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By Fernanda Ferrante, Wagner Reis Modesto Ribeiro, Eduardo Pena Carvalho

CSN Mineração S.A. is the second largest exporter of iron ore in Brazil and is among the five most competitive in the market. Casa de Pedra currently has an approximate production capacity of 30 million tons per year. The fleets of small trucks 6x4 and 8x4 models are responsible for the ore movement, traveling an average distance of 10 km between origin and destination. 116 trucks of this size are used in CSN Mineração for the handling of products. Every month this fleet consumes an average of 550,000 liters of fuel. The objective of the work is to do a fuel consumption analysis by truck through the embedded telemetry system. The reports generated through this system provide the specific consumption of each equipment and also the specific consumption of each Driver. As reports are generated it is possible to assess which equipment had a higher specific consumption and, in this case, the respective trucks with greater consumption are directed to the Maintenance team for analysis and action in the event that a problem is identified in the equipment. At the same time, the analysis of the drivers who had the highest specific consumption and conducted a practical and theoretical training, addressing the techniques for a safer and therefore economical direction, is carried out. In 2019, the economy of fuel consumption type S10 was 204 thousand liters, which represents 9% of all consumption foreseen for the period.

Oct 3, 2019

By S A. Ravishankar

An overview of flotation reagents used in sulfide and non-sulfide separations, from an industrial perspective, is given in this presentation to highlight the current applications knowledge. The historical and theoretical aspects, which are well documented in numerous books and reviews, will only be highlighted, when necessary, to support the theme of this paper, viz critical analysis of reagent research, design, selection and optimisation with an emphasis on relevance to plant needs and practice. The three types of flotation reagents; viz collectors, frothers and modifiers, used currently in the industry are briefly reviewed; pitfalls and gaps, arising from somewhat arbitrary and reductionistic practice in reagent applications, are identified; and the impact of environmental regulations on current and future reagent development is discussed. The importance of frothers and modifiers, which have received less overall attention than collectors, is highlighted. The need for a rational, holistic (or ætotal systemÆ, ætop-downÆ) approach for reagent design, selection and optimisation is discussed with a view to provide remedies for pitfalls and a platform for filling gaps in reagent chemistry and applications, and to develop reagent technology that can deliver robust solutions to plant needs. Flotation Matrix 100TM, a comprehensive package designed at Cytec to incorporate all the elements of the holistic approach û viz definition of mineralogy and plant needs, rule-based expert system rational reagent selection, and laboratory and plant best practices û will also be described.No paper available for this abstract

Jan 1, 2005

By Fulvio Tonon

And Rabcewicz said ?tunnels should be driven full face whenever possible.? ADECO, which stands for ?Analysis of Controlled Deformations in tunnels,? now allows us to fulfll Rabcewicz?s dream in any stress-strain condition. In order to achieve that dream and its consequent control over cost and schedule, however, NATM must be abandoned for the ADECO. The paper presents the basic concepts in the ADECO approach to design, construction and monitoring of tunnels together with some case histories, including: full face excavation for Cassia tunnel (width of 22 m, height of 14 m) in sands and silts under 5 m cover below an archeological area in Rome, Italy; Tartaguille tunnel (face area > 100 m2) advanced full face in highly swelling and squeezing ground under 100 m cover where NATM led to catastrophic failure, France; and 80 km of tunnels (face area > 100 m2) advanced full face in highly squeezing/swelling ground under 500 m cover for the high-speed railway line between Bologne and Florence, Italy (turnkey contract).

By Roy F. Abernethy

This publication by the Federal Bureau of Mines contains the free-swelling indexes for 2,812 samples of coal received from January 26, 1948, to July 15, 1957, and the Hardgrove grindability indexes for 2,339 samples of coal received from June 23, 1947, to July 15, 1957. These data consist of the origin of the sample, bed name, and analysis. Summaries show the high, low, and average values for each bed. The free-swelling index is a relative measure of the caking properties of a coal when burned on a grate, and the Hardgrove grindability index is used to estimate the relative ease of grinding coals. Development and standardization of these test procedures were at a much later date than those for the more familiar tests, such as proximate and ultimate analyses and calorific value determinations. The newer tests are valuable in supplying supplemental information, particularly for assisting in evaluating coals used in certain types of combustion processes.4/ Data from such tests are important to designers of burning equipment, operating engineers, and purchasing agents. Data from these newer tests are scarce and scattered through a number of publications. Special projects were started to determine the free-swelling and grindability indexes, in addition to the regular analyses on the tipple samples collected by Bureau engineers. Since the start of these special projects, all the coal fields of commercial importance have been adequately covered in the sampling program.

Jan 1, 1961

By F. G. Crack, R. V. Ramani, R. L. Frantz

Management for mine construction and development differs from that needed for routine mine production and maintenance. An integrated approach to managing mine development projects must consider contract documents; management organization of a project; the project manager's role and the field supervisor's responsibility; and the use of scientific techniques for planning, scheduling, executing, and controlling projects. Professional project management encompasses the following: • Preparing contract documents that establish technical and financial schedules, and detail the responsibility for the physical work commitment. • Developing a project's organizational structure, to clearly define the roles of the project manager and the field supervisors. • Establishing project management and field supervisor relationships, to avoid ambiguity in assigning responsibility and to ensure desired project progress. • Using management science techniques, particularly networking techniques such as the critical path method for planning scheduling, executing, and controlling projects. Project Versus Production Management Project management differs from routine production management in the following ways: • Uniqueness: A project is unique. Production operations tend to be repetitive. The magnitude of one-time capital expenditures for many facets of mine development warrant special skills and attention. These professional project development skills must already be available by prior experience in the management team. • Personnel: In projects, personnel are usually assigned on a specialty basis and frequently change with the project activity. On the other hand, production personnel work together, more or less permanently. • Management Structure: In a project there may be several staff-line relationships that are not clearly defined and change with changing project activities. In a production situation, the lines of communication and authority are usually well defined. • Time Frame: A difference between project and routine production management is that project activities have comparatively less well defined durations and often tend to be relatively short-term. Production usually has both long-term and short-term plans and well defined long-term and shor-term goals. In project management, formal, critical, short-term reviews are frequently required. In production management, five year plans can be formally adjusted quarterly and annually. Short-term weekly or daily reviews can be informal. • Response to Delays: Delays in a development project may occur without anyone being immediately aware of their existence or suspecting the magnitude of consequence. In contrast, any delays in the production process can be easily identified from prior results comparison. Additionally, the response is quick, usually in a set routine. This can be traced back to the management structure and personnel. • Control Techniques: Measurements of project progress for control are not easily made due to the variety of activities that are carried on at the same time by different work groups. The yard-sticks of performance measurement for individual activities, let alone for the total project, are not easily established. However, due to the difficulty in detecting project delays, a workable control system is vitally important to a project manager. To apply a scientific project control technique such as "management by exception" requires specific planning and monitoring from the project manager for each activity in the project. Production and productivity are quick and effective yard-sticks of measuring performance in a routine operation. Control techniques required in production management usually revolve around these measures. Construction Contracts The construction contract is an important document that establishes contract scope, technical and financial details of the work, and achievement deadlines. It may also serve as the contract document to pay for work done and to verify field progress with planned progress. In practice, it is a good idea to develop a job-specific contract. This whole area is replete with legal precedence and procedures, and it is not the intent here to deal with the intricacies of establishing a contract document. But it is necessary to have an understanding of major contract types. Construction contracts are extremely important legal documents. They may vary in work specifications and enforcement of the provisions. Due to their nature, they must be composed with legal help and will take some time to compile. Even with all the precautions and provisions, it is not uncommon to find owner and contractor disagreeing. Therefore, it is important to include a way to resolve any difference quickly and to incorporate aspects of the contract as part of an overall management control tool for efficient project management.

