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By William A. West

One manifestation of anelastic properties in solids is the mechanical elastic aftereffect, which may be described briefly as follows: If a stress is applied to a solid body, a deformation or strain is produced. On removal of the stress, this deformation disappears, at least in part. As a first approximation, this appearance or disappearance of deformation usually has been considered instantaneous. Actually, however, for a very wide variety of substances, on application of stress the instantaneous deformation is followed by a further slow yielding, which continues, although at a rapidly diminishing rate, for as long as the stress is applied. Similarly, on removal of the stress, the instantaneous recovery from deformation is followed by a further slow recovery, which continues, although at a rapidly diminishing rate, often for a long time. This latter phenomenon has been called the "elastic after-effect." Experiments upon the elastic after-effect in metals, when properly designed and when properly interpreted, are capable of giving quite precise information regarding the relation between stress and strain in the various constituent parts of the metal. For example, if certain parts of the metal, such as grain boundaries or slip bands, behave in a viscous manner—that is, if therein—the relaxation spectrum will contain lines or bands associated with the relaxation of shear stress within these parts. No attempts have heretofore been made to utilize elastic after-effects for obtaining such detailed information. The purpose of the present paper is to explore the possibilities of properly designed and interpreted experiments on the elastic aftereffect in metals. Since new procedures and principles are employed in this study, an attempt has been made to record each step taken. Elastic after-effect observations are susceptible of simple interpretation only when the stress level employed is so low that all effects are linear with the stress. Just how low the stress level must be can he determined only by experiment. An advnntage, other than simple interpretation, is associated with low stress levels. When all effects are linear, derived quantities, such as the relaxation spectrum, are independent of the stress distribution. It is, furthermore, possible to employ the type of deformation that is most convenient from the experimental standpoint; for example torsion. It appears that in experiments involving both loading and unloading the following would be observed: I. Instantaneous deformation, recoverable instantaneously in whole, or in part. 2. Delayed deformation, recoverable slowly in whole, in part, or not at all. 3. Permanent deformation, the difference between total deformation and total recovery. In the work here described, unloading experiments only were made. Wires were

Jan 1, 1947

By C. Ernest Birchenall, Robert F. Mehl

Application of diffusion laws in the customary form to experimental studies in binary metallic solid solutions has shown the diffusion cocfficient to vary with concentration for all systems investigated. The factors determining this variation have not been ascertained. However, the question of whether the diffusion coefficient would become a constant, independent of concentration throughout a single phase if the concentration gradient in the diffusion equation were replaced by an activity gradient has been an attractive subject for speculation. Wagner¹ derived an expression for the force acting on a diffusing particle in terms of the chemical potential. This was also the approach chosen by Jost2 in his monograph. From a somewhat different point of view, Eyring3 and his co-workers have used activity gradients when dealing with diffusion in concentrated nonideal solutions. The only actual test with experimental data is that given by Darken,4 though this is more qualitative than quantitative. Many others opposed the application in any way of thermodynamic concepts to kinetic phenomena, including diffusion processes. A rigorous examination of this principle requires good data expressing the relationship between activity and concentration for solid solutions for which reliable diffusion work has been done. The literature provides such information only for the interstitial solution of carbon in gamma iron (austenite) and for the substitutional copper-zinc solutions (alpha brass). Activity data for carbon in austenite at 800°C and 1000°C are available from the recent work of Smith5 on the equilibrium of hydrogen-methane and carbon monoxide-carbon dioxide mixtures with gamma iron. Combining these with the diffusion studies of Wells and Mehl6 makes possible a quantitative test for this interstitial solid solution. The vapor-pressure determinations for zinc over brass by Hargreaves7 allowed the calculation of activities in this system over a wide range of temperatures and concentrations. Extensive investigation of diffusion in this substitutional solid solution has been carried out by Rhines and Mehl.8 Activities in Brass9 If the vapor phase of zinc is assumed to behave as an ideal gas, any solid or liquid solutions that are in equilibrium with the same partial pressure of zinc at the same temperature have the same thermodynamic activity of zinc. In order to assign a numerical value to the activity azn, it is necessary to choose some standard reference state to which an activity value of unity is arbitrarily assigned. It is customary to choose the liquid or solid state of the pure material. Then azn is defined numerically by

Jan 1, 1947

By C. S. Smith, E. W. Palmer

IN 1934, when Gregg and Daniloffl wrote their excellent monograph on the alloys of iron and copper, the most recent literature on the constitution of the alloys indicated a narrow single-liquid area for 20" above the liquidus with a closed liquid mis-cibility gap above this. Since that time, however, a number of investigators have confirmed the much earlier studies of Mushet2 and Stead3 who, among others in the nineteenth century, had described the true state of affairs. Liquid copper and iron are completely miscible in the absence of carbon, but small amounts of carbon cause liquid segregation. In 1934, one of the writers' mentioned evidence for the absence of liquid separation in carbon-free alloys at temperatures up to 1700°C. Two years later, Mad-docks and Claussen5 unequivocally established the absence of liquid segregation and published a revised diagram, reproduced in fig. 1. They also studied the limits of the two-liquid area in ternary alloys of iron, copper, and carbon as a function of carbon and iron content. In the same year Simpson and Bannister" and Schumacher and Souden7 described in some detail the properties of alloys containing 50 to 75 pct Cu. More recently Hodges et al.16 have developed the copper-rich alloys for use as high-strength conductors. In 1937, Iwase, Okamoto, and Ameniya8 published data on the miscibility gap in ternary alloys of iron, copper, and carbon that supported the conclusions of Maddocks and Claussen, and definitely located the two-liquid area at temperatures of 1450" and 1540°C. They also reported that additions of 1 pct Al, Ni, Pb, Sn, or Zn caused no segregation in 50 pct Cu alloys at 1540°C. The use of copper in amounts approximating 1 pct has found industrial employment to an increasing degree in both wrought and cast steels, for such steels are capable of being precipitation-hardened following normalizing, and have high yield strengths. This is summarized by Gregg and Daniloff,1 Sallitt,9 and Lorig and Adams,10 while Alexander" gives additional information on the heat treatment of copper-steel castings. Lippert12 has described Digby's two-phase steels containing copper and chromium. The work described in the present paper was done in the years 1932 to 1934, at which time much of the information was new. The excellent work subsequently done in other laboratories but more promptly published makes the present paper in part only a confirmation of what is now well known. There has not, however, been published any unified study of

