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By J. C. McKinnell

The appraisal of an oil lease may often be mad,? through production decline analysis, which requires description of the functional relationship between the oil production rate and either cumulative production or time. Heretofore, attempts to define the function appropriate to a given set of production data have depended to some extent on subjective procedures. The purpose here is to introduce an objective solution, obtained by combining the principle of least squares with the theory of equations. MATHEMATICAL ANALYSIS The fundamental differential equation appropriate to a general class of decline curves may be written. Solution of Eq. 1 for general boundary conditions may be written in terms of either the cumulative oil production or time: These equations constitute the mathematical expression of the so-called hyperbolic decline. Their complete description for a given set of production data requires the numerical evaluation of the three parameters1.', n, D, and (go),. For the special case of n = 0, Eq. 2 becomes q. = (q.), - DiN with the corresponding expression in terms of time being q. = (qa),e...........(5) Similarly, for the special case of n = 1, Eq. 3 becomes with the corresponding expression in terms of cumula- tive oil production being q. = (q.),e " '.......(7) Eqs. 4 and 5 constitute the mathematical description of the so-called exponential decline; Eqs. 6 and 7 are the mathematical description of the harmonic decline.',' Returning to the hyperbolic expressions, Eqs. 2 and 3 may also be written, q: = sNp + b........ (8) and where a = 1 - n; s = (n— 1)D,(q0);"; b = (go):-"; a'=-n;s/= nD,(qo);"; and b' = (go);-. Note that both Eqs. 8 and 9 are linear in either time or cumulative production with respect to an exponential function of the production rate. In other words, a straight line relationship results for both variables when associated with the appropriate power of q,. This fact is of prime importance in the application of statistical analysis. . STATISTICAL ANALYSIS For a given oil lease, the time, production rate and cumulative production are recorded records. To establish predictive formulas from Eqs. 2 and 3, it remains to determine numerical values for the three parameters [n, D, and (q,) .] through an investigation of the past history. Upon interpreting a, s and b as parameters, Eq. 8 may be expressed for every time interval of interest, i, over the past history as follows. (q,): = s(Np), + b........(10) In general, Eq. 10 will not be satisfied exactly, because of the assumptions in the expression of Eq. 1, and the errors and anomalies universally associated with production data. It will instead define the residual, s(Np), + b- CO=d......(11) Squaring both sides and summing over all the data points, m, under consideration yields

By F. H. Wilson, R. M. Brick

With the papers of Palmer and Smith1 and of Burghoff and Bohlen,2 published in 1942, understanding of the problem of the development of ears on deep-drawn brass cups was brought to the point where, from a practical standpoint, producers of brass sheet could keep earing under control. However, these very practical results raised questions concerning the reasons for the observed behavior. Since plastic deformation is fundamentally a function of crystallographic slip, these reasons must be considered in the light of the textures to be found in the annealed sheet. Various attempts have been made. to interpret the mechanism of ear formation by correlation with the preferred orientation and the anisotropy of the sheet. However, none of these has satisfactorily explained why ears are usually found in the rolling and transverse directions for copper but at 45' to these directions for brass. This paper offers additional data on these two related subjects and has been divided into two sections The first section provides a survey of the recrystallization textures of brass as affected by annealing temperatures and prior reductions, and an account of the caring behavior which accompanies these textures. The second section reports new data on the anisotropy that accompanies a characteristic texture for brass and endeavors with partial success to establish the factors that account for the difference in earing behavior between copper and brass Earing BehavioR oF Brass Review of Textures The recrystallization texture of severely rolled brass was first reported by Bass and Glocker.3 The preferred orientation to which this texture, obtained from metal annealed at 500°C., was most akin was (II3)[I12] This texture has been confirmed by Bauer, von Göler and Sachs;4 Brick;' Brick, Martin and Angier;6 and Cook and Richards7 who, in general, used annealing temperatures under 500°C. Bass and Glocker3 also reported the recrystallization texture at 850°C. to be the same as at 500°C. They analyzed their textures by means of single photograms obtained with white radiation. The photo-grams for both temperatures are reproduced in their paper, and there is a strong similarity between the two. However, for the latter temperature, the number of spots registered on the film was remarkably large for the grain size to be expected, and the authors made no mention of using a technique that would integrate a large enough area of the specimen to produce so many spots. The only other attempt to determine textures resulting from high temperature

