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Executive JOHN M. LOVEJOY, Chairman ERLE V. DAVELER G. B. WATERHOUSE WISER JUDSON WILLIAM WRAITH J. V. W. REYNDERS, Consultant Finance HENRY KRUM, Chairman PAUL D. MERICA R. M. ROOSEVELT H. G. MOULTON, Consultant Admissions. RALPH M. ROOSEVELT, Chairman GEORGE D. BARRON, Vice-chairman JOHN L. CHRISTI PHILIP KRAFT W. A. SINSHEIMER

Jan 1, 1936

By J. Richter, D. Schulze

J. Richter and D. Schulze (Deutschen Akademie der Wissenschafte zu Berlin)—Introduction. In a recent paper R. G. Garlick and H. B. Probst reported on experimental results of investigations of room-temperature slip in zone-melted tungsten single crystals.17 In the paper it was pointed out that slip lines could be detected with an optical microscope only after about 10 pet plastic strain of the crystal. In our investigations we could observe slip lines in tungsten single crystals of defined orientations already with an elongation of 0.02 to 0.03 pet.18"9 Experimental Technique and Results. The tungsten single crystals were produced from 4 to 5 mm sintered rods* as starting material by electron- beam zone melting. With single-zone-pass melting a speed of 0.5 mm per min was used, while three-pass melting could be handled at a speed of 3 mm per min. Crystal axis orientations were located in the shaded area of the stereographic triangle, see Fig. 6. Orientation 1 is located at about 18 deg and orientation 2 at about 5 deg on the great circle from [011] to [ill]. This corresponds approximately to the orientations P and M referred to by Garlick and Probst. Our single crystals had a length of about 70 mm and were profiled solely by electrolytic means, leaving grip ends at both ends of the crystals. Between the latter, a cylindrical crystal of 45 to 50 mm length and about 2.4 mm diam was obtained. The crystals were deformed at room temperature in a commercial tensile-testing machine to obtain a strain of 0.02 to 5 pet. The average strain rate e = eP/t for all tensile tests amounted to approximately 10 -6 to 10-5 per sec, with ep representing plastic strain and t the duration of applied stress. In Fig. 7 a crystal is shown elongated by 0.03 pet. The picture was obtained by means of an optical microscope. Figs. 8 and 9 give electron-microscopic pictures of slip lines of crystals elongated by 0.07 and 1.1 pet, respectively. For crystals with the orientation 1, see Fig. 6, only the two main slip systems (101)[111] and (110)[111] were found. With the crystals of group 2 the two main slip systems are again evident, with

Jan 1, 1965

By C. M. Smith

HOWARD N. EAVENSON, acting for the last time as president of the Institute, presided at the annual business meeting on Tuesday afternoon at 4 o'clock. He spoke briefly of his visits with Local Sections last fall, and read a scholarly address on "Mineral Fuels and Civilization," scheduled for early publication in these columns. Karl Eilers presented the Treasurer's report, showing last year's income to be $134,967.44, compared with expenses of $133.266.51. Comparable figures for 1933 were $121,689.90 and $115,462.60. The Institute's peak income was in 1923 about $208,000. Newell G. Alford read the report of the Membership Committee showing 750 new members elected and placed on the rolls in 1934, compared with 328 in 1933. Losses by resignation last year were 81, compared with 262 in 1933; and 691 were suspended for non-payment of dues, compared with 747 the year before. Total membership, including 579 Student Associates, was 7742 at the end of 1934. Applications for membership have been coming in freely the last few months.

