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By Harmon E. Keyes

Harmon E. Keyes (Chemical & Metallurgical Engineer, Eagar, Ariz.)-Chemical dissolution of chalcocite by acidic ferric sulfate is well known. Resulting elemental sulfur may be oxidized to sulfuric acid by heated ferric sulfate. Laboratory tests at Southwest Experiment Station, USBM, Tucson, generally confirmed stoichiometric relations of 1 part Cu dissolved to 1.750 parts ferric iron reduced, using CP chemicals, dried ore samples, and apparatus cleaned with potable water. Recirculation with open-drainage percolation to increase copper in leaching solvent was followed successfully when appropriate, both in laboratory and Pinto Valley pilot tests. Before 1924 attempts to produce ferric sulfate by aerating ferrous sulfate solution were known. Initial oxidation was satisfactory, but rate slowed below practicality as oxidation progressed and acidity increased. Also, due to hydrolysis of ferric sulfate, a ferric precipitate of hydroxide and basic sulfate resulted. Both laboratory and pilot plant tests gave similar results, regardless of whether CP ferrous sulfate or scrap iron cementation discard solution was used. Rapid oxidation of ferrous hydroxide by air alone is well known to analytical chemists. I demonstrated a process to produce acidic ferric sulfate solutions by precipitating ferrous hydroxide with milk of lime, aerat-

Jan 1, 1973

By F. W. DeVries

The subject article is an excellent comparison between two potential oxidants, molecular oxygen and hydrogen peroxide, as used in the Palangana field at the time of the trials. The tests showed no advantage to using hydrogen peroxide; however, it would be unwise to generalize that the experience in these trials was universally true. During the time of the work cited, extremely high levels of an unusual impurity were recycling in the lixiviant, which substance was a catastrophically destructive catalyst for peroxide. Since this material was not removed before recycle, it was not surprising that much of the peroxide fed was decomposing in the feed piping and never made contact with the uranium mineralization. Under these conditions, indeed, peroxide showed no improvement over oxygen. This is, however, perhaps the most adverse environment encountered to date in US in-situ uranium leaching. In other operations, peroxide has proved advantageous where two factors have been exploited: 1.Despite the tendency for Hz02 to decompose to water and oxygen in the in-situ leach environment, its higher redox potential before decomposition has provided higher leach rates. In some formulations, overloading beyond the O2 saturation equivalent with peroxide has allowed higher oxidant levels, and higher leaching rates, when overloading with molecular O2, led to vapor-locking.

Jan 1, 1983

By J. L. Weeks

Discussion by J.L. Weeks Discussion I wish to comment on Kissell and Sacks's paper "Inaccuracy of area sampling for measuring the dust exposure of mining machine operators in coal mines." It is well established in industrial hygiene that area sampling is not an accurate measure of personal exposure. To measure personal exposure, one must use a personal sampler. Kissell and Sacks, using data from coal mining, reached the same conclusion. This is the right answer but it is the wrong question. This issue arises because the machine-mounted respirable dust continuous monitor (MMRDCM) is being considered to monitor coal-miners' exposure to respirable dust. This device may be mounted on a continuous mining machine, and it would take a modified area sample. I refer to it as "modified" because a mining machine is not really a fixed location, as is the typical area sample. The concern with whether this machine would provide an accurate estimate of the machine-operator's exposure, however, overlooks important features of the MMRDCM. Specifically, it displays dust concentration as it occurs and at the place where it is needed, not 10 days later, as is the case with the current system. Used in this way, it allows for timely intervention to control exposure to dust and it leads to greater first-hand knowledge of specific conditions and mining practices that result in excess exposure. If one knows the dust level is excessive at the time the dust is being generated, it is possible to use known and effective methods of dust control to reduce exposure. By measuring again, one can determine whether control methods have worked. This is a generic procedure followed in any industrial process: measure, adjust and measure again. It leads to more effective and more efficient dust control and is preferred to taking a sample, waiting 10 days for the results and then trying to apply that information to a situation that no longer exists. The MMRDCM also records the dust level automatically, and it runs continuously, making it harder to tamper with. Dust monitoring in underground coal mines has been corrupted by some operators having submitted fraudulent samples (and being convicted on criminal charges because of it), weakening the credibility of the current system. The MMRDCM is, in part, a response to this corruption, and an effort to focus attention on dust levels and dust controls rather than on the perpetrators of fraud. Use of the MMRDCM is an evolutionary change from the current system. With the current system, one takes a personal sample of exposure of the "designated occupation" (DO, defined at 30 CFR 70.2 (f)), the occupation regularly exposed to the highest level of dust on a section. Typically, on sections using continuous mining machines, this is the mining-machine operator. The rationale behind DO sampling rests on some of the findings that Kissell and Sacks report. They reviewed several studies that showed that dust concentration varies with location on a mining section and that there is a concentration gradient with the highest concentration occurring closest to the face. The logic behind DO sampling strategy is that if the dust concentration at the place where it is highest is below the exposure limit, then concentration elsewhere on the section is also below the limit. In this way, one will have achieved the objective or keeping dust concentration below the exposure limit for all miners on the section by measuring the exposure of only one miner. The