Jan 1, 1945

TO THE BOARD OF DIRECTORS AND MEMBERS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS GENTLEMEN Submitted herewith are the report of the Treasurer for the year 1937 and the reports for the same year of the following standing committees: Admissions, Membership, Papers and Publications, Library, Student .Relations, Speakers for Local. Sections and Student Societies, and Mining and Metallurgy. To these reports members are referred for further details. Finances.-Income for the year was the largest since 1930, the figure being $189,394, an increase of $18,803 compared with income for 1936, exclusive of a special Rocky Mountain Fund appropriation of $2500 in that year for visits to western schools and Local Sections. Major items of increase were: $8,000 from current dues and arrears; $7,700 from advertising in MINING AND METALLURGY and the two periodical "Technologies"; and $4,800 from sales of TECHNICAL PUBLICATIONS (pamphlets) and TRANSACTIONS volumes for both current and former years. Initiation fees and clues from new members declined $2,300, principally because of the larger 'proportion of Junior Members to Members among the new enrollments. Junior Members pay no initiation fee and dues are $10 compared with $15 for Members.

Jan 1, 1938

By George Sachs

I deeply appreciate the honor of being selected to deliver the twentieth Annual Lecture of the Institute of Metals Division. The subject of my paper is extremely involved and voluminous, therefore I shall discuss only some more recent experimental material and speculate somewhat on the physical and mechanical fundamentals of these changes. The flow and the rupture of a solid material are rather different phenomena. It is therefore surprising that up to a rather advanced stage in metallurgical science these two fundamental phenomena have been simultaneously treated and forced into the general conception of the "failure" of solid material. Only in this century, and particularly during the last 20 years, have the very different physical meanings of flow and rupture been clearly recognized. Several hundred of the more recent publications deal with these subjects.1 LAW OF SIMILARITY The basic values commonly considered responsible for the mechanical behavior of any material are the stresses. From this standpoint both a large and a small article made from the same homogeneous metal and of geometrically similar shapes should behave identically, i.e., they should deform geometrically in a similar manner, if subjected to the same stress values at corresponding points. This "law of similarity" was introduced about 60 years ago simultaneously by Barba2 and Kick3 and was derived from the classical theory of elasticity. As far as the plastic behavior of a metal is concerned, this rule appears to be valid. The conventional properties of large and small tension or compression test bars, machined from larger sections, are identical; while the force required to deform a section is proportional to its cross-sectional area and the work consumed in deforming geometrically similar articles in a geometrically similar manner is proportional to its volume. The general trend of the stress-strain diagram of a metal is independent of the section size (Fig. I). No exceptions from this rule are known. However, if the deformation of a metal is continued until rupture occurs, and the breaking stress or the work consumed is measured, a test bar of large cross section appears to fail before or at lower stresses than does one having a small cross section. Thus, the specific impact energy has been often found to decrease with increasing size of the test specimen, particularly for materials with a limited ductility.4 Another exception from the rule of similarity is offered by fatigue-strength values, which usually decrease with increasing section size. 5,6 The conclusion must be drawn from these experimental facts that the ductility of a homogeneous metal decreases with increas¬ing section size (Fig. x). This effect has been actually confirmed by Docherty,7 who observed that in static notch bending tests large specimens failed earlier and in a more brittle fashion than small specimens ma-

Jan 1, 1941

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. 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 S. C. Schaeker, A. W. Schlechten, A. H. Larson

