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By E. Lifshin, R. E. Hanneman

QUANTITATIVE applications of the electron micro-beam probe frequently involve the evaluation of complex mathematical expressions and/or the analysis of large amounts of experimental data. The purpose of this communication is to describe briefly a versatile and useful computer program system that is applicable to analyze rapidly a wide variety of practical microprobe problems. This system consists of a group of ten FORTRAN programs that can be stored on tape, cards, or in the memory disc of the computer. These programs, or links, can be run individually or in any prespecified sequence without interrupting the operation of the computer or without destroying information which is being transfered from one link to another. For the program system described here a GE-235 computer with disc storage was used, so that the DCHAIN method of program linking was employed. Included in the library are programs to: 1) initiate analysis of a new set of data and transfer control between all other programs in any predetermined manner; 2) generate theoretical calibration curves of composition vs relative intensity; 3) generate empirical deviation parameters from least-square fits of experimental calibration data from standards of known composition; 4) convert raw X-ray data to corrected composition; 5) determine inter diffusion coefficients by Matano analysis of con centrat ion -distance data on a uniaxial diffusion couple; 6) determine activation energies and frequency factors of temperature-activated processes such as diffusion; and 7) generate calibration curves for determination of the thickness of thin films using microanalysis. A detailed description of these computer programs and their underlying principles is available on request from the authors."' The first program to generate theoretical calibration curves of corrected relative intensities vs composition uses the Poole and Thomas atomic number correction' and the Philibert absorption factor' with a voltage-dependent mass absorption coefficient for electrons in the alloy. A modified Castaing fluores- cence correction is also used which includes the effects of both Ka and KO radiation and over voltage.' Once the theoretical curves have been calculated in 1 wt pct intervals, these results are least-squares fit to obtain Ziebold deviation parameters' which are stored in COMMON in the computer memory. The net discrepancies between the original theoretical calibration curve and the regenerated curve using the Ziebold parameter are computed. Although this link is explicitly written for K-K fluorescent interactions, it can be applied to K-L, L-K, and L-L interactions as previously disc~ssed."~ Similar programs have also been written to utilize the Wittry fluorescence correction, Birks combined corrections, and various other corrections.' These modified programs have proved to be quite useful for quantitative comparisons of the results of the various theories. The program for conversion of raw X-ray data to corrected composition includes corrections for drift, backround, and instrumental dead time. The corrected intensities are converted to composition by use of the Ziebold equation"2 and parameter obtained from the program system. The results can be obtained for either atom or weight fractions. In addition to accurately computing interdiffusion coefficients the Matano analysis program calculates least-square smoothed values of concentration, concentration gradient, and curvature for each point on the raw input concentration profile. In order to obtain high accuracies a unique method of performing a least-square polynomial fit to incrementally advancing profile segments which overlap is used.' This program has been successfully modified for use in ternary diffusion problems3 and can readily be modified to handle analysis of diffusion profiles which include phase boundary discontinuities. This link is generally applicable to analysis of interdiffusion data obtained by other techniques as well as by the microprobe. The primary function of the next program is to least-squares fit experimental diffusion data to the normal Arrhenius function: D = Doexp(-Q/RT), to obtain values of Do and Q. In addition the probable error and one, two, and three u statistical confidence limits of DO, Q, and log D are evaluated. This program is also directly useful for analysis of any other simple temperature-activated processes including conductivity, and certain deformation and chemical processes. The program to generate calibration curves for film-thickness determination using the microprobe is based on a numerical integration of the equation derived by Cockett and ~avis.' Values of film thickness obtained by this program for copper on various substrates are in good agreement with measurements made by other techniques. Versions of the above program system have been prepared for use with or without a remote teletype connection to the computer for processing on either a real-time or time-share basis. The instrumentation coupling a microprobe to a teletype for automatic data collection and analysis by the presently described program system has been reported elsewhere by the authors.' If teletype equipment is not used to communicate with the computer, standard methods of card reading and tape reading can be used. In either

Jan 1, 1967

IT will be noticed, from the following contributed papers on the various plant, what an infinite number of parts are required to be kept in active operation in order to derive a resultant product of commercial value from the ores and materials received at the works. Crude ores and concentrates, in every degree of complex structure and resistance to treatment, are arriving daily from near and distant places, moreover their metallic contents are so varied that an outsider, unacquainted with the operations, would naturally wonder how it is possible that the rare elements are to be sorted out and classified into their true order, to meet industrial requirements.The proposition is necessarily not a simple one and owners of mining properties have naturally refrained from smelting their complex ores on account of the technical difficulties of attaining high efficiency and recovery of the metals, where limitations are imposed in procuring a variation of ores that lead to the best smelting and refinmg result. This difficulty obviously imposes many disabilities on the smelter, who is prepared to accept all such complex ores, and it may be said that were therenot available a large weekly supply of lead concentrates from the company's own mine at Broken Hill, of standard quality, much of the material being treated in the world today would certainly not be marketable.In order to sustain full efficiency, each section of the works must maintain its.true balance and synchronize with the requirements of such other departments as are dependent on its partially treated materials. This harmony of operations is not only imperative as regards tonnage output, but also relies on the condition of the resultant treatment by each plant, no large variations being permissible.The various officers are, therefore, dependent on one another to keep the order of the operations flowing regularly. This is accomplished by constant intercommunication and observation, as...

