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By C. J. Pritchard, R. E. Gundersen

I commend the authors on examining an interesting method of shaft lining and attempting to improve safety in a dangerous environment by remotely installing the shaft lining. It is important, though, to not trade off shaft lining safety for long-term mine safety by lining an intake shaft with combustible material. In many operations, the mine utilities are installed next to the lining of the intake shaft, supplying a possible ignition source if damaged or overloaded. Although the polyurethane studied in the paper is of relatively high density, no mention is made of the flame retardency of the samples. When exposed to heat, small amounts of polyurethane will melt and bum but are extinguished when the heat source is removed. If large surface areas of combustible polyurethane - a tunnel or mine shaft- are exposed to ignition heat sources that are not removed or extinguished early, an uncontrollable, fuel rich fire may result with high carbon monoxide levels, low oxygen concentrations, and greatly increased burning rates that can have devastating effects on the ventilation system and miners' safety. Although these heavy polyurethanes lend themselves to a "pouring" application around the annulus of the shaft liners and is a continuous process, past experience with atomizing and frothing polyurethane spray systems indicates a high degree of maintenance and operator attention to the nozzle1 delivery system. This may require more miner's time to be spent in the shaft maintaining the foam system, negating some of the safety advantages of the system. If polyurethane foams are to be used in mines, they must be of the highest quality available in terms of flame spread, heat emitted while curing, and contaminants emitted while curing and spraying. In addition, employees must be given adequate training and be thoroughly informed in all aspects of polyurethane foam safety procedures. As witnessed by our fellow miners in South Africa, we can accept no less.

Jan 1, 1991

By H. Nemutolluhi

Discussion by G.E. Agar In the April issue of Mining Engineering there is a technical note "New size laboratory ball mill for Bond Work Index determination" written by M. Nematollahi which is very confusing. My recollection is that a description of an experimental procedure should be such that someone skilled in the art should be able to reproduce the results. Applying this test to this particular article would according to me cause a failure to be registered. There are apparently three batch laboratory test procedures referred to in the article. One of these is the traditional Bond test with all its limitations such as dry grinding followed by exclusively dry screening, two attributes which fail to simulate conventional industrial grinding. There is a second procedure (NSBM) which the author is advocating as an improvement of the Bond procedure but from the description I doubt that anyone would be able to repeat the procedure. For instance, is the grinding to be done wet or dry, if wet at what pulp density, and how is the screening to he done, wet or dry or a combination? On top of that uncertainty the author refers to a simplified "Anaconda" test. No reference is provided for this procedure and in the text the results of the technique are referred to "Denver wet ball mill" results and say nothing of Anaconda results. Reply by H. Nematollahi I think that the method proposed to determine the Bond Work Index in this paper is clearly described in the paper as follows: •The method of grinding is dry (Ref. paragraph I, subject Method description); •The size of ball mill, the quantity and size of balls are noted (Ref. paragraph 1, subject Test equipment); and The test procedure is described in detail (Ref. paragraphs 1, 2 and 3, subject Test procedure). As it is noted in the paper, the test has been worked out under the same condition as Standard Bond Test with ball mill, so dry (screening should be dry also), but using a smaller ball mill and a smaller quantity of sample. Considering the above mentioned points, I believe that the method has been fully and clearly described and it ought to be repeatable as well. The Anaconda test is a method for determination of Work Index and could be done by any types of laboratory wet ball mill (Yan, R.F., et al., cf. References). I applied this method using a laboratory Denver ball mill (Ref. paragraph I subject Determining the Bond Work Index). So the results referred to Denver wet ball mill can be equated the same as Anaconda method.

Jan 1, 1996

By Jay F. Smith

The Alan Wood BOF Shop consists of two 140 ton furnaces with a rated yearly capacity of 1-1/4 million ingot tons, he hot metal for the BOF Shop is supplied by two 18 foot blast furnaces which produce an average of 2000 tons per day, To achieve the rated ingot ton capacity with this limited supply of hot metal, the preheating of scrap is necessary. This is accomplished in the furnace by using an oxygen-natural gas burner. Piping Arrangement The natural gas and oxygen are piped into the Shop through 8-inch lines to their respective valving stations. As can be seen from Figure 1, the flow of natural gas passes through a flow control valve which is common to both furnaces, after which it divides into two 6-inch lines forming two identical and independent gas control lines, one for each furnace.