PARRAVANO and Malquori' studied the equilibrium of H2S-Hz with molybdenum and its lowest sulfide which they believed to be MoS2. Mc Cabe' has shown that its composition is actually Mo2S3 and determined its dissociation pressure by means of Knud-sen effusion measurements. Stubbles and Richard- son3 have recently studied the equilibrium of gas mixtures of H2S-HZ with the two-phase solid mixtures of Mo-MozS3 and Mo2S3-MoS2. The latter investigators found that M02s3 deviated slightly from the stoichiometric composition, but they did not determine the homogeneous region of the disulfide phase. Morimoto and Kullerud, studied the Mo-S system by quenching, microscope, and X-ray methods and concluded that the disulfide is stoichiometric. The present investigation was concerned with the measurement of the sulfur vapor pressure variation with composition at 1100°C in the homogeneous region of "MoS2". These measurements were made by reacting: 1) molybdenum powder (99.97 pct Moj with sulfur vapor, and 2) MoS1.g9 (formed by reaction of Mo + H2S) with sulfur vapor in a quartz capsule. Conditions were controlled to form an equilibrated phase within the homogeneous region of the disulfide. The quartz capsule was sealed off initially under a vacuum and the residual gases were gettered by titanium powder contained in one end of the capsule. A mixture of Mo + S or MOS,., + S was in the other end. The section containing the titanium powder was heated for 24 hr at 700°C and then removed by flame sealing. The end of the capsule containing the charge was then heated to 1100°C. The other end of the capsule was maintained at a temperature which would produce the desired sulfur pressure in the capsule (liquid sulfur distilled from the charge mixture was retained in this end). After equilibration, the capsule was removed from the heating assembly and rapidly air-cooled. It is assumed that equality existed between the total sulfur pressures (PT) in the two ends of the capsule and not between the partial pressures of the different molecular species (S, SZ, Three separately controlled heating elements were used to maintain the proper temperature gradient over the length (approximately 12 in.) of the capsule. A thermocouple-Wheelco "Capacitrol" system was used for temperature control of the two end heating elements within 2"C. The center heating element was controlled directly by a " Power -stat". Separate controlling and measuring thermocouples were used for both end heating elements. Pt-Pt(l0 pct Rh) thermocouples were used for 1100°C and Chromel-Alumel thermocouples were used for lower-temperature control and measurement of the assembly. Silver foil was wrapped around the end of the capsule containing the liquid sulfur to insure a constant temperature zone. The thermal gradient over the entire length of the capsule was measured to: 1) ascertain that the length of the constant temperature zone of the liquid-sulfur end and the sulfide end was sufficient, and 2) ascertain that the liquid-sulfur zone was the zone of lowest temperature. The data obtained in this investigation are shown in Fig. 1 and Table I. The total sulfur pressure (PT) and p(S2) were calculated from the data of Braune et UZ.~ The compositions of the equilibrated disul-

Jan 1, 1964

By R. Sporcic, P. J. Mudra

During the past year personnel of the Roof Control Research Group of the Bureau of Mines designed and developed encapsulated hydraulic cells for measuring pressure changes in coal in situ. Preliminary results from feasibility tests in progress in the laboratory and field indicate that the cells respond favorably to changes in pressures associated with a coal-mining environment. The ultimate objective is to use these cells to obtain engineering information relating to coal bump or coal outburst phenomena. Mining research has experienced a remarkable growth during the past decade and from all indications should surge forward at even a greater pace in the future. This increased interest in mining research has been brought about by the ever-multiplying number of technical problems being encountered by the mining industry in its effort to produce pay-dirt tonnages safely and economically from greater underground and surface pit depths. Among the various divisions in the field of mining research, the study of ground stress has received a large part of the overall attention. Numerous technical papers have been written with regard to ground stress conditions around mine openings and yet the total usable knowledge concerning this subject is extremely limited. Research teams around the world are endeavoring to bridge the gap between theoretical and laboratory approaches and the solution to design problems in the field. The problem of ground stress is not a new one for the coal mining industry. Operators in both eastern and western coal fields of the United States as well as in many foreign countries have long been plagued with a number of ground stress problems, one of which is commonly referred to as the coal-mine bump. This term or phenomenon has been aptly defined by earlier investigators as the violent and sudden failure of coal and adjacent rock. Direct results of such failures have been the loss of human lives and thou- sands upon thousands of dollars of sustained mine damages. In an effort to alleviate the magnitude and frequency of these failures, mine operators have employed and are presently employing various corrective techniques. These include: Inducing failure in heavily stressed areas by augering large-diameter holes into stressed pillars, using extensively yield-able steel arches in both long-term haulage and short-term face entries, backfilling unused or abandoned entries with mine waste to gain additional support, and using systematic pillar coal panel extraction techniques including mechanized longwall mining. The Health and Safety Activity of the Bureau of Mines has for a number of years contributed considerable time, funds, and talent in an effort to define better the ground stress problems associated with coal-mine bumps. As a part of this investigative program, in situ ground pressures are presently being studied in coal mines located in West Virginia and Utah. The description and development of the device being used to measure these pressures is the specific topic of this paper. CHOICE OF INSTRUMENTATION After consideration and evaluation of the various instruments and techniques that are being used by researchers in the field of rock mechanics to detetmine in situ stresses, a simple hydraulic system was selected for detailed investigation. Aside from simplicity, a hydraulic system is relatively inexpensive and also eliminates the need for electricity in its installation and operation. The hydraulic device referred to is, in essence, a simple unidirectional pressure-measuring cell. Hydraulic cells, which had been used for measurement of pressures in hard rock, were investigated but found not entirely suitable for use in coal, particularly since they involved (1) preparation and emplacement of cement grout at the test site, and (2) a waiting period before the cells became operational. At the outset, it was decided that certain design parameters be established. The cell should be simple and inexpensive, constructed of materials readily obtainable and easily built in the laboratory or field by unskilled labor. It was further decided that it was desirable to encapsulate the cell in a suitable mate-