Jan 1, 2003

By G. Chi, M. C. Fuerstenau, R. C. Bradt, A. Ghosh

Technical Papers, Mining Engineering Vol. 49, No. 12, pp. 70-75, Discussion by McIvor, R. and Fink, R. P. We must challenge what we consider to be dubious statements in the above-mentioned article. Much of what is reported was published elsewhere over a year ago (i.e., in their reference: Chi, G., Fuerstenau, M.C., Brandt, R.C. and Ghosh, A., 1996, "Improved comminution efficiency through controlled blasting during mining," International Journal of Min¬eral Processing, Vol. 47, p. 93). There is nothing unusual or significant about a 10% or more difference in grindability between two materials of apparently similar origin and other attributes (such as chemical assays, hardness and specific gravity). Consider also that: • the materials came from different locations in the pit; • only two sets of four blastholes were considered per blast: • spatial orientation with respect to the face and other blastholes was also altered; • only two pairs of data were collected; • the impact of sampling error and bias, • both of which could be significant in this case; and • normal experimental error in parameter measurement and calculation. It is clearly inappropriate to draw any conclusions with regard to cause-and-effect relationships without first presenting a thorough error analysis. A substantial number of randomly selected test and control areas might provide meaningful statistical evidence of the claimed effect of the variables being studied. Even that appears doubtful, however, because Figures 3 and 4 show about as much variation in crushing energy for the two "regular" conditions vs. regular and altered conditions. On a separate, but also important issue, broad experience with autogenous/semiautogenous milling has shown that smaller or weaker feed material results in reduced tonnage. ? Reply Thank you for the opportunity to respond to the comments of Messrs. Mclvor ant Fink. The points raised are addressed in the order of presentation. As the commenters noted, there are parallels between this article and a previous manuscript. The reason for these complementary articles is that the audiences for the two publications are different, although there is obviously some overlap. We believe that the different audiences each profit from the technical aspects of the two manuscripts. We are not in agreement that a grindability difference of 10% is insignificant. The laboratory work is corroborated by data obtained at plant scale, which confirms that an increase in throughput of the same magnitude (between 5% and 10%) is achieved when the blasting pattern is modified, i.e., reduced from 9 to 8 m (29.5 to 26.2 ft). This increase in throughput translates into substantial power savings for ore grinding. No differences in appearance in the rock were noted between the two adjacent areas. Rock in both areas belonged to the same rock mass/block, which was quite homogeneous and without geological features in between that could create drastic differences in comminution characteristics. Given the resources, we would have sampled from all of the holes. Additional data would certainly have been desirable, as would have been additional funding to expand the study. Their comment, "spatial orientation with respect to the face and other blastholes was also altered," is not clear. Figure 1 does not show the initiation sequence. Without the initiation sequence, we do not understand how the commenters concluded that spatial orientation with respect to the face and other blastholes was altered. The commenters may be trying to make the point that the four-hole configurations with respect to the original bench face are not exactly the same. In fragmenting the