Jan 1, 1935

By R. F. Nielsen, R. G. Bentsen

Jan 1, 1966

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970

By Philip B. Bucky

CONTENTS [PACEPACE r. What Is a Rock Burst?2 4. How Can Rock Bursts Be Predicted? . 35 Jack Spalding2Jack Spalding35 A. F. Robertson 2, 5A. F. Robertson35 W. R. Crane 2A. B. Yates and P. J. Shenon. . . . 35 G. S. Rice 2W. R. Crane 35 P. J. Shenon 2G. S. Rice 35 L. C. Graton 2B. F. Tillson 36 2. What Are the Causes of Rock Bursts? 6 5. How Can Rock Bursts Be Controlled?. 36 Jack Spalding6Jack Spalding36 A. B. Yates and P. J. Shenon . 7, 12, 29A. F. Robertson 36 A. F. Robertson 12, 28W. R. Crane37 W. R. Crane 15A. B. Yates and P. J. Shenon. . . . 37 G. S. Rice 15Oscar Weiss38 Oscar Weiss15G. S. Rice37, 42 P. B. Bucky21R. D. Hoffman42, 43 P. H. Bird 21, 26, 28R. D. Hall 42 M. K. Hubbert26R. H. Cromwell42 G. Wheeler 26. J. Shenon 42 B. F. Tillson26, 28P. B. Bucky42, 44 T. T. Read 27B. F. Tillson 42, 44 A. B. Yates 43, 44 3. How Can Rock Bursts Be Prevented? . 30P. H. Bird 43 Jack Spalding. . . . • . • • • • . 306. General Discussion . A. B. Yates and P. J. Shenon. . . . 31Jack Spalding44 A. F. Robertson32R. D. Parker49 W. R. Crane 35C. Baring Horwood 51 G. S. Rice 35P. B. Bucky 52] FOREWORD THIS symposium brings together points of view, experiences and ideas on rock bursts from a goodly portion of the globe. Some conceptions, particularly those regarding the necessity of depth, have been fairly well shattered, as we find that they are present in the water tunnels of New York, on the surface at marble quarries in Vermont, and in the coal mines of the United States, as well as in the deep mines of the South African and Kolar gold fields, and in the nickel, copper and gold mines of Canada. Their occurrence under such a variety of conditions is, therefore, a challenge,

Jan 1, 1942

By E. H. T. Whitten

Fundamental principles of trend surface analysis are briefly reviewed. Recent analyses of several granite masses illustrate the method of estimating the quantitative regional composition and also variation trends. Mineralogi-cal, bulk chemical, and other quantitative variates can be employed. Such results should improve gravimetric surveys (etc.) relying on correction terms based upon estimated rock composition. For the first time realistic estimates of the mean composition of rock bodies can be made with the aid of trend components. Deviation maps hold promise for delimitation of disseminated mineralized areas. Deviations comprise residual "anomalies" after removal of trend components. In petrogenetic work such deviations have been shown to reflect local influences (e.g., contamination of magma by assimilation of xenoliths or country rocks of the envelope). Similarly, mineralization should be reflected as deviations standing out from background trends. Actual examples are given. Present results largely involved projection of data onto a horizontal plane, but if sufficient data are available use of three spatial coordinates increases accuracy for prediction in "unexposed" areas. Regression analysis shows that statistical correlations between variates for regionally distributed specimens are often strong (particularly with percentage data). Hence, in preliminary surveys more easily determined variates may sometimes be employed to gain first estimates of the distribution of components more economically significant. The sampling plan is of paramount importance. Unless a suitable sampling plan is devised and adhered to rigorously during collection of the samples, all subsequent analysis is liable to strong bias and to yield spurious estimates of the truth. For a wide variety of purposes it is becoming necessary to assess the quantitative composition and variability of rock masses and mineralized zones of various types. In petrology and petrography this is something of a break with tradition, because virtually all descriptions heretofore have been qualitative. Although vast amounts of qualitative data have been compiled, little is known about the quantitative behavior of rock components. However, if variability of rocks could be understood and expressed with sufficient accuracy, there would be considerable advantage to both economic and petrogenetic problems. For example, if, on the basis of a limited series of observations, the three-dimensional geometry of a disseminated orebody (or ore-bearing formation) could be predicted accurately, it would be possible to extrapolate with confidence the structure into unexposed areas. The following example based upon the geometry of an igneous cone sheet illustrates the point. The significant rock-unit gives outcrops at a number of points on the exposed surface ABCD (Fig. 1A). Study of n exposures may enable a geologist to predict that the rock-unit is circular in form and thus indicate where the unit can be expected in unexposed terrain. Such observations are made at sites with u, v coordinates, but, if subsurface information is available at sites with uvw coordinates, it will eventually become possible to predict accurately the three-dimensional form of the rock mass. Geologic rock masses or mineral deposits are not generally as regular and symmetrical in geometric form as the body illustrated in Fig. 1A. However, even where the broad limits of a major rock mass are known, a more acute problem arises in attempting to obtain detailed quantitative estimates of its internal variability; it is difficult to predict the variability of a mass from a limited number of observa-