Jan 1, 1963

By J. Murray Riddell, George A. Morrison

THIS paper is a companion to the one by George A. Morrison on Mining a Deep Limestone Mine in Ohio.[+] Barberton is 8 miles west of Akron, Ohio, and 23 miles south of Cleveland. The underground mining of limestone at Barberton constitutes the world's deepest limestone mine. The stratigraphy is as follows: 0-20 ft. Loam, clay, sand and gravel. Water bearing. 20-40 ft. Fractured. sandstone. Water bearing. 40-110 ft. Sandstone with interbedded shale, slightly fractured. Water bearing. 110-314 ft. Sandstone with interbedded shale, slightly fractured. Water carrying. 314-2197 ft. Shale with occasional seams of sandstone, which varies in thickness from a few inches to 4 feet. Dry. 2197-2247 ft. Limestone. Dry. 2247-2742 ft. Dolomitic limestone. Dry. 2742-2767 ft. Salt. Dry. 2767- Dolomitic limestone. Dry. All of the strata dip to the southeast, about 0.5 per cent from the horizontal. The top 110 ft. of the crust is water-bearing. The rock strata are naturally fractured to a depth of 314 ft., sufficient to allow the passage of water. In the shaft-sinking operations, a stra was encountered at a depth of 520 ft., and flows of methane gas were pierced at depths of 1350 and 1952 feet. Specifications for the mine plant called for, in part, the sinking of two vertical shafts and a hoisting plant capable of producing at the rate of 300 tons per hour. No. I shaft is 550 ft. west of No. 2 shaft. Each shaft measures 8 by 17 ft. outside of steel. General features of the design (Fig. I) are: Principal set members, 6-in. H-section; connecting angles (studdles), 3/8 by 4 by 4-in. angle irons; spacing of sets, 8 ft. centers; spacing of bearer sets, generally, 160 ft.; bearers, of 12-in. I-beams. Each bearing set featured a concrete ring about the periphery of the shaft, steel to rock, and 8 ft. in height; permanent guides, 6 by 10-in. long-leaf yellow pine, 85 per cent heart. THE SHAFT-SINKING OPERATION The preliminary shaft-sinking work consisted of driving interlocked steel piling about the exterior of the shafts to depths of 35 and 32 ft., respectively, and of such horizontal dimensions as to ultimately permit the pouring of a concrete collar 2 ft. in horizontal thickness. Following the pouring of a shaft collar, a temporary wooden headframe for shaft-sinking purposes was erected. The head-frame, while ordinary, featured: (I) a storage pocket of 300 cu. ft. capacity with truck servicing facilities, and (2) pneumatically operated dump doors, which were actuated by the hoistman, thus caring for the dumping of the "ball-and-chain"

Jan 1, 1944

By C. G. Dunn, F. W. Daniels, M. J. Bolton

IN recent papers on interface energies in metals¹,² the concept of an equilibrium of forces has been used in the measurement of interfacial tensions. Mathematically the equilibrium of three forces is given by the relations: where the 2's are the interfacial tensions (interface energies per unit area of interface) of three phases or grains meeting at angles 21 22 and 23 (212 relates to the 1-2 boundary formed by grains 1 and 2;223 to the 2-3 boundary, etc.). If these relationships are valid, one can calculate relative values of the interface energies from measured boundary angles on specimens which have been brought to equilibrium. Since Eq 1 may be derived through a mathematical process of minimizing the grain boundary energy under the restriction that the ?'s be independent of boundary orientation: the concepts of surface tensions and equilibrium of forces are not particularly essential. To deal with the general case involving dependence of boundary energy on boundary orientation, it becomes desirable to drop certain concepts formerly held (namely that energy per unit area is identical with force per unit length or surface tension) and to use the energy concept alone. It is appropriate, therefore, to use E in place of ? in deriving and using the more general equations that express the anisotropic nature of the grain boundary energy. Herring3# ' recently has derived the required general equations using the principle of minimization of energy. Specifying the boundary orientations in terms of angles (4) measured with reference to crystal axes within the grains, Herring's equations take the form E23 + E21 cos?8 + E12 cos?2 — sin ?12 + sin?2-?E12/?12 =O [2] where the partial derivatives are measured in the direction of counterclockwise rotation of the boundaries. Eq 2 implies that an infinitesimal displacement of the triple point along the 2-3 boundary produces no change in the boundary energy. Similar equations apply for infinitesimal displacements along each of the other two boundaries. From such equations Herring obtains the following general relationship (1 + E1 E2) sin?8 + (E2 — E1) cos?3 ________ E38______________ = (1+ E2 E8) sin ?1+ (E3— E2) cos ?1 __________^5____________[3] (1 + E sin ?2, + (E1 — E8,) COS ?2 1 E28 where E1 = 1/E23- E25 and PC and c8 have similar expressions. It is apparent that Eq 3 reduces to Eq 1 when the c's vanish. Eq 3 also reduces to Eq 1 when the E'S are all equal. Shockley and Read' have pointed out one limitation to these equations. When E plotted versus 4 appears as an energy cusp, as their theory requires, for example, for the energy near a twin boundary position, then Eq 3 (and therefore Eq 1 also) no longer applies if one boundary is in the minimum energy position. One of the equations of form Eq 2, however, applies if the infinitesimal displacement is along the boundary associated with the energy cusp. From the foregoing treatment it will be apparent that equilibrium angles alone are not sufficient in general for calculating relative interface energies.

