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By R. H. . T. Garnett

Contributed remarks on paper published in the Transactions, Mining industry section, vol. 100, September- December 1991, A121--45

Jan 12, 1992

By L. O. Howard

R. HATCH, Garfield, Utah.-The object of the meeting, I believe, is to determine the proper chemical composition to insure long wear of a ball in a mill, This might also apply to rods. I feel that there is only one way of determining accurately the wearing qualities of balls in mills, and that is by actually wearing out 400 or 500 tons of different kinds of balls. Two things add to the wearing qualities of a ball: (1) the tenacity, with which the particular particles of iron or steel are cemented together; (2) the individual hardness of each particle. My experience is that a ball that has a Brinell of 550 to 650 will give comparatively long life. There is considerable difference of opinion as to the best steel and iron alloys necessary to produce a satisfactory grinding ball. Some favor chrome, some manganese and some nickel. Personally, I believe cast iron alloyed with chrome makes the best ball for small sizes; for large sizes (3 1/2 in. and up) steel alloyed with manganese is best. L. 0. HOWARD, Pullman, Wash.-How would this method apply to lining? A. KissocK, New York, N. Y.-I do not subscribe to that exactly. As I am connected with the Climax Molybdenum Co. you would hardly expect me to. We have been much interested in trying to work out this grinding-ball problem and have spent a great deal of thought and effort on it. As we are associated with the American Metal Co. and have a number of properties of our own, we are in position to try our ideas on ourselves first. We have tried different compositions, but have not done anything very remarkable with them yet, except that we have been able to say that the combination of chrome and molybdenum has given the best wearing ball. Mr. Hatch feels that iron is the best medium for grinding, but since toughness as well as hardness is a factor in wearability we feel that a well made steel is better for this purpose. Another difficulty with cast, or chilled, iron is lack of uniformity from day to day or from heat to heat and the impossibility of producing balls free from blow or shrinkage holes which materially affect their life. If cast iron is made hard it becomes brittle and lacks stretch or toughness. This prevents its use in the larger sizes, as breakage is a serious handicap to efficiency. We have tried hard and brittle balls and softer but very tough balls and have proved that maximum hardness, with sufficient toughness to prevent breakage, is the most important factor in resistance of a steel to abrasion. It is well known that chromium is one of the best hardening agencies for either iron or steel, and molybdenum is recognized as an element capable of introducing toughness. In other words, the proper combination of chromium and molybdenum permits unusual hardness with still sufficient toughness to stand up under severest impact. It is yet too early to give any actual mill results of this new combination and though we are proving our ideas at our own properties we have to depend on others to help us make the data more general and more worth while and would like to get some tests

Jan 1, 1928

By G. Johnston, P. K. Chatterjee, S. Holguin

M. Gershon The article is an excellent one, providing a basis for the conduct of the major tasks in underground mine planning and scheduling. I object to only one word. Since that word is featured in the title, it is a strong objection. The word used erroneously is optimization. There is no optimization performed in the article. By definition, an optimization is an approach that yields the best of all possible solutions. We can limit this definition to its narrowest sense, the optimization techniques of operations research such as linear programming, or broaden it to include less sophisticated search procedures that find the best mine plan or schedule. No such claim is made in the article. No optimization of any kind is performed. The major tool used is a simulation, which, in truth, is probably more appropriate for this problem than any optimization. But simulation does not optimize. It only allows for quick evaluation of many options, leading to the selection of the best plan "of those tried," not "of all possible plans." This article, of course, is not the first mining paper to make this error. It seems that the word optimization is used more to impress people than to refer to any act of optimizing. It is used in a way that implies "try to optimize"or "come close to optimize," but not to really do it. It is usually appropriate to quietly ignore this error. But when Dr. Chatterjee, who has done so much good work in true optimization projects and whose work I have come to admire, makes such an error, it is time to publicly dispute it. Having discussed this very point with him in the past, I am sure that he will agree. If he can support this position in his response, perhaps people will start to listen and we can reduce the number of false claims of optimization. This should be easy for him in this case since the approach he used, simulation, is the more appropriate one anyway.

Jan 8, 1988

By M. Gershon

The article is an excellent one, providing a basis for the conduct of the major tasks in underground mine planning and scheduling. I object to only one word. Since that word is featured in the title, it is a strong objection. The word used erroneously is optimization. There is no optimization performed in the article. By definition, an optimization is an approach that yields the best of all possible solutions. We can limit this definition to its narrowest sense, the optimization techniques of operations research such as linear programming, or broaden it to include less sophisticated search procedures that find the best mine plan or schedule. No such claim is made in the article. No optimization of any kind is performed. The major tool used is a simulation, which, in truth, is probably more appropriate for this problem than any optimization. But simulation does not optimize. It only allows for quick evaluation of many options