Jan 7, 1982

By S. Storchheim

MORE and more attention is being paid to the bonding of metals in their solid states. For a better understanding of this technique for joining metals and how it is affected by changes in temperature, pressure, and time at temperature and pressure, a detailed report concerning nickel to aluminum bonding has been published.' In order to broaden the knowledge accrued, some additional work concerning solid state joining of aluminum to copper and aluminum to zirconium was performed. The investigation of the Al-Cu system was considerably more extensive than the investigation of the Al-Zr system. For the A1-Cu system, not only were tensile sudies made but intermetallic penetration rate investigations also were carried out. The effect of temperature on intermetallic penetration rate for the A1-Cu system was determined at 11 tsi pressure, held 2 min. Procedure Apparatus: The hot pressing technique was the means of solid state reaction used and required the equipment depicted in Fig. 1. The following procedure was involved: The two metals to be reacted were placed in an aquadag-lubricated 18-4-1 tool steel die, 16 in. high by 1.440 in. ID, between punches of 1.366 in. diam made of the same material. A thermocouple well was located in the die body 3½ in. down from the top of the die, while another well was located centrally in the bottom punch 8½ in. from the bottom of the die. This die assembly was located in three cylindrical ceramic heating furnaces placed in tandem. Each furnace was controlled individually by a Variac power transformer. In turn, the die and furnaces were placed in a water-cooled stainless steel pot which could be evacuated. A cover, which contained a centrally located Wilson seal with an 18-4-1 1 in. diam ram running through it, was bolted on the pot. After sealing, the pot was evacuated by a roughing pump to 200 microns pressure, after which a diffusion pump was used to bring the pressure down to 5 to 15 u. At this pressure, the furnaces were turned on. As soon as they started to heat, out-gassing of the entire unit raised the pressure to 30 to 400 p. By the time the specimens were at temperature ready to be pressed, approximately 4/2 hr, the vacuum pumps had re-established the 5 to 15 u pressure. Once the desired temperature was reached, the required pressure was applied for a predetermined length of time to the 1 in. ram, through to the top punch, and to the specimen. When the time for keeping the specimen under pressure had elapsed, the pressure was released, the energizing coil current turned off, and the assembly allowed to cool. After cooling, the die was removed from the pot and the specimen was ejected. Specimen Preparation: Two different types of specimens were made for this investigation. One was for subsequent tensile testing, while the other was for determination of intermetallic alloy zone penetration into the parent metals. Tensile Bars—Commercially rolled copper pieces in. thick or zirconium sheet pieces 1/32 in. thick and 1.366 in. diam were placed between commercial 2-S aluminum rod 1 in. thick and 1.366 in. diam. This sandwich in turn was slipped into a 2-S aluminum sleeve 1.438 in. OD and 1.370 in. ID. This sleeve lined the couple up and prevented the aquadag lubricant from getting in between either the A1-Cu or Al-Zr interfaces. Immediately prior to the specimen assembly, the copper or zirconium was abraded on the flat surfaces with 320 grit silicon carbide paper, producing clean smooth surfaces. The aluminum was chemically cleaned just before assembly by: l—degrease in acetone, 2—distilled water rinse, 3—immersion for 3 min in 5 pct NaOH at 70" to 80°C, 4—distilled water rinse, 5—immersion for 2 min in 50 pct HNO3 solution at room temperature, 6—distilled water rinse, and 7—drying in a blast of gas. After the A1-Cu sandwiches were hot pressed and ejected, the specimens were machined such that the aluminum sleeve was removed, and the remaining aluminum was then threaded; the bar so produced was tested later for tensile strength. In all the instances where Al-Cu couples were tested, the specimens broke during the test at the Cu-A1 interface and never within the aluminum or copper. The ultimate tensile strength values at times showed considerable scatter for a set of given reaction conditions. Because of this, as many as three to five specimens were made for a particular set of conditions. The trend of the average tensile strengths obtained was not as conclusive as was the trend of the maximum tensile strengths, the latter values being obtained under optimum reaction conditions. Therefore, the values of ultimate tensile strength given herein are maximums.

Jan 1, 1956

By H. C. Brown

SINCE 1934 the steel industry has been utilizing the spectrograph for supplementing wet chemical analysis in the production control of electric and open hearth furnaces. This means of control made great strides during the war years because of the general acceptance of the spectrograph and the increased emphasis that was placed on rapid control methods. However, in the post war era, with the demand still on increased production, it became apparent that a still more rapid and economical means of production control was needed. Since the spectrograph had been used mostly in the analysis of low alloying and residual elements, it also became apparent that equipment was needed to extend the spectrographic technique to the analysis of the high alloying elements in stainless steel. For these reasons, companies manufacturing spectrographic equipment were prompted to start development work on direct reading instruments. In June 1949, the Applied Research Laboratories of Glendale, Calif., announced that a direct method of spectrochemical analysis for stainless type steels had been developed. This paper will describe the use of the Applied Research Laboratories Production Control Quantometer in the quantitative control of stainless, silicon, and plain carbon steels being made at the Butler Pennsylvania Div. of the Armco Steel Corp. The Armco Butler Div. has one 70-ton electric furnace and six 150-ton open hearth furnaces. The electric furnace is employed in the making of all types of stainless steel and the open hearth furnaces are used for the production of silicon, wheel, and plain carbon steels. The ARL quantometer was purchased primarily for the purpose of controlling the steelmaking in the electric furnace, but its use has been extended for the analysis of final tests (ladle tests) on a number of different types of stainless, silicon, and plain carbon steels. Because of this additional work by the quantometer, substantial savings in manpower and time have been realized by the laboratory. In the analysis of a set of preliminary tests from the stainless steel furnace, approximately 40 min in laboratory time are saved due to quantometric analyses. Despite the fact that more specialty grades of stainless steel are being made in the electric furnace, the average tons per hour have been increased since the quantometer was put into operation. Specialty grades require more furnace time than regular commodity grades of stainless steel. The installation of the ARL production control quantometer was completed on March 13, 1952. By May 1, 1952, the instrument was calibrated for nickel, chromium, manganese, silicon, and molybdenum, which are the elements necessary for the production control of the stainless steel furnace. Within the following month, training of personnel on the quantometer was achieved and a study of the accuracy of the instrument showed that the results obtained were sufficiently accurate for control purposes. Therefore, on June 11, 1952, the quantometer was placed on production control for all types of stainless steels. Starting September 11, 1952, the instrument was gradually placed on ladle analysis (final tests) as the analytical curves were refined and additional curves were drawn. The quantometer has been relatively free of breakdowns since placing it on production control. The samples from only one stainless steel heat have had to be analyzed by wet chemistry because of instrument trouble. The previously existing heat-time record was also bettered by 15 min on a commodity grade of 18-8 stainless steel. Scope of Control In general, the quantometer determines all elements necessary for the production control of all types of stainless steel heats and for the ladle analysis of various types of stainless steel heats. It is also used in reporting final results for silicon, manganese, chromium, nickel, molybdenum, tin, copper, and aluminum on all silicon steel grades and manganese, chromium, nickel, molybdenum, tin, and copper on several plain carbon steel grades. Table I shows the elements and the concentration ranges of these elements in the various types of stainless, silicon, and plain carbon steel that are determined on the quantometer. A study of the results obtained on ladle test samples of stainless steel types 410, 430, 430 Ti, 446, 301, 302, 304, 304L, 305, and 17-7 PH will be discussed. Also included in the study are the results obtained on ladle test samples of a number of silicon steels. Apparatus In order to take full advantage of the potentials of the production control quantometer, the unit has been placed in an air-conditioned room with relative humidity control. The temperature is maintained at 73'22°F and the humidity at 45&5 pct. The air conditioning serves as a precaution to minimize the amount of adjustment and calibration needed during operation. It also reduces contaminating fumes and dust and thereby lessens the necessity for maintenance on the equipment. The quantometer is composed of three units: the high precision multisource unit, the 1.5 meter vertical spectrometer, and the console. The source unit supplies excitation conditions varying from spark-like discharges to arc-like discharges. The voltage to the source unit is supplied by a motor-generator