Jan 1, 1951

By S. K. Asunmaa, W. D. English, N. A. Tiner, W. A. Cannon

This paper discusses the reaction of metal surfaces with fluorine. Fluorination reactions result in the formation of metal fluoride films which are "passive" toward further reaction of the metal with fluorine. These films are very adherent, and do not easily detach from the substrate metal by mechanical flexing or thermal shock. Exposure of passive films to a humid atmosphere produces hydrated metal fluorides which cause secondary fluorination reactions upon reexpo-sure of the metal surface to fluorine. The surface films formed range from 10 to 30A in thickness and they pow at the expense of surface oxide films. The apparent film formation is completed rapidly in 15 to 30 min on stainless steel and nickel surfaces. On copper and on Monel surfaces, the film at first grows rapidly, then increases slowly over an extended period of time. Passive films are formed at all fluorine pressures in the range from 0.1 to 1.4 atm at room temperature. ALL metals react when exposed to fluorine. These reactions generally produce surface films which consist of metal fluorides. The rate of reaction is largely determined by the extent to which these films are protective. Although there is an extensive literature concerning reactions of oxygen with metals, there are very few investigations reported concerning fluorine-metal reactions. Brown, Crabtree, and ~uncan' investigated the kinetics of the reaction of gaseous fluorine with copper metal which had been freshly reduced in hydrogen. The reaction rate was independent of pressure over the range from 6 to 60 torr. A logarithmic rate law was obeyed in the temperature range from 25" to 300" ~. There was some deviation at higher temperatures which could have been the onset of a parabolic law. The calculated film thicknesses ranged from about two molecular layers, 10A, for 5 hr exposure at room temperature to thirty-five molecular layers for 5 hr exposure at 200" . The authors concluded that no single mechanism could explain all the observations. O7Donnell and spatkowski2 studied the reaction of fluorine with copper at 450°C at pressures from lo to 133 torr. The reaction was found to be pressure -dependent and followed a logarithmic rate law. It was not entirely diffusion-controlled, and fluorine was thought to be the migrating species in the reaction. Miscellaneous metal-fluorine reactions were investigated by Haendler et ~1.~ Reaction products were identified but no rate data were determined. Air Prod- ucts and Chemicals, Inc., have conducted an investigation of reactions between fluorine and various metal powders at room temperature and 85° C. Fluoride film thickness as a function of time of exposure was reported on the assumption that the reaction takes place between fluorine and metal to form the normal metal fluoride. Surface areas of the powders were only estimated so the relative film thicknesses may not be exact. The data showed reaction rates which were generally logarithmic in character, the rate of film growth virtually ceasing after a few hours exposure time for some alloy powders. The effect of moisture on fluoride films was also investigated by measuring additional reaction with fluorine after exposure of passivated powders to atmosperic moisture. The fluorination of iron was studied by 0'~onnell~ at temperatures from 225" to 525" ~ and at pressures ranging from 20 to 200 torr. In all ranges, the reaction followed a logarithmic rate law and was dependent on the square root of the gas pressure. The author concluded that fluorine gas passes through pores in the film. As the film grows, the blocking of pores leads to a rapid decrease in reaction rate; hence a logarithmic rate law is observed. Jarry, Fischer, and Gunther' investigated the mechanism of the reaction of fluorine with nickel at about 600" to 700°C. On the basis of the metallographic examination of fluoride scales growing on the nickel and from separate radioautographic data, it was claimed that fluorine is the migrating species in the reaction. This is in sharp contrast to the growth of oxide films on nickel where it has been shown that nickel ions migrate through the scale to the gas-solid interface to react with oxygen. Few investigations have been reported of the reaction of fluorine with metal oxides. Such investigations should be of great significance for a better understanding of passivation in view of the ubiquitous oxide films on technical alloys. Haendler et al.3 studied the reaction of fluorine with oxides of copper, tin, titanium, zirconium, and vanadium. Copper (I) oxide reacted as follows in the temperature range 150" to 300"~: temperature above 300" ~ was required for the CuO to react to form additional copper fluoride. Ritter and smith7 also investigated the reaction of fluorine with copper (11) oxide. An oxide powder comprised of spherical particles with a fairly high surface area was reacted with fluorine, starting at room temperature and increasing to 100° C over a period of 3 or 4 hr. The initial reaction was slow until the fluoride film thickness reached about to or 15R at which time the reaction rate accelerated, then decreased again. Most of the kinetic data was obtained during this final phase of reaction. The authors conclude that the film grows slowly at first until the stresses developed in the distorted lattice are sufficient to rupture the initial

