titus and Franklin Counties. At the close of the year 54 oil and gas fields were producing in the district. There were 13 other fields, 11 oil and 2 gas, which have been abandoned. The East Texas field led the district in the number of completions for the year. During the year about 622 wells (oil and distillate wells included) were completed and 80 wildcats were drilled. Production and Proration During the year 170,424,685 bbl. of oil (distillate production included) were produced in the district—a decrease of 2.6 per cent from the 175,053,729 bbl. (distillate production included) during the preceding year. The district's production for the year 1938 was 182,369,484 bhl. As usual, most of the district's annual production was in the East Texas field, which produced 139,095,694 bbl. (distillate production in- cluded) during 1940, or 81.6 per cent of the total oil produced as compared with 141,333,317 bbl. (80.7 per cent) for 1939. The December estimated daily average production in the district was 424,565 bbl. The district accounted for 34.9 per cent of the state's annual production, compared to 36.7 pcr cent of the state's 1939 production. The decrease in production for 1940 may be attributed to changes made in proration schedules. Any material changes in the district's annual production may be considered for the most part as a reflection of proration-schedule changes affecting the East Texas field, since it is by far the most important field in the area. The entire state was subject to 71 shutdown days for the year; the East Texas field to 131; and the Rodessa field (Cass County, Texas, portion) to 5 days. No important changes were made in field rules and regulations during the year regarding the allocation of oil in individual fields in this district. Discoveries The Hawkins field is in southeastern Wood County in and principally north of the town of Hawkins. Development to date indicates that the field is somewhat of an elongated anticline trending slightly east of north and the proved oil area appears at this time to cover approximately 4000 acres. The oil production has been secured from the Woodbine sand, Upper Cretaceous; a considerable quantity of gas has been encountered in the Sub-Clarksville formation (Eagleford shale) in the higher part of the structure. It appears that a free gas

Jan 1, 1941

President MRS. THOMAS T. READ 9 Windmill Lane Scarsdale, N. T. First Vice-President MRS. FELIX E. WORMSER Acorn Lane Larchmout, N. T. Second Vice President MRS. W. SPROTT BOYD The Carlyle, Madison Ave. and 76th Street New York, N. Y. Third Vice-President MRS. LOREN W. KEMP El Chico, Plainfield Avenue Metuchen, N. J.

Jan 1, 1944

By H. D. Outmans

Present first-order theory for frontal stability and viscous fingering of immiscible liquids is improved by including the nonlinear terms in the equations describing conditions at the interface of the liquids. This leads to the revision of several conclusions which were based on first-order theory. They concern the growth rate and changing shape of a sinusoidal disturbance, particularly in relation to the wave number of this disturbance. Nonlinear aspects of effective interfacial tension are discussed and it is shown that this tension is not simply a positive proportionality constant in a linear relation between pressure difference and curvature at the interface. Scaling requirements are determined from the dimensionless groups which govern fingering. Gravity and interfacial tension invalidate a previously formulated conclusion that the shape of a finger after a given displacement is independent of the displacement velocity. Also, similarity of fingering (and, hence, of sweep efficiency in case of an unstable front) requires geometrical similarity of the initial disturbance in the model and the reservoir with a scale factor which is the same as the one for scaling down the dimensions of the reservoir. INTRODUCTION The critical velocity at which the transition zone in the vertical displacement of immiscible liquids becomes unstable was calculated by ill. More recently, the same was done for nonvertical displacements and it was also shown that the stability is affected by an effective interfacial tension between the liquids. 2-4 Although in the oil reservoir a stable front is always desirable from a recovery point of view, the necessary velocity may have to be so low that the corresponding production rate is not economical. In that case, a knowledge of the fingering unstable front is necessary for predicting recovery at break- through. Studies in this direction have not gone beyond the very moment at which fingering first occurs.5,6 Conclusions about stability and fingering in these references are all based on linear theory. In this theory the nonlinear terms in the equations describing conditions at the front are neglected. The usual justification for this lack of mathematical rigor is that the nonlinear terms can be made small relative to the linear terms and, supposedly, small causes produce only small effects. It has been recognized, however, that this is not necessarily true in the nonlinear problems of hydrodynamics.7 The hydro-dynamic stability and fingering of the front between two liquids, accelerated in a direction normal to the front, for instance, is strongly influenced by the nonlinearity of the boundary conditions.8-10 Since these boundary conditions are not unlike those arising in the problem of stability and fingering of the front during a slow immiscible displacement in porous media, it was thought that there, too, the nonlinear terms should be taken into consideration. A summary of the results obtained in linear theory and a comparison with experimental data precede the nonlinear theory developed in this paper. This summary serves to introduce some quantities which will be used in the further develop ment. It should also be pointed out that the method of higher-order approximation by which the nonlinear stability problem is solved has application in other reservoir studies.11 SUMMARY OF LINEAR THEORY 1. A plane interface remains stable if its velocity is smaller than a critical velocity. vc = (p2-p1)gn/(l/A2- l/A1 .........(1.1) This equation is derived for uniform flow in a thin layer inclined to the horizontal plane. The displacement takes place in a direction normal to the intersection of this layer and the horizontal plane. The undisturbed (line) interface is normal to the velocity. Fluid 1, the upper fluid (gas), is displacing Fluid 2 (oil). (VcQS would be the injection rate in cc/