Jan 1, 1951

R. F. McELVENNY.- The next item is: "Center and other methods, vs. side charging." That was all discussed in the Carson case, and I do not know but what many of the plants are still using center charging. Some are using side charging. Did I understand that where you use the wet charge it is all side charging on the wet ore? B.-G. C. HONEYMAN.- We were on center charging for about a year with wet ore. R. F. McELVENNY.- Then you went to side charging. Has anyone any remarks to make on side versus center charging? E. A. BARNARD.- We have one side and one center, both on deep bath. It is an experimental proposition so far, but the side charge looks very favorable.. R. F. McELVENNY.- This is with calcine? E. A. BARNARD.- This is with calcine on a floating charge proposition.. They are both water jacket. The charge acts very similar on both center and side charging. The calcine spreads much the same as it does on the center charge. It will run down 75 ft. on the furnace side as well as the center. The advantage is in taking care of secondaries and things of that nature. C. BARDWELL.- Do you get any side wall protection from it? E. A. BARNARD.- No. R. F. McKENZIE.- Do you not project the side wall up to protect the skewback? E. A. BARNARD.- There is a slot projection down around the top of the bath; but the repairs on the side wall have been practically the same; that is, they, have been practically the same as they have on the center charge. A. H. RICHARDS.- A point I would like to make is that if you have any doubt about the center charging, we feel that we get better tonnages and lower fuel ratios and better slags with center charging than we ever got with side. Different kinds of charges would, of course, vary, and I could readily see that if you had the same advantage with deep bath smelting that you mention you would probably get just as good a slag and as good fuel ratios. E. A. BARNARD.- In fact, I think the calcine charge spreads more on the side than on the center charge. A. H. RICHARDS.- If you maintain a deep bath. E. A. BARNARD.- That is one thing we have to be careful about, to hold the charge back.

Jan 1, 1930

By P. W. Andrews, R. B. Toombs

ECONOMIC STRUCTURE OF MODERN INDUSTRIAL ECONOMIES The role of minerals in modern industrial economies may be examined in several ways. There are relationships with the various sectors of the economy: the primary, secondary, and tertiary industrial groupings and activities. Mineral supply and demand activities can be measured in terms of national accounts criteria. The economic policy objectives of the modem industrial economy are based to a considerable extent on the needs of the nation for economic supplies of miner- al materials. There is an important role for minerals relative to national security in peace and in wartime and many national policies are directed toward ensuring adequate sup- plies of minerals. Environmental control in the modem industrial economy is increasingly concerned with matters related directly to the production and use of minerals and these matters, in turn, bear importantly on conservation in mineral supply and demand. Mineral polices include specific provision for research and development activities concerned with the production and the use of minerals. In all, national policy objectives will be shaped in considerable part by the circum- stances of mineral supply and demand: the relative degree of availability from domestic and foreign sources, the state of the mineral-processing industries, and the degree of development of the mineral-using industries, and per capita and total changes in requirements. Goods made from mineral raw materials are the basis of all advanced societies and although this is taken for granted, every country is continually dealing with problems of mineral supply and demand. Considering that in the first 50 years of this century the consumption of mineral materials in a highly Industrialized country such as the United States increased by six times while the population was doubling, it becomes apparent that if a country is to enjoy rapid economic growth it must have access to huge and ever-growing supplies of mineral materials at lowest possible cost. Adequate supplies of mineral materials and wise usage of mineral resources have always been among the most important determents of a nation's survival The importance of access to adequate mineral supplies is increasing every year and this has significant international, as well as national, implications because of the unique locational characteristics of mineral resources. It is generally acknowledged that no particular type of natural resource is essential to a high level of national income or to economic progress. A country's endowment of natural resources need not exercise a determining influence on the course of its national income over time, provided it is able to trade. What is required for economic progress is the availability of a substantial quanti-

Jan 1, 1976

By D. L. Katz, M. J. Rzasa

The derivations of three methods of computing the static pressure gradients in natural gas wells have been presented to show the assumptions made. Charts were developed from which the pressure gradients may be read when the well-head pressure, the well fluid gravity, depth, and the average well temperature are given. A chart for estimating the well fluid gravity from the condensate content and separator gas gravity is included. The effect of the increased average well temperature after flow on the calculation of the static pressure gradient is discussed. Introduction Reservoir pressures have been calculated from well-head pressures for gas wells for many years. As the pressure measurements become more accurate, the need for a reliable calculation of the static pressure gradient often arises. This paper will develop the several methods for computing the pressure gradient in gas wells and make a comparison between them. The method of calculating static pressure gradients in common use is Eq. I (ref. I) or its counterpart which includes a factor for the deviation of the gas from the ideal gas law. P2 - P1 = P1(e0.0000347GX _ I) Eq. [I] in which P1 = pressure at well head, lb. per sq. in. abs. PP = pressure at bottom of well, Ib. per sq. in. abs. G = gas gravity X = depth of well, ft. An alternate method is to compute the average density of the gas in the well and multiply by the well depth in a manner similar to that used for liquid gradients. Derivation of Formulas A static pressure gradient is a special case of the general fluid-flow equation. Consider a pound of fluid flowing in a vertical column from point I to point 2, Fig. I. By an energy balance for fluid flowing from I to 2: U1 + P1V1 + u12/2g + X1 + q = U2 + P2V2+ u22/2g+X2 +W [2] in which U = internal energy, ft-lb. per lb. P = pressure, lb. per sq. ft. V = volume, cu. ft. per lb. u = average linear velocity, ft. per sec. X = height above datum, fl. q = heat absorbed by fluid, ft-Ib. pcr lb. W = work done by system, ft-lb. per lb. An energy balance on the fluid itself gives: U = ?TdS - ?PdV + etc. [3] in which T = temperature, deg- R- S = entropy, ft-lb. per deg. R. per lb.