Jan 1, 1918

Although Mn, Fe, Cu, Ni, and Co have been the main interests since the ferromanganese nodules had been found, the other major components such as Si and Ca might be very important controlling factors in the processing due to the locally variable content. It is because of the fact that SiO2 and CaO are added to decrease the smelting temperature in the reduction-smelting method for manganese nodule processing. We have compiled the 707 chemical data for KODOS (Korea Deep Ocean Survey) ferromanganese nodules, which have been acquired from 1994 to 2001 and have been also standardized from 2001 to 2003 to avoid the discrepancy between the data sets. All 707 chemical data were used for the hierarchical cluster analysis to get the elemental correlations and also classified by the morphological types. The averages from each station were classified by the facies groups (Fig. 1) and the localities. Then all data are plotted on the SiO2-CaO-MnO phase diagram at 1773°K to compare with the best compositional area in the nodule smelting. Variations and distributions of SiO2 and CaO as well as those of Mn, Fe, Cu, Ni and Co in KODOS ferromanganese nodules were also reviewed. The mineral phases assigned by the cluster analysis are CFA (Carbonate Fluorapatite), Fe-oxide, Al-silicate, and Mn-oxide. MnO contents are generally higher than SiO2 contents in most of the morphological types except for the Is- and It-type. The Dt- and Tt-type show wider range and the E-types show high anomaly in their CaO contents. The stations which belong to facies group A and B show generally higher MnO contents than SiO2 contents, however, the stations of facies group C and D show wide range in their MnO and SiO2 contents.

Jan 1, 2004

By Robert E. Charles

Much has been said about digital computer control of metal and mineral ore dressing processes, but little has been done. This pa- per discusses what practical use can be made today of a digital computer in an ore concentrator and how such application can be made successfully. A hypothetical, but commercially common, grinding and flotation circuit is presented in terms of analog measurements which can and are being made in existing plants and a centralized computer control system which is reasonable in terms of today's technology. Dangers and possible disadvantages of such an approach are discussed as well as estimated benefits. Possible future benefits are presented in terms of improved control technology. Development of new measuring devices is not considered as a criterion for computer benefits. The control systems described have been utilized successfully in existing ore dressing operations. However, the degree of success or failure of analog systems is generally left to the interpretation of management rather than absolute analysis. Many factors affect the economic operation of a mineral recovery circuit such as size of facility, flow sheet design, number of operating personnel, percent of recoverable mineral in the ore body, loss to tails, and haulage rates. In existing mills where little or no instrumentation has been used, it is extremely difficult to prove or disprove the advantage of analog control systems on one mill line versus its sisters due to the lack of standards and the lack of ability to separate final products by ton.

Jan 1, 1969

By Donald B. Evans, Robert D. Pehlke

The solubility of nitrogen in liquid Fe-A1 alloys has been measured up to the solubility limit for formation of aluminum nitride using the Sieverts method. The activity coefficient of nitrogen decreases slightly with increasing aluminum content in the range of 0 to 4 wt pct Al. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from fhe elements dissolved in liquid iron has been determined to be: ?F" = -59,250 + 25.55 T in the range from 1600º to 1750ºC. The solubility of nitrogen in liquid iron alloys and the interaction of nitrogen with dissolved alloying elements in liquid iron have been the subject of a number of research investigations.' Most of this work, however, has been reported for concentrations well below those necessary for the formation of the alloy nitride phase. Data in the concentration region near the solubility limit of the alloy nitride, particularly for systems exhibiting stable nitrides, are important in evaluating the denitrifying power of various alloying elements. They are also useful in determining the stability of a given nitride if it is to be used as a refractory to contain liquid iron alloys. In view of the importance of aluminum as a deoxidizing agent in commercial steelmaking and the fact that its nitride, AIN, is a highly stable compound and has merited some consideration as an industrial refractory, the following investigation was undertaken. The use of the Sieverts technique provided a measurement of the equilibrium nitrogen solubility in liquid Fe-A1 alloys as a function of nitrogen gas pressure up to 3.85 wt pct A1 in the temperature range of 1600º to 1750°C. The values obtained by the Sieverts method were checked by means of a quenching method in which liquid iron was equilibrated with an A1N crucible under a known partial pressure of nitrogen gas, and the solubility of A1N in liquid iron determined by chemical analysis. EXPERIMENTAL PROCEDURE The theoretical considerations involved in determining the solubility product of a solid alloy nitride phase in liquid iron by measuring the point of departure of the nitrogen gas solubility from Sieverts law have been discussed by Rao and par lee.' The principal problem is to determine the variation of nitrogen solubility in an alloy as a function of the pressure of nitrogen gas over it with sufficient precision to establish the break point in the curve at the solubility limit of the alloy nitride phase. A fairly large number of data points are required to do this. A second problem is the determination of the composition of the precipitated solid nitride phase. This is necessary in order to define completely the thermodynamic relationships. The Sieverts apparatus used to make the nitrogen solubility measurements in this investigation is of essentially the same design as that described by Pehlke and E1liott.l The charge materials were Ferrovac-E high purity iron supplied by Crucible Steel Co. and 99.99+ pct pure aluminum. Recrystal-lized alumina crucibles were used, and were not attacked by the liquid alloys. The hot volume of the system which was measured for each melt ranged from 46 to 50 standard cu cm and was found to decrease linearly with decreasing pressure and with increasing temperature. The temperature coefficient of the hot volume at 1 atm pressure of argon gas was essentially constant for all experiments at a value of -6 X 10-3 cu cm per "C. The melt temperature was measured with a Leeds and Northrup disappearing filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature scale was calibrated against the observed melting point of pure iron taken as 1536°C. The emissivity of all melts was assumed to be that of pure iron, taken as 0.43. The charge weights ranged from 110 to 140 g and the range of aluminum contents covered was from 0 to 3.85 wt pct. Aluminum additions were made as 12 to 15 wt pct A1-Fe master alloys previously prepared in the system under purified argon. The compositions of the master alloys were checked by chemical analysis and found to be in agreement with the charge analyses. Vertical cross sections of the master-alloy ingots were used as charge material for the equilibrations in order to minimize the effect of any segregation which might have occurred during solidification of the master alloys. Determinations of the solubility product of