Jan 1, 1972

By R. J. Pindred

Discussion by R.J. Pindred In his paper, Davis presents an overview of risk. He also introduces the Capital Asset Processing Model (CAPM) as a foundation for selecting the appropriate discount rate for a mining project. While applying portfolio theory is more defensible than the ad hoc adjustment of discount rates, the CAPM is not a panacea. CAPM shortcomings [The CAPM, as Davis stated, is expressed in the equation: ri=rf+pi4) where ri is the project discount rate rf is the risk free interest rate (3i is the project beta, and 0 is the market risk premium (rm - rf)] Application of the CAPM is more difficult than Davis indicates. Valuation is prospective, while the CAPM parameters are historical. Beta is determined from a regression analysis of historical data, while the beta needed for valuation is the expected beta. Betas are known to be unstable and the regressions that generate them often have low explanatory power. The difficulty of estimating a "project" beta must also be considered. Thus, the beta that is used in the CAPM will be based on the analyst's judgment. Like Cavender's discount rate, this judgment can lead to different project NPVs. Subjectivity in valuation cannot be avoided by a mechanical application of the CAPM. The risk-free rate, which Davis identifies as a short-term real rate of 4%, is also subject to scrutiny. A mining project is not a short-term investment and no single risk-free rate is appropriate for all of the cash flows. The hypothetical mine discussed in Cavender's paper is a six-year project. One might argue for the application of a risk-free rate from the Treasury yield curve at the duration of the project (in a bond-duration sense). This, too, is inappropriate. The risk-free rate should be matched to the timing of the cash flow. These rates can be determined by calculating the implied forward rates from the yield curve using a procedure known as "bootstrapping." It is likely that each of the project's cash flows would be discounted at a different rate. Commodity prices Davis criticizes the "ad hoc adjustment to the discount rate." Yet, in his discussion of the value of stochastic simulation, he suggests that the gold price be modeled as a "random walk, with or without a trend." This is essentially an arbitrary modeling of price risk. Consider that a liquid market in gold futures exists. The futures' price curve, which is closely related to the market's estimate of future spot gold prices, should be used to provide inputs to the model. This is especially true of a relatively short six-year project. Alternatively, as Davis correctly points out, a risk-averse investor can sell the commodity short to hedge price risk. Is it any more correct, in the portfolio sense, to account for price risk at all ?? References Cavender, B., 1992, "Determination of the optimum lifetime of a mining project using discounted cash flow and option pricing techniques," Mining Engineering, Vol. 44, No. 10, pp.1262-1268 Fabozzi, F.J., 1993, Bond Markets, Analysis and Strategies, Second Edition, Prentice Hall, Inc. Higgins, R.C., 1992, Analysis for Financial Management, Third Edition, Richard D. Irwin, Inc. Solnik, B., 1991, International Investments, Second Edition, Addison Wesley Reply by G.A. Davis Pindred discusses two issues related to my paper, the shortcomings of the Capital Asset Pricing Model (CAPM) and which commodity price values to use in the valuation exercise. Even though these topics are not directly related to the use or misuse of Monte Carlo simulation, they are important points to take into consideration in valuation exercises. Since I do not appear to have addressed these issues satisfactorily in my original paper, I will comment on each here. Pindred agrees with me that applying portfolio theory, and specifically the CAPM, to the selection of project discount rates is more defensible than ad hoc methods. But he then points out that the application of the CAPM to project valuation is more difficult that I indicate. It is true that the CAPM is a difficult tool for project valuation in general,. But the application of the CAPM to mining projects is one of the easiest I can think of. The biggest problem with using the CAPM for project valuation is coming up with an expected project beta. I suggest a project beta for gold projects of 0.45. The "true" value might be 0.35, 0.55 or whatever. Pindred correctly notes that the selection of the appropriate project beta is based

Jan 1, 1996

By B. E. Grant

There are several exceptions from the practical operating viewpoint that might be taken with the paper. The author recommends using a "curve" in plotting safety factors of ropes and suggests that the U. S. Bureau of Mines change its present "step curve" method to the "curve" method. From an engineering theoretical point of view that is possible, but from a practical standpoint it is not possible. Rope manufacturers fabricate their ropes in diameter gradients of 1/16 in. to 1/4 in. which automatically sets up a step pattern gradient. If ropes were manufactured in the diameter gradients of 1/1000 of an inch or thereabouts, the curve method could be used. Also, from a practical standpoint, if an operator is to hoist from a depth of 4000 ft, for example, he will determine the size of the rope necessary for that depth, and it is only natural that he will have safety factor to spare at lesser depths, and in plotting this excess capacity the natural end result is a curve. The U. S. Bureau of Mines tables are set up so that the operator will know what size rope at the required safety factor he will need at his maximum depth. He is not concerned with lesser depths. W. A. Boyer (author's reply)-Mr. Grant states, "Rope manufacturers fabricate their ropes in diameter gradients of 1/16" to 1/4" which automatically sets up a step pattern gradient." There is no connection or relationship between the "size" pattern gradient and the present "factor of safety" step pattern gradient. The inherent factor of safety values for any particular size of rope with a given connected load when plotted for various depths is a curve, and with modern rope material and construction the inherent factor of safety curve is quite far removed from the present recommended factor of safety step curve. This is shown quite clearly in Figs. 3 and 4 of my paper.

Jan 11, 1954

Three -dimensional boundary value problems are difficult to solve. Indeed, while the separation of the scalar wave equation can be effected in 11 different coordinate systems, an analytic solution requires that the boundaries, both external and internal, possess the same symmetry as the coordinate system. Numerical methods are thus of great importance for the solution of such problems; however, despite the availability of high-speed, large memory digital computers , the solution to a significant three -dimensional problem is by no means trivial. It is unfortunate that the results reported here by Jones are invalid. Jones discusses a model in which a three-dimensional island lies off a linear coastline where all the interfaces lie in the coordinate planes in a Cartesian system. A downward plane em wave polarized with the electric field parallel to the linear coastline, and two of the islands coast, is incident downward. This, of course, requires that the incident electric field is perpendicular to the other faces of the idealized Cartesian island. The significant equation used by Jones for his finite difference calculations is [ ] where n2 = sµ? . is the conductivity, µ=µo is the permeability of the appropriate medium, and w is the angular frequency of a Fourier component of the incident field. We see that the displacement current term is omitted, which is an excellent approximation for the parameters of interest in this model. In the similar equation for the y- component of the diffusion equation, the same considerations which we are about to discuss are equally valid. It can be seen from the equation that the field components are related and thus any errors introduced will be propagated into all three components. The difficulty arises when Ex or E is perpendicular Y to one or other of the surfaces of discontinuity in s. The continuity of current at the air-earth interface (upper surface), e. g., jy, requires