Jan 1, 1945

By D. S. Pye, J. P. Gallus

Successful hydraulic pressure treatment of oil and gas wells that have long producing intervals, multiple pay zones, fluid thief zones, or natural or induced fractures has long been a serious problem plaguing the petroleum industry. High fluid-injection rates, straddle packers, ball sealers, and either liquid or solid additives to the treating fluids are being used to cope with this difficult and costly problem.l-6 The use of ball sealers and straddle packers is limited, in practice, to wells that have been completed with perforated cemented casings or liners. Well stimulation with ball sealers and straddle packers is usually successful as long as the cement remains competent. The other techniques of diverting are used with all types of completions. However, there are two significant disadvantages of the high rate method: excessive horsepower requirements, and the need of large treating-fluid volume. Consequently, most well stimulation techniques that involve diverting depend upon ball sealers or granular materials. Liquid diverting agents, and some of the solid ones in use today, frequently will cause formation damage. On the other hand, the most popular particulate diverting agents often are so soluble in the treating fluid that they become largely ineffective; their particle size is severely reduced as they dissolve while being transported through thousands of feet of pipe to the formation face down hole. In our attempts to deal with the shortcomings of these diverting agents, we experimented with a large variety of potentially suitable deformable materials the solubility of which could be controlled. Following are the criteria for the diverting agent sought: 1. The material must be effective in reducing fluid loss to thief zones, including existing fractures and very high permeability layers in the formation to be pressure treated. 2. The material must have enough strength to bridge under the treating pressure. 3. The material must be insoluble or slowly soluble in the treating fluids so that the particles retain sufficient size to be effective after they reach the formation face. 4. The material must be completely soluble in the produced oil or condensate liquid so that it can be removed readily; it must not cause formation damage. A number of products consisting of various polymers blended with waxes and other solid hydrocarbons were examined. All these materials satisfied the criteria for a diverting agent and also exhibited some degree of plastic deformability. On the basis of initial tests of strength and hardness, several blends of wax and polymer were selected for extensive testing in the laboratory and the field. These compounds have congealing temperatures ranging from 140 to 190F; they are insoluble in water and soluble in oil. They conformed, therefore, to the criteria specified for a theoretically superior diverting agent. Laboratory and field tests were conducted using these wax-polymer materials to demonstrate that the use of a deformable diverting agent can significantly improve fluid diverting performance. Data in this

Jan 1, 1970

By F. W. Glaser, Benjamin Post

A LTHOUGH most transition metals form a wide variety of boride compounds, the existence of only one zirconium boride, ZrB2, had been established prior to this investigation.' The crystal structure and some properties of a hitherto unreported zirconium boride, ZrB12, are described in this paper. Only one other dodecaboride of a transition metal, UB12, has been reported up to the present.' Chemical analysis of the new compound showed 44 pct Zr and 56 pct B, compared with 41 pct Zr and 59 pct B computed for ZrB12. The difference is within the range of error of the analytical method employed. ZrB12 shows marked metallic properties. It is obtained as a fine black powder. Measurements of electrical resistivity were made at —79°C, + 22°C and +64°C. At 22°C the electrical resistivity is approximately 60 microhm-cm. Over this range the temperature coefficient of resistivity is +0.00162. The thermal conductivity at room temperature is 0.122 watts per cm per "C. The product of the electrical resistivity and thermal conductivity is therefore 8.05, which is not far from the normal Wiedemann-Franz ratio (approximately 7.5 at room temperature). These measurements were made on hot pressed samples which were not always high density specimens. The hardness of ZrB12 on the Rockwell A scale varies between 92 and 92.5. Crystal Structure Determination Single crystals of ZrB12 of a size suitable for X-ray diffraction analysis could not be obtained and powder samples had to be used. Filtered Cu radiation was used throughout. Powder diagrams were indexed on the basis of a face-centered cubic unit cell. After correction for film shrinkage, a Bradley and Jay extrapolation³ to ? = 90" indicated that a, = 7.408 ±0.002A. The volume of the unit cell is 406.5A.V he assumption that there are four "molecules" of ZrB12 per unit cell leads to an X-ray density of 3.63 g per cc. The measured density is 3.7 g per cc (as measured by the immersion method). Relative intensities of reflections were determined by integrating the intensities of diffraction peaks using the count register of a North American Philips wide range spectrometer. Intensities measured in this way showed good agreement with photographic intensities estimated visually using multiple film techniques. The usual Lorentz, polarization, and multiplicity corrections were applied to the observed intensity measurements. There are striking similarities between ZrB12, and UB12. The unit cell of the latter is also face-centered cubic and contains four molecules. a, = 7.473, compared with 7.408 for ZrB12. The radius ratio rB/rU is 0.57; rB/rZr is 0.54. In both ZrB12, and UB12 the four metal atoms in each unit cell are in special positions; only the boron positions need be determined. The latter may be inferred from the extent to which diffraction of X-rays by the 48 boron atoms reinforces or weakens the diffraction by the metal atoms. This effect is relatively much greater in the case of the zirconium compound. In their determination of the crystal structure of UB12, Berthaut and Blum' assumed holohedral symmetry (space group Oh5 , Fm3m) and reported that the U atoms are in positions 4(a): 000; 01/2 1/2; ½ 0 ½ ; ½ ½; the boron atoms were reported to be in positions 48(i) with x = 1/6: ½xx; ½xx; x½x; x½x; xx½; xx½; ½xx; ½xx; x½x; x½x; xx½; xx½