Jan 1, 1964

By R. H. Kolb

A long term project at Shell Development Co.'s Exploration and Production Research Laboratory has been the improvement of the accuracy and the ease of BHP measurements. As a result of these efforts, two complete and separate systems have now been built for the automatic logging of BHP variations. The first of these is a small-diameter instrument suitable for running through production tubing on a single-conductor well cable. During the development of this instrument, as much emphasis was placed on providing a high degree of usable sensitivity and repeatable accuracy as on obtaining the advantages of surface recording. The second system combines the benefits of automatic, unattended recording with the convenience of a permanently installed Maihak BHP transmitter.' THE CABLE INSTRUMENT For many years the standard instrument for BHP determination has been the wireline-operated Amerada recording pressure gauge or one of several other similar devices. This gauge records on a small clock-driven chart carried within the instrument, and although relatively precise readings from the chart are possible, they are difficult to ob-tain. a Both the maximum recording time and the resolution of the time measurements are limited by chart size, and when a slow clock is required for long tests, the precision of the time measurement is often inadequate. Since it is impossible to determine the data being recorded until the gauge has been returned to the surface, wasted time often results when a test is protracted beyond the necessary time or when it is terminated too soon and must be re-run. Clock stoppage or other malfunctions which would be immediately apparent with surface recording remains undetected with down-hole recording; the test is continued for its full term with a consequent loss in production time. As new uses for subsurface pressure data evolved, the shortcomings of the wireline instrument became increasingly apparent, and the concurrent development of a surface-recording pressure gauge and the associated high-pressure well cable service unit' was undertaken. Description of the Instrument Because of its ready availability and advanced degree of development, the Amerada bourdon-tube element was chosen as the basic pressure-sensing device. This element converts a given pressure into a proportional angular displacement of its output shaft, and a suitable telemetering system was designed to measure accurately the extent of this displacement and to transmit the measurement to the surface and record it. The telemetering system furnishes a digital record printed on paper tape by an adding machine-type printer. The present arrangement provides a resolution of one part in 42,000 over the angular equivalent of full-scale deflection, giving a usable sensitivity of better than 0.0025 per cent of full scale. An additional refinement simultaneously records on the tape the time or the depth of the measurement, also in digital form. When the instrument is placed in operation, an adjustable programer can be set to initiate a read-out cycle automatically at selected time intervals. When subsurface pressures are changing rapidly, readings may be recorded as frequently as once every 10 seconds; when pressures are more nearly stabilized, the period between readings may be extended to as much as 30 minutes. Because the instrument is surface-powered as well as surface-recording, the maximum period of continuous logging is (for all prac. tical purposes) unlimited. The subsurface instrument is a tubular tool, 1 1/4-in. in diameter and 6.5 ft in length, operating on 12,000 ft of conventional 3/16-in. IHO logging cable. The transmitting section, mounted above the bourdon-tube element in place of the regular recording mechanism, contains no fragile vacuum tubes or temperature-sensitive transistors. This unit has been laboratory-tested to 1 0,000 psi and 300°F and has performed dependably during a number of field operations. The down-hole transmitting arrangement can be fitted to any standard Amerada pressure element, regardless of range and with no modification of the element itself. Calibration To obtain a repeatability commensurate with the sensitivity and resolution of the instrument, it was necessary to develop a special calibrating technique. The manufacturers of the Amerada recording pressure gauge claim an accuracy of only 0.25 per cent of full scale, which is a realistic figure for normal calibrating and operating procedures. An exhaustive investigation was made of the errors inherent in the bourdon-tube element, itself, independent

By Pedro S. Zúñiga S.

El presente trabajo señala la optimización de los parámetros de perforación en el yacimiento minero de Cuajone a través del control de presión hidráulica y velocidad rotacional en la operación de máquinas de acuerdo a las formaciones geológicas consideradas. En este sentido, se busca mejorar el rendimiento respecto al desgaste de brocas y conservación de la máquina perforadora.

Oct 14, 1980

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 Ross C. Anderson, William I. Weisman