Jan 1, 1961

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

By H. E. Biber

DURING the production of tin plate a thin layer of FeSn2, is formed at the interface between the steel sheet and the protective tin coating. Because excessive amounts of this alloy layer are undesirable, the kinetics of its formation is a subject of interest in the tin-plate industry. A recent study of this subject at our laboratory uncovered a relationship which should be of general interest to anyone studying kinetics of reactions in metallic systems. It had been previously concluded that, at any given temperature in the range 175" to 330°C, the Fe-Sn alloy layer would have a parabolic growth rate.1,2 However, our studies showed that this rule apparently holds only when the tin plate is heated very slowly to the "reaction" temperature; when the tin plate is rapidly heated, considerably different growth rates occur. An example of this effect of heating rate on growth behavior is contained in the accompanying results of alloy-layer growth measurements at 240°C in oil baths stirred at 10,500, 1800, and 0 rpm. The heating curves for these three conditions are given in Fig. 1, and the growth data are presented in Fig. 2. With the rapid heating rate, provided by the stirring at 10,500 rpm, the alloy layer had three distinct stages of growth. In the initial stage, which persisted well beyond the time required to heat the tin plate to bath temperature, the alloy layer formed very rapidly. The growth followed a rate law of the form w = ktn where n > 1. This initial stage was followed by a growth-retardation stage of about 50-sec duration in which little additional alloy was formed. In the third stage the growth again followed a rate law of the form w = ktn, but here « =0.3. With the intermediate heating rate provided by stirring at 1800 rpm, the three-stage nature was less pronounced and the slope of the third stage increased (i.e., n > 0.3). With the slow heating rate provided by the unstirred oil bath, the alloy layer grew in two stages. The initial rapid-growth stage persisted only until the specimen was heated to bath temperature, no growth retardation was observed, and the slope of the main portion of the plotted data was greater than in the stirred baths, having a value of almost 0.5. Similar results were obtained for other bath temperatures in the range 200" to 300°C. This effect of heating rate on growth behavior may be due to changes in the rate of nucleation of FeSn, crystallites. The iron and tin are in contact from the onset of heating. Thus the initial formation of FeSn, occurs not at the "reaction" temperature but rather while the tin plate is being heated to that temperature. Because nucleation is in general temperature-dependent, different heating rates could cause different over-all nucleation rates, which in turn could cause different growth behaviors. A more detailed discussion of the growth of Fe-Sn alloy layer and the effect of heating rate will be published shortly.