Jan 1, 1953

By V. Kondic, W. M. Rumball

HUNT and Jackson' have recently suggested that binary eutectics might be classified according to the entropy of fusion of the component phases. Such a classification was in fact proposed2 some time ago by the authors and the purpose of this communication is to present some supporting evidence. As pointed out by Hunt and Jackson' typical metals of low entropy of fusion, ?S, tend to form normal eutectics (using Scheil's terminology3). Where one phase is metallic (low ?S) and the other nonmetallic (high AS) then anomalous structures are formed. These anomalous structures may either be regular (e.g., Bi-Sn)or irregular (e.g., A1-Si). Finally Hunt and Jackson suggest that where both phases are of high ?S regular faceted structures are formed. In the proposed classification2 the ratio of the entropies of fusion is taken as the quantitative parameter, i.e., ?Sa/?SB = E, where e > 1.0. An extensive literature survey has been carried out2,4 for reliable photomicrographs of eutectic structures. The structures, numbering 151, have been classified into two classes, viz., normal (i.e., lamellar and rodlike) and anomalous. The latter group has been arbitrarily subdivided into regular and irregular anomalous eutectics. Details and sources of the structures are given elsewhere.2,4 In the absence of better thermodynamic data the value of E has been determined for each of the systems making the following assumptions and approximations: l) The entropy of fusion of solid solutions may be calculated additively;5 ii) Inter metallic compounds are treated similarly but with the addition of the following term for fully ordered structures.5 -4.573(Ni lOg10 Nl + N2 log10 N2) where Nl and N2 are the atomic fractions. It might be argued that the entropies of fusion are meaningless as the eutectic phases form at some temperature (T,°K) below their true melting point (Ta or Tb). As AS, = Lo/To if La the latent heat of fusion of a, is assumed independent of temperature, the actual entropy change AS& is given by La/Te. The ratio of entropies of fusion then becomes Fig. 1 shows E' plotted against cumulative totals for normal and anomalous systems from which it is seen that normal eutectics predominate at low values of E'; e.g., some 90 pct of normal systems lie below E' = 1.5 with 65 pct of anomalous systems above this value. Fig. 1 also shows that the regular anomalous structures occur mostly at low values of c' possibly suggesting growth more akin to normal than anomalous growth. The choice of c as a classification parameter was based on nucleation concepts, it being observed that metals widely separated in Sundquist and Mondolfo's8 nucleation series were anomalous and those close together normal. The basis of these classification views is really outside the intended scope of this communication but it is hoped to explain them fully in the near future.7 Having arrived at this entropy of fusion classification by nucleation considerations it is interesting to note that Hunt and Jackson's ideas are based on growth considerations. Elsewhere one of the authors4 has shown that an even better classification of the metallographic structures reviewed is obtained from purely conventional heterogeneous nucleation concepts. It has been found that systems having a value of the parameter +b less than 0.28 are almost certainly normal and above this anomalous: V, is the gram atomic volume. This parameter is nevertheless closely related to c and c', these being an approximation of p. The parameter is also related to the other classification3,8,9 which have met with any success in the past. All these classifications are to be reviewed shortly by the authorsU7 A significant thing about the classifications based on

Jan 1, 1968

By S. A. Mersol, C. T. Lynch, F. W. Vahldiek

The room-temperature Knoop hardness of single -crystal titanium diboride has been determined. Variations in microhardness have been correlated with orientation and structural imperfections in the crystals. Maximum differences in hardness values of 750 kg per sq mm with respect to orientation and 450 kg per sq mm with respect to substructure were found. The effects of etchants, load on indenter, and degvee of cracking of indentation were studied. The average hardness was determined as 2800 kg per sq mm on the as-grown crystals. Annealing increased the average hardness to 3375 kg per sq mm. ThE microhardness of polycrystalline titanium diboride approximating the stoichiometric composition TiB, has been studied by several investigators. The values for the Knoop hardness number range from 2710 kg per sq mm (Khn = 2710 kg per sq mm) to 3400 kg per sq mm.'-4 Samsonov et al.' reported a Vickers hardness number of 3400 kg per sq mm (Vhn = 3400 kg per sq mm) at 120-g loads for a 98 pct Ti + B material of 96 pct theoretical density. Recently Dunegan measured the Vickers hardness and obtained 2060 kg per sq mm with a 10-g load (Vhnlo = 2060 kg per sq mm), 1425 kg per sq mm for Vhnloo, and 1320 kg per sq mm for Vhnlooo. We have obtained a Khnloo = 3000 * 350 kg per sq mm for hot-pressed polycrystalline TiB2 that was 99.1 pct Ti + B and 96.6 pct of theoretical density. The present investigation has been made on single-crystal titanium diboride boules, and is believed to be the first such study on TiB, crystals of known orientation. EXPERIMENTAL The single crystals were prepared by a Verneuil-type process using an electric arc by the Linde Division of Union Carbide Corp. The largest specimens were 6 mm in diameter by 12 mm long. The crystals were of theoretical density (4.50 g per cm3) with a Ti + B content of 99.8 pct. The major impurities present were: 0.03 pct (by weight) 0, 0.06 pct C, 0.01 pct Si, 0.05 pct Fe, 0.01 pct Cr, and 0.01 pct Ni. The crystals were boron-rich, the average boron content being 31.S7 wt pct (stoichiometric value is 31.12 wt pct), and titanium-poor, the average titanium content being 68.2 wt pct (stoichiometric value is 68.88 wt pct). Titanium was determined gravimetrically by cupferron precipitation and boron by titration of H3B03 from a NaOH-fused specimen after removal of titanium with BaC03. The outer edge of the boule accounted for some of the excess boron. An electron-microprobe analysis showed that the titanium content increased from 60.0 wt pct at the edge to 68.5 wt pct at D, ~ 1000 p, where D, = distance from outer edge (see Fig. 5). X-ray measurements indicate that the boules are single crystals with considerable substructure. Upon etching this structure is seen in the form of a Widmanstatten-type rhombohedral line pattern in the basal (c) plane and a parallel "lines" pattern in the prism (a) planes. A typical WidmanstHtten-type pattern is seen in in Fig. 1. Electron microscopy reveals that the lines are less than 1 p across, which does not allow direct electron probe or microfocus X-ray determination of their composition. The identity of the second phase has not been established. It might be a higher boride or a nonstoichiometric TiB2. On annealing above 2200°C the precipitate is dispersed and dissolves in the matrix. The best etchants found were HF/HNO/HO, KF(CN)$NOH/HO (Murakami's Etch), and A large number of other etchants were previously Studied. The acidic etchant produced an acicular or "needles" pattern in the (a) planes which is an etchant effect on the "lines" pattern.