THE manufacture of anhydrous sodium sulphate or salt cake from natural deposits in the United States has been in general somewhat of a marginal undertaking. Competition from foreign sources and from large quantities of byproduct sodium sulphate produced domestically in the manufacture of hydrochloric acid and other chemicals has existed and continues. For example, most of the sodium sulphate produced is a byproduct or co-product in the manufacture of hydrochloric acid through the reaction of sodium chloride with sulphuric acid. In recent years, many manufacturers of rayon have installed equipment to recover sodium sulphate from waste spin bath liquors; today this is an important source. Before World War II large quantities of sodium sulphate were imported from Germany. In 1949 imported material from Europe again appeared on the domestic market. Natural sodium sulphate from Canada in substantial quantities also enters the United States markets. Despite this kind of competition, numerous attempts have been made to exploit various natural deposits of sodium sulphate in this country, but only a very few of these have survived economically over a period of years. One of these few operations is the plant of the Ozark-Mahoning Co. located 13 miles south of Monahans in West Texas. Several factors contributing to the successful life of this plant may be summarized as follows: 1—Geographical location. Monahans is reasonably close, freightwise, to the Kraft paper mills in Texas, Arkansas, and Louisiana; the Kraft paper industry is the greatest consumer of sodium sulphate in the United States. 2—Availability of natural gas as low cost fuel. Proximity of the natural gas fields of West Texas has been a tremendous asset, as the availability of low-cost natural gas is to all industry throughout the Southwest. 3—The nature of the deposit. The occurrence of sodium sulphate brines in southeastern New Mexico and West Texas has been very well described by Lang,' who writes that the brines are found in the Castile formation of the Delaware basin. Here weathering has altered the anhydrite so that a relatively porous gypsiferous zone overlies a dense impervious mass of anhydrite. This porous zone provides traps where percolating ground waters that have picked up soluble salts may lodge. These traps or pockets are the natural brine reservoirs exploited at Monahans. Although several hundred wells have been drilled, currently some 25 wells serve to supply brine to the plant. All are within 1 1/2 miles of the plant and are conveniently tied together by an electric power system serving electric motors driving the pumps. Having the raw material in the form of a brine which can be pumped from shallow wells makes possible much simpler and more efficient handling than if it were in form of solids. By contrast, other deposits of sodium sulphate, such as those in Arizona, Nevada, and North Dakota, are in the form of the solid minerals, thenardite and mirabilite, which present somewhat more of a mining and mineral dressing problem.' The largest producer of sodium sulphate from natural sources in the United States is at Searles Lake, Cal., and there a brine also is utilized. 4—Water. Substantial quantities are needed for cooling towers and for operation of gas engines. An area underlain with brine is not a promising source of fresh water, but fortunately, after a long search, an adequate supply was found nearly two miles from the plant. It may be appropriate to discuss briefly the grades of sodium sulphate offered on the market. Salt cake is the name usually applied to the grade of sodium sulphate used by the Kraft paper industry. It may be a low analysis byproduct, 95 to 97 pct sodium sulphate, with as much as l 1/2 to 2 pct residual acid, or it may be a natural product. Usually salt cake is considered a low grade product, but a great deal of a higher grade of material is marketed under this name. The specifications for glassmakers' salt cake are somewhat higher than those of the paper industry, usually requiring 98 pct sodium sulphate. Technical anhydrous sodium sulphate is a high grade material and usually exceeds 99 pct sodium sulphate. It finds the biggest market in the textile industry and is used as a builder in some synthetic detergents. Glauber's salt, Na2SO4. 10H20, is usually of high purity. Preferred for some uses, it normally has been recrystallized from an anhydrous salt. A unique manufacturing process has been developed at Monahans. This process results in the production of an exceptionally high grade of salt cake, and qualifies for nearly all uses, including many which specify the technical anhydrous grade. All of the finished product, which is very white, passes a 10-mesh U. S. Standard screen, and is retained on a 200-mesh U. S. Standard screen. It is over 99 pct Na2SO4 with main impurities being sodium chloride and magnesium sulphate. Iron content is less than 0.01 pct. As mentioned, the raw material at Monahans is a brine drawn from wells. Attention was first attracted to this location because a so-called alkali

Jan 1, 1954

By D. H. Gieskieng

THE advent of curved jaw crusher wearing plates made an approach other than segmental layout analysis desirable for prediction of capacities. For some time it had been known that the drawing board capacities of crushers using these plates had to be considerably modified by complicated experience factors to achieve agreement with results. Because these apparent capacities could be readily increased severalfold by minor crushing chamber shape changes, it was necessary that the utmost precaution be taken in predicting capacities of jaw plates modified for nonchoking, special wear characteristics, or any other reason. To this end the laboratory and field tests outlined by the author in a previous paper1 were made on Blake-type jaw crushers. The results of these tests were summarized in a simple first degree equation applicable to crushers using either straight or curved jaw plates. This equation first outlines the maximum capacity potential of a given crusher, then reduces this figure in accordance with installation circumstances by means of a realization factor. It was found subsequently that this equation, with the addition of an eccentric throw factor, is applicable to standard types of single-toggle or overhead eccentric jaw crushers as far as maximum capacity potential is concerned. However, these crushers have realization factor curves somewhat different from those outlined for the Blake type. While this paper is concerned principally with standard type single-toggle crusher capacities, the evaluation of data obtained with these machines is simplified by comparative reduction to the 10 x 7 in. Blake-type equivalents upon which the summary of the preceding paper was made. Convertibility of data from one type of crusher to the other also tends towards confirmation of both. The agreement of these data is sufficient to be considered complimentary. Consequently the feed factors, f, previously reported for Blake crushers are slightly adjusted to an average with the single-toggle crusher results. Blake-type equation: C = f.d.w.y.t.n.a.r [I] Single-toggle type equation: C = f.d.w.y.t.n.a.e.r [21 where C is the capacity in short tons per hour through the crusher, f is a feed factor, dependent upon the presence of fines in the feed, and the surface character of the jaw plates used. Values of f : Smooth Plates Corrugated Plates With normal fines 0.0000414 0.0000319 Fines scalped out 0.0000368 0.0000252 Large pieces only . 0.0000312 0.0000215 d is the apparent density of the broken product in pounds per cubic foot. (If the true specific gravity of the feed is known, 40 pct voids may be assumed and d becomes 37.4 times sp gr). w is the width of crushing chamber in inches. y is the openside setting of the crusher, in inches. In the case of corrugated jaw plates it is measured from the tip of one corrugation to the bottom of the valley opposite. t is the length of jaw stroke in inches at the bottom of the crushing chamber. It is the difference between open and close-side settings. n is rpm, or crushing cycles per minute, a is the nip-angle factor. It is unity for 26" and 3 pct greater for each less nip-angle degree. A nip-angle of 20" has an a value of 1.18, and an angle of 30" has an a value of 0.88, see Fig. 1. r is the realization factor. It is unity for perfectly uniform choke feeding and usually less for actual operating conditions according to the method of feeding used and the probabilities of hang-ups involving the size of feed and crusher opening. Approximate values are given by the curves in Fig. 2. These values are further reduced by intermittent feeding, e is the throw or diameter of gyration of the single-toggle crusher eccentric in inches. As evident in Fig. 1A, variation of feed size will generally have little effect on nip-angle if both jaw plates have flat areas. Jaw plates having continuous curvature, as in Fig. 1B will have different nip-angles, depending upon the size of feed. For test work as described in this paper this effect was accounted. For general compilation of capacities for average feeds it is suggested that the nip-angle be taken at the various settings computed, at an arbitrary level, such as is indicated in Fig. 1C. Data Evaluation To bring the Blake and single-toggle type crusher capacity test results to common terms for evaluation, all data are converted to terms of 10 x 7 in. Blake-type performance at conditions of 100 lb per cu ft, 10 in. chamber width, 250 rpm, 0.65 in. stroke, 3-in. openside setting, and 18° nip-angle. (The nip-angle of the 10x7 in. Blake is 18° at 3-in. setting.) The single-toggle crusher performances are also divided by the eccentric throw to bring this effect to unity. As outlined,' laboratory and field tests made on Blake-type crushers ranging from 10 x 7 in. to 60 x 48 in. were summarized along the foregoing conditions of speed, stroke, etc. This resulted in groups of data which correspond to feeds with fines, feeds