Jan 1, 1999

By H. I. Smith

CONTENTS [PAGE Problems of Mining and Processing Mineral Aggregates (TP 1649, by NATHAN C. ROCKWOOD, Min. Tech., Nov. 1943. Discussion by H. I. SMITH, IRVING WARNER and the author) t Mica in War (TP 1749, by RUSSELL G. WAYLAND, Min. Tech., July 1944. Discussion by H. S. SPENCE) 3 Three Roofing-granule Plants in Pennsylvania (TP 1787, by RICHARD M. FOOSE, Min. Tech., Jan. 1945. Discussion by H. I. SMITH)5 Methods of Prospecting and Mining Optical Calcite in Montana (TP 1896, by E. W. NEWMAN, Min. Tech., Nov. 1945. Discussion by W. C. STOLL and FRANK C. ARMSTRONG, and the Glass Sand and a Glass Industry in Puerto Rico (TP 1939, by HOWARD A. MEYERHOFF and J. EARL FRAZIER, Min. Tech., Nov. 1945. Discussion by A. M. SHORT, the author and PHILIP The "Bonanza" Mica Operation of Purdy Mica Mines, Limited, Mattawsn Township, Ontario (TP 2154, by HUGH S. SPENCE, Min. Tech., March 1947. Author's supplement and discussion by JOHN A. BAKER, E. J. LINTNER, and the author) 7 Process for Manufacture of Dead-burned Magnesite and Precipitated Calcium Carbonate from Dolomite (TP 2155, by ROBERT D. PIKE, Min. Tech., March 1947. Discussion by 0. C. RALSTON and the author) 9] Problems of Mining and Processing Mineral Aggregates H. I. SMITH*-Mr. Rockwood has presented a very interesting paper on problems of the mineral aggregate industry in meeting specification requirements, which apparently are ever decreasing in tolerance. May I call attention to a method of mineral separation that may be of value in separating the flat aggregate particles from the more angular ones and possibly the soft particles from the hard. The method is the old Pardee spiral coal separator, extensively used many years ago in the anthracite region for separating rock and bone from anthracite coal.1 The success of the process depends on the relative coefficient of friction of the aggregate particles to be separated rather than on their relative specific gravity. The flat and the soft particles normally will slide more slowly and stay on the inner spiral until they reach the delivery spout at the bottom whereas the round and the angular pieces will work to the outer edge and fall off into a spiral of larger diameter. The capacity of the separator is increased materially by having three inner spirals, with a separate feed for each, on which the particles travel more slowly, and one outer spiral from which the more rapidly traveling pieces slide to the bottom. IRVING WARNER*-I have long been convinced that much of the equipment and methods developed for mineral dressing might be advantageously employed in the mineral aggregates industry, and more particularly in the production of sand and gravel. The two industries are not well acquainted with each other or their problems. They have separate trade publications. The difficulty with the situation is that there are few large sand and gravel plants and few provided with technical services in their own organization or by retainer. This does not refer to engineering organizations but rather to improvement of plant technic in processing.

Jan 1, 1947

By R. F. Kovar, R. N. Torbin, R. E. Gundersen

I have to express my .surprise and must send a note of warning concerning the use of polyurethane foam as described in a paper by R.N. Torbin and R.F. Kovar, entitled "Innovative Shaft Lining Method," published in your February 1989 edition. In September, 1986, 177 miners lost their lives when they were exposed to fumes downwind from a fire in a tunnel lined with polyurethane foam. Whilst polyurethane exhibits reasonable fire retardent properties in small-scale tests, mass use in a tubular configuration, exacerbated by the furnace effect of cross-radiation, can lead to a rapid, uncontrollable conflagration. I do not wish these comments to detract from the engineering achievements of the authors but rather to sound a loud warning as to the application of the system. Any shaft designed for human access- be it for transport or shaft work - and any intake airway, should not consider the use of polyurethane foam. It only needs a slip with a cutting torch or an electric fault to initiate a disaster. Many countries have banned or restricted the use of polyurethane foam in the workings of a mine and maybe alternative foams (e.g. phenolics) can be used or developed