Jan 1, 1973

Gerald Sherman, Bisbee, Ariz. (written discussion*) .—The fact that, after a change in the hours of labor, as much work is found to be done in 8 hr. as was accomplished in 10, probably results from the more rigid examination of operating methods that is made when the management faces new and more difficult conditions. Although A better working pace will prevail, most of the gain will result from economies of plan and only a part of it from the improved effciency of labor. The Iabor of shoveling is so severe that it may be easily believed that a working period of less than 7 hr. will give maximum results, but there arc many other occupations about a mine in which this is not true, and in which the rate of accomplishment is in proportion to the time employed, up to 9 or 10 hours. Mr. Harley's study of shoveling has becn thorough, and demonstrates the benefit of investigation and education even in such simple work, but his reference to methods of payment opens a subject even more important in mine management. The efficiency of labor may be excellent, but unless a method of equitable payment accompanies it, the result will be only temporary. With strict but sympathetic supervision, a good average day's work can be obtained; but with the exception of those unusual men who cannot be restrained from working to their limit, an average daily wage does not bring out the remarkable performance of which many men are capable. There is also a considerable variation in the average amount accomplished, dependent on the supply of Iabor. This can readily be shown by any labor record that covers several periods of shortage or superabundance of labor. An increase in the daily wage in the time of labor shortage does not necessarily bring out an increased day's work; there is usuaIly a decrease in labor efficiency at such times regardless of the wage, whenever a daily rate is used. Rewards to individuals for exceptional performance appearing as an increased rate of pay cannot be made in a large organization without bad feeling. In a small organization, an individual's ability may be so well recognized that different rates of pay can be applied. Exceptional work can only be obtained by a method of payment based on the valuable results accomplished. As a basis for such payment, an

Jan 1, 1920

Contribution by G. Narsimhan It was with much pleasure that I went through D.F. Malan's excellent paper. The following explanatory and critical note has been the result of my deep study of the paper. Although by qualifications and experience I have been a chemical engineer, involved over four decades with problems in the modeling and simulation of transport-limited (heat and mass) chemical reactions in multi-phase systems, I have of and on interested myself in challenging problems in extractive metallurgy. This is the first time I have veered of to continuum mechanics, at the age of 71! Author's reply. I thank Professor Narsimhan for his extensive contribution to the paper. It provided me with the stimulus to derive an extended model. However, there are some inaccuracies in his arguments that need further discussion. Professor Narsimhan's main concern is that there is not a good enough fit between the derived viscoelastic Kelvin model and the experimental data supplied by Güler1 (see Figure l1 on page 218 of my paper). I will therefore explain the choice of a viscoelastic model in more detail and also make specific comments on the arguments given in his contribution.

Jan 1, 1996

By L. W. Saperstein

P.J. Ehret By and large, I agree with many of the precepts discussed in the Saperstein paper. I believe there is much more that can be done on the local level to involve both government and planning in the mine permit review process. Admittedly, much can be done to improve discussion between the state regulatory authority, local authorities, and mine operators. However, I strongly disagree, as suggested in the paper's conclusion, that such a system, as outlined in Saperstein's paper, could result in a reduction of review time or a lowering in the cost of permitting. The implementation of such a system by its very nature would only add a new level of bureaucracy to an already cumbersome process. This system, in my opinion, would only add to the cost of permitting and the time necessary to obtain a permit. Admittedly, it would achieve the result of adding local influence into the permitting process, but at what off-setting cost? It has been my professional first-hand experience and observation in the permitting and lands unsuitable processes to note that under the present system, local governments that do feel they have a stake in local mines and actively ad¬vocate their position (not simply comment), have had significant input into the conduct of mining and reclamation plans in their areas. Mining companies that mine in these areas are aware of local interests and attitudes, and do consider them in their plans. Simply put, local governments that want to get involved and want to play significant roles can and do. Those that do not advocate a position or have no input to offer do not. Although the present system is not as direct in effect in regard to local control as Saperstein's, it does work. It does so without the red tape that would result from developing miniature regulatory authorities in every county in which mining occurs. Although local input is important, there are many more sections of the Surface Mining Control and Reclamation Act (SMCRA) than Sections 508(a)(8) and 522(a)(3)(A) that also are important. It appears Saperstein's paper may overindulge these sections. An additional specific comment is made in regard to the statement that while local areas benefit from mining (wages, salaries, and purchases), they also endure environmental deterioration caused by mining affects. It is believed that the whole purpose for which SMCRA and its resulting regulations were enacted and developed was so mining would not be permitted if significant environmental deterioration could occur. Therefore, it could be argued that this point under current law is moot. Reply by L.W. Saperstein P.J. Ehret writes in a reasoned and rational way and makes some good points. The arguments in favor of central control of the designation process reflect all of the benefits associated with central environmental control: consistency of enforcement, efficiency of operation, ease of communication among enforcing agency, etc. Nonetheless, the decision to mine or not to mine is a landuse decision which, in substance, is similar to the decision to build a shopping mall, a new highway, or a housing subdivision. Although, state and federal governments' interests in the protection of public welfare are real and are expressed properly in mining laws and mining enforcement agencies (OSM, Illinois Department of Mines and Minerals, etc). I continue to maintain that the permitting and designation processes should originate with local government, which is in keeping with the American tradition of delegation of the land-use decision to local or regional government.