Jan 1, 1952

By H. J. Morel-Seytoux

Methods of predicting the influence of pattern geometry and mobility ratio on water flooding recovery predictions are discussed. Two methods of calculation are used separately or concurrently. The analytical method yields exact solutions in a convenient form for a unit mobility ratio piston-like displacement. A few typical pressure distributions, sweep efficiencies and oil recoveries are presented for various patterns. For non-unit mobility ratio, one may resort to a numerical method, such as that of Sheldon and Douherty. 1,2 Because the domains of applicability of the analytical and numerical techniques overlap, the exact solutions provide estimates of the errors in the numerical procedures. The advantages of the analytical and numerical methods can be combined. To develop a numerical technique as independent of geometry as possible, the physical space is transformed into a standard rectangle. The entire effect of geometry is rendered through one term, the "scale-factor", derived from mapping relations. The scale factor can be calcu-lated from the exact unit-mobility ratio solution for the particular pattern of interest. By this means recovery performances for arbitrary mobility ratio con be obtained for many patterns. A sample of tesults obtained in this manner is presented. INTRODUCTION Pattern geometry and mobility ratio are two major factors in making a waterflood recovery prediction. Because assisted recovery has become increasingly important to the oil industry, pattern configuration and mobility ratio also assume a greater significance in the assessment of the economic value of recovery projects. The influence of pattern geometry and mobility ratio in shaping a recovery curve and on the other quantities of interest to the reservoir engineer is the main subject of this paper. Much effort has already been spent on estimating quantitatively the influence of either pattern or mobility ratio or both on oil recovery. The literature reports many investigations of this nature. 3-9 However, many results or methods of recovery prediction presented in the literature cannot be considered fully satisfactory. Even for unit mobility ratio and piston-like displacement, where analytical solutions are available, the literature shows discrepancies. For non-unit mobility ratio, the divergence in the results is extreme. For infinite mobility ratio in a repeated five-spot, depending on the investigator, the sweep efficiency ranges from 0 per cent to 60 per cent. With respect to the influence of pattern on recovery, only the repeated five-spot has received much attention. Other confined patterns and pilot configurations have received very little attention. Two calculation methods are presented in this paper, either separately or concurrently: the analytical method of potential theory and the numerical method of finite-difference approximation. The analytical method is more restricted in scope than the finite-difference method, but it has the definite advantage of providing exact solutions within its range of applicability. If a unit-mobility ratio piston-like displacement is assumed, the analytical approach is possible. A few typical results are reported in this paper; the detailed description of the general method and of a great variety of results will be the subject of other articles. Fornon-unity mobility ratio, we must resort to a numerical scheme. The numerical technique is that which was described by Sheldon and Dougherty.l,2 It is not limited to piston-like displacement. However, mainly single interface results will be presented here. Because the respective domains of applicability of the analytical and the numerical method overlap, useful comparisons of exact and numerical solutions can be made for a variety of patterns. The advantages of the analytical and numerical approaches can be combined. The reason for the success of this analytical-numerical approach can be summarized in the following two points: 1. The numerical solution for arbitrary mobility ratio can be programmed most efficiently when the physical space in which the displacement actually takes place is transformed into a standard shape; and 2. This can be done with remarkable simplicity whenever an analytical expression for the pressure

Jan 1, 1966

By Rajamani R. K.