Jan 1, 1965

Jan 1, 1967

By H. T. Kennedy, S. G. Dardaganian, J. L. Clanton

This paper presents equilibrium ratios measured on oil and gas samples taken from the Kelly-Snyder field at the reservoir temperature of 128°F. From these data smoothed curves were constructed for the reservoir fluid up to the bubble-point, 1,874 psia. A material balance calculation, based on the use of equilibrium ratios instead of the usual solubility and shrinkage meayr~rements is made on the field and compared to the con\.entional method. DETERMINATION OF EQUILIBRIUM RATIOS The equilibrium ratios, or K values were obtained by recombining separator samples of oil and gas taken when the reservoir was above its bubble point, and thus represented the reservoir fluid before any change had occurred due to the evolution of gas. The well sampled had a gas-oil ratio of 617 cu ft of high pressure sepalator gas per barrel of separator oil. and a bottom-hole temperature of 128°F. Samples were brought to equilibrium by agitating for 24 hours in a thermostat, maintained at the proper temperature within 0.2ºF, mercury being added when necessary to maintain the pressure constant. Samples of oil and gas were then taken by constant pressure displacement, and analyzed by low temperature frac-tionation. Equilibrium ratios were determined at 128°F and 500, 800, 1,000 and 1,400 psig. At the latter pressure, there were indications that the gas samples were contaminated with small quantities of oil, and only data taken at the first three pressures were included in Fig. I. This figure has been extended to higher and lower pressures by the use of the Fluor charts for 3,000 psi convergence pressure, on which the experimental points fit well. MATERIAL BALANCE EQUATIONS The possible errors involved in conventional material balance equations have been analyzed by Muskat1. Where the errors occur in field measurements, or in obtaining effective averages from variables such as gas-oil ratio and pressure, they will evidently be involved in any attempt to estimate the content of the reservoir. On the other hand, substantial errors may be introduced in conventional material balance calculations by: (1) the neglect of the amount of oil dissolved in gas at high pressures and temperatures in the reservoir, but which condenses under separator conditions; (2) the assumption that the separation of oil and gas in the reservoir may be duplicated by a differential liberation in the

By L. W. Pommier, F. B. Brien, A. K. Bhasin

In the field of mineral processing, although many operations are applied to suspensions of ore particles in fluids, there is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. Previously proposed equations, based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids, are exam ined in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. As more knowledge is acquired in regard to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow predictions of conditions to achieve optimum results for engineering purposes. In the field of minerals processing, many operations are applied to suspensions of ore particles in fluids. The differential movement of solids of various sizes and densities in suspensions is of utmost importance to gravity concentration, wet classification, flotation, hydrometallurgy, and pipeline transport of solids. The subject is also of importance to other branches of engineering; for example, those involved with soil mechanics, ceramic slips, and oil-well drilling fluids. There is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The problems encountered in the direct application of the well-known Stokes and Newton's Laws to non-Newtonian systems have been examined in a previous paper.' Equations were proposed based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids. This present paper examines these equations in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. It is thought that, as more knowledge is acquired as to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow prediction of conditions to achieve optimum results for engineering purposes. The purpose of this paper is to make an initial assessment of the nature and magnitude of pertinent suspension variables. In order to avoid too voluminous a document, the examination of kinetics and mechanisms will be omitted at this time. THEORY A Newtonian fluid is defined as a fluid in which the stress is proportional to the rate of strain, 2 i.e.: H = viscosity; see Table I. for list of symbols The following equations are conventionally used to assess the motion of spherical particles moving under laminar and turbulent flow conditions through Newtonian fluids: When these relationships are applied in practice to suspensions, the liquid density is substituted by a composite suspension density, and viscosity is usually taken as that of the suspending liquid or an approximated "apparent viscosity." However, suspensions are non-Newtonian in character3 and thus, more than one viscosity parameter is required to describe their behavior. A number of models have been proposed for non-Newtonian fluids;2,4 among these the simplest is the Ostwaldde Waele or power-law model for incompressible fluids which for one dimensional flow may be reduced to:

Jan 1, 1970

CONTENTS PAGE ANDERSON, ARVID E., and CAMERON, FRANK K.-Recovery of Copper by Leaching, Ohio Copper Co. of Utah. Discussed by Thomas B. Brighton, H. C. Goodrich, Arvid E. Anderson, Thos. P. Billings, Frank K. Cameron 2 BEESON, J. J.-Mining Districts and Their Relation to Structural Geology. Discussed by Charles Keyes, Chas. A. Porter 4 DOBBEL, CHAS. A.-Deep-hole Prospecting at the Chief Consolidated Mines. Discussed by G. W. Crane 10 CRANE, G. W.-Notes on the Geology of East Tintic. Discussed by G. W. Crane, H. E. Havernor, N. O. Lawton 11 SACKETT, B. L., BARDWELL, CARLOS, JACOBSON, SIMON, and JENSEN, N. H. Lead Smelting in Utah. Discussed by D. W. Jessup, B. L. Sackett, E. H. Laws 13 BARDWELL, E. S., and MILLER, Roy H.-Pulverized Coal as Fuel for Copper Refining Furnaces. Discussed by L. D. Anderson, E. S. Bardwell, C. P. Crawford 15 WIGTON, G. H.-The Chief Consolidated Volatilization Process and Mill. Discussed by Thomas Varley, S. G. Olmstead, V. O. Lawton, O. C. Ralston.... 16 JESSUP, D. W.-Evolution in the Preparation of Ores for Lead Blast Furnaces. Discussed by W. Spencer Reid, D. W. Jessup, Carlos Bardwell 19 ALLEN, H. P., and MADGE, WM. C.-Chloridizing Mill of the Standard Reduction Co. Discussed by Thomas Varley, H. R. Hanley, H. P. Allen, George H. Dern 20 TUCKER, E. L., and HEAD, R. E.-Effect of Cyanogen Compounds on Floatability of Pure Sulfide Minerals. Discussed by Blarney Stevens 24 Mix, B. E., and BARKER, L. M.-Method of Unloading Ores and Coarse-crushing Practice at Magna Plant of Utah Copper Co. Discussed by W. C. Madge,B. E. Mix 25 KEIGLEY, C. T.-The New Byproduct Coke Plant of the Columbia Steel Corporation. Discussed by W. M. Grant, C. T. Keigley, A. C. Feilder 25 JACKSON, P. W.-Blast Furnace Plant of the Columbia Steel Corporation. Discussed by W. R. Phibbs, H. M. Henton 26 OLDRIGHT, G. L., KEYES, H. E., and WARTMAN, F. S.-Production of Ferric Sulfate and Sulfuric Acid from Roaster Gas. Discussed by G. D. Van Arsdale William E. Greenawalt, G. L. Oldright 27 MAZANY, M. S.-Braden Copper Company Caletones Smelter. Discussed by A. B. Young, G. L. Oldright 36 HARRINGTON, D.-Safety Methods in Utah Coal Mines. Discussed by Edward K. Judd, Otto Herres, Benedict Shubart, A. C. Watts, D. Harrington 36

Jan 12, 1925

By John Chipman, Wayne L. Worrell

Using recent thermodynamic data for the carbides and oxides of tantalum, columbium, and vanadium, the stable solid phases aboue 1300°K and at 1 atm CO(g) pressure in each M-C-O system have been determined. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures necessary to obtain these metals by carbothermic reduction under reduced pressures. TANTALUM, columbium, and vanadium react with carbon to form the M,C and MC carbide phases. The M,C carbides have narrow homogeneity ranges, but the MC phases possess considerable ranges of homogeneity.' The free energies of formation of the MC carbides were recently measured, and those of MC and M2Ccarbides have been estimated., (The notations MC and MC denote, respectively, the carbide compositions at the carbon-rich and at the metal-rich boundaries of the homogeneous MC phase.) In this paper, these carbide data are combined with thermodynamic data for the oxides to predict the stable phases in the Ta-C-O, Cb-C-O, and V-C-O systems at specified temperatures and oxygen pressures. M-C-O PHASE DIAGRAMS The solid phases in equilibrium above 1300°K for each M-C-0 system are shown in Figs. 1, 2, and 3. Above 1300°K, the vapor would consist entirely of carbon monoxide; and these phase diagrams were obtained by specifying the vapor pressure of CO(g) to be 1 atm. The temperature at which any two solid phases become unstable is specified along the two-phase equilibrium lines in each diagram. To simplify the diagrams, all solid phases in the Ta-C-O and Cb-C-O systems are represented as stoichiometric compounds. However, the homogeneity ranges of VO and VC are indicated, because they form a complete series of solid solutions.3 It also should be noted that the homogeneity range of