Jan 4, 1984

By P. J. Ehret

By and large, I agree with many of the precepts discussed in the Saperstein paper. I believe there is much more that can be done on the local level to involve both government and planning in the mine permit review process. Admittedly, much can be done to improve discussion between the state regulatory authority, local authorities, and mine operators. However, I strongly disagree, as suggested in the paper's conclusion, that such a system, as outlined in Saperstein's paper, could result in a reduction of review time or a lowering in the cost of permitting. The implementation of such a system by its very nature would only add a new level of bureaucracy to an already cumbersome process. This system, in my opinion, would only add to the cost of permitting and the time necessary to obtain a permit. Admittedly, it would achieve the result of adding local influence into the permitting process, but at what off-setting cost? It has been my professional first-hand experience and observation in the permitting and lands unsuitable processes to note that under the present system, local governments that do feel they have a stake in local mines and actively advocate their position (not simply comment), have had significant input into the conduct of mining and reclamation plans in their areas. Mining companies that mine in these areas are aware of local interests and attitudes, and do consider them in their plans. Simply put, local governments that want to get involved and want to play significant roles can and do. Those that do not advocate a position or have no input to offer do not. Although the present system is not as direct in effect in regard to local control as Saperstein's, it does work. It does so without the red tape that would result from developing miniature regulatory authorities in every county in which mining occurs. Although local input is important, there are many more sections of the Surface Mining Control and Reclamation Act (SMCRA) than Sections 508(a)(8) and 522(a)(3)(A) that also are important. It appears Saperstein's paper may overindulge these sections. An additional specific comment is made in regard to the statement that while local areas benefit from mining (wages, salaries, and purchases), they also endure environmental deterioration caused by mining affects. It is believed that the whole purpose for which SMCRA and its resulting regulations were enacted and developed was so mining would not be permitted if significant environmental deterioration could occur. Therefore, it could be argued that this point under current law is moot.

Jan 1, 1985

By Wallace W. Wilson

This DaoerAA calls to attention for the first time, to the writer's knowledge, a purported recovery of oil by substantially horizontal gas cycling that is considerably in excess of 50 per cent of the oil originally in place. The average angle of dip along the path of travel of the gas is less than one degree of arc. The best recovery by gas cycling previously brought to the writer's attention1 occurred in the case of the Mile Six Field in Peru, where about 68 per cent of the original oil in place has so far been recovered. In this case, however. the recovery was greatly aided 1)y the high dip angle of about 17.5". An approximate estimate of recovery was made by the method developed by the writer' for the case of the Cook Ranch Field, using an average relative permeability ratio function dictated by past experience with a number of good quality sandstones. A result of about 40 per cent recovery of the original oil in place wa* obtained after the 8.5 pore volumes of cumulative gas cycling undergone by the Cook Ranch Field. Tile writer desires to emphasize what appears to him as the sound engineering practiced at Cook Ranch, and also the care attending the taking of data and the high quality of the calculations made. It is impossible to take issue on factual grounds with any of the conclusions drawn in the paper. It is, however, desired to point out the difficulty of explaining the unexpectedly favorable oil recovery on ordinary theoretical grounds. It would be of interest to know whether relative permeability ratios have been measured on the Cook sand. The operator is inclined to attribute some of the excess benefit to settling of the oil across the bedding planes into the lower part of the sand. It is difficult for the writer to appreciate the importance of such an effect, inasmuch as the concomitant opening of excessive vacated pore space in the upper part of the sand would he expected to cause excessive bypassing of the gas. REFERENCE 1. Welge. H. J.: "A Simplified Method for Computing Oil Recovery by (Gas or Water Drive." Trans. AIME, (1952), 195, 91. AUTHOR'S REPLY TO MR. WELGE Welge has poined out clearly the difficulty of applying material-balance procedures in calculating the Performance of low-pressure, dispersed gas injection operations. There can be no argument that even with the most favorable assumptions of K,/K,, and with cumulative gas cycling in excess of normal expectations, the calculated oil recovery will be considerably less than the 72.5 per cent recovery realized from this project to Jan. 1, 1951. There probably are at least two reasons for the unusually high recovery from this reservoir, the effects of which would be difficult or impossible to calculate by known methods: 1. The operator did not use the same injection wells for the entire operation, and exercised considerable control over producing GOR by changing the locations of injection wells whenever well performance indicated excessive bypassing. Fifty-six wells were used for injection, not over 29 of which were in use simultaneously. This procedure resulted in frequent shifting of the fluid movement patterns in the reservoir and undoubtedly increased the ultimate recovery. The writer knows of no satisfactory procedure for calculating the effect of this practice. 2. Vertical movement of oil across the bedding planes of the reservoir rock hy gravity drainage tended to maintain a relatively high oil saturation, and hence a favorable K,/K, ratio, in the lower sections of the reservoir. As pointed out by Welge, this condition has aggravated the tendency for high producing GOR, but at the same time it has resulted in increased oil recovery. As may be seen from the performance charts for the various battery areas, operating (GOR'S have been quite high for the last several years of reported history.