Jan 1, 1965

By Arthur Hockman, Howard W. Jaffe, Howard F. Carl

THE problem of establishing practical techniques for evaluating natural corundum ores arose from the desire to improve the existing purchase specifications for crystal corundum procured by the Federal Government for stockpiling. Such purchase specifications had been developed for a large number of products, including minerals and ores considered to be critical and strategic because of the country's dependence on foreign sources of supply. It will be apparent to anyone considering the subject of purchase specifications that the determination of whether or not a submittal meets the specifications is a prime consideration. Consequently satisfactory specifications for minerals should not only incorporate physical, chemical, and mineralogical requirements that are practical but should also establish the means by which both buyer and seller can be assured that materials meet stated requirements. The Munition Board's Material Purchase Specification for corundum, dated February 1954, covered two grades of crystal corundum intended primarily for abrasive use. It established limits of size and of composition: Grade A, at least 95 pct +3 mesh and 92 pct alumina (Al2O3); Grade B, at least 95 pct +7 mesh and 90 pct alumina. It also specified that "of each lot of material, not less than 95 percent shall have a hardness equal to or exceeding nine (9) on Moh's Scale." These specifications were unsatisfactory for several reasons. They did not allow the purchase of lower grades of corundum being used by industry. Neither did they specify exactly what a corundum ore actually was, except that it should contain so much alumina and have a certain scratch hardness. Nothing was said about the abrasive qualities of the material that was to be purchased primarily for abrasive use. During the period 1946 to 1948 supplies of the two grades defined in the then current specifications continued to decrease. Early in 1949 industry recommended that the finer sizes of corundum known as "crystal corundum concentrates," ¼-in. to 16-mesh material, be added to the stockpile specifications and that lower grades of crystal corundum also be included. In the spring of 1949 the National Bureau of Standards and the Bureau of Mines were asked by the Munitions Board to cooperate in developing more practical specifications for grading natural corundum ores. The National Bureau of Standards indicated that it would investigate physical test methods for determining abrasive characteristics of corundum, and the Eastern Experiment Station of the Bureau of Mines at College Park, Md., stated that it would consider the mineralogical aspects of the problem. Members of these two agencies, in consultation with representatives of the Office of Materials Resources of the Munitions Board and of the Federal Supply Service of the General Services Administration, and with the cooperation of industrial suppliers and consumers of abrasive corundum, developed, in a fairly short time, more practical specifications for six grades of corundum ores. The new specifications, issued January 1951, were for corundum, natural crystals, as by this time high-purity synthetic corundum was available and widely used. Nevertheless, for certain specific applications the natural product was preferred over the synthetic material. It has been extensively used in forming snagging wheels. It breaks into more or less cubical particles, whereas artificial corundum fractures into splintery shapes. These produce irregular cuts in glass, while the more symmetrical shape produces a more uniform ground surface. For this reason natural corundum has been preferred for certain types of lens grinding. Pure corundum is clear, colorless alpha alumina (A12O3), but it is rarely found in nature in this form. The most important gem varieties include the blue and yellow sapphires and the ruby. Minute impurities of titanic oxide impart a blue color,

Jan 1, 1955

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By Robert E. Green, Kenneth Reifsnider

A microscopic X-ray diffraction technique was employed for the simultaneous study of the behavior of several families of lattice planes, whose local orientatiotz changes are manufestations of internal distortions resulting from specimen deformation. Photographs taken using aluminum were single crystals 1/64 in. In diam are presented which illustrate the appearance of various types of deformation- or growth- induced structural variations. Slip and lattice bending were detected in tensile tests for strains as small as 0.1 pct. Evidence of deformation bands, lineage structure, and void formation wns also shown. AmONG the most important methods of studying internal stresses in metals is the utilization of various X-ray techniques. The general subject of X-ray metallography has been treated in a most excellent manner by Taylor,1 and the use of X-rays for the direct observation of imperfections in crystals has recently been reviewed in an article by Newkirk2 and in the book edited by Newkirk and Wernick.3 Since the inception of metallographic X-ray analysis, there have been numerous technological developments and refinements, each with its particular advantages and disadvantages and, acrording to these, its particular applications. X-ray diffraction techniques can be divided into two general categories, that of X-ray diffraction microscopy and that of X-ray diffraction macroscopy. In the former are included such methods as those of Berg-Barrett, Lang, and Schultz2,3 which are concerned with microscopic imperfections such as dislocations. The second category includes all work concerned with the study of the condition of a crystal lattice structure as indicated by the marroscopic detail in its diffraction patterns. An example of this is the study of the diffraction manifestations of inhomogeneous plastic deformation as manifested by formation of deformation bands and inhomogeneous lattice rotations. The method used in the present investigation was an X-ray diffraction macroscopy technique. The geometry and analytical aspects of the method were similar to those of Julien and Cullity.4,5 The source was collimated with a single slit in a manner simi- lar to the "parallel beam'' method of Barth and Hosemann6 except that a continuous spectrum of radiation was employed. The apparatus produced large-beam transmission Laue patterns of thin cylindrical aluminum-wire crystals, which were deformed either in tension or torsion. Although the conventional X-ray target and interposed slit were not capable of the high resolution obtainable with a fine-focus X-ray source as employed in a microfocus apparatus, resolution was a secondary consideration in our technique, and was sacrificed to obtain sufficient intensity along a sizable length of the specimen. By using a grid indexing technique similar to that of Barth,7 we were able to study several diffraction lines from various planes simultaneously. The results of these tests give additional information with regard to the inhomogeneous deformation of single crystals, and the indexing procedure used provides a correlation between portions of the test specimen and portions of a diffracted beam. EXPERIMENTAL TECHNIQUE The experimental arrangement used is shown schematically in Fig. 1. A source of continuous X radiation from a vertically mounted Machlett X-ray tube possessing a copper target and operated at 20 kv and 10 ma was passed down a horizontal lead tube 80 cm long which terminated in an adjustable vertical brass slit. The slit opening was adjusted to correspond with the diameter of the test specimen. In front of the brass slit it was possible to place a screen wire mesh, one horizontal strand of which was a lead wire which served as a fiduciary mark, the screen itself serving as an indexing system as will be described later. Behind the screen was the test specimen which consisted of an aluminum single crystal wire 1/64 in. in diameter and 3 in. long. These 3-in.-long crystals were cut from