Jan 1, 1969

Lead-zinc production in Canada accounted for 19% of the total value of metals and minerals produced in 1976, says Keith C. Hendrick, president of Noranda Sides Corp. Mine production of recoverable zinc w as 1. 158 million toils of 27.4% of free world production in 1976. Slab zinc pro¬duction was placed at 472,000 tons that year. Canadian mine production of recoverable lead was 247,000 tons or 10.6% of the free world production. Refined lead that year was at 177,000 tons.

Jan 11, 1977

By J. Norman Bulkley

As electrical power is used to a greater extent on the Rand than in any other mining center, it is thought that a short description of the methods used and results obtained may be of interest. In comparing Rand practice with that on other fields, several general factors should be borne in mind: First, the mines are all working on large tonnages of low-grade ore (average. $6.50). The annual crushing rate is about 27,000,000 tons. Second, the mines are all grouped udder the financial and engineering control of mining houses, so that the results of a group, rather than an individual mine, are open for study, and practice follows more uniform lines. Third, coal of fair quality (about 12,000 B.t.u.) can be obtained for $2 to $3 per ton., Good supplies of condensing water are, however, scarce, and have to be carefully stored. Power Supply Power is supplied by the Victoria Falls & Transvaal Power Co., Ltd., and its subsidiary, the Rand Mines Power Supply Co. Both companies, which are practically one from an engineering point of view, operate the following stations, all feeding into the same system.

Jan 2, 1916

'T. C. MERRIMAN, New Haven, Conn. (written discussion *).-This most interesting paper gives much carefully obtained and valuable data. However, there are two points in connection with the commercial application of such data that might possibly be a source of trouble and mis-understanding. In the first place, the examination of thin sections of annealed brass, subjected to standard Brinell test.(500 kg. on a 10-mm. diameter ball) at thicknesses from 0.075 to 0.150 in. (1.9 to 3.8 mm.) indicates that cold work has been performed on the specimen during the application of the load sufficient to extend way through the section, and have the hardness of the metal affected by the backing. If the usual steel support is used, this effect is very evident. If a piece of soft brass is used as a support, there is an indentation in the surface of the support accompanied by a bulge on the under side of the tested specimen opposite the impression made by the 10-mm. ball. The result is that Brinell specifications (governmental or otherwise) on stock for a certain purpose may not be fair in all cases, since manufacturers, owing to differences in equipment, etc., may not all use precisely the thickness and conditions of stock on which the Brinell specifications were based. This would mean that the government Brinell specification might not give them the temper of stock best suited for their manufacturing methods. The concluding paragraph of this paper, stating that "the hardness of cartridge brass may be determined with greater accuracy by the Brinell hardness measurement than by attempting to judge it from the grain size" appears to be in line with the movement of the last year or so among brass manufacturers toward substitution of the Brinell test for microscopic examination as an acceptance test on cartridge brass. The statement may he strictly true that the Brinell test is the best test for hardness, but it is not, as the statement might readily be construed, a sufficient test of suitable condition. For instance, some cartridge brass might accidentally have been overheated to a point where it would be distinctly unsafe to use for the manufacture of small arms cases and then be so rolled (reduction 3 to 5 per cent.) as to pass perfectly proper Brinell specifications. Under such conditions the microscope would reveal its unsuitability where the Brinell test had failed so to do.