Jan 1, 1991

H. H. Bleakney (Dept. of Mines and Technical Surveys, Ottawa, Canada)— The work of Dr. Machlin and his colleagues at Columbia University is so scholarly that one hesitates to take issue with them. Nevertheless the writer feels compelled to enter a demurrer to the mechanism of intercrystalline cracking proposed in this paper. The principal obstacle to its acceptance is found in its preoccupation with purely mechanical influences and its disregard for the chemical effect of impurities. The writer believes that the destruction of metallic cohesion by concentration of impurities at the grain boundaries is a necessary and sufficient condition for the development of intercrystalline cracking; and he believes that discussion of the numerous mechanical explanations proposed should wait until some valid objection to the chemical hypothesis has been advanced. It is nearly twenty years since Gillett" drew attention to the possibility that the chemical influence of precipitation might be the cause of intercrystalline cracking. As early as 1935, Greenwood'" remarked that grain-boundary precipitation of impurities in lead appeared to promote intercrystalline cracking. Again in 1939, Scott commented as follows on a paper by Thielemann and Parker:'" "There are at least two familiar phenomena that can influence grain-boundary cohesion: 1) intergranular oxidation; and 2) grain boundary precipitation. An important consideration in this work, therefore, is to determine which, if either, of these factors is responsible for the low values of cohesive strength observed." In 1952. the writer presented evidence," some original and some abstracted, which indicated that in copper, silver, aluminum, lead and iron, intergranular cohesion was a function of the purity of the metal. In 1954 Glen, discussing a paper by Ridley and Tapsell14 indicated his belief in a precipitation mechanism for the intercrystalline embrit-tlement of molybdenum steel and suggested that with an absolutely pure metal it would be almost impossible to obtain an intercrystalline crack. This suggestion has

Jan 1, 1959

C. G. Dunn (Generai! Electric Research Laboratory)— The author is to be commended on his attempt to calculate the residual strain energy from information on the dislocation density within the subgrains and a surface energy associated with the subgrains. However, much closer agreement between a calculated critical size of a nucleus and the observed size of grains that did not continue growing can be obtained if a reasonable correction is made in obtaining the energy of the surfaces of the subgrains. For example, since the sample is a single crystal with a cold-rolling reduction of 70 pct in thickness, one needs either an average disorientation for this or an average subgrain boundary energy rather than the 2.5 deg disorientation of a bent crystal, which was used by the author. From either the Laue photographs of the author or the pole density plot of Koh and Dunn 16 for a (113) [332] cold-rolled crystal the