Jan 1, 1964

By J. H. Swisher

An experimental study has been made of the possible mechanisms for foam stability in the system CaO-SiO2-Cr2O3, where Cr2O3is the foaming agent. The degree of lowering of surface tension by Cr2O3 was determined at 1600 "C for high -silica melts. Measurements were also made of foam stability under standardized conditions. The results of the two sets of measurements then were correlated by applying the Gibbs and Marangoni theories of film elasticity. It was demonstrated that the Marangoni elasticity effect is probably the largest single contributor to foam stability, although the high uiscosity of' silicate melts makes some contribution in controlling the rate of drainage of liquid from bubble lamellae. ThE tendency of metallurgical slags to foam has frequently been observed during steel-refining operations. In the open-hearth furnace,this tendency is considered undesirable because it slows down the rate of heat transfer from the burners to the molten-metal bath. On the other hand, it is sometimes desirable to have a "foamy" slag in the basic oxygen converter.' A more effective blanket over the steel bath is made by a "foamy" slag, and loss in yield of metal due to splashing is minimized. In addition, a flush slag can be removed more easily in this condition. Since slag-foaming problems in the field have been attacked largely on an empirical basis, it appeared desirable to obtain a better basic understanding of the mechanism of foam stability. The experimental work was directed almost entirely toward the behavior of Cr2O3 as the foaming agent in CaO-SiO,-Cr2O3 melts. In the first stage of the investigation, the degree of lowering of surface tension by Cr2O3 was determined at 1600°C. The second stage consisted of measuring foam stabilities under standardized conditions. The two sets of experimental results then were correlated by applying various theories of foam stability. For convenience in interpreting the surface-tension and foam-stability results reported here, a portion of the CaO-SiO2-Cr2O3 phase diagram2 is reproduced in Fig. 1. EXPERIMENTAL 1) Surface-Tension Measurements. Very little information is available in the literature on the lowering of surface tension of slags by foaming agents. Kozakevitch 3 mentioned that the addition of 1.5 pct Cr2O3 lowered the surface tension of FeO slightly. In another system, some data on the lowering of surface tension of foaming slags by P2O5 were reported by Cooper and Kitchener.4 The technique used for the surface-tension measurements was the maximum bubble-pressure method,' using a single tube immersed to various depths in the melt. This method has been used extensively in high-temperature systems, such as in liquid metals, slags, and glasses.6,7 It has the advantage that the contact angle between the liquid and the tube material need not be known. The equation used for calculating surface-tension values from maximum bubble-pressure measurements is the Schroedinger equatioq5 which can be written as follows:

Jan 1, 1964

By W. A. Scheuch

ORDINARILY secondary copper, unless electrolytically refined, is reclaimed directly as foundry ingots used in the manufacture of copper-rich alloy castings. This use does not require the elimination of the impurities to the degree required if the recovered metal is to be used for electrical purposes where a high electrical conductivity is of prime importance. However, as a part of the general policy of reusing its own scrap and by-products wherever possible, the Western Electric Co. at its Hawthorne Works is recovering its secondary copper as wire bars which are delivered to its own rod and wire mill and there processed into wire of high electrical conductivity. This departure from the usual recovery scheme has been accomplished through the careful classification and sorting of the material entering the furnace charges and the careful control of the subsequent melting and refining in a reverberatory furnace. Tests conducted over a period of approximately four years have shown that the quality of wire bars produced from selected secondary copper is equal to that of wire bars produced by the electrolytic refineries. The interest which has been exhibited in the process by those who have seen it has prompted the following general description. It is the authors' opinion that the recovery of secondary copper will become more and more an important factor in the copper production industry. The description is largely of the refining furnace and its operation, but it must be remembered that careful classification and sorting of the scrap materials to eliminate impurities are just as important as the furnace operation toward obtaining a satisfactory final product. Classification and sorting do not lend themselves easily to description; they must just be done. It should also be recognized at the outset that constant intelligent supervision is requisite to the success of the process because there are so many ways in which impurities can find their way into the final product.