Jan 1, 1955

By Benny Langston, Frank M. Stephens

Although little information is available concerning small-scale equipment for dust collection in laboratories, it is possible to adapt standard equipment for laboratory use. Dust from laboratory processes may be collected by cyclone separators, filters, electrostatic separators, scrubbers, and settling chambers. IN recent years much attention has been given to recovery, treatment, and disposal of dusts discharged into the atmosphere from operations of industry. considerable data has been accumulated on both operation and design of dust-collector equipment for commercial installations. On the other hand, there is almost no published data on design and construction of small-scale equipment to handle dust problems that arise in the ore-dressing laboratory. Dust-collection equipment such as multiclones, single-cyclones, scrubbers, chemical and mechanical filters, settling chambers, and electrostatic separators has proved its efficiency for collecting dust in industry. In the laboratory, however, the engineer is faced with the problem of collecting small quantities of dust, inexpensively, without diverting the major effort from the metallurgical problem to the problem of collecting dust produced by the process. For most applications standard dust-collection equipment is too large for use in the laboratory; however, for control of dust in large working areas it is often possible to use a standard dust collector, such as an air filter, with branch ducts to eliminate a health hazard. For example, the well-furnished sample-preparation room containing small jaw crushers, rolls, and pulverizers, in addition to the riffles and screens necessary for preparation of samples, presents a perennial source of dust. The authors' experience has shown that a combination system consisting of overhead branch ducts to the individual equipment and floor ducts with grills, where applicable, connected to a central dust collector effectively removes dust generated in preparation of samples. Fig. 1 is a sketch of a downdraft dust-collector for table installation. Similar systems can be built with floor grids. For portable equipment such as laboratory vibrating screens this type of installation with a steel grill to support the heavy load is reasonably efficient. Overhead branch ducts to individual crushing and grinding equipment, although efficient, must be carefully controlled by dampers to prevent excess loss or a change in the composition of the sample. Change in sample composition can result from excess velocity, which causes selective removal of constituents of low specific gravity. Fig. 2' shows the theoretical effect of terminal velocity on spherical particles of different specific gravities in air and water under action of gravity. Fig. 3 shows the effect of air velocity on composition of CaCO, coal mixtures. Although the entrainment of dust particles in a moving air stream is the basic mechanism by which all dust-collection equipment functions, usually intake velocity of the dust-collection system must be controlled to prevent loss of part of the sample. As an example of what may happen when excess velocities are used, a mixture of 50 pct coal and 50 pct limestone was crushed to —10 mesh and fed to a pulverizer equipped with an overhead dust-collection system. Fig. 4 shows the overhead dust-collection equipment used in this test. The pulverizer was set to give a product 95 pct —100 mesh in two stages. Velocity of air passing over the lip of the pulverizer was measured with an anemometer. After grinding, the finished product was analyzed to show the amount of calcium carbonate present. Fig. 3 shows graphically the increase in calcium carbonate as velocity through the dust-collection duct was increased. These data show that at a velocity of 1 ft per sec little if any of the coal was entrained by the overhead draft. At the maximum velocity, about 6.5 ft per sec, approximately 7 pct more coal was entrained than calcium carbonate. From an operating standpoint, this problem can be remedied easily by dampering the line to control velocity. The lowest velocity commensurate with satisfactory dust control should be used to prevent excess loss and, in some cases, selective dust loss. Collection of Dust in Laboratory Processes As in industry, the engineer desires to collect efficiently the dust produced by processes being investigated on a laboratory scale. However, in the collection of laboratory dusts he is faced with two additional problems: 1—The volumes of gas and the quantity of dust that must be recovered are small when compared with the capacity of standard dust-collector equipment, which must be scaled down in design except for collection of dust from large pilot-plant operations. 2—In addition, because of the variety of problems studied in the process laboratory, the engineer cannot design today a dust collector that will meet the conditions imposed by the processes of tomorrow. Sometimes, therefore, he must compromise collection efficiency to minimize the cost of fabrication and the amount of time diverted from the metallurgical to the dust-control problem. For collection of dust from laboratory processes a cyclone separator, filters, electrostatic separators, scrubbers, and settling chambers can usually be adapted for small-scale operations. The following

Jan 1, 1955

By D. G. Westlake

Polycrystalline tensile specimens of various Zr-0-H alloys have been tested at 298°, 178°, and 77°K. Solute oxygen and hydride precipitates in quenched alloys made individual contributions to the yield strength at 0.2 pct strain which combined to produce a resultant strength increment, a,., Ductility changes which were ohserved can he interpreted in terms of the various oxygen and hydrogen concentrations, testing tem -peratures, and dispositions of the hydride. ADDITIONS of oxygen in solid solution were known to increase the yield and tensile strengths of polycrystalline zirconium as early as 1951.' More recently, the critical resolved shear stress (CRSS) for prism slip in zirconium single crystals was also shown to be affected by the solute oxygen impurity.' This latter work also demonstrated that large increments of strength could be contributed by the finely dispersed zirconium hydride precipitates that are present in quenched Zr-H alloys.3 It was concluded that the combined strengthening due to alloying could be expressed by where to is the increase in the CRSS due to solute oxygen alone and TH is the increase due to finely dispersed hydride precipitates. Eq. [I] is analogous to one used to express the combined strengthening effects of work hardening and neutron radiation damage.4 Eq. [1] was verified only indirectly and for only small amounts of the impurities—up to 0.14 at. pct 0 and 0.63 at. pct H. The present investigation was undertaken to obtain a more direct verification of the validity of the form of Eq. [1] for this system and also to determine the combined effects of oxygen and finely dispersed hydride precipitates on the tensile strength and ductility of polycrystalline zirconium. EXPERIMENTAL PROCEDURE Tensile specimens were machined from the same rolled billet of Kroll zirconium used in the earlier study.' These measured 38 by 4.7 by 0.5 mm and had 10-mm gage lengths which were 2.8 by 0.5 mm. Each specimen was ß-annealed in vacuo at 1173°K for 15.5 hr and a-annealed at 1073°K for 4 hr to D. G. WESTLAKE, Member AIME, is Associate Metal l ur-gist, Metallurgy Division, Argonne National Laboratory, Argonne, III. Manuscript submitted July 17, 1964. IMD______________ give an equiaxed structure with grain diameters averaging 0.06 mm. Oxygen was added by allowing the metal to react with a known quantity of oxygen during the 0 anneal and known quantities of hydrogen were added during the a anneal. Each alloy was encapsulated in Pyrex under vacuum, annealed at 873°K for 4 hr, quenched into ice water, and polished by immersion in a solution of 46.75 vol pct H2O, 46.75 vol pct concentrated HNO3, and 6.5 vol pct HF (49 pct) at 298°K. Special heat treatments given to a few specimens are described in the results below. Tensile tests were done on an Instron machine and were begun within 20 min after the quench, except where specified otherwise. Tests at 298°K were in air, at 178°K in acetone, and at 77°K in liquid nitrogen. All tests were at a strain rate of 8x sec-1. RESULTS AND DISCUSSION Yield Stress at 298°K. The compositions of alloys and the corresponding yield stresses (0.2 pct strain) are given in Table I. A plot of the yield stresses of the oxygen alloys, A, B, C, and D, indicates that varies linearly with CO1/2, where Co is the oxygen concentration, Fig. 1. This is in accord with Fleischer's6 theory for solution strengthening if the oxygen atoms do not cluster, or the cluster size remains constant with increasing oxygen concentration. In Fig. 1, it appears that if one could prepare some oxygen-free zirconium its yield stress would be very low. Therefore, we shall assume that for the oxygen alloys is equivalent to O0, the strength increment contributed by the presence of oxygen. The relationship between0.2and Co is expressed by 0.2 = 31.3 CO1/2, when the yield stress is in kg per sq mm and the concentration is in at. pct. Each of the hydrogen alloys, Al, A2, A3, and A4, contained 0.081 at. pct 0 as an impurity. In Fig. 1, it appears that this small amount of oxygen makes a significant contribution to the strength which cannot be ignored when we evaluate the contribution of the finely dispersed hydride. Let us assume the validity of the following equation: a0.2 = (a2o+a2R)1/2 [2] which is analogous to Eq. [I] for single crystals, and calculate values of UH for the hydrogen alloys by using the experimental values of 0.2 and o (0.081 at. pct) = 8.9 kg per sq mm. For 0.36 at. pct H, oH = 6.47; for 0.72 at. pct H, OH = 11.30; for 2.16 at. pct H, OH = 19.4; and for 3.60 at. pct H,