By L. J. West, R. M. Perrry

This chapter describes the rock mechanics studies performed for a high cut at a nuclear power station in Pennsylvania. Two units presently are being constructed on the Susquehanna River. When these units are completed, they will generate approximately 2100 MW of electricity. It was necessary to excavate about 1 million cu yd of rock to prepare the site. This excavation resulted in a high cut on the west and north sides of the station area with a maximum height of about 200 ft. The location of the high cut with respect to the plant facilities is shown on Fig. 1. The recommended slope angles ranged from 1 ½ (horizontal) to 1 (vertical) for the upper residual soil to ½ to 1 for the deeper competent rock. Because of the significant height of this cut and the fact that the slope is immediately adjacent to the proposed nuclear facilities, extensive stability analyses were performed prior to, during, and after excavation to evaluate the steepest angle at which the slopes could be safely cut. The studies consisted of evaluating both qualitatively and quantitatively all apparent factors which could affect the stability of the slopes. These factors include the strength of the material, the zones of weak material which are present along the planes of schistosity, the prominent joint systems, the ground water, and postulated seismic effects. FIELD AND LABORATORY STUDIES A comprehensive program of field explorations was performed to evaluate the geologic characteristics of this site. This program consisted

Jan 1, 1970

By G. Richards Gwinn

Graphite is one .of the so-called minor nonmetals that have become of major importance during the present conflict. Requirements of the domestic industry for graphite are relatively small and uses have changed so greatly in the past 25 years that different types, with few exceptions, are more nearly interchangeable in use. However, the quality of the graphite required for crucibles is exacting and under present manufacturing practices only a small part of the world production can be utilized economically by this industry. Graphite, for the domestic crucible industry, was supplied almost entirely by imports from Madagascar and Ceylon before the present war. The quantity required has been increased by the war and the greatest demand is for Madagascar flake. The fall of France to Germany in 1941 and the Japanese expansion southward threatened our supply of crucible-grade graphite, therefore the domestic industry was revived to supplement imports and to act as insurance in the event of complete stoppage of imports. Two plants were constructed for the Government, one at Ashland, Alabama, called the Crucible Flake Graphite Co., operated by Haile Mines, Inc., and one near West Chester, Pennsylvania, operated by the Benjamin Franklin Flake Graphite Co. Loans were made by the Reconstruction Finance Corporation to the Alabama Flake Graphite Co. at Ashland, the Ceylon Graphite Co., at Goodwater, Ala., and the Southwestern Graphite Co., at Burnet, Texas. However, by the end of 1943 the import situation had improved and it was no longer necessary to continue Government assistance to mine and stock-pile the high-cost domestic material. Graphite is found in virtually every country of the world. Most occurrences are of no economic importance because of their poor quality, prohibitive mining and milling costs, inaccessibility, and poor location with reference to the industrial centers where graphite is used. The principal commercial deposits are found in Ceylon, Madagascar, Chosen (Korea), United