Jan 1, 1961

K. T. Aust and J. W. Rutter (General Electric Research Laboratory)—We find it difficult to reconcile the activation energies determined by Gifkins with his general conclusion that "migration during both creep and grain growth can thus be treated on the basis of the same model" (that of Lucke and Detert). Gifkins finds the activation energy for grain boundary migration during creep to be 24.5 kcal per rnol and that for grain boundary migration during grain growth to be 7.5 kcal per mol. The calculation carried out by Gifkins of the activation energy for grain boundary migration during grain growth, using the Lucke and Detert model, gives a value of 20 to 24.5 kcal per mol, rather than his experimental value of 7.5 kcal per mol. The theory of Lucke and Detert was developed to account for the rates of migration of grain boundaries in the presence of impurities during grain growth. The theory does not take into account the effect on the boundary migration of another, simultaneous process such as creep deformation and would be expected, therefore, to be applicable only to migration during grain growth. The fact that Gifkins measured a different activation energy for boundary migration during grain growth (7.5 kcal per mol) from that during creep (24.5 kcal per mol), although the specimens were of the same composition, shows clearly that such an effect exists under his experimental conditions; the presence of a simultaneous creep deformation markedly affects the boundary migration process in comparison with what would be observed under the same conditions but without the creep deformation. The failure of McLean's equation (Eq. [4] of Gifkins' paper) to give a satisfactory dislocation density difference for boundary migration during creep is not surprising, since the activation energy which must be used in this equation refers only to the elementary atom transfer process of grain boundary migration. This activation energy value is approximately 6 kcal per mol for zone-refined lead, as determined in both the grain boundary migration experiments of Aust and Rutter31, 32 and the grain growth experiments of Bolling and Winegard.33 Using this activation energy value, McLean's equation gives reasonable agreement with observed migration rates for grain boundaries moving free of the influence of impurities.31, 32 The value of 24.5 kcal per mol is probably associated with the presence of impurity atoms, as Gifkins suggests. It should be noted, however, that this value was obtained using lead of only one composition and measurements at only two temperatures. The work of Aust and Rutter3"' on the effects of tin, silver, and gold on grain boundary migration in zone-refined lead in the temperature range from 320" to 200°C, as well as the work of Bolling and Winegard34 on the effect of silver and gold on grain growth in zone-refined lead, shows that the measured activation energy is markedly dependent upon the kind and amount of solute present. Gifkins' work does not permit evaluation of the effect of the 8 ppm of impurities other than oxygen present in his specimens. One incidental point: the symbols used to designate the experimental points of Fig. 6 appear to be in incorrect order in the figure caption. As the caption is printed, it would indicate that larger grain sizes were obtained after annealing at 47°C than at 100°C, which does not agree with the text (point M, p. 1019). Finally, it seems clear from Gifkins' results that any serious attempt to determine whether grain boundary migration and grain boundary sliding during creep occur with the same activation energy, as Gifkins suggests and McLean rejects, must take into account the effects of impurities on these two processes, Although the work of Weinberg35 indicated that adding small amounts of copper, iron and silicon to aluminum did not affect the grain boundary shear behavior, it should be noted that his starting material contained approximately 60 ppm of impurities. Gifkins' results indicate impurity effects at an impurity level of 8 ppm, suggesting strongly that the most significant impurity range to be investigated lies substantially below that value. R. C. Gifkins (author's reply) — As Drs. Aust and Rutter suggest, the results under discussion may have to be reinterpreted in the light of their own work on grain boundary migration, which was not available to me when the paper was written. Because of their work, Aust and Rutter attach more importance than I did to the activation energy for grain boundary migration during annealing (7.5 kcal per mol) obtained from a "direct" plot of log-rate against the reciprocal of absolute temperature. At the time it was obtained, this value seemed rather low, although it was similar to the value obtained by Bolling and Winegard.36 It was then, and still is, difficult to accept this value because of the low value of the index in the power law for grain growth, which seemed to indicate the influence of impurities. It was also concluded that the low value of the activation energy might have arisen from the manner of selecting rates of grain growth which were truly comparable at the two temperatures. There were many other indications in these experiments and those on recrystallization during creep3? that an impurity, probably oxygen, was of importance. The model for grain-boundary migration which Lucke and Detert had proposed was an obvious possibility and its use yielded an activation energy for boundary migration during annealing of 20 to 25 kcal per mol.

Jan 1, 1961

By C. H. Gerould

I would like to take a moment to consider our polystyrene-silica replica technique, which was developed at the Dow Chemical Co. and which was mentioned in the paper just given by Mr. Thielsch. He stated that he feared that our replica technique would cause difficulty due to deformation of the metal as a result of the application of pressure during the molding process. We at the Dow have never had any reason to suspect that any deformation of the metal was occurring during the molding process. Our procedure has been to heat the polystyrene to a temperature of 160°C. before applying any pressure, at which temperature the polystyrene is a viscous liquid. By so doing the pressure of the polystyrene against the metal is essentially hydraulic and is therefore applied equally in all directions, which we feel should not cause deformation. Our work using this replica technique has brought forth several indications that deformation of the specimen is negligible. These indications are: I. Direct comparisons have been made between the light and electron microscopes when studying a specific spot on a metal surface. These "same spot" studies were obtained by first taking micrographs at high magnification, with a light microscope, of a specific structure that could be readily recog-

Jan 1, 1947

By H. [Eyring], B. J. Zwolinski

[ ] The authors are to be commended for their excellent work on the activities of components in the solid state. It is, however, felt that certain points require clarification with reference to diffusion in the solid state. It is a well established point that any rate process in a non-ideal system can be expressed by the general equation [ ] where ko is the specific rate in an ideal system, and ?A, ?B ... , the activity coefficients of the reactants and ?± and ?M,?N the activity coefficient of the activated complex and the intermediates, respectively. With reference to diffusion, the following simplified treatment in correcting for non-ideality is proposed. The same free energy change is involved in moving a particle from a solution of one activity to a solution of another activity,