Jan 1, 1952

By B. Mather

Discussion by B. Mather I was very glad to see an article on alkali-silica reactivity of concrete aggregate in Mining Engineering. It is a topic that should be reexamined every 45 or 50 years. The last paper (that I am aware of) that examined this topic in Mining Engineering was Rexford (1950), who, at the time, was chief of the Petrography Section, South Pacific Division Laboratory, Corps of Engineers, Los Angeles, CA. The paper was presented at the AIME meeting in Los Angeles in October 1948. Professor Leming's discussion generally reflects the current state-of-the-art; but it provides no references for more detailed information. I wrote a paper titled "How to avoid excessive expansion of concrete due to alkali-aggregate reaction," which was included in the Proceedings of the Second International Conference on Alkali-Aggregate Reactions in Hydroelectric Plants and Dams (Mather, 1995). In it, I emphasized that it was the hydroxide ion (not the alkali ion) that caused the pore fluid in the concrete to dissolve reactive silica, producing alkali-silica gel capable of taking up water, thereby, causing swelling and rupturing of the concrete. Excessive expansion will not occur unless there is a sufficient amount of potentially expansive alkali-silica reaction product and water. However, this will not occur unless there is a sufficient quantity of reactive aggregate and unless there is a mechanism by which the pH of the pore fluid can get well above the normal value of about 12.6. In many cases it is sufficient that the cementitious medium not only contains portland cement but also contains ground granulated blast-furnace slag (GGBFS) or a pozzolan such as fly ash, silica fume, metakaolin, volcanic glass or calcined shale - any of which may have been included for economic reasons. If, however, the person selecting the ingredients for concrete knows that the aggregate is reactive (with no alternate nonreactive aggregate available) and if the person knows that the only available portland cement has a high alkali content (i.e., more than 0.6% Na2Oe; Na2Oe = % Na2O + 0.658 x % K20), then it becomes irresponsible not to establish what reasonable precaution one should take. Professor Leming suggests using one of the following: 30% Class F fly ash, 50% GGBFS or 7% to 10% silica fume. My view is that one should prepare test specimens with the cement and aggregate to be used and then expose these both with and without at least two dosages of each of the various alternative materials (slag, pozzolan and lithium salts), so that the required dosage to control the expansion is established. Then, economic considerations can dictate the final selection. I would point out to the author that GGBFS is not a pozzolan and is not an admixture, but, rather, it is a latent hydraulic cement. An admixture is, by definition, a material other than hydraulic cement. I commend him for suggesting that aggregate producers should become more active in knowing about the reactivity of their products and the precautions needed to permit those products to be safely used in concrete. ? References Mather, B., 1995. "How to avoid excessive expansion of concrete due to alkali-aggregate reaction," Proceedings, Second International Conference on Alkali-Aggregate Reactions in Hydroelectric Plants and Dams, US Committee on Large Dams, Denver, CO, pp. 421-439. Rexford, E.P, 1950, "Some factors in the selection and testing of concrete aggregates for large structures," Mining Engineering, Trans. AIME, Vol. 187, pp. 395-402. Reply by M.L. Lerning Mr. Mather has once again provided a cogent and useful discussion. I am grateful to him for bringing these issues to my attention, as well as to the readers, and I am grateful for his discussion of several important factors in alkali-silica reactivity. Mr. Mather's discussion of the mechanism of alkali-silica reactivity (ASR) notes the critical role of the hydroxide ion. While the alkali hydroxides are highly soluble (reducing the solubility of the other primary hydroxide in pore solution, i.e., calcium hydroxide, and providing hydroxide ions that initiate alkali-silica reactivity), it is, as Mr. Mather quite correctly notes, the hydroxide ion that attacks the silica structure. This point was not clearly stated in my original article. As noted in the text, the requirements for mineral admixtures to mitigate or control ASR vary widely depending on the specific characteristics of the materials

Jan 1, 1998

By M. E. Gershon

I would like to congratulate Professor Gershon on an idea that is obviously valuable and is certainly new to me. It has, however, to be further developed, in that one can get fallacious results by limiting oneself to positional weights. In the example problem, the positional weight of one block was 8.6 (the 8.0 value in the paper was incorrect) for 36 units in the cone, for a mean block value of 0.239. The positional weight of the second block was 4.4 for 15 units, for a mean block value of 0.293. Surely one would expect the second block to be rated higher. Additionally, the time value of money adjustment cannot be determined by depth, because the time that a block is mined is determined by the mining sequence, not depth. Figure 1 shows a slightly altered version of Professor Gershon’s pit. The overall value of the pit is the same, as are the total values under each of his blocks. The values in the right-hand cone have been reversed top to bottom, and the values in the rest of the pit adjusted to keep the central cone total unchanged. All values have been multiplied by 10. Figure 2 shows the sequence of mining, at three blocks per year, for Professor Gershon’s pit, and Fig. 3, the sequence for a pit under the other block. Table 1 shows the value and discounted value (157. ) of Professor Gershon’s pit, and Table 2 shows similar values for the second pit. It is apparent that the second pit schedule is more valuable than the first.

Jan 12, 1987

By C. J. Hall

I would like to congratulate Professor Gershon on an idea that is obviously valuable and is certainly new to me. It has, however, to be further developed, in that one can get fallacious results by limiting oneself to positional weights. In the example problem, the positional weight of one block was 8.6 (the 8.0 value in the paper was incorrect) for 36 units in the cone, for a mean block value of 0.239. The positional weight of the second block was 4.4 for 15 units, for a mean block value of 0.293. Surely one would expect the second block to be rated higher. Additionally, the time value of money adjustment cannot be determined by depth, because the time that a block is mined is determined by the mining sequence, not depth. Figure 1 shows a slightly altered version of Professor Gershon's pit. The overall value of the pit is the same, as are the total values under each of his blocks. The values in the right-hand cone have been reversed top to bottom, and the values in the rest of the pit adjusted to keep the central cone total unchanged. All values have been multiplied by 10. Figure 2 shows the sequence of mining, at three blocks per year, for Professor Gershon's pit, and Fig. 3, the sequence for a pit under the other block. Table 1 shows the value and discounted value (15%) of Professor Gershon's pit, and Table 2 shows similar values for the second pit. It is apparent that the second pit schedule is more valuable than the first.