States, U. S. S. R., Canada, Germany, and Mexico. Graphite is a typical international mineral in that it is utilized mainly in countries noted for industrial activities, whereas the two islands, Ceylon and Madagascar, which produce the major part of the world's high-grade graphite, are virtually devoid of any manufacturing establishments requiring its use. The industry thus is violently disturbed by wars. Types oF Graphite Used in Crucibles Graphite of various kinds and from many countries has been used for making crucibles. Passau (Bohemian) flake was first used in Europe, but by the middle of the seventeenth century crucible formulas were established largely on Ceylon graphite and German Klingenberg clay. Ceylon graphite is granular and the grains are subdivided into more or less

Jan 1, 1948

By G. Richards Gwinn

Graphite is one .of the so-called minor nonmetals that have become of major importance during the present conflict. Requirements of the domestic industry for graphite are relatively small and uses have changed so greatly in the past 25 years that different types, with few exceptions, are more nearly interchangeable in use. However, the quality of the graphite required for crucibles is exacting and under present manufacturing practices only a small part of the world production can be utilized economically by this industry. Graphite, for the domestic crucible industry, was supplied almost entirely by imports from Madagascar and Ceylon before the present war. The quantity required has been increased by the war and the greatest demand is for Madagascar flake. The fall of France to Germany in 1941 and the Japanese expansion southward threatened our supply of crucible-grade graphite, therefore the domestic industry was revived to supplement imports and to act as insurance in the event of complete stoppage of imports. Two plants were constructed for the Government, one at Ashland, Alabama, called the Crucible Flake Graphite Co., operated by Haile Mines, Inc., and one near West Chester, Pennsylvania, operated by the Benjamin Franklin Flake Graphite Co. Loans were made by the Reconstruction Finance Corporation to the Alabama Flake Graphite Co. at Ashland, the Ceylon Graphite Co., at Goodwater, Ala., and the Southwestern Graphite Co., at Burnet, Texas. However, by the end of 1943 the import situation had improved and it was no longer necessary to continue Government assistance to mine and stock-pile the high-cost domestic material. Graphite is found in virtually every country of the world. Most occurrences are of no economic importance because of their poor quality, prohibitive mining and milling costs, inaccessibility, and poor location with reference to the industrial centers where graphite is used. The principal commercial deposits are found in Ceylon, Madagascar, Chosen (Korea), United States, U. S. S. R., Canada, Germany, and Mexico. Graphite is a typical international mineral in that it is utilized mainly in countries noted for industrial activities, whereas the two islands, Ceylon and Madagascar, which produce the major part of the world's high-grade graphite, are virtually devoid of any manufacturing establishments requiring its use. The industry thus is violently disturbed by wars. Types oF Graphite Used in Crucibles Graphite of various kinds and from many countries has been used for making crucibles. Passau (Bohemian) flake was first used in Europe, but by the middle of the seventeenth century crucible formulas were established largely on Ceylon graphite and German Klingenberg clay. Ceylon graphite is granular and the grains are subdivided into more or less