Jan 1, 1947

By R. L. Dietrich

[ ] We at The Dow Chemical Co. have recently done some work on the deformation of magnesium alloys and although it is far from complete there have been a few observations which may be of interest in connection with this paper. In the first place, I should like to point out that the deformation of polycrystalline magnesium alloys has not been completely explained by the work on single crystals. Bakarian and Mathewson found slip on the ( 101) and {002) planes, and (102) twinning as the deformation mechanisms in magnesium single crystals, but in compression when the (002} planes were within ii° of parallel t0 the compression surfaces, fracture occurred at all temperatures up to 340°C (644°F). In commercial working processes, particularly in rolling, an orientation is quickly produced which should be unfavorable to further deformation by the three established mechanisms. The first few reductions in rolling quickly produce an orientation having

Jan 1, 1947

By G. Sanders

Discussion by G. Sanders The studies reported on in this paper were initiated to draw attention to the severe contamination problem in the Section 30 drilling program at Chimney Creek. The lithologic-subset sampling study reached a different conclusion from that presented in your paper, and I wish to comment on your subsequent analysis of the data and your conclusions. Request for more complete data In the section on subsampling, you mention that the subordinate lithologies were separated and sampled, yet only the dominantlithology gold value is plotted in Fig. 4. In a contamination study, the reader is interested in the assay values for the individual subsets. Please include a table of the subsample assay data in your reply. Also, please indicate which analytical methods were used to arrive at the gold values in the subsampling study. Turning barren rock into low-grade ore Figure 5 is very revealing and typical of all of the cross sections in Section 30. Note the long strings of low-grade mineralization spread out for hundreds of feet below the ore zones. There were some very high gold values found in certain contaminated fractions during the subset sampling. The conclusion, here, was that the distinctive, strongly-mineralized dolomite layer was probably loose and crumbly and continued to disintegrate during drilling. This caused salting of the unmineralized rock samples below. Missing the high-grade part of the ore body In your statistical analysis, you directly compare the reverse circulation assays to the diamond drill assays in Section 30. Two points argue against a direct comparison and suggest the differences are greater than the 3 % that you report. First, any core loss in a gold zone most likely means that the true gold values are greater. The drillers lost significant amounts of the clay-rich, Section-30 gold mineralization. Also, the initiated salt-mud system, an attempt to improve the core recovery, met with little success. Second, the practice of not sampling core geologically, but instead sampling on even 5-foot intervals, adds a deliberate dilution to the core assay values by including a portion of nonmineralized rock in the first and last samples of each high- grade intercept. The result is often a pair of low-grade assay values on either side of a high-grade gold zone. In reality, a high-grade gold zone has a very sharp assay wall that is often bounded by barren rock. This sampling method may make the diamond-drill core assays more like the reverse circulation values and may help explain the statistical similarities you found. However, it does not represent the true gold values in the high-grade parts of the deposit. You cannot deny that, by careful geological sampling of the drill core, higher and sharper assay values will be obtained. The low core recovery and the diamond-drill-core sampling method used act together to lower the diamond-core assay values. The 3% difference you found between the reverse-circulation and diamond-core assay values could be much larger when you consider what the true diamond-drill core values would be with optimum core recovery and a geologic sampling method for the core. Should statistics have been applied here? The statement "... that reverse circulation holes have overestimated the values of some ore zones and underestimated the values of others" (p. 345) is not correct. The subsampling confirmed what the cross sections hinted at in Section 30. Namely, beneath the high-grade zones, the reverse circulation holes created, by contamination, large intercepts of low-grade ore in regions of barren rock. Because the low-grade material was not there to begin with, this is not a process of overestimating low-grade mineralization. The next statement that "the average result is similar to that of the diamond drill holes" may apply to the data set numerically, but it is not true when viewed spatially on cross sections. Adjacent reverse circulation and diamond drill holes are almost impossible to correlate, high-grade zone values vary widely and many low-grade intercepts make no geologic sense. The subset sampling and cross sections presented in the first part of the paper show that the reverse circulation portion of the data set has some serious problems, as highlighted above, and should not have been dealt with statistically at all. Conclusion Each ore body is different, and each drilling method presents unique sampling problems. In this case, the diamond drill is the

Jan 1, 1994

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 y(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: [ ] where N is the total number of samples, Xi is the sample value at the i - th location, Xi+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 arbitrary 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 one-dimensional 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 11, 1985

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

By R. E. Crater

Brown, Gaudin, and Loeb in their study of intergranular comminution by heating attempt to find one explanation for all types of rock in terms of the properties of the phases present. The only necessary condition for intergranular cracking by heating is the setting up of high stresses at the grain boundaries. Such stresses may be set up in multiphase isotropic mixtures if the thermal expansions of the phases are different, in non-cubic single phases because of the anisotropy of thermal expansion in the various crystallographic directions, and in materials containing quartz because of the a-ß transformation at 575°C. In addition, for intergranular comminution by heating, the cooling and not the heating is most important.