Jan 1, 1988

By E. Tulcanaza

M.S. Azun I do not at all agree with the basic points of the author's conclusion. The use of lognormal or normal model to respond to the attribute distribution function should be carefully questioned. If fitting a distribution function of regionalized variables is the main purpose, one may employ one of certain well-known families of distributions, such as Tukey's lambda functions. For instance, the distribution function of gold assay values studied by Krige (Krige, 1978) may fit the lognormal model well, but one should not exclude that the basic idea of using the distribution function of observed data is to have insight of the physical mechanism that gives rise to the regionalized variables. In Applied Geostatistics, there are many examples considering only lognormal or normal model for the distribution function of geostatistical data even if the observed distribution function has more than one mode. Of course, using lognormal or normal model always brings easy computation for the statistical properties of attribute under investigation. Still, I object to adopting any of those models without having any "statistical inference." As seen from the author's paper, lognormal and normal model produce the same average grade (0.746% copper) and almost the same sample variance. Therefore, which model explains the probabilistic behavior of ore deposit is always an important question that should be replied by the geostatistician using not the common sense but the statistical and probabilistic methods. For kriging procedures, such as linear kriging, one should describe either second order stationary properties or bivariate properties of regionalized variables. Second order properties, such as correlogram function or semivariogram function, are the inputs of the so-called kriging equations. Selecting one of any useable models for the observed second order properties, such as spherical model, is not easy since the models are not based on the correlations structure of the regionalized variables. How those models being used in Applied Geostatistics can be distinguished is another important problem. One may develop many fitting models to respond to the observed second order properties of regionalized variables. However, I suggest that the model should be based on the probabilistic behavior of geologic process. The author used spherical model for copper, wolfram, and silver grades from isotropic sector (Fig. 2, 4, 3b) and exponential model for silver grades obtained along raises in isotropic sector (Fig. 3a). It seems that those semivariograms given in Fig. 3b for isotropic sector and Fig. 4 may be described by the random model implying that regionalized variables do belong to renewal process (Azun, 1983). If I knew the total number of data points used in estimation, I may prove that my conclusion is correct. Recalling the test for the first order sample correlogram value, the test procedure is introduced such that the independence is rejected if [ ] where Za/2 is the a/2 percentile of standard normal random variable and N is the total number of samples used in estimation (Azun, 1983). For the other observed semivariogram functions I suggest the author might try to use the so-called "Markovian model" describing not only the correlation structure of regionalized variables, but also the physical mechanism that produces the regionalized variables. The Markovian model for correlogram function is, [ ] The Markovian model for the other second order properties of ReV are also derived. T ve B, in the above equation, show, for example, structural change and mineralizational variation in a considered deposit, respectively (Azun, 1983). In selecting any model, it is not easy to search for the "best" response to the observed second order properties of ReV's. The Markovian model, based on a theoretical understanding of underlying mechanism, gives more information about the occurrence of regionalized variables and respond to all properties. Random model and the so-called hole effect structure can be easily defined as a special form of the Markovian model (Azun, 1983). An estimation of any second order properties of regionalized variables may be computed through (N-1) lag. However, the dependency between the regionalized variables may be deemed to have "died out" after the so-called stationarity width (range). In practice, the estimation is carried out through 25% of the total number samples available. Therefore, the large fluctuations around the zero level and variance for correlogram or covariogram function and semi-variogram function, respectively, cannot be observed. Since the number of pairs involved in the estimation of higher second order properties is small, the estimation variance at those lags is large. There is no need to show higher order estimated second order properties. After using one of any kriging procedure for block estimation, the distribution function of average grades has the same mean as the drilling sample grades but

Jan 3, 1985

By M. S. Azun

I do not at all agree with the basic points of the author's conclusion. The use of lognormal or normal model to respond to the attribute distribution function should be carefully questioned. If fitting a distribution function of regionalized variables is the main purpose, one may employ one of certain well-known families of distributions, such as Tukey's lambda functions. For instance, the distribution function of gold assay values studied by Krige (Krige, 1978) may fit the lognormal model well, but one should not exclude that the basic idea of using the distribution function of observed data is to have insight of the physical mechanism that gives rise to the regionalized variables. In Applied Geostatistics, there are many examples considering only lognormal or normal model for the distribution function of geostatistical data even if the observed distribution function has more than one mode. Of course, using lognormal or normal model always brings easy computation for the statistical properties of attribute under investigation. Still, I object to adopting any of those models without having any "statistical inference." As seen from the author's paper, lognormal and normal model produce the same average grade (0.746% copper) and almost the same sample variance. Therefore, which model explains the probabilistic behavior of ore deposit is always an important question that should be replied by the geostatistician using not the common sense but the statistical and probabilistic methods. For kriging procedures, such as linear kriging, one should describe either second order stationary properties or bivariate properties of regionalized variables. Second order properties, such as correlogram function or semivariogram function, are the inputs of the so-called kriging equations. Selecting one of any useable models for the observed second order properties, such as spherical model, is not easy since the models are not based on the correlations structure of the regionalized variables. How those models being used in Applied Geostatistics can be distinguished is another important problem. One may develop many fitting models to respond to the observed second order properties of regionalized variables. However, I suggest that the model should be based on the probabilistic behavior of geologic process. The author used spherical model for copper, wolfram, and silver grades from isotropic sector (Fig. 2, 4, 3b) and exponential model for silver grades obtained along raises in isotropic sector (Fig. 3a). It seems that those semivariograms given in Fig. 3b for isotropic sector and Fig. 4 may be described by the random model implying that regionalized variables do belong to renewal process (Azun, 1983). If I knew the total number of data points used in estimation, may prove that my conclusion is correct. Recalling the test for the first order sample correlogram value, the test procedure is introduced such that the independence is rejected if [Ir(1) I > Za/2 N1/2] where Za/2 is the a/2 percentile of standard normal random variable and N is the total number of samples used in estimation (Azun, 1983). For the other observed semivariogram functions I suggest the author might try to use the so-called "Markovian model" describing not only the correlation structure of regionalized variables, but also the physical mechanism that produces the regionalized variables. The Markovian model for correlogram function is, [p (h) = T 1ih , h>1 ,] The Markovian model for the other second order properties of ReV are also derived. [T veß], in the above equation, show, for example, structural change and mineralizational variation in a considered deposit, respectively (Azun, 1983). In selecting any model, it is not easy to search for the "best" response to the observed second order properties of ReV's. The Markovian model, based on a theoretical understanding of underlying mechanism, gives more information about the occurrence of regionalized variables and respond to all properties. Random model and the so-called hole effect structure can be easily defined as a special form of the Markovian model (Azun, 1983). An estimation of any second order properties of regionalized variables may be computed through (N-1) lag. However, the dependency between the regionalized variables may be deemed to have "died out" after the so-called stationarity width (range). In practice, the estimation is carried out through 25% of the total number samples available. Therefore, the large fluctuations around the zero level and variance for correlogram or covariogram function and semivariogram function, respectively, cannot be observed. Since the number of pairs involved in the estimation of higher second order properties is small, the estimation variance at those lags is large. There is no need to show higher order estimated second order properties. After using one of any kriging procedure for block estimation, the distribution function of average grades has the same mean as the drilling sample grades but