Jan 1, 1948

By A. L. Field, P. H. Royster

The first report on the slag viscosity work of the Bureau of Mines was made by one of the authors1 in 1916. It was concerned chiefly with the method of measurement. A paper2 on this phase of the work was presented to the Institute in February, 1917, and a similar paper3 was communicated to the Faraday Society. PuRpose and Scope of the Slag Viscosity Tables Following the development of a suitable method, the next step in the investigation was the measurement of slag viscosity over a wide range of temperature and composition, and the arrangement of this experimental data in the form of tables for the use of the blast-furnace operator. It is believed that this information, if used intelligently, should help the operator to reduce losses in production caused by off-grade pig iron, to improve fuel economy, to promote operating efficiency, and to extend present-day practice to meet the increasing need of smelting lean and complex ores. In the experimental part of the work it was carly, observed that the temperature-viscosity relations of a slag were determined, for practical purposes, by the relative proportions of the three major constituents, lime (CaO), alumina (Al2O3), and silica (SiO2), provided the percentage

Jan 1, 1918

By C. R. Clark, G. Swift, D. S. Roberts

The purpose of this investigation was to measure PVT behavior of various types and combinations of heavy hydrocarbon components from the paraffinic, naphthenic and aromatic classes where the relative proportions Of the various components were selected to approximate those of natural gas or gas condensate systems. Synthetic mixtures were used so that the compositions Of the various components could be measured accurately. n-Heptane, methylcyclohexane and methylbenzene were used to represent the paraffinic, naphthenic and aromatic components of the heavy fraction. In the mixtures studied, the heavy fraction composition was held constant at O. O5-mole lraction, the balance being methane except for one mixture where 0.10-mo1e fraction of an intermediate component, propane, was added. The PVT data for the mixtures were determined in a variable-volume, constant-mass apparatus at psuedo-reducedtemperatures from 1.84 to 2.00, over a pseudo-reduced pressure range from 2.3 to 12.0. The experimental results showed that, regardless of the type of heavy material (paraffinic, naphthenic, aromatic, or combinations thereof) mixed with methane or methane and propane, the compressibility factors at equal values of pseudo-reduced temperature and pressure varied by less than 2.2 percent. INTRODUCTION PVT data is used for natural gas and gas condensate fluids in determining reserves of reservoirs and performance of wells, in metering produced fluids, and in recombining samples for laboratory studies. While there are vast amounts of PVT data reported for natural gas and gas condensate systems from which useful correlations have been developed, ' the compositional analyses for these systems and the resultant correlations typically were made with components analyzed through some arbitrary carbon number, usually C6, with the residue reported as a lumped "heavy" fraction. The heavy fraction was stoichiometrically recombined on the basis of an apparent molecular weight to give the final compositional analysis. It is virtually impossible to make a systematic analysis of the effect that variation of the relative amounts of paraffinic, naphthenic and aromatic constituents of the heavy fraction of natural systems might have on PVT behavior. Because there is considerable latitude in the relative amounts of these constituents, one speaks of crudes or condensate liquids as being "paraffin base", etc. It is of interest to determine if changes in the relative amounts of these three types of hydrocarbons in the heavy fraction cause significant changes in PVT behavior. If so, steps should be taken to describe better the nature of the heavy fraction in PVT correlations. If not, more confidence can be placed in the correlations presently employed. DESIGN OF THE EXPERIMENTAL INVESTIGATION We attempted to determine if changes in the base of the heavy fraction would cause significant changes in the PVT behavior of gas or gas condensate fluids. Synthetic mixtures were used to enable us to systematically vary the base of the heavy fraction and to analyze accurately the fluids. We found that the heavy fraction of naturally occurring condensate systems seldom exceeds 0.05-mole fraction. Thus, the mole fraction of the heavy fraction in the synthetic systems studied was set arbitrarily at 0.05, to maximize whatever deviations in PVT behavior that might occur. Further, we judged that since the C7 hydrocarbons normally are present in greater quantities than higher carbon number hydrocarbons in naturally occurring systems, the use of n-heptane, methyl cyclohexane, and methylbenzene to represent the paraffinic, naphthenic, and aromatic species in the heavy fraction would be most appropriate. Finally, to enable us to compare our