Jan 4, 1919

By R. G. Agarwal, Ramey Jr. H. J., Al-Hussainy R.

Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited infomlation on the subject has been available until recently. This study was performed to show the qiiantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appear to depend in an important was on: (I) the prodirction rate and manner of production; (2) the residual gas saturation; (3) aquifer propertie.); and (4) the volumetric displacement effciency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state tnethorl. the Hurst modified steady-state method, and various unsteady-state methods such ac. those of van Ever-dingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should he investigated early to permit adequtrtr planning lo optirtize the pay reserves. INTRODUCTION In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.'a Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,1 the Hurst modified steady-state method and various unsteady-state methods such as those of van Everdingen-Hurst. Hurst, and Carter-Tracy. Interesting applications of these solu- tions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,14 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high. A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation. The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reser.voir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.' However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions. CALCULATION METHOD Water-drive gas reservoir performance can be estimated in a manner completely analogous to oil reservoir calculations: a materials balance is written for the reservoir, and a water influx equation is written for the aquifer. Siniltaneous solution provides the cun~ulative water influx and the reservoir pressure. When reservoir performance data (gas produced and reservoir pressures) are available, it is usually possible to match performance data to determine the initial gas in place and the water influx parameters —

Jan 1, 1966

By Richard F. Link, George S. Koch

Advantages and disadvantages of deflecting (wedging) diamond-drill holes to obtain sampling data are compared with the alternative of drilling additional holes. The discussion is based on a statistical analysis of a large set of deflection data from exploratory boreholes in South African gold mines. Representative cost comparisons show the conditions under which deflections are likely to be desirable.

Jan 1, 1969

Discussion of the paper of E. C. HARDER, presented at the Pittsburgh meeting, October, 1914, and printed in Bulletin No. 94, October, 1914, pp. 2573 to 2586. I. C. WHITE, Morgantown, W. Va.-I have seen some of the great iron-ore deposits described in this paper. -One of these in the State of Minas Geraes appears to be an immense mountain of iron ore about 2,000 ft. in height. All over its surface from bottom to top may be seen large masses of rich iron ore, varying in weight from a few pounds to several tons, and from all that one can judge without exploitation, the quantity of available ore is certainly very large in this particular mountain. Whether it will prove a mere surface deposit or shell, like the famous Iron Mountain of Missouri, is for future exploration to determine. The question of transportation is the main factor in determining the availability for exportation of these Brazilian iron ores. There is no coal in Brazil that can be manufactured into coke without expensive previous treatment, since the best of the raw coal in the States of Rio Grande do Sul, Santa Catharina, and Parana, contains about 35 per cent. of ash, of which about 6 per cent. is sulphur, and coal of this composition cannot be utilized in iron smelting without purification. When I was chief of the Brazilian Coal Commission in 1904 to 1906, I had a cargo of this coal shipped to Balk, Germany, and treated in the great coal-testing plant of the Humboldt Engineering Works, located just across the Rhine from Cologne. It was found that by crushing and washing the Brazilian coal, it yielded 33 per cent. of briquetting coal, containing only 10 to 12 per cent. of ash (of which 1 per cent. was sulphur), and 42 per cent. of slack coal, with 25 per cent. of ash and low in sulphur, so that about 33 per cent. of the Brazilian coal could be converted into coke of fair quality, as shown by the following average of three analyses, using air-dried coal, of briquets made from the Barro Branco coal bed, State of Santa Catharina: Moisture 1.56 Volatile matter 31.66 Fixed carbon 56.73 Ash : 10.05 Total 100.00 Sulphur 1.34 Phosphorus 0.003 B.t.u 13,395

Jan 4, 1915

By Roshan B. Bhappu, Zeki M. Dogan

Two magnesite ores containing 3.15% and 8.73% SiO2 and a calcined magnesite product assaying 2.6% Si02 were first reduced in size to -20 mesh by roll crushing. 'They were then treated dry on a high intensity magnetic separator to reduce their silica content by rejecting iron-stained silicate minerals in the magnetic fraction and obtaining marketable magnesite or calcined magnesite as a nonmagnetic product.