The design of tumbling mills has progressed from the Bond work index concept of the 1950s to the population balance concept of the 1980s and then made a quantum leap forward with the discrete element method in the 1990s. The failure of a SAG mill at the Grasberg mine site set in motion the inquiry into the role of shell lifter geometry on the profile of the charge motion within the mill. Quickly, it became evident that this could only be accomplished by tracking individual motion of ore particles and grinding balls and not by study of en masse motion of the charge that had been established previously. The discrete element method (DEM) which was prevalent in the civil engineering literature at that time proved suitable to tackle this simulation problem. In 1991, the two dimensional simulation of laboratory scale mills was validated with the DEM. Later this simulation method evolved into ?MillSoft?? a simulation software package for the design of lifters in ball and SAG mills. MillSoft?simulations proved that cataracting charge motion is not conducive to the life of lifters. The old rule of thumb that the number of shell lifter rows should equal twice the diameter of mill in feet was shattered by simulation results. Instead, the number of rows equal to the diameter of the mill in feet, providing that the lead angle of lifter is around 25 degrees, was established as being more optimal. This bold design change was first implemented and tested by Mark Sherman at Alumbrera Mines in Argentina. Two 36-ft SAG mills responded extremely positively to the design change. This success was immediately repeated at Collahuasi, Pelambres and other mines in South America. The design change has so far exceeded expectation that there is not a single SAG mill around the world today that does not employ a relief angle on its shell lifter. The DEM method has advanced in the hands of the author, mining companies and universities, notably in Australia and South Africa. Today, three-dimensional simulation of charge profile and slurry transport is a standard in the design of mills. There is strong pursuit of a virtual comminution machine with DEM in Australia. In South Africa, an experimental method known as positron emission tracking is emerging as a method for tracking particles in grinding mills. The computational burden of computing with millions of particles in three-dimensional simulations has been eased to less than a day with a technique known as GPU computing. Keywords: DEM method, GPU computing, SAG mill, tumbling mill simulation, discrete element method

Sep 1, 2012

By Michael A. Poling

Ladies and gentlemen, I appreciate this opportunity to be with you, and to share my outlook on the future of Federal coal leasing. I'm told that you wanted the best speaker on this subject in the world. Perhaps it's a reflection of these trying financial times, but I'm glad you finally agreed to settle for the best speaker your budget would afford. I have been asked to give you some insight on the status of Federal coal leasing, and how the budget problems facing the Department will affect the coal program. So I've polished up my crystal ball, and I'll try to give you a peek at the future. Before I do that, however, let me first go back in time - to when this Administration took office in 1981. We had a coal program then, after a hiatus of ten years. But that program was untested and - for reasons well known to all of you - did not work well in practice once we began operating the program. We went back to the drawing board and redesigned the program so that it can do what it is intended to do. We've made the program more predictable. That means that when future lease sales are scheduled, those sales will be reflective and reactive to the need to lease coal. On February 26, Secretary Hodel unveiled a framework for resumption of Federal leasing program activities, ending a more than two-year suspension of regional coal sales. The new program will provide the opportunity to satisfy market demand for acquiring and developing new leases, assure the government of fair market value for its coal reserves, and provide a stable supply of coal for this country's energy needs. The new program grew out of the Department's response to recommendations of the Linowes Commission and the Office of Technology Assessment, coupled with a supplemental environmental study. The Linowes Report, issued in 1984, contained 36 recommendations and three Judgments on leasing levels, tract selection, sale procedures, appraisal methods, key statutory and related factors, and organization and management of the leasing program. Major changes in the new leasing program reflect these concerns. We have developed a definition for captive tracts and devised procedures to appraise their value to the adjacent coal or mine owner. Other steps include a coal lease appraisal guide which describes our appraisal methodology and is available to the public. Improvements have also been made in the gathering of lease assignment information to help in estimating the value of potential lease tracts. To improve market analysis, a three-tiered system will be used to ensure that steps of the lease sale decision process are undertaken in the context of coal supply and demand. Regional Coal Teams will thus have the advantage of long range, regional and tract specific market studies to help them determine whether sufficient demand is expected first to warrant the initiation of activity planning, then to set regional leasing levels, and finally to actually offer specific tracts for lease sale. Sale procedures will also be improved in many ways to encourage competition, improve the chances for receiving adequate bids, and to evaluate whether bids represent fair market value. We made additional modifications to the program in response to the OTA recommendations. Regional Coal Teams have been given a larger role in recommending key decisions concerning the amounts of coal to be studied and the actual selection and scheduling of tracts for lease sale. These recommendations will be accepted unless the Secretary can cite an overriding national interest factor, or a governor's request to modify the recommendations. Smaller, more frequent sales will be held, to better judge market conditions and prevent over- or under-leasing. Public participation guidelines have been written, to document all opportunities for the public to comment at various stages in the planning process. We also decided that resource management plans prepared after the passage of FLPMA in 1976 must be completed, in order for a new round of lease sale planning to begin. The BLM will also beef up its procedures for consulting with affected Federal agencies during the planning process, to assure that the purposes and values of those agencies are considered and factored into land use decisions. To assure consistent use of an adequate data base in coal lease decision-making, Regional Coal Teams will develop standards and guidelines for data adequacy, and document the use of these standards. These procedures will also be applied to the unsuitability criteria screening process. Thus, the new leasing system announced by Secretary Hodel: is fully responsive to recommendations made by the Linowes Commission and the Office of Technology Assessment for improving environmental planning and fair market value procedures; gives the regional coal teams a major say in determining leasing levels, and on the timing,

Jan 1, 1986

By Wenying Liu, Marek Pawlik

Long-chain ionic surfactants, with fatty acids and amines as the most important representatives, are widely used as collectors in froth flotation. These surfactants, generally referred to as weak electrolyte collectors, frequently form solid insoluble precipitates within a certain pH range. However, the action and behavior of these colloidal precipitates in froth flotation systems are not well understood and has not been well decoupled from those of dissolved forms. The objective of this study was to understand and compare the role of colloidal precipitates with that of the dissolved forms at gas-liquid and gas-liquid-solid interfaces. Using primary amine as the model surfactant, experiments were carried out to measure: the maximum volume of bubbles generated in the presence of dissolved and precipitated forms of the surfactant; surface tension for both forms of the surfactant using the drop shape and maximum bubble pressure methods; and contact angle using the sessile drop method. The experimental results showed that: in the presence of the precipitate, bubble volume was smaller, which was correlated with the lower surface tension and higher contact angle measured; the surface tension of solutions containing surfactant precipitate was affected by the surface age of liquid droplets. This study enhances understanding of the interfacial behavior of long-chain ionic surfactants under different conditions, which would help improve the efficiency of reagent utilization in froth flotation.