Jan 1, 1965

By R. G. Schaal

The Magma Mine at Superior, Arizona had an unimpressive beginning as a. worked out silver mine that was purchased in 1910 for $130,000 and then incorporated into the Magma Copper Company which has been continuously mining the deposit since 1915. Copper is the principal metal produced. However, zinc, gold, silver and iron have also contributed to the total metal product. Prior to 1973, the production rate of 1500 tons per day was maintained by hoisting 4 and 5 ton pay-loads at speeds up to 1100 FPM through four small hoisting shafts. The hoists used included 8' and 7' diameter double drum, double clutched doc. and a.c. motor driven geared units built as early as 1917. One old timer that did yoeman's service for many years was an 8' Bollen Pulley with a.c. geared drive that utilized an endless rope system with mechanical grip and release mechanism built into the pulley's throat. Primary power for all of these old production hoists was 25 Hertz. Exploration that was completed in 1967 developed a reserve of 10 Million tons of 5 per cent copper which was sufficient to justify new capital expenditures for enlargement of productive facilities to 3300 tons per day. To reach the new reserves a 22' I.D. concrete lined vertical shaft was sunk to an initial depth of 48431. A 12 ½ diameter adit was bored from the mill side of the mountain to intercept the shaft at a point about 1100' below the collar. This 9200' long adit provides the right-of-way for the mine to mill railway and egress for heavy supplies from rail head as well as a conduit for potable water, electric power, compressed air and mine drainage. Mine operating levels begin 3582' below collar and thereafter have been cut at 100' vertical intervals. Skip loading stations have been installed 4282' and 46821 below collar with an in-shaft skip dump station located 800' below collar. This provides for 4500 tons of storage above the mine to mill train loading station located 1100' below collar. Ore and waste are moved horizontally from stope chutes and drift headings by rail haulage to transfer raises which channel all material to the two mentioned skip loading stations. The 22' diameter shaft crossection is arranged with the two skip compartments on the south side separated from the manway and utility compartments by the cage compartment. The cage counterweight operates in a portion of the southwest quadrant of the shaft. The hoisting plant consists of two conventional Nordberg double drum, single clutch, geared, d.c. motor driven units that are identical except for the drives and automatic controls. The drums are 15' diameter x 105" face with LeBus grooving for 2-1/8" diameter wire rope wound in three layers. Mechanical design emp1o::ed is the same as has been used for the past twenty- five years. One drum is attached to the main shaft by 2 large bolted integral shaft flenge. The loose drum is engaged by a 4-arm positive tooth clutch meshing with radially cut teeth of the clutch ring which is bolted to the drum. The drums are one-piece steel plate weldments having a finished weight of 60 tons each and are mounted upon a 36" diameter shaft that also weighs 60 tons. With the addition of brake rings, clutch, bull gear and rope, the total dead weight adds up to nearly 250 tons that is supported by just three double row spherical roller pillow block bearings. There is no bearing between the drums. All pinion shafts as veil as all head sheave journals are supported in the same type of antifriction bearings.

Jan 1, 1975

By A. R. Gregory

A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy. S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King, 1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. 5- and P-wave velocity measurements on Bandera sandstone and Solenholen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2 and by Gregory 3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fate sand by Gregory, 3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King 1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8 A new shear wave velocity laboratory apparatus has been developed for testing rock samples under elevated pressures. This apparatus employs liquid-solid interfaces as mode converters. The technique for generating pure shear waves at liquid-solid interfaces was developed from studies of critical angle methods.6 Two identical transducers are placed in contact with opposite ends of the rock sample, one transducer acting as an ultrasonic energy emitter or generator and the other acting as an ultrasonic energy receiver or motor. The P-wave energy emitted from the piezoelectric crystal in the generator transducer is converted into pure S-wave energy at the Drakeol-aluminum