Jan 1, 1929

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush's work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By S. A. Hovanessian

The method of characteristics which reduces the Buckley-Leverett mnlineur, partial differential equation to two first-order, linear differential equations is applied to the solution of a waterffood recovery problem for multiple lines of producing wells and one line of injection wells. The application of the method is described by a numerical example, and a brief theoretical background is given. From the results of this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple sets of producing wells. INTRODUCTION In this paper, the method of characteristics is applied to the solution of a waterflood recovery problem with multiple lines of producing wells and one line of injection wells. The application of the method to this type of recovery problem considerably simplifies the procedure of obtaining a numerical solution. It differs from the method described by Kern1 because it eliminates the need for integration in obtaining saturation fronts. In addition, the saturation history at any location within the field is obtained from a single diagram (time vs distance with saturation as a parameter)'. The paper includes a brief theory of the method of characteristics and its application to the solution of oil recovery problems. A numerical example is worked out, and the cumulative oil recovery-vs-time curve for a system with multiple sets of producing wells is obtained. This curve is then compared with the recovery curve of a system with only one set of producing wells. From this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple lines of producing wells. However, the recovery time is considerably longer for multiple sets of producing wells.

By Maxwell Gensamer

Jan 1, 1960

By F. D. Richardson

STAFF: Editor, Gerhard Derge Carnegie lnstitute of Technology Schenley Park Pittsburgh, Pa. 15213 Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Jack H. Scoff, President; Richard C. Cole, Past-President; Harold 0. Emerick, President-Elect; Ralph L. Hennebach, Treasurer; Robert W. Shearman, Secretary; Donald A. Parks, Assistant Secretary; Leslie S. Wilcoxson, Assistant Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. E. Lund, Chairman; T. E. Dancy, H. O. Emerick, P. R. Gouwens, R. E. Grace, J. H. Jackson, H. H. Johnson, A. E. Lee, Jr., R. R. Nosh, R. D. Pehlke, and Paul Queneau. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extroctive Metallurgy Division: R. E. Grace, Choirmon; G. M. Bell, D. W. Bridges, J. M. Cigon, G. W. Heoly, T. A. Henrie, R. D. (Holli-doy, C. E. O'Neill, C. S. Somis, A. W. Schlech-ten, and Charles Shull. Iron and Steel Division: R. D. Pehlke, Choirmon; T. P. Floridis, Arnulf Muon, G. R. St. Pierre, E. T. Turkdogan, L. H.Von Vlock, and J. M. Uys. lnstitute of Metals Division: H. H. Johnson, Jr., Chairman; J. B. Clark, Vice Choirmon; M. R. Achter, G. F. Bolling. J. O. Brittoin, G. P. Conard, II, R. S. Davis, L. A. Girifolco, G. T. Hohn, J. P. Hirth, L. Himmel, G.T.horn, George Krauss, J. D. Livingston, R. D. Manning, H. M. Otte, S. V. Rodcliffe, R. E. Reed-Hill, H. C. Rogers, E. ScaIa, O. Sherby, M. T. Simnad, G. R. Speich, E. A. Steigerwald, R. A. Swolin, W. A. Tiller, W. R. Upthegrove, J. B. Wagner, Jr., Derek Wolton, H. W. Weart, W. W. Webb, and D. Published seven times yearly in February, March, April, June, August, October, and December by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 345 East 47th Street New York, N. Y. 10017. Telephone PLAZA 2 -6800. Subscription $30 per year for non-AtME members m United States and North, South, and Central America; $32, foreign; $7.50 for AlME members Single copies, $6.00, single copier foreign, $6.50. The AiME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1964 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AiME New York Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts. Second dost postaas poid ot New York, N. Y.,ond Ann Arbor, Mich. Volume 230, Number 6.

Jan 1, 1964