Jan 1, 1965

By G. H. Miller

With the recent advances which have been made in science and technology and the increased use of mathematics in this area, the question of the best mathematics courses for a mining engineer to take is of major importance. The question becomes even more difficult to answer due to the recent increase in the number of different mathematics courses in the last two decades offered by the mathematics departments. Therefore, the National Study of Mathematics Requirements for Scientists and Engineers (NSMRSE) was designed to provide some answers to these questions. Approximately 10,000 scientists and engineers were selected for the Study, These individuals were placed in two categories: (1) The Awards Group, recipients of national honors or awards and those recommended by the members of the Board of Advisors as having national and international reputations in their areas of specialization and (2) The Abstracts Group, persons exceptionally productive in their research, based on the number of journal articles listed in the last five years in the Engineering Index, Scientific and Technological Aerospace Reports, Chemical Abstracts, Biological Abstracts, and the Physics Abstracts. The NSMRSE Course Recommendation Form and the Instruction and Course Content Sheet were constructed with the aid of the Board of Advisors and other consultants. For the Study, 40 courses were selected by the mathematical consultants. In order to make sure that the basic content of the mathematics courses was the same for all respondents, a brief resume of each of the 40 courses was given. The NSMRSE Course Recommendation Form consisted of seven sections. These sections were as follows: Section 1, 38 different specializations; Section 2, orientation of work (applied through theoretical); Section 3, highest degree obtained; Section 4, place of employment (academic, nonacademic); Section 5, administrative capacity (administrative or nonadministrative); Section 6, age groups (five-year intervals). Section 7 contained the 40 courses which were to be marked according to five categories: (1) Course Length, 3 to 36 weeks; (2) Applied-Theoretical Orientation, a five-point scale; (3) Course Level, freshman through graduate; (4) Knowledge of Course; and (5) Use of Course Content in Work. The Analysis The report of the data is based on the replies received from 44 mining engineers. This group was part of the Awards and Abstracts Group for all engineers. The resume of the recommended courses is reported in quintiles (upper fifth to lower fifth), since recommendations of this kind are not precise. The results of the Study are based on recommendations of the most active research men in engineering in the U.S. today; therefore, the reader should realize that these course recommendations represent an upper bound of mathematics requirements for the Ph.D. in both undergraduate and graduate work. Conclusions and Recommendations 1) Mining engineering students who plan to be active research specialists should take all those courses which are "very highly recommended" (80-10070) and "highly recommended" (60-79.9%). Those courses in the upper two quintiles and recommended by most mining engineers are: first-year calculus, third-semester calculus, elementary differential equations, applied statistics, and machine computation. Courses of "moderate recommendation" (40-59.9%) are: vectors, intermediate ordinary differential equations, the first course in partial differential equations, elementary probability, and linear programming. 2) The great majority of mining engineers indicated that they prefer a course which is concerned primarily with applications. Only the standard courses such as first-year college mathematics, calculus, differential equations, and advanced calculus received a recommendation for 50% theory and 50% practice. Therefore, all mathematics courses given to mining engineers should contain many applications and little theory. Engineers in both the applied and the combination (ap-plied-theoretical) groups indicated a definite need for applications in all courses. 3) In general, recommendations were for mathematics courses to be given for short intervals of time such as 3, 6, or 12 weeks. Only the standard courses mentioned previously received the usual one-semester or one-year recommendation. Therefore, it is of value to combine several related courses into a one or two-semester course so that the mining engineering student could acquire important mathematical knowledge at an early date in order to prepare him for his research. 4) There was little use for the newer courses in modern mathematics such as the functional analysis sequence, the modern algebra sequence, and the group theory sequence. In addition, there were uniformly very low recommendations (0-19.9%) for multilinear algebra, complex variables, mathematical logic, special functions, integral equations, approximation theory, analytic mechanics, integral transforms, and geometric algebra. Therefore, these courses should be given a low priority. 5a) Comparisons among mining engineers with different backgrounds showed that the combination ap-plied-theoretical group recommended more mathematics than the applied group. 5b) There was little difference in recommendations between the administrative group and the nonadminis-trative group. 5c) Analysis of age groups showed that those in the lower age groups gave significantly higher recommendations to courses such as the first course in partial dif-

Jan 1, 1971

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation' can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation' in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

By I. R. Kramer

I. R. Kramer (Martin Co.)—In a recent paper Nakada and Chalmers24 reported some observations of effects of surface conditions on the stress-strain curves of aluminum and gold single crystals. It is of interest to compare these observations with the results published previously in this journal and to comment on their general conclusions. In brief, Nakada and Chalmers concluded that the removal of the surface layer of a prestrained specimen lowered the stress-strain curve for aluminum but not that for gold. Further, they concluded that the surface work hardening of aluminum is confined to a depth not more than l0-3 cm. In our results25 published previously, it was pointed out that when prestrained specimens of aluminum and gold were polished to reduce the thickness upon reloading the initial flow stress decreased markedly. Further if a sufficient amount of metal was removed, the yield point failed to appear. With continued application of the load the stress-strain curve became coincident with that of the virgin crystal. We have found this behavior in some 100 determinations to hold consistently for gold, aluminum, and copper in both single and poly-crystalline specimens. The amount of strain required before the curves coincided depends upon the amount of metal removed but it is usually less than 0.01. This type of behavior is the same as that reported for metarecovery by other investigators.29 For aluminum specimens which have been prestrained and then heated to temperatures above 50°C we have consistently found that the stress-strain curve was typical of the orthorecovery28 type. In this case the stress-strain curve always lies below that of the virgin specimen. With respect to Ref. 24 the curves for aluminum are always below that of the virgin curves, while those for gold become coincident. This observation indicates at least for aluminum that the specimens must have been heated to a temperature high enough to cause recovery by an alteration of the internal dislocations. In addition, a recovery would be expected because of the removal of the surface work-hardened layer. Nakada27 had reported that, with his particular apparatus in which a perchloric acid polishing solution was used, the temperature of the specimen increased 65°C. The curves presented in Ref. 24 for gold do not permit one to detect the initial flow stress upon reloading after the surface-removal treatment. In fact, contrary to the method used by Nakada and Chalmers, the change in the stress-strain curve produced by a surface-removal treatment cannot be described in terms of a decrease in stress at strains much higher than that at the initial flow stress because of the coincidence of the curves at the higher strain values. With regard to the depth of the work-hardened surface layer, our data show for aluminum single crystals (7.5 by 0.3 by 0.3 cm) that the initial flow stress remained constant after 12 x 10-3 cm had been removed from the thickness. This depth was independent of the prior strain. For gold crystals this depth is somewhere between 10 x 10-3 and 20 x 10-3 cm. Y. Nakada (author's reply)— Kramer states,28 "for aluminum specimens which have been prestrained and then heated to temperatures above 50°C, we have consistently found that the stress-strain curve was typical of the orthorecovery28 type. In this case the stress-strain curve always lies below that of the virgin specimen." However, Cherian et a1.26 discovered that aluminum polycrystals annealed at 32" and 100°C showed the metarecovery behavior. They showed that the orthorecovery behavior did not appear until the crystals were annealed at 150°C. Kramer suggests28 that the drop in the flow stress of aluminum crystals after the surface removal by electropolishing24 may be due to the recovery caused by the temperature rise which may occur during the electropolishing.27 However, as indirectly stated in Ref. 24, the current density used in these electro -polishing experiments was 0.15 amp per sq cm. According to ref. 27, this current density should cause a temperature rise of only 40°C. This may cause the metarecovery but not the orthorecovery. Furthermore, as stated explicitly in Ref. 24, the surface removal was accomplished by chemical etching as well as by electropolishing. The results were the same for both electropolishing and etching. During the etching, the specimen temperature did not rise above 35°C. Some aluminum crystals were placed in water at 35° C for 30 min. These crystals did not show the decrease in flow stress. Therefore, it is quite clear that the flow-stress drop after the surface removal is not caused by a high-temperature recovery. However, as Kramer points out,28 it is quite possible that the internal dislocation structure may have been altered because of the removal of the highly work-hardened surface layer. However, how much this rearrangement contributes toward the flow-stress decrease is not known at present.