Jan 1, 1970

By A. J. Teplitz, J. K. Rodgers, E. M. Pohoriles

This note is presented in order to call attention to a newly developed laboratory apparatus that appears to have interesting possibilities for the study of lost circulation of the pressure-parting type, for a more realistic evaluation of sealing materials for this type of loss, and for investigation of other aspects of hydraulic fracturing. A study of lost circulation, conducted jointly by operating divisions of the Gulf Oil Corp. and the Gulf Research & Development Co., has been in progress for the past few years. Earlier phases of the study dealt with mechanical factors contributing to loss of returns in laminar type sediments.' One aspect of this type of loss which has been widely discussed in the literature and elsewhere concerns the geometry of the fractures into which such losses occur. This subject is not merely a philosophical one, but has an important bearing on procedures for combating lost circulation difficulties and on other well operations. The further course of the collaborative studies previously mentioned has produced some information on this subject which, though limited in amount, is believed to be significant. In several typical cases of lost circulation in laminated shale and sand formations, the wells have been surveyed with instruments2,3 capable of detecting the points of loss with considerable accuracy. These wells were located in the Gulf Coast of Texas and Louisiana, in the Texas Panhandle, and in the Rocky Mountain area. In each of these instances the loss was shown to be occurring at some distance removed from the bottom of the hole and sharply confined to a very narrow interval, less than 1 ft in thickness. It is rather difficult to imagine that fractures of a vertical nature' would be of the limited extent indicated by the surveys in these wells. Furthermore, the high rates of loss at relatively low pressure differentials observed in some of these instances together with the narrow intervals involved would appear to require the radial flow pattern which would be associated with a more or less horizontal fracture plane. In view of the foregoing observations and records of successful squeeze cementing operations, in attempting to construct a laboratory apparatus For simulating pressure induced lost circulation, it was decided that the design should be based on a horizontal type of fracture. It was realized that5,6 Vhe production of horizontal fractures in a formation with non-penetrating fluid requires some mechanism for transmitting vertical components of the hydraulic forces to the plane of parting. This was accomplished, as will be evident in the description of the apparatus that follows, by providing recesses in the wall of the borehole which are believed to be representative of wellbore configuration found in Gulf Coast wells. The possible influence of such borehole irregularities on both pressure fracturing and the treatment of lost circulation appears to have been neglected in many studies of these subjects. It is believed that the present apparatus, incorporating features that take into account some of the factors mentioned, will provide means of gaining a further understanding of pressure induced fracturing and possibly for more realistically evaluating the numerous sealing agents, particularly the non-time-setting materials employed in treating the pressure-parting type of loss. DESCRIPTION OF APPARATUS The test cell used in the laboratory investigations is shown in Fig. 1. A schematic diagram of the entire system is shown in Fig. 2.