Jan 1, 2014

By M. Uszko

The paper presents the conditions for determining the selection of methods for methane drainage in Polish hard coal mines. Various factors for the evaluation of methane drainage performance are used, including the methane drainage effectiveness ratio. However, as will be discussed there are limitations to the methane drainage ratio approach resulting from the characteristics of the deposits extracted in Kompania Weglowa S.A. coal mines.

Aug 1, 2013

By A. Policard

The bodies of mammals possess a very efficient mechanism for ridding themselves of inhaled dust. When the lung is healthy this mechanism works very well, and dust is quickly and completely expelled from the lung either by the respiratory tract or the lymphatics. The mechanism, however, is easily upset, and slight alterations in the condition of the ciliated epithelium or the circulation of lymph are sufficient to interfere with it, therefore the second mechanism comes into play and the dust is fixed and immobilized in some part of the lung. This, however, is not a real cleansing process, since the lung becomes a dust-trap, and may become'pneumokoniotic. The mechanism is protective at first, but later, when the accumulation of dust is considerable, it gives rise to trouble. The lung cannot become, so to speak, a physiological dust-trap, and still retain its normal structure and function; pneumokoniosis begins, which is essentially a disease due to the mechanical presence of large amounts of inert foreign material.

Jan 1, 1947

By V. H. Gottschalk

SEVERAL years ago a group in the metallurgical division of the U. S. Bureau of Mines began a study of the application of new developments in physics to metallurgical problems'. Among these developments were the extensions of what may be termed by analogy the "sound spectrum." Electromagnetic waves, from X-rays to radio waves, have been quite thoroughly explored for metallurgical use, but the sound spectrum, extending from low-frequency vibrations involved in certain types of metal failure by fatigue through the range of audible sound to inaudible vibrations having frequencies of many kilocycles, has had only meager consideration from metallurgists. Because of the general interest in the process recently demonstrated by St. Clair3 for flocculating smoke by means of sound waves, this article is written to point out possible applications of sound and supersonic (ultrasonic) waves in the metallurgical industry.

Jan 1, 1937

By J. H. Swisher

The rate of internal sulfidation of austenitic Fe-Ti alloys in H2S-H2 gas mixtures is controlled primarily by sulfur diffusion, with counterdiffusion of titanium playing a minor role. At temperatures below 1100°C, enhanced diffusion along grain boundaries becomes important. The rate of internal sulfidation at 1300°C is approximately equal to the rate computed from the sulfur diffusion coefficient. The diffusion coefficient of titanium in y iron has been determined from electron microprobe traces in the base alloy near the subscale interface. The solubility of sulfur in Fe-Ti alloys has been measured in the temperature range from 1150° to 1300°C. The equilibrium sulfur content is found to increase with titanium content, due to the large effect of titanium on the activity coefficient of sulfur. The Ti-S interaction becomes stronger as the temperature decreases. TITANIUM as an alloying element in stainless steels is an effective scavenger for interstitial impurities, carbon in particular. Titanium is known to form stable sulfides; however extensive thermodynamic data on the Ti-S system are not available. Schindlerova and Buzek1 have shown that the Ti-S interaction in liquid iron is moderately strong. There have been no previous studies of the Ti-S interaction in solid iron. Internal sulfidation of Fe-Mn alloys was the subject of a recent investigation by Herrnstein.2 He found the rate of internal sulfidation to be an order of magnitude greater than predicted from available solubility and diffusivity data. A satisfactory explanation for the discrepancy could not be given. In the present study, the solubility of sulfur in austenitic Fe-Ti alloys was measured using a standard gas equilibration technique. Fe-Ti alloy specimens were also internally sulfidized. The rate of internal sulfidation was measured as a function of temperature and alloy composition. Supplementary electron micro-probe measurements were made to provide additional information on the nature of the internal sulfidation process. EXPERIMENTAL The starting materials were alloys containing 0.12, 0.24, 0.38, and 0.54 wt pct Ti. The alloys were made in an induction furnace by adding titanium to electrolytic iron that previously had been vacuum-carbon-deoxidized. The major impurity in the alloys as determined by chemical analysis was carbon. The carbon content of the alloys averaged about 100 ppm; metallic impurities were presented in concentrations of 50 ppm or less. Specimens were made in the form of flat plates, 0.03 by 2 by 4 cm for the equilibrium measurements and 0.5 by 1.5 by 3 cm for the rate measurements. The experiments were performed in a vertical resistance furnace wound with molybdenum wire and containing a recrystallized alumina reaction tube. In the gas train, flow rates of the reacting gases were measured using capillary flow meters. The source of H2S was a mixture of approximately 2 pct H2S in H2, which was obtained in cylinders from the Matheson Co. A chemical analysis was provided with each cylinder. The H2-H2S mixture was diluted with additional hydrogen to obtain the desired ratio of H2S to H2, and the resulting mixture was diluted with 30 pct Ar to minimize thermal segregation of H2S in the furnace. Argon was purified by passage over copper chips at 350°C and subsequently over anhydrone. Hydrogen was purified by passage over platinized asbestos at 450°C and then over anhydrone. The H2-H2S mixture was purified by passage over platinized asbestos and then over Pas. The samples used in the solubility measurements were analyzed for sulfur by combustion and iodometric titration. The subscale thickness in the internally sulfidized samples was measured on a polished cross section, using a microscope with a micrometer stage. Electron microprobe traces for titanium in solution were made on several samples that had been internally sulfidized. A Cambridge microanalyzer was used, and the known titanium content at the center of the specimen was used as a calibration standard. The procedure for the microprobe measurements will be described further when the results are presented. RESULTS AND DISCUSSION Equilibrium Data. Fig. 1 shows the sulfur concentration as a function of gas composition for three alloys equilibrated at 1300°C. The dashed line is based on data published by Turkdogan, Ignatowicz, and pearson3 for pure iron. The breaks in the curves are the saturation points for the alloys. The fact that the initial slope decreases with increasing titanium content indicates that titanium interacts strongly with sulfur in solution. To obtain information on the composition of the precipitating sulfide phase, the measurements described in Fig. 1 were extended to higher sulfur partial pressures. These results are shown in Fig. 2. (The initial portions of the curves are reproduced from Fig. 1.) The highest PH2s /pH2 ratio used is believed to be below the ratio required for the formation of a liquid sulfide phase. Time series experiments were used to study the approach to equilibrium in the samples. It was found that equilibrium with the gas phase was reached in less than 4 hr at 1300°C.