By R. B. Adair, J. S. Browning

The laboratory batch and continuous flotation pilot plant tests demonstrated the technical feasibility of recovering high grade mica concentrates from weathered mica pegmatite ores of Alabama and Georgia. The research indicated that combinations of anionic and cationic collectors may be used effectively for flotation of fine size mica from weathered pegmatite ores. In continuous tests, concentrates containing 98.5% mica were obtained from the Georgia pegmatite ore; the Alabama pegmatite ore concentrates contained 98.4% mica. The recoveries were 91 and 89% respectively. INTRODUCTION The principal uses of fine ground mica are as a filler in wallboard joint cement, as a filler and surface coating for roofing, as an ingredient in paints, and in oil well drilling mud. The mineral has other uses in the manufacture of rubber, wallpaper, plastics, welding rods, electric insulation, house insulation, and textiles, and as an annealing agent in metal treatment. In recent years, more than 99% of the domestic mica produced has been scrap and flake mica (mica which does not meet specifications for sheet mica and is used for producing fine ground mica). There has been a continued increase in mica production for several years, the 1963 production of scrap and flake mica totaling 117,251 tons.1 Ground mica is obtained primarily by crushing and milling pegmatites and schists. To a lesser extent, mica is produced as a byproduct of kaolin washing and feldspar and spodumene flotation operations. The processes used in recovering mica by crushing and milling pegmatites are generally simple, consisting of various combinations of alternate roll crushers and trommel screens that separate the mica and gangue at screen sizes coarser than 6-mesh. As these processes are designed to recover only coarse mica, high losses in the plant rejects are common. Large tonnages of tailings from the crushing and screening plants have been accumulated in a number of areas. Methods for treating such products were developed by the Bureau of Mines in 1941,2 but have not been generally applied. More recently, mica flotation research has been completed and published by the Bureau of Mines.3 These methods required complete removal of 150- to 200-mesh materials from the flotation feed with consequent fine mica losses. Later, the Bureau of. Mines investigated methods for-recovering fine size mica from pegmatite ores after desliming sufficiently to remove clay materials, but not so drastically as to remove the fine sands. This report summarizes the results of these studies. The process developed was effective on pegmatite ores from two locations and should be applicable to the commercial treatment of other mica-bearing pegmatite ores and fine rejects that have been accumulated at various mica-milling operations. DESCRIPTION OF ORES The ores used in the investigation were obtained from the Dixie Mines, Inc., Heflin, Alabama, and the Ruberoid Corporation, Hartwell, Georgia. The sample from Alabama contained muscovite and quartz, with a high percentage of clay, and minor amounts of biotite, kaolin, limonite and tourmaline. The mica in the ore was essentially all minus 4-mesh in size and was free of attached mineral grains. The Georgia sample contained muscovite and quartz, with minor amounts of biotite, kaolin, and limonite. The mica in the ore, which was essentially all minus 4-mesh, was liberated. Petrographic analyses of the two samples are given in Table I. THE ANIONIC-CATIONIC MICA FLOTATION METHOD Previous investigators2,3 have reported that complete desliming of mica ores at 150- to 200-mesh was required prior to flotation with cationic collectors to obtain satisfactory selective separation of the mica from the other mineral components. Numerous tests were made at the Tuscaloosa Metallurgy Research Center to determine if some reagent combination could be used to selectively float finer size mica without complete desliming. The investigation led to development of a process using a simple reagent com-

Jan 1, 1967

By R. W. Kraft

A comprehensive analysis of the crystallographic and metallographic structure of several Al-CuAl, lamellar eutectic grains solidified under equilibrium conditions has been performed. A consistent pattern was discovered which was interpreted in terms of a detailed atomistic model of an interface describable as: Interface II {111} AL 11 {211} <101>Al <120> ? Several arguments are presented to substantiate the theory. It is compared in detail with another interface model characteristic of the Wid-manstatten precipitate of CuAl2 in A1 at low Cu levels. In addition, a concept is proposed to help explain the structure of the compound CuAl2. It has been shown that the eutectic alloy between A1 and CuA1, can be forced to solidify as substantially parallel lamellae throughout a relatively large volume&apos; by appropriately controlling the solidification parameters of growth rate, thermal gradients, and impurity level and by causing solidification to proceed in a unidirectional fashion from one end of an ingot to the other. A typical ingot solidified in this manner shows three distinct zones along the length of the ingot, Fig. 1. At the head end is a region consisting of many different grains, some of which are elongated slightly in the direction of solidification. After a few centimeters of growth, this polygrained region gradually merges into the second zone which consists of a very few elongated coarse grains. The third zone at the tail end is a region of eutectic colonies caused by segregation of impurities. Microscopic examination of transverse and longitudinal sections of the ingots reveals that during the initial stages of growth (zone I) the lamellar structure is frequently highly distorted and twisted but that it straightens out in zone 11. This characteristic pattern suggests that nucleation of a eutectic grain begins randomly at the head end of the ingot, and that some particular orientation relationship between the phases is more favorable from an energy consideration than others for one reason or another, so that some grains grow and others which are less favorably oriented do not. The favorably oriented or "low energy" grains continue to grow until excess solute rejected at the advancing liquid-solid interface destroys the parallel lamellar structure by forming a cellular rather than a substantially planar interface. When this occurs, the parallel lamellae fan out and eutectic colonies are formed because the lamellae grow perpendicular to the local interface. Questions naturally arise as to the crystallographic nature of the "low energy" grains. What do the grains which persist into zone II have in common? Can this explain the stability of such grains during growth? To answer the first question it is necessary to determine the crystallographic orientation of the lamellae of each phase relative to one another. This has been done for Al-CuAl2 eutectic alloys by two different techniques on specimens prepared in different ways.2&apos;3 The results were different from each other and from a third orientation relationship between A1 and CuA1, reported for overaged A1-Cu alloys.4 The three orientation relationships are summarized below to illustrate their similarities and their differences. (001) ? 11 (001) A1; [l00] ? 11 [l00] Al Eutectic, Ref. 2 (001) 8 1) (001) A1; [1001 ?11 [1101 A1 Eutectic, Ref. 3 (001) ? 11 (001) A1; [l00] ? 11 [310] Al; Widmanstfitten, Ref. 4 It is not surprising that different orientation relationships were found by Ellwood and Bagley,&apos; and Takahashi3 since the solidification conditions were quite different. Nor is it surprising that Mehl, Barrett, and Rhines 4 found still another value since they were studying another type of alloy. Nevertheless, it would be expected that some logical and systematic pattern could be found if all the alloys were at equilibrium since the same two phases are