Jan 1, 1956

By David A. Thomas, Eugene S. Meieran

MECHAMCAL, electrical, and other property measurements are often more easily made on wires than on sheets. In order to carry out transmission electron microscopy on the same material used for property determinations, we have developed a method for preparing thin foil specimens of wires. The technique was developed for 0.030 in. diam tungsten wires, and is a modification of the thinning techniques used by Wilsdorf, et al 1 A length of wire is first ground to about 0.010 in. thick by mounting the wire in low melting temperature wax, hand grinding a longitudinal flat, removing and reversing the wire in the mount, and then grinding a second parallel flat. The 0.030 in. wide and 0.010 in. thick strip is cut into 1/8 in. lengths to fit in the specimen holder of the electron microscope. Next the specimen is gripped in platinum-tipped tweezers (the anode) and placed 2 mm below a hol- low copper cathode with a 0.010 in. ID nozzle. Electrolyte, 10 pct NaOH, flows by gravity feed through the nozzle onto the specimen, as shown in Fig. l(a). Polishing is carried out until a shallow impression is made on one surface, and then the specimen is turned over and the opposite surface indented. The metal between the two impressions should be about half the specimen thickness, as is shown by the heavy line in the cross section in Fig. l(b). The entire specimen is then electropolishedin 2 pct NaOH until a hole appears at the location of the indentations. The apparatus is shown in Fig. 2, and is essentially the same as that used by Wilsdorf et al. at The Franklin Institute. Light is reflected by a mirror onto the bottom surface of the specimen! which is viewed by a stereoscopic microscope placed above it. Polishing is carried out until light is seen, indicating that a hole has formed, and then immediately stopped. The specimen is washed in water. alcohol, and ether, and is then ready for examination. The specimen should be reversed in its platinum clip during electropolishing to insure equal polishing on both sides of the impression. For tungsten, indenting at 120 v and 0.04 amp takes less than 1 min, and final polishing, at 10 v and 1 amp, less than 5 min. The portion of the specimen available for transmission microscopy surrounds the hole, as is seen by the dashed lines in Fig. l(b). Slight electroetch-ing accompanying electropolishing reveals the mi-crostructure, as seen in Fig. 3(a) by light microscopy. Low-magnification electron microscopy, as in Fig. 3(b), enables the same areas and grains to be viewed and identified when subsequently examined at high magnification. Fig. 4 is a typical structure of

Jan 1, 1963

By W. David Leyshon

This paper compares the general characteristics of Florida phosphate rock for the manufacture of fertilizers and phosphoric acid. The subjects covered are relative reactivity for superphosphate manufacture and various properties of the rock for use in phosphoric acid production, including gypsum filterability, sulfuric acid consumption, foaming, relative cor-rosiveness, chemical composition, and others. Comprison will include rocks of North Africa, the western U.S., and other locations. This paper reviews some of the important properties of phosphate rock, giving particular attention to a comparison of Florida phosphate with some of the major phosphates produced in the world. It also discusses some of the techniques available for evaluatine Phosphate. rock for phosphoric. acid and fertilizer use. The use of Florida rock outside the U.S. has been increasing steadily, evidence in itself of certain desirable properties of this rock. Table I is a list of the major producers and exporters of phosphate rock as of 1965. Florida, meaning in this case Central Florida, was the largest producer of phosphate rock and the largest exporter of rock. Of a total world production estimated at 60 million tons, about 50 million tons were produced during 1965 by the areas listed in Table I. One major producing area omitted from Table I and from subsequent evaluations in this paper comprises Nauru, Ocean, and Christmas Islands, whose output totaled about three million tons in 1965. This phosphate is marketed entirely by the British Phosphate Commissioners, primarily in Australia and New Zealand, and does not get into the world market elsewhere to a significant degree at the present time. South Africa, Egypt, Israel, and North Vietnam also produce lesser quantities of rock for the international market, and these materials are also excluded from this review. The phosphate industry is now seeing the introduction of several new areas that will be significant factors in the rock market in the future. The North Carolina and North Florida areas each have capacity at present or in the near future for producing about three million tons per year. The Djebel Onk mine in Algeria has a potential of about 800,000 tons per year. In addition, announcements have been made of significant development of deposits in Peru and in the Spanish Sahara, and sizable expansions are planned in several of the existing areas that are now of minor importance. Competition for the rock market appears to be increasing so that more attention will probably be paid to evaluating phosphates available from different areas. It is not possible here to go into all the properties of even a few of the materials listed in Table I. However, it is practical to discuss some comparative properties important for making phosphoric acid and fertilizers, and to touch on the techniques used for the evaluation of various phosphate rocks. Table II gives typical analyses of the major phosphate rocks available in the world as of 1965. There is, of course, an inherent danger in labeling any analysis as typical, but it appears that variations between two samples of rock within one given area are generally less than between two samples from different areas. The analyses listed were compiled from several years of data so they may not be representative of the present output of any particular area. The range of grades represented by these analyses goes from 66 BPL for Gafsa rock to 85 BPL for Kola

Jan 1, 1968