Jan 1, 1986

By M. A. Schimmelpfennig, A. D. S. Gillies

M.J. McPherson Having worked on the thermodynamics of air/liquid-water mixtures passing through the surface fans of deep mines, I find this paper of great interest and congratulate the authors on producing it. There are two matters, however, deserving discussion. First, the authors have described the classical theory of fog formation with fogging occurring at "supersaturation." In fact, the process of fog formation begins well below 100% humidity. The more strongly hygroscopic nuclei in the atmosphere will attract water molecules and begin to grow at a relative humidity perhaps as low as 70%. The process is a dynamic one with both condensation and evaporation taking place throughout the mixture on microscopic liquid surfaces. As saturation is approached, the rate of condensation accelerates rapidly producing the familiar reduction in visibility. Hygroscopic nuclei are present in all natural atmospheres and under the appropriate conditions of pressure and temperature, will produce clean fogs. However, if the air is polluted by particulates from combustion or other processes then the resultant coagulation with growing liquid particles may produce dense (and sometimes photochemical) smogs. It is this process that is likely to occur in underground mines when moist air is cooled below dew point. Second, the authors have summarized very well the individual measures that might alleviate the problem. In particular, I agree that neither heating nor refrigerating the air, by themselves, provides a satisfactory solution. However, there is a combination of these that provides a neat and effective control of fog formation. This involves a small, self-contained refrigeration unit within a duct but without the usual external heat rejection facility. The air is cooled below dew point and, hence, dehumidified on passing over the cold evaporator coils. The heat from the condenser is rejected back into the air downstream from the water eliminator, as shown in Fig. 1. The duct configuration can be designed to create good mixing at the outlet. I have used a climatic simulation program to illustrate the effect, assuming a 500-m (1,640 ft) long airway of cross section 60 m2 (645 sq ft), an airflow of 9 m3/s (318 cu ft per sec), inlet conditions of 19/19.25°C (66/67°F) wet bulb/dry bulb temperatures, a virgin rock temperature of 17°C (63°F) and typical rock thermal properties for a hard-rock mine. I have also assumed that 10% of the rock surface is wet. Figure 2 shows the variation in temperatures along the airway if no measures are taken. The relative humidity remains close to 100% and condensation will occur throughout the length of the airway. Before any such installation is designed, the exercise must, of course, be repeated for each location with accurate data. However, this example demonstrates the potential of the system. The idea is not new - the principle is sometimes used in air-conditioning plants for buildings. Figure 3 shows the effect of removing 30 kw of heat by evaporator coils sited 40 m (131 ft) along the airway and rejecting that heat (plus another 10 kw of compressor and fan power) into the air at 60 m (197 ft). Condensate water is produced, at a rate of 0.45 L/min (0.12 gpm). The result of this sequential cooling/dehumidification/heating process is to separate the wet and dry bulb temperatures along the length of the airway. The relative humidity increases from 80% at the duct outlet to 92% at 500 m (1,640 ft). The airway is maintained free from fog.

Jan 11, 1983

By M. J. McPherson

Having worked on the thermodynamics of air/liquid-water mixtures passing through the surface fans of deep mines, I find this paper of great interest and congratulate the authors on producing it. There are two matters, however, deserving discussion. First, the authors have described the classical theory of fog formation with fogging occurring at "supersaturation." In fact, the process of fog formation begins well below 100% humidity. The more strongly hygroscopic nuclei in the atmosphere will attract water molecules and begin to grow at a relative humidity perhaps as low as 70%. The process is a dynamic one with both condensation and evaporation taking place throughout the mixture on microscopic liquid surfaces. As saturation is approached, the rate of condensation accelerates rapidly producing the familiar reduction in visibility. Hygroscopic nuclei are present in all natural atmospheres and under the appropriate conditions of pressure and temperature, will produce clean fogs. However, if the air is polluted by particulates from combustion or other processes then the resultant coagulation with growing liquid particles may produce dense (and sometimes photochemical) smogs. It is this process that is likely to occur in underground mines when moist air is cooled below dew point. Second, the authors have summarized very well the individual measures that might alleviate the problem. In particular, I agree that neither heating nor refrigerating the air, by themselves, provides a satisfactory solution. However, there is a combination of these that provides a neat and effective control of fog formation. This involves a small, self-contained refrigeration unit within a duct but without the usual external heat rejection facility. The air is cooled below dew point and, hence, dehumidified on passing over the cold evaporator coils. The heat from the condenser is rejected back into the air down-stream from the water eliminator, as shown in [Fig. 1]. The duct configuration can be designed to create good mixing at the outlet.