Jan 1, 1975

By Francis Cameron

Gloomy predictions that domestic mineral reserves are approaching exhaustion are unwarranted and may be harmful, this author contends. Specific mineral forecasting errors in the Paley Report are cited to support this contention, and steps that can be taken to insure a progressive mineral industry capable of keeping pace with the major raw material needs of the nation through advancing technology are suggested. Mining is both exciting and rewarding —although at times somewhat frustrating— and we all can have real pride in our industry, in its people, and in its accomplishments. It is, however, with concern that I have noted a deterioration in this Country in what might be called mining's stature and in the growth of a belief in many quarters that our mineral reserves are rapidly approaching exhaustion. In other words, there is a popular image that we are fast becoming a "have not" nation in many respects and that the domestic mining industry can no longer be considered, in the vernacular of Wall Street to offer much in the way of "growth potential." I do not subscribe to this hypothesis, nor do I be-li4ve that the record of the mining industry bears this out. However, let me add that we can, in time, talk ourselves into this frame of mind and we can hasten the day when this very well might come about by unnecessary and unwise legislation or regulation. My remarks today are basically designed to give my reasons for refuting this negative philosophy and to review our record. With your help, I know we can improve our image, and the public's recognition of our industry's peculiar problems. The progress of our civilization over the centuries has been fundamentally based upon proper use of raw materials, both agricultural and mineral, and upon energy, human or otherwise. As the standard of living has progressed century by century, the demands for mineral raw materials have increased in an irregular, but steadily rising progression. Fortunately, those minerals on which we depend most, i.e., iron, coal, petroleum, copper, aluminum, lead, and zinc have been neither too difficult to find nor to process into useful form. Iron, the most useful of all metals, is present in various amounts in most rock types and soils. Gold, seemingly the most generally desired (but certainly not the most useful of all metals), occurs in sea water in a far greater total tonnage than has been won from all of the world's known gold mines. If the latter is true, then why do we not see large installations treating sea water for the recovery of its gold content? The answer, of course, is that even the French, who seem, from their recent actions, to value gold above all else, have not devised a way of doing this at a profit. Theoretically, it is possible, but not with today's technology at a cost which would justify the effort. Man has exploited only those mineral concentrations which accidents of nature have placed within his so far limited means of finding and utilizing. What we geologists and engineers refer to as an orebody is nothing more than a concentration of minerals, exploitable with available knowledge, that will yield a value greater than the value attached to the energy and capital required to produce it. What is "ore" and what is not "ore" is, in the end, a matter of economics. The economic problem stems from the physical and chemical character of mineral deposits. The good Lord stacked the cards heavily in favor of rising costs by limiting the amount of the higher grade ores easily available. As the best and most accessible ores are depleted, it becomes necessary to work harder and with greater ingenuity to produce more from less accessible and lower grade resources. The quantity of mineral raw materials we can have in the future will be determined largely by what we can afford to pay for them in terms of human effort, capital outlay and production energies. We will always have the problem of cost with us and our only real means of keeping ahead of rising costs is by continually improving our technical abilities. We, in this country at least, no longer have open to us large and unexplored virgin wildernesses in which a pick-and-shovel prospector might uncover an untouched mineral bonanza. The rest of the world also has few conventional frontiers left in which the explorer-prospector is free to roam. We do, however, have enormous land areas unexplored, and untouched po-

Jan 1, 1969

Discussion of the paper of DAVID COLE, presented at the New York meeting, February, 1915, and printed in Bulletin No. 9S, February, 191.5, pp. 431 to 444. R. H. RICHARDS, Boston, Mass.-The Butchart riffle seems to violate, according to our preconceived notions, some of the very essential principles of the Wilfley riffle, and therefore ought not to succeed, but it does. On this account it must conform to other very important principles, or it would not succeed. It would beinteresting to know what these principles are which enable it to succeed. E. P. MATHEWSON, Butte, Mont.-I cannot, explain the principles on which this riffle acts, because I have not given it personal attention. All I can say is that I first saw the riffle in operation several years ago at the Steptoe Valley mill in Nevada, and I was told that a man had been around there guaranteeing that these riffles would make the table do twice as much work and do it better than with the ordinary Wilfley riffles. I heard nothing further about it for a long time. I heard about a year ago, from David Cole, the author of this paper, that the riffles were a success, and that he was using them at Morenci, and if, we were interested he would send the inventor to show us how they worked. As we knew of David Cole's reputation, we invited Mr. Butchart to come up and show us how his riffles worked. We did not have sufficient confidence in the invention to guarantee Mr. Butchart his traveling expenses, but lie came up entirely at his own expense and put in a set of the riffles on one table. It was known as a roughing table in our No.

Jan 5, 1915