Jan 1, 1962

By A. J. Griest, A. P. Young, P. D. Frost

A study was made of the effect of ß grain size on the tensile ductility of a-ß titanium alloys haet treated to strengths in the range 165,000 to 180,000 psi. It was concluded that the primary cause of $ embrittlement is the large grain size which is obtained so rapidly in many a-ß titanium alloys when heated into the ß field. It was also found that grain-boundary a and acicular intragranular a in the microstructure are not necessarily detrimental to the tensile ductility if the prior ß grain size is sufficientlv fine. BETA embrittlement occurs in a-ß alloys when the finish hot-working or stages of the subsequent heat treatment have been done at temperatures in the ß field. In order to avoid this embrittlement, for-gings must be finished at temperatures under the ß transus. For better workability, it would be desirable to forge at temperatures in the ß field. For this reason, research has been conducted to determine the cause of ß embrittlement. Although ß grain size has been considered as a possible contributing factor to ß embrittlement, only limited research has been done to evaluate its effect. The effect of addition elements on ß grain growth in unalloyed titanium has been studied by Liu.&apos; Complete mechanical property data, however, were not obtained for correlation with grain size. Ogden and coworkers2 have investigated the effect of both a and ß grain size and grain shape in Ti-Cr-Mo alloys. Their data indicated that tensile ductility was relatively insensitive to ß grain size at annealed strength levels (140,000 psi ultimate). No study has apparently been made to determine the relationship between ß grain size and ß embrittlement in a-ß alloys heat treated to high strength (180,000 psi ultimate). The high-strength condition is that in which ß embrittlement is particularly severe. Beta grain size is not easily varied through the use of a range of annealing times and temperatures in the ß field, because of the rapidity with which ß grain growth occurs. Short-time heating techniques are needed to obtain the smallest ß grains. EXPERIMENTAL PROCEDURE In this research, the experimental procedure was as follows: 1) Tensile and microimpact specimen blanks were resistance heated to produce a range of ß grain sizes. 2) The tensile and microimpact blanks were then solution-treated in the a-ß field and aged to produce predetermined ultimate tensile strengths in the range 165,000 to 180,000 psi. Tensile and impact ductility were then correlated with a grain size for constant strength levels. Materials—The alloys Ti-6A1-4V, Ti-4A1-4Mn, and Ti-16V-2.5Al are representative of the heat-treatable a-ß types in which ß embrittlement can be severe. The compositions and ß transi of the heats studied are given in Table I. The Ti-16V-2.5Al heat was melted and fabricated to 1/4 in. round at Battelle; the other alloys were obtained as 1/4 in. round rolled from commercial heats. The micro-structures of the as-rolled alloys were fine a-ß mixtures. This structure is typical of titanium alloys hot-worked extensively in the a-ß field. Resistance-Heating Treatments to Establish ß Grain Size—For direit resistance heating, a 1/4-in.-diam s~ecimen was heated with a 3000-watt transformer rated for 1000 amp with adjustable secondary voltage. The apparatus included a spray quench fixture. Both heating and quenching periods could be automatically controlled. For temperature measurements, 28-gage Chromel-Alumel wires were tack-welded to the specimen at its midpoint. A high-speed recorder-controller was used to control the heating cycle.

Jan 1, 1960

By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR&apos;s are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By H. S. Choi, I. Iwasaki

The effect of temperature as a parameter in ore flotation has not been systematically studied, although for some ores it has been known for many years that selectivity and grade of concentrates can be improved by conditioning or flotation at moderately or substantially elevated temperatures. In 1934 Coghill and Clemmer&apos; stated that "elevated temperature seems to make hard water more tolerable" in soap flotation, and a cursory examination of the literature indicates that some earlier investigators were aware of beneficial results obtained by floating above room or mill-water temperatures. Tartaron,2 Mitchell et aL.,3 and particularly Hamilton et al.&apos; have shown that high pulp temperatures give high recovery and selectivity in soap flotation of fluorite from a variety of gangue minerals. As a result of the work of these and of other investigators, high-temperature flotation has been successfully applied to industrial flotation of fluorite. Falconer" stated: "The use of high temperature conditioning (above 35°C and preferably above 60°C) in connection with the soap flotation of nonsulphide ores, as covered in B. Kalinowski&apos;s French Patent No. 847,-215, Dec. 7, 1938, is claimed to provide more intense activation, better separation of values from gangue, and reduction in quantity of reagents." The various investigations quoted above clearly demonstrate the improvements to be realized by increasing the temperature at which fluorite is floated, and it is surprising that little or no information has been published on systematic investigation of the same method as applied to other ores. The present article describes comparative results obtained at room temperature and at elevated temperatures by otherwise conventional flotation of iron ores, by single-mineral flotation in the Hallimond tube, and by contact-angle measurements. It is not the purpose of this article to evaluate the commercial feasibility of high-temperature flotation of iron ores, although preliminary calculations show that the cost should not be excessive and that the gains to be realized may well outweigh the extra cost of heating the pulp. LABORATORY FLOTATION TESTS Experimental: All flotation tests reported in this article that use a laboratory Fagergren cell were made on ore A (either containing the primary slimes or deslimed at 20µ as specified) following the preparatory procedures described elsewhere- or this particular ore. Ore A contained hematite, goethite (limonite), quartz, chert, and minor quantities of magnetite. Confirmatory tests made on other ores show that the same general principles apply to ores of similar mineralogy and structure. Conditioning was performed by adding the collector, as a soap, to the vigorously stirred and heated pulp. Conditioning time was 5 min, the pulp contained 60 pct solids, and the equivalent of 0.5 Ib of fatty acid was added per ton of original (unde-slimed) ore. The pH of the pulps ranged from 6.8 to 7.1 (25°C measurement) during conditioning. The pH was adjusted in the flotation cell by addition of either NaOH or H2SO4, the values reported being those of the pulp cooled to 25°C. During conditioning and flotation the pulp temperatures were controlled within l° to 2° by immersion of Variac-controlled Calrod elements in the conditioning beaker and in the cell, and by the use of water, heated to the appropriate temperature, for transferring pulp, adjusting pulp volume, and washing. Selectivity indexes have been calculated on the same basis as those reported in the article by Cooke, Iwasaki, and Choi." Results: Table I gives the results obtained by floating deslimed ore A with pure oleic acid at 25" and 50°C, and Fig. 1 shows the selectivity indexes plotted against pH of flotation. Inspection of Table I

Jan 1, 1961