Jan 3, 1959

By R. D. Longyear

[Some Problems Involved in the Interpretation of Diamond-drill-hole Sampling and Surve ing (paper by J. J. Collins, Mining Tech., Jan. 1946). ............... I Geologic Interpretation of Magnetic Exploration on the Mesabi Range, Minnesota (paper by R. H. B. Jones, Mining Tech., July 1946) ................... 2] DISCUSSION R. D. LONGYEAR.*-Mr. Collins is to be commended very highly for the brief summary he has made of the currently used methods of taking diamond-drill sludge samples and the principles involved in evaluating the results. This paper should stimulate further discussion and research on this vitally important problem. It is particularly imperative that geologists and engineers know when assay results on sludge recovery can be accepted quantitatively and when they must be considered only qualitatively. In most cases where the sludge recovery is less than 95 per cent or more than 125 per cent, it is safest to consider the assays as of qualitative value only. Certain cases, however, are known where a relatively small proportion of the sludge sampling will give a reasonably accurate measure of the value of the total sample. One such case is ore in which the valuable mineral is of approximately the same specific gravity as the waste mineral, such as chalcopyrite in a massive pyrite body. The essential point is to determine the degree of accuracy of sludge sampling in any given drilling project and to weigh the results accordingly. It should be emphasized, however, that sludge sampling can be made reliable in many localities where careless practice produces unreliable results. In many instances, it is desirable to empty the core barrel in the core shack instead of at the drill, so that the engineer can examine the core as it first comes from the core barrel. It should be pointed out, however, that the drill * E. J. Longyear Co., Minneapolis, Minnesota. runner should be permitted to study the core to guide his future drilling. It is hoped that with the return of more normal conditions after the war geologists, engineers, contractors, and manufacturers will be able to carry on more research along the lines of improved core-barrel design and drilling technique with the objective of increasing core recovery so as to eliminate as far as possible the necessity of relying upon sludge samples. H. M. ROBERTS.*-Whoever in the future will have to do with the search for ore bodies and their exploration will have frequent occasion to refer to the clear and comprehensive summary on diamond-drilling methods by John Collins. His review of the experience of the last 40 years in this technique is invaluable. As Dr. L. D. Ricketts wrote in 1932, "The principles on which an art is founded are usually few and necessarily basic in nature, but he who wishes to achieve the power to select his aides and give success to important undertakings that may be intrusted to him in the future must ordinarily undergo years of drudgery in order to gain the experience that will enable him to distinguish such fundamentals through the haze of reinforcing detail that clothes and tends to disguise them."[t] Ricketts went on to say that since the beginning of the century there has been much

Jan 1, 1946

Joseph K. Stone, Jr. (Kaiser Engineers, Oakland, Calif.)—I would like to compliment the authors on their clear presentation of the results of their study of the pneumatic processes. We hope that the Inland Management decision to make this information available to all will induce others to release additional valuable fundamental data which they have accumulated in the field. There are two points upon which we would like to comment. In the discussion of Table VII it was indicated that the "oxygen consumptions were about the same as has been reported for other oxygen steelmaking processes". This conclusion is apparently based upon the consumption of 2100 cu ft per ton shown in Table VII. The data in Table IV also permits calculation of 2520, 2280, 2250 and 2700 cu ft per ton in heats 1 to 4, respectively. These figures are in the same general range as those reported for the Kal-Do and Rotor Processes using Thomas iron, but considerably above the following figures for four of the operating L-D Process Plants while using iron which is similar to American basic iron: Donawitz 1760 cu ft per ton Adapted from Cuscoleca' LinZ 1900 cu ft per ton Trenkler & Hauttmann2 Dofasco 1850 cu ft per ton D. O. Davis:3 In addition to the differences between the consumption of gaseous oxygen in the Inland operation and in the L-D Process, there is another closely related difference. The L-D plants for which data are cited are using approximately 1 pct ore while the authors' process used about 7 pct of sinter. Assuming 65 pct Fe in the sinter, the difference amounts to 400 to 500 cu ft