Jan 1, 1965

By J Price, M. R. Geer, H. F. Yancey

COAL mine operators recognize coal as an abrasive material, because the wear of drilling, cutting, and conveying equipment is reflected as a cost item for replacement of parts. Similarly, industrial consumers of coal experience abrasive wear on all coal-handling equipment. Operators of pulverized fuel plants are doubtless most keenly aware of the abrasiveness of coal, because under the high contact pressures developed between coal and metal in pulverizers, abrasive wear is increased many fold. Moreover, experience in operating pulverized fuel plants has demonstrated that some coals are much more abrasive than others. Hardgrove' stated that maintenance costs entailed by the wear of grinding elements is often a more important variable than the cost of the power required to pulverize different coals. Craig2 also reports that one coal may cause pulverizer parts to wear several times faster than another. It is apparent, therefore, that those concerned with pulverizing coal could profitably employ a method for estimating the abrasiveness of different coals, just as they utilize standard tests for thermal value, grindability, and ash-fusion temperature to assist in selecting the most suitable and economical coal to use in a particular plant. The objective of this investigation was to develop a test procedure that would be suitable for general use in estimating the abrasiveness of coals. However, few, if any, of the standard tests now used for evaluating the properties of coal are the product of a single investigation or the result of a single investigator's efforts. Rather, in each case, a testing procedure was devised by one investigator, used by others on a wider variety of coals, and finally refined completely as the result of the joint efforts of a number of interested people. Thus, the test procedure for estimating abrasiveness developed in the course of this work may not be refined sufficiently in its present form for general use, but it may serve as the starting point from which an acceptable test procedure can be developed. The method has been used thus far on only about a dozen coals, and there has been no opportunity to attempt a correlation between experimental results and actual plant experience. Only wider use of the procedure by other investigators and correlation with plant experience can determine to what extent the method will have to be modified to render it suitable for general application. Test Method Although the literature contains no record of an attempt to devise a method for estimating the abrasiveness of coal that could be used industrially, several investigators have tested properties of coal that are closely related to its abrasiveness. The abrasiveness of a material generally is considered to be related to its hardness, and hardness tests for coal have been employed by Heywood,' O'Neill," and Mathes. Also, the resistance of coal to abrasion, a property that presumably is related to the abrasiveness of coal, was measured by Heywooda and by Simek, Pulkrabek, and Coufalik.2 11 these investigators tested only individual pieces of coal. Since coal is a heterogeneous material having components of varying properties, tests of this type can yield results having little more than academic interest. Only a test method that utilizes a representative sample of coal can give results that are useful industrially. The abrasion tests used for various other materials have been considered for adaptation to testing the abrasiveness of coal. The tests used for metals,7-9 paving and flooring,'" and rubber," cannot be used because coal is not sufficiently abrasive.~ The present experimental work was begun before World War II and was conducted by three research fellows"'" working under a joint agreement between the University of Washington and the Bureau of Mines. After a great deal of preliminary work with a variety of apparatus and materials, a test procedure was developed which consisted of rotating a test disk 2Yz in. diam in a steel mortar containing the coal sample. The shaft carrying the test disk at the lower end and a 100-lb load on the upper end was free to move vertically. The bed of coal in the mortar was kept fluid by low-pressure air admitted through a port near the bottom of the mortar. Measurable wear on an Armco iron disk could be obtained in this test procedure, but, despite extensive efforts to eliminate them, several major disadvantages remained in this test method. First, with most coals the amount of wear on the iron disk did not exceed a few milligrams. Second, a single type of disk was not applicable for all coals. A smooth iron disk gave satisfactory results with both bituminous and sub-bituminous coals, but hardly any wear with anthracite or coke. A disk having studs or projections gave more satisfactory abrasion losses with anthracite and coke and presented no operating difficulties with free-burning bituminous and sub-bituminous coals. It could not, however, be used with caking coals because these coals formed a

Jan 1, 1952

By H. H. Kellogg

Equations representing the standard free energy of formation as a function of temperature, for thirty metallic chlorides, are presented and plotted on a free-energy vs. temperature diagram. The use of these data for calculations on reduction of metallic chlorides, refining of metals with chlorine, and chlorination of metallic oxides and sulphides is illustrated. CHLORINE metallurgy' has attracted metallur- gists for more than a century because the unusual properties of the metallic chlorides—low melting point, high volatility, and ease of formation from the oxides—make possible many useful extractive processes. Interest in chlorine processes is undergoing a renaissance due to present availability of chlorine at relatively low prices, and to recent advances in technology. During the present century there have accumulated a considerable number of reliable values of the thermodynamic constants for the metals and their chlorides. These data permit the calculation of free-energy equations for many metallurgically important reactions. Consideration of free-energy values makes possible certain predictions of the direction and extent of a given reaction, as well as the effect of temperature, pressure, and composition upon the result. Reaction rate, although not predictable from free-energy data, is usually sufficiently great at elevated temperatures that diffusion of the reactants and products to and from the zone of reaction determines the actual rate. Thus, if the free-energy indication is favorable, the chances are good that a high temperature metallurgical reaction will proceed at a reasonable rate, if adequate provision for rapid diffusion has been made. This paper presents standard free-energy equations for a number of metallic chlorides, based on data which are scattered throughout the literature. The equations are presented in a form that simplifies their use, and typical examples are given of the application of free-energy data to metallurgical processes. Free Energy of Reaction The free-energy change (AG) of a reaction is the true measure of the "driving force" of the reaction under a given set of conditions, and this is related to the standard free-energy change (AGO) of the reaction as follows: For the reaction: bB + cC = dD + eE ?G = ?G°+RTln ADd. AEA / ABb. ACc where A, = activity of constituent (i) T = absolute temperature, OK R = gas constant The criterion of a spontaneous reaction from left to right, at constant temperature and pressure, is a negative value for the free-energy change (?G). The standard free energy of the reaction is equal to the free energy of the reaction when all the reactants and products are at unit activity, since under these conditions the second term on the right-hand side of eq 1 is equal to zero. The concept of activity is treated fully in many textbooks on chemical thermodynamics1 and in a recent article by Chipman.2 Briefly, the activity (A,) of a constituent (i) is a measure of the reactivity of this constituent relative to its reactivity in some arbitrary standard state. For liquids and solids the standard state most often used is the pure liquid or solid constituent. Thus the activity of a pure liquid or solid in a metallurgical reaction is equal to unity. Gases under moderate pressure and at elevated temperatures behave very nearly as 'idea1 gases,' and the standard state is chosen as the gas at 1 atm pressure. The activity of an ideal gas is therefore equal to its partial pressure, and this relation is sufficiently exact for real gases in most metallurgical reactions. For a liquid or solid solution there is in general no simple way to express the activity of a constituent as a function of its concentration, and activity must be determined by experiment. A few solutions follow a so-called 'ideal' behavior, and if the pure constituent is chosen as the standard state, the activity of a constituent in an ideal solution becomes equal to its mol fraction. When a reaction reaches a state of thermodynamic equilibrium at constant temperature and pressure, AG becomes equal to zero and eq 1 reduces to: [ADd . AEe ?G°=RTln Abb ¦ Ac c equilibrium [2] The brackets surrounding the activity term are used to emphasize that each of the activities is an activity under equilibrium conditions—not just any arbitrarily assigned value. The bracketed term is the equilibrium constant (K) of the reaction. Eq 2 makes possible the calculation of equilibrium activities for a given reaction, if AGO is known at the desired temperature. The standard free-energy equations presented in this paper were calculated from the fundamental thermodynamic values of enthalpy of formation at 298°K (AH°,), standard entropy at 298°K (So298), heat capacity as a function of temperature (Cp), and enthalpies of transition, fusion, vaporization, and sublimation for the various constituents. Where possible the data reported in the recent "Selected Values of Chemical Thermodynamic Properties," published by the Bureau of Standards," were used. A large number of data came from the publications