Jan 1, 1969

By R. R. M. Cousens, W. S. Garrett

Discussion: L. T. Campbell Pitt: When Mr Garrett and I discussed the design and construction of plugs and bulk head doors to resist great water pressures in mines about ten years ago, we visualized an emeregeny when there would be no time for site preparation. We could not however, anticipate a problem of such magnitude and urgency as the one described in the paper under discussion. The paper very clearly describes the flooding and the measures taken to save the mine. The complete flooding would have been a national disaster. The account of the combat between man and water reads like the account of a military operation. It was an endeavour which achieved success because there was a master plan, tenacity and, in fact, heroism. The paper is of necessity a long one. In my contribution I will mention some historical facts and factors that I believe have relevance to the flooding and the saving of the mine. It is of great satisfaction to me to have been one of the two initiators of a new approach to underground plug design and construction. The investigation was taken over by a Chamber of Mines Committee which combined our early work with further research and the resulting data had a significant bearing on the West Drie emergency plug designs. The final plug length was correctly based on the requirements to obviate leakage. A plug to have structural strength only would have been very much shorter but so ineffective as to have become a waste of labour, material, and in consequence, wasted the limited time available to prevent flooding of the whole mine. The figure of 75 lb per sq in. sheer stress provided a very ample margin, in my opinion, but under the very difficult site conditions and the limitations of plug material suitable for the very unusual construction, justified such a figure. There must have been considerable temptation to reduce the safety margin due to the urgency to complete and commission the plugs, but it is much to the credit of the directors of this operation that nothing less than a safe design was permitted. In about 1945 Blyvooruitzicht Gold Mining Company, which was then mining in to the West Driefontein area to assist in early development, decided to protect themselves from a possible inrush of water from the latter mine. A bulk head door was accordingly designed and installed on 2 level between 1945 and 1948 at 4,218 ft below surface. Since West Driefontein paid for it, Gold Fields consulting mechanical engineers collaborated with their colleagues of Rand Mines who completed their design after a few modifications were agreed. This door was never used to prevent an inrush into Blyvooruitzicht but the exercise was very useful to Gold Fields when the high pressure doors initially installed on 10 and 12 levels between Nos. 2 and 3 shafts to enable isolation of one section of the mine from another were designed. At that time the capacity of West Driefontein to cope with an inrush of water was comparatively small because the storage in stoped areas and the installed pump capacity were much less than in later years. These doors together with others of the same design were later moved to the lower levels served by sub vertical shafts. In addition, doors to prevent flood water entering the pump chambers on 18 level were installed at each end of that level, and designed for a head of 360 feet so that water would have to reach 16 level before the pumps were flooded. All these doors were called upon to hold water and it is reported that only a small plug in one of the doors and a 4 in. dia flanged pipe joint failed. The lesson is that in these cases the smallest details warrant as much attention as the major ones. That these were the only equipment failures when so much depended on equipment, is very much to the credit of design engineers, both of the Gold Fields head office and companies who supplied both mechanical and electrical equipment. Until I had read the paper I wondered why the policy of isolation by bulk head doors was not continued as the development moved eastward towards the Bank Compartment and particularly when it pierced the Bank dyke. The reasons have been given in the paper. It was unreasonable to expect provisions to be made to counter the remote contingency that the large installed pumping capacity and mine capacity to store water would be exceeded during a peak inrush. When pumps were being considered for West Driefontein, it was decided that the Gold Fields standard underground main pumps at that time of 1 million gallons per 24 hours would be too small. Three alternatives were considered. 1. Very large units that would require underground sub assembly and dismantling of both pump and motor. 2. The largest pump and motor that could be conveyed as a complete pump or motor from surface to the pump chamber. 3. Pumps of higher speed to reduce dimensions and weight. It was decided to adopt alternate 2 because of avoidance of transporting pumps in parts and assembling underground. Alternative 3 was not favoured because high speeds would have introduced problems of more exact rotor balancing. I believe the decision was correct and in the crisis enabled comparative easy transport of pumps and motors to surface for overhaul and, if required, transfer to other pump stations. The standard pump thus became a 10 stage 1,500 rpm pump with a capacity of approximately 2 million gallons per 24 hours against a static head that varied

Jan 3, 1969

By M. S. Azun

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function ?(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [1 N-hy*(h) = 2(N h) i21 {Xi-Xi+h}Z, h=0, 1, N-1] where N is the total number of samples, Xi is the sample value at the i - th location, X i+h is the sample value at the i +h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2,…., up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any ar¬bitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of onedimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. ? References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity. ?

Jan 1, 1986