Jan 1, 1959

R. Schuhmann, Jr. (Purdue University)— Fulton and Chipman's results on rate of silica reduction from slags are analogous in many was to the results of Parlee, Seagle, and Schuhmann10 on rate of alumina reduction from alumina crucibles. Both investigations have given comparably low rates of reduction and slow approaches to equilibrium. Accordingly, we may hypothesize that the rate-determining step is the same in both kinds of experiments; that is, oxygen diffusion across the stagnant boundary layer on the liquid-metal side of the interface between the liquid metal and the oxide phase (slag or solid oxide). I suggest that silica reduction involves the following consecutive steps: I) At the slag-metal interface: SiO2(slag) Si+ 20 II) Transport of oxygen from slag-metal to gas-metal interface: a) diffusion across liquid-metal boundary layer at slag-metal interface. b) convection within the body of liquid metal. c) diffusion across boundary layer at metal-gas interface. 111) At the metal-gas interface: C +O- CO (gas) Iv) At the graphite-metal interface: C (graphite) -C At steelmaking temperatures it is reasonable to assume that equilibrium is attained in all three chemical reactions (I, 111, and IV) right at the respective interfaces. Convection within the stirred liquid metal (step IIb) is also rapid. Transport of Si and C should be orders of magnitude easier than transport of 0, because of the relatively high concentrations of Si and C. Accordingly, we might expect the overall reaction rate to be determined by boundary-layer diffusion of oxygen, either IIa or IIc. Fulton and Chipman's demonstration that bubbling CO through the system had no major effect on reaction rate indicates that IIc is not the slowest step. Therefore, it becomes logical to estimate the maximum rate for step IIa and to compare this theoretical estimate with Fulton and Chipman's experimental data. If oxygen diffusion across the liquid metal boundary layer at the slag metal interface (step IIa) is rate-determining, In this equation, dn sio, /dt is the rate of silica reduction in moles per sec,A is the area of slag-metal interface in sq cm, Do is the diffusivity of oxygen in sq cm per sec, 6, is the boundary layer thickness in cm, c,* is the oxygen concentration right at the slag-metal interface in moles per cubic cm, and co is the oxygen concentration in the body of the liquid metal, also in moles per cubic cm. Equilibrium data" on the silicon deoxidation reaction in liquid iron and steel at 1600°C indicate that the oxygen contents of the liquid metal in Fulton and Chipman's experiments at 1600°C probably fell in the range of 0.5 x10-3 x10-3wt pct. That is, the maximum conceivable value of co*-co for the system under consideration was on the order of 10"5 mole oxygen per cubic cm. On the basis of previously published data,1O,11 it is estimated that Do/0 will fall somewhere in the range from 10-3 to 10-1 cm per sec. The surface area A in Fulton and Chipman's experiments was approximately 20 sq cm, and the weight of metal involved was about 500 grams. Combination of all these figures with the above rate equation leads to an estimate that the rate of silica reduction should fall within the range from 0.002 to 0.2 wt pct Si per hr. This estimate is consistent with the experimental data. For example, Fulton and Chipman's Fig. 2 shows a change of about 0.3 pct Si in 10 hr, corresponding to an average rate of 0.03 pct per hr. According to the proposed hypothesis, increasing the temperature will increase the reaction rate ill two ways: 1) by increasing oxygen diffusivity and 2) by increasing the oxygen concentration (oxygen solubility) in the liquid metal. The combination of these two effects accounts for the high value of the observed activation energy. Summarizing, I propose that the rate of silica reduction, like that of the carbon-oxygen reaction, is diffusion controlled and that low oxygen concentration in the liquid metal is the major factor accounting for the very low observed rates of silica reduction. John Chipman (author's reply)—The authors thank Professor Schuhmann for his interesting contribution. His proposed explanation may well prove to be the correct one. There is clearly a need for much further experimental work on this problem, and further research is in progress.

Jan 1, 1961

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Jan 1, 1946