Jan 1, 1984

By Bunting S. Crocker

Bunting S. Crocker (Executive Vice President, Kilborn Engineering Ltd., Toronto, Ont., Canada)-This is an interesting report on laboratory-scale testing with pebble charges in 12-in.-diam mills, and the author correctly concludes that useful laboratory testing can be done. In the opening paragraphs he states, "laboratory pebble-milling tests have been considered too difficult to perform and not relevant enough to the actual grinding situation"!! This is definitely not so! The writer published detailed tests done in a 12-in.-diam mill comparing pebble and steel balls in 1952 6 and again in 1954 7. We note that our review paper in 1963 was the only one mentioned in the References. The author states that "a smooth lining is more frequently used in commercial-scale pebble grinding." The writer has designed some 22 plants treating 134,000 tpd in North America and Australia. He has also visited pebble installations in Norway, Sweden, Finland, and South Africa. All these plants correctly use heavier lifters than would be considered standard for ball mills of a similar size. Smooth liners are not recommended in wet ore treating plants. In the 1952 paper6 it was clearly demonstrated in the test work that the individual ore pebbles had to be the same weight-not the same diameter or size-as the steel balls if comparable grinding results were to be obtained. In the tests performed in this study most of the pebbles "passed 50-mm round hole screen openings and remained on a 40-mm round hole sieve. Correspondingly most of the ball mill experiments were performed with 50 or 40-mm steel balls". Thus, the balls and pebbles were essentially the same size or diameter. This means we are comparing apples and oranges. When the feed being ground is fine enough the pebbles will be superior. When the feed is coarse the steel balls will be the better. This is similar to grinding tests in which two sizes of steel balls are compared. In the middle of the article, "Crocker5 has reported that equal weights of pebbles and steel balls achieve the same grinding capacities under similar conditions …", then he proceeds to question this postulate. In the eight reports that I have published, I have never made this statement. What I have said is "for comparable grinding, the individual pebbles in the mill charge should be the same weight as the individual steel balls." This is not the first time that I have been misquoted on this point! It is most unfortunate that this test work has been done with a ball and pebble of the same diameter and not the same weight. It is impossible to properly evaluate the results. I also regret the fact that the screen analyses of the tests were not shown. Many of us who have been 40 years or less in the grinding game can easily read screen analyses at a glance. We can tell whether the top meshes are being ground by the ball charge, etc., etc. The graphs are fine for the summary or to illustrate conclusions but are often misleading in the report itself. However, we do agree that useful pebble grinding tests can be done in a 12-in. mill.

Jan 1, 1973

By F. W. Brackebusch

In the paper presented by F.W. Brackebusch on the "Basics of paste backfill systems," paste fill was presented as a backfill process that offers many advantages over other alternatives such as hydraulic fill and rock fill. It was observed, however, that the mechanics of paste-fill transportation in pipelines is not fully understood and that the success of its implementation in practice depends on the precise control of the proportions of fines, aggregates and water in the mixture. The author emphasized the necessity for laboratory and full-scale testing to determine the suitability of a material to be used as paste fill. Although experimental testing is definitely an important operation in the design of a reliable paste fill, advances in the understanding of the fundamental laws that govern paste flow in pipelines are equally relevant. Ideally, the results of such efforts would provide predictive models for the rheology of the paste and the corresponding pumping-energy requirements. In an attempt to achieve this objective, an ongoing research program has been active at McGill University's Department of Mining and Metallurgical Engineering. Preliminary results showed that the underlying mechanics of paste-fill flow in pipelines may be described in terms of what is known as "plug flow," as depicted in Fig. 1. Although this flow mechanism has been known qualitatively for many years, few attempts managed to offer a comprehensive model (Gandhi, 1987; Duckworth, 1986). In our model, it is assumed that coarse aggregates present in the mixture form a porous core, which is filled with paste (fines and water) and is surrounded by an annular non-Newtonian (Bingham-plastic) lubrication layer, which enables the mixture to flow with pressure losses that are easily overcome by common positive-displacement pumps. In summary, our model predicts the thickness of the annular lubricating layer, which controls the magnitude of the pressure losses. This is done either by collecting data on the apparent viscosity of the Theologically-active fine fraction and using an analytical equation (Bouzaiene, 1994), or is done by measuring the void content of the coarse aggregates and deducing the thickness as a function of the fine- to coarse (weight or volume) fraction ratio in the mixture for a given pipe diameter and solids concentration. Our model predictions showed good agreement with data from Duckworth et al. (1986), as shown in Fig. 2.? References Bouzaiene, R., 1994, "Hydraulic transportation in mining," Ph.D. dissertation in progress, McGill University, Dept. of Mining and Metallurgical Engineering, Montreal, P0, Canada Duckworth, A., Addie, G.R., and Maffei, J.R.,1986, "Mine waste disposal by pipeline using a fine slurry carrier," Proceedings of the 11th International Conference on Slurry Transportation, Slurry Transport Association, Washington DC. Gandhi, R.L., 1987, "Effect of rheological properties of fines fraction on slurry hydraulics," Proceedings of the 12th International Conference on Slurry Technology, New Orleans, LA.

Jan 1, 1996