Jan 1, 1951

By Bruce Kennedy, Charles Bruce

MINERAL EXPLORATION 'The Function of Exploration Mineral exploration aims at locating the presence of economic deposits and establishing their nature, shape, and grade. As all ore bodies are finite, exploration is essentially the lifeblood of the mining industry. It is divided into two phases, reconnaissance and target investigation. It involves geological mapping, geophysical prospecting (aerial and ground or both), geochemical surveys, prospect drilling, and/or exploratory under-ground workings. Successful exploration is followed by development drilling, mine development, and eventually operation. In underground mining, the term "ore" is applied rather loosely to metalliferous rock that can be profit- ably mined, but nonmetallic industrial minerals and energy related materials constitute a large and growing portion of the tonnage extracted by underground methods each year. It is appropriate, therefore, to consider exploration as the search for any useful substance occurring in the earth or in the oceans that is of sufficient value as to volume, grade, chemical and physical com- position, and location as to make extraction by mining commercially profitable for the investment required. The Selection Process The search for ore includes hundreds of mineral commodities. The more successful exploration organizations tend to restrict the search to the mineral commodities for which they have strong exploration expertise and which have a high probability of being concentrated in areas open to exploration and development in sufficient volume, grade, and proximity to the surface to warrant the large expenditures of risk capital in finding an ore body. Special expertise is needed to engage in mineral exploration and development for the extended periods required for success. Individual prospectors continue to discover mineral occurrences, but it generally takes an organization with strong financial resources to carry the exploration process forward to the point of developing "ore." Still greater corporate resources in the form of management, engineering, and sales capability are needed to develop an ore body into an operating mine. In the past, companies other than those engaged in mining rarely conducted exploration, since they lacked the technical skills and know-how to bring a mine to fruition. A notable trend in recent years has been the success of other resource-oriented firms, such as petroleum companies, that have not only acquired the necessary skills to engage in exploration for hard minerals, but are doing so on a far more intensive scale than known in the industry heretofore. The desire to diversify from increasingly regulated oil and gas, the potential for the discovery of a bonanza, and the large scale of mining projects for these capital-intensive firms are the attractions. US government and certain international organizations, such as the United Nations, have fielded sizable exploration programs in the past decade on behalf of Third World countries wherein many of the world's higher grade deposits and scarce mineral resources are located. The level of overall mineral exploration in the industry is, regrettably, closely geared to the business cycle. Accelerated search during the periods of strong demand, shortages, and high prices, together with the long lead times necessary to develop mineral finds, often creates surges in supply which invariably are followed by a collapse in prices. The trend is, therefore, to exploration funding by larger better-endowed firms having the staying power to weather the cyclical nature of mining. Tax incentives, tariff policies, and other incentives have a decided impact on the level and nature of exploration. Surface mining regulations and environmental forces have fostered a renewed interest in under- ground development despite the lower average costs of surface mining. Spiraling inflation has caused mining costs to outpace prices for many mineral substances. Organizations increasingly are directing their search away from high- grade but limited tonnage occurrences toward low-grade disseminated bulk tonnages amenable to mining on a vast scale. Mining continues, therefore, to grow even more capital-intensive with half-billion-dollar mine-mill- smelter complexes now commonplace, compared with the hundred-million-dollar projects of a decade ago. Reconnaissance Exploration Having elected to search for specific mineral commodities, the exploration company narrows its focus to a reconnaissance of those regions offering the best potential. A working hypothesis which is constantly up- dated concerning the geologic controls for ore occurrence guides the search. The possibilities for discovery are best in areas of existing mines and known ore bodies, where the probabilities are high for additional ore occurrences. In such areas, published data on the trends and geologic controls of known mineral occurrences aid the search. Even in some remote territories, a variety of geologic data is available to the explorationist. The major sources of basic geologic data are the libraries of the US Geological Survey (USGS), the state geological surveys, the American Institute of Mining, Metallurgical, and Petroleum Engineers (AIME), the US Bureau of Mines, and various institutions such as Colorado School of Mines. Overseas, virtually all of the countries have their own geologic survey groups which are associated directly, or indirectly, with their respective ministries of mines. The objective of reconnaissance exploration is to narrow the search by pinpointing target areas having interesting mineralization. These favorable areas are then investigated in detail to delineate potential ore bodies.

Jan 1, 1982

By R. R. Judd, H. W. Paxton

The rate of dissolution of cementite was studied in three low-carbon materials: a zone-refined Fe-C alloy, an Fe-0.5pct Mn-C alloy, and a commercial low-carbon steel. The materials were spheroidized, ad then held isothermally at temperatures above the Al. The isothermal anneal was interrupted periodically by a water quench and the specimens were analyzed by quantitative metallography for the amount of aus-tenite formed during the anneal. The results of this study were compared with an analytical model for the process, which assumes that carbon diffusion in aus-tenite is the rate-controlling step for the cementite dissolution process. The correlation between the model and the experimental data is excellent for the zone-refined Fe-C alloys; however, the Fe-0.5 pct Mn-C alloys and the commercial steel deviate from the calculated model. This deviation is thought to be a result of manganese segregation between the carbide and the matrix. The rate of nucleation of austenite at carbide interfaces was reduced by the manganese addition and enhanced by the presence of ferrite-ferrite grain boundaries. PREVIOUS investigations of the nucleation and growth of austenite from ferrite-carbide aggregates are not entirely satisfying for at least one of several reasons. The most prevalent of these is a lack of quantitative data. Engineering studies have been run on many steels with little control over important parameters such as composition and initial aggregate structure. The data obtained are valid only for material with identical chemistry and thermal history. A more informative approach to the problem of aus-tenitization would be to determine the mechanism that controls the rate of solution of carbide in austenite and how it is modified by alloying elements. This information could then be used to calculate an austeniti-zation rate for any material, provided its composition and structure are known. The object of the present work is to establish the rate-controlling step for cementite dissolution in Fe-C austenite and to investigate the modification of this rate by small manganese additions. The composition and structure of the material used were carefully controlled and all measurements were designed to allow a quantitative analysis of the kinetic process that controls the austenitization rate. A MODEL FOR DISSOLUTION OF CEMENTITE Cementite dissolution has been analyzed mathematically by a model that approximates the material used in the experiments. This model postulates a regular ar-array of identical cementite spheroids with 4 C( diam, embedded in a grain boundary- free ferrite matrix. The analysis provides a detailed description of the dissolution of one carbide spheroid and a generalization of the solution by summation over all the carbides in the material. The carbides may be isolated by defining identical, space-filling cells of ferrite around them. If the cell dimensions are greater than the diameter of the austenite sphere resulting from complete dissolution of the carbide, and no interaction (through diffusion in ferrite) takes place between cells during the dissolution process, the model need concern only one cell, since the solution in each cell is identical. In the experimental material, the dimensions of the cell, the carbide, and the final austenite sphere are approximately 24, 4, and 8 p, respectively; use of the single cell is therefore justified. The experimental observations are made on the austenite nodules that form around each carbide during the dissolution process. The model concerns the growth of these austenite nodules. The attendant shrinking of the carbide can be obtained from the same analysis by an extension of the calculations. Several a priori assumptions are necessary to make the analysis of the growth problem tractable. They are: 1) carbon diffusion through the austenite nodule is the rate-controlling process; 2) local equilibrium exists at all interfaces, 3) the austenite nucleus that forms on each carbide instantaneously envelops the carbide; 4) during the austenite growth process, the diffusion flux of carbon in ferrite is insignificant; 5) a quasi-steady state exists in the austenite concentration field; that is, at any instant during the dissolution process, the austenite carbon concentration gradient closely approximates that for a steady-state solution; and 6) the effects of capillarity on the dissolution rate of the carbides can be neglected. Referring to Fig. 1, a mass balance at the y-a interface for an infinitesimal boundary movement gives: Where rb is the outer radius of the austenite shell, C1 and C are carbon concentrations at the interface in austenite and ferrite, respectively, see Fig. 2, is the diffusion coefficient of carbon in austenite for the concentration of carbon at the interface, and t is time. The fifth assumption permits the austenite carbon concentration to be approximated by the Laplace solution for the spherical case. Therefore, where C(Y) is the carbon concentration at r, and A and B are constants. Local interfacial equilibrium fixes the boundary conditions for the diffusion problem. They are:

Jan 1, 1969

By R. L. Moment

The anisotropic elastic behavior of rolled beryllium sheet has been measured, using a pulse echo technique, and compared with X-ray diffraction data. Calculated elastic stiffness constants compared favorably with published values for beryllium single crystals which were attributed to the strong (0002) rolling plane texture. Variations of Young's modulus in the yolling plane could be associated with the velative distribution of (0002) planes out of their ideal position in the rollitzg pkule. WHEN a metal is subjected to cold working such as drawing, forming, or rolling, a crystallographic texture develops which can significantly alter its physical properties. One method for detecting this texture is X-ray diffraction, but Alers and Liu' have recently pointed out how the prediction of anisotropic physical properties from pole figures alone is not always accurate due to differences in interpretation. Variations in Young's modulus with orientation or, more completely, the values of the effective elastic constants of the worked metal, also serve to indicate the presence of a texture. In fact, as Alers and Liu' pointed out, calculated variations in Young's modulus for assumed orientations, when compared with experimental data, can be used to eliminate some of the uncertainty in interpretation of X-ray pole figures. Thus, elasticity measurements can serve not only to clarify any unusual elastic behavior of worked metal, but also to detect and in part determine the nature of its texture. X-ray determination of the texture of rolled beryllium has been reported by Smigelskas and Barrett,2 who found a strong texture of (0002) in the rolling plane with (1070) planes normal to the rolling direction. In the case of metal rolled at room temperature, they reported that [1010] directions also appeared at positions 60 and 120 deg from the rolling direction in the rolling plane, while in more recent work Keeler3 found these directions were also tilted towards the rolling plane. The texture for beryllium rolled at 80O0C, however, only showed (1010) planes normal to the rolling direction and the spread of (0002) planes out of the rolling plane was less. In looking for elastic anisotropy one might consider unidirectional rolling of a metal as introducing an or-thorhombic symmetry through reorientation of the grains, since the three deformations, compression, extension in the rolling direction, and extension in the cross direction, are orthogonal to each other and unequal in magnitude. Thus the rolled sheet could be treated like an orthorhombic single crystal and the nine stiffness constants of the elasticity tensor used to calculate the anisotropy of Young's modulus, the shear modulus and Poisson's ratio. In this case we could write: which is symmetric about its diagonal. Borik and Alers4 have recently used this approach on rolled die steel with very good results. They found, however, that instead of displaying orthorhombic elastic symmetry their specimens could be considered tetragonal in which case Cr1 = c22, c13 = Ca, and c44 =cjj. This conclusion was made solely on the basis of the measured tensor elements, and serves to point out the advantage of this method for studying the anisotropy of rolled metals. Their calculated values for Young's modulus as a function of angle in the rolling plane also checked very well with direct measurements made on different specimens using the resonance technique. In the present study, cross-rolled beryllium was used which had been unidirectionally rolled about 11 pct for the final reduction. This imparted a slight anisotropy in the rolling plane which was detected both by X-ray techniques and elasticity measurements. For purposes of discussion in this paper, the rolling direction is that direction in which the most reduction passes were made and cross direction is the normal to the rolling direction in the rolling plane. It was also decided to consider the rolled sheet as displaying orthorhombic symmetry for the purpose of obtaining elasticity samples with the direction defined as in Table I. Any change in the final symmetry attributed to the sheet would then be made on the basis of the measured elastic stiffnesses. The final data would then be compared with that expected from the X-ray study and that reported for beryllium single crystals. EXPERIMENTAL PROCEDURE Rolling Schedule. The samples used in this study were taken from a large sheet which, because of its size, had to be unidirectionally rolled for the final reduction. The resulting texture was that of cross-rolled metal with a slight unidirectional texture superimposed. A cast beryllium ingot, 9.500 in. sq by 3.325 in. thick, was cross-rolled to 81 pct reduction followed by unidirectional rolling for an additional 11 pct to give a total reduction of 92 pct. The thickness of the final sheet ranged from 0.265 to 0.280 in. Reduction up to 67 pct was done at 980°C and the final 25 pct at 870°C. Analysis for metallic impurities showed aluminum 0.06 pct, iron 0.19 pct, and silicon 0.11 pct, giving a beryllium purity of 99.64 pct.

Jan 1, 1968

By John Chipman

The concentration of a solute in a dilute ),zetallic solution may be measured by any of several parame- ters including weight percent, atom fraction, atom ratio, and lattice ratio. The ratio of filled to unfilled interstitial sites is useful for interstitial solutes. A variable 2 proportional to this ratio is used as a measuve of concentration. For component 2 irz a bitzary solution z2 = n2/Ym - nz/b) where b is the numberber of interstitial sites per lattice atom. For a t~lul-ticortzporzent solution this becomes zz = n2/(nl + Cvjnj) in which Vj = - l/b for an interstial solute and +1 for a substitulional solute. In the infinitely dilute solution the activity of an interstitial solute 2 is proportional lo z2. At finile concentration the departure from this limiting law is expressed us an activity coefficient, his coefficient is a function of concentra1io)z expressed as tevactiolz coeffcient 8; is analogous to the jark~iliar e£ bul is found to be independent of concentvation in certain solutions for which data are available. It is found that the same equations may be used to express the activity of a nonmetallic solute, sulfur, in liquid solutions of iron containing other solutes, both metallic and nonmetallic. For a nonmetallic solute or for one which strongly increases the actiuity of sulfur, it is convenient to assign arbitvarily a value vj = — 1. When this is done the derivative is found to be constant in each of the ternary solutions studied. The activity coefficient of sulfur in a complex liquid iron solution may be expressed as where nk is a second-order cross product determined in the quaternary solution Fe-S-j-k. The equation is used to calculate tlze activity of sulfur i)z three sevetl- component solutions. IN thermodynamic calculations concerning dilute solutions it is unnecessary to invoke laws and relations which extend across the concentration range to include concentrated solutions. In most binary metallic systems, as arkeen&apos; has recently pointed out, there exist two terminal composition regions of relatively simple behavior, connected by a central region of much greater complexity. When the solute is a nonmetal there is only one such region and in many systems the concentration range is extremely limited. It is the purpose of this paper to suggest a method for the calculation of activities in such a terminal region in which one or more solutes are dissolved in a single solvent of predominantly high concentration. HENRY&apos;S LAW In the usual textbook statement of Henry&apos;s law, concentration is stated in mole fraction. This has the advantage that it makes Henry&apos;s law thermodynamically consistent with Raoult&apos;s law. Since all measures of concentration at infinite dilution are related by simple proportion it follows that mole fraction, molality, atom ratio, weight percent, or any other unit of concentration can be used with the appropriate constant. At finite concentrations, however, calculations based on the law depend upon the unit employed. Deviations from Henry&apos;s law at finite concentrations depend upon the composition variable employed. They are evaluated in terms of activity and interaction coefficients2 which have become familiar features of metallurgical thermodynamics. It is the purpose of this paper to propose a measure of concentration for metallic solutions containing interstitial or nonmetallic solutes by means of which the calculation of activities in complex solutions may be simplified. The discussion will be restricted to free-energy interaction coefficients3 typified by Wagner&apos;s c|a BINARY SOLUTIONS The several measures of concentration which are to be considered are shown in line a of Table I. The corresponding activity coefficients are in line b and the deviation coefficients, sometimes called self-interaction coefficients, are in line c. Henry&apos;s law simply states that the activity coefficient approaches a constant value at infinite dilution. By adoptihg the infinitely dilute solution as the reference state and defining the "Henrian" activity as equal to the concentration in this state, the activity coefficient is always unity at infinite dilution. This convention is far sim~ler and more useful in dilute solution than emploiment of the &apos;Raoultian" activities and it will be used in the following discussion. The several definitions and equations of Table I will be referred to by means of their coordinates in the table. Early observations of deviations from Henry&apos;s law in metallic solutions were shown graphically4 rather than analytically. For the case of sulfur in liquid iron5 the slope of a plot of logfs vs (%S) was constant in the range 0 to 4.8 pct S, indicating constancy of eh2&apos; in Ic. He was proposed by wagnerz and has been widely adopted. The a function of IIIc recently employed by ~arkenl was designed specifically for dilute solutions. Darken has shown that the value of a12 remains essentially constant for many binary solutions within a substantial range of compositions. The atom ratio is directly proportional to the molalitv.<, a conventional measure of concentration. IVb and C served as the basis for smith&apos;s6 classic studies of

Jan 1, 1968

By H. J. Ramey

The wellbore acts as a storage tank during drawdown and build-up testing and causes the sand-face flow rate to approach the constant surface flow rate as a function of time. This effect is compounded if non-Darcy flow (turbulent flow) exists near a gas wellbore. Non-Darcy flow can be interpreted as a flow-rate dependent skin effect. A method for determining the non-Darcy flow constant using this concept and the usual skin effect equation is described. Field tests of this method have identified several cases where non-Darcy flow was severe enough that gas wells in a fractured region appeared to be moderately damaged. The combination of wellbore storage and non-Darcy flow can result in erroneous estimates of formation flow capacity for short-time gas well tests. Fortunately, the presence of the wellbore storage eflect permits a new analysis which can provide a reasonable estimate of formation flow capacity and the non-Darcy flow constant from a single short-time test. The basis of the Gladfelter, Tracy and Wilsey correction for wellbore storage in pressure build-up was investigated. Results led to extension of the method to drawdown testing. If non-Darcy flow is not important, the method can be used to correct short-time gas well drawdown or build-up data. A method for estimation of the duration of wellbore storage effects was developed. INTRODUCTION In 1953, van Everdingen and Hurst generalized results published in their previous paper3 concerning wellbore storage effects to include a "skin effect", or a region of altered permeability adjacent to the wellbore. Later, Gladfelter. Tracy and Wilsey4 presented a method for correcting observed oilwell pressure build-up data for wellbore storage in the presence of a skin effect. The method depended upon measuring the change in the fluid storage in the wellbore by measuring the rise in liquid level. To the author&apos;s knowledge, application of the Gladfelter, Tracy and Wilsey storage correction to gas-well build-up has not been discussed in the literature. It is, however, a rather obvious application. Gas storage in the wellbore is a conlpressibility effect and can be estimated easily from the measured wellbore pressure as a function of time. Several approaches to the wellbore storage problem have been suggested. As summarized by Matthews, it is possible to minimize annulus storage volume by using a packer, and to obtain a near sand-face shut-in by use of down-hole tubing plug devices. Matthews and Perrine have suggested criteiia for determining the time when storage effects become negligible. In 1962, Swift and Kiel&apos; presented a method for determination of the effect of non-Darcy flow (often called turbulent flow) upon gas-well behavior. This paper provided a theoretical basis for peculiar gas-well behavior described previously by Smith. Recently, Carter, Miller and Riley observed disagreement among flow capacity k,,h data determined from gas-well drawdown tests conducted at different flow rates for short periods of time (less than six hours flowing time). In the original preprint of their paper, Carter et al. proposed that the discrepancy in flow capacity was possibly a result of wellbore storage effects. Results of an analytical study of unloading of the wellbore and non-Darcy flow were recorded by carter.14 In the final text of their paper, Carter et al.!&apos; stated that they no longer believed wellbore storage was the reason for discrepancy in their kgh estimates. In view of the preceding, this study was performed to establish the importance of non-Darcy flow and well-bore storage for gas-well testing. In the course of the study. a reinspection of the previous work by van Everdingen&apos; and Hurst&apos; was made, and the basis for the Gladfelter, Tracy and Wilsey&apos; wellbore storage correction was investigated and extended to flow testing. WELLBORE STORAGE THEORY As has been shown by Aronofsky and Jenkins,11-12 Matthews," and others, flow of gas can often be approximated by an equivalent liquid flow system. The following developnlent will use liquid flow nomenclature to simplify the presentation. Application to gas-well cases will be illustrated later. First, we will use the van Everdingen-HursP treatment of wellbore storage in transient flow to establish (1) the duration of wellbore storage effects, and (2) a method to correct flow data for wellbore storage. DURATION OF WELLHORE STORAGE EFFECTS When an oil well is opened to flow. the bottom-hole pressure drops and causes a resulting drop in the liquid level in the annulus. If V. represents the annular volume in cu ft/ft of depth, and p represents the average density of the fluid in the wellbore, the volume of fluid at reservoir conditions produced from the annulus per unit bottom-hole pressure drop is approximately: res bbl-- (V, cu ft/ft) (144 sqin./sq ft) psi -(5.615 cu ft/bbl)(pIb/cuft) ........(I)

Jan 1, 1966

By C. A. Rowland

Introduction Ball mills are lined drums, either cylindrical in shape or modified cylinders that have either one or both ends of the shell, consisting of conical sections, that rotate about the horizontal axis. Fig. I I shows a cylindrical mill, Fig. 12 a conical ball mill, and Fig. 13 a Tricone ball mill (Hardinge tradename). Steel or iron grinding media, generally in the shape of spheres, are used to grind the ore to the specified product size. In order to obtain more contact area for grinding and to simulate the shape of worn balls, balls have been made with two concave surfaces diametrically opposite each other. Some concentra¬tors, such as Erie Mining Co., have used slugs cut from worn and broken rods to supplement the balls in ball mills and save money otherwise lost as rod scrap. Cylindrical and conical shapes have been tried instead of balls, but balls remain as the most common shape grinding media used in ball mills. Ball mills were a logical development from the earlier pebble mills that used hard natural pebbles such as flint pebbles or sized ore pebbles (obtained from the ore itself) as grinding media. In the early 1900s36 it was found that when cast iron or cast steel balls were used in place of flint or ore pebbles, the mills drew more power and gave greater production capacity. Advances in technology have resulted in the manufacture of ball mills up to 18 ft diam inside shell, drawing up to 8,000 hp. Ball mills are employed to grind ores, especially the more abrasive ores, to finer sizes than can be produced economically in other size¬reduction machines such as roll crushers, hammer mills, and impactors. Ores can be ground dry-dry grinding-or in a slurry-wet grinding-using ball mills. Dry grinding nominally refers to less than I %v moisture by weight. If the moisture content increases by several percent, dry grinding capacity is significantly reduced as shown in Table 17. The usual range of solids content in wet ball-mill slurries is from 65 to 80% by weight. Wet grinding is used to prepare the feed material for unit opera¬tions such as flotation, magnetic separation, gravity concentration, and leaching that require a slurry of liberated valuable mineral and unwanted gangue particles. Dry grinding" is employed to produce feed for agglomeration, pelletizing, and pyrometallurgy processes that require feed that is dry or nearly so and for finely ground industrial mineral products used in the dry state. Dry grinding is also used when minerals cannot be dewatered economically to the required moisture level or when the ground product reacts unfavorably with liquids. For example, cement clinker must be ground dry. Dry grinding requires about 30% more power than wet grinding for comparable size reduction .28 The total power required in a dry¬grinding ball-mill plant including drying may be double that required for a wet-grinding plant. Grinding-media and liner consumption in dry grinding reported as pounds of metal consumed per kilowatt-hour per ton of ore" is 10-20% of that used in wet grinding. The Wabush pellet plant, Point Noire, Que.3o reported ball consumption dropped from 6.3 lb per ton of ore ground to 2.5 lb per ton of ore ground when they converted from wet to dry grinding, and a 30% increase in power consumption. A number of comparisons made on wet and dry grinding of cement raw materials show metal consumption in dry grinding to be 10% of that in wet grinding. The capital costs for wet grinding are generally lower than for dry grinding. When thickening and filtering of the wet-ground product are required, dry grinding may have a lower capital cost. With open-circuit grinding the ball-mill discharge passes directly to the next processing step without being screened or classified and no fraction is returned to the ball mill (Fig. 14). In closed-circuit grinding the ground material, undersize, in the ball-mill discharge is removed either using a screen or a classifier with the oversize being returned to the mill for additional size reduction (Fig. 15). The over¬size material that is returned to the ball mill is called the circulating load. Open-circuit ball-mill grinding requires more power than closed¬-circuit grinding for products containing similar amounts of top-size material. The less the amount of oversize allowed in the product, the longer the ore must remain in the ball mill when grinding in open circuit. This increases the production of extreme fines and thus the consumption of more power. The power required for open-circuit ball-mill grinding can be estimated using the multipliers listed in Table 18 and knowing the power required for closed-circuit grinding to yield the desired product particle size. For example, assuming the desired grind size is 90% passing some specific top size, open-¬circuit grinding would require 1.40 times the power to achieve similar results as closed-circuit grinding.

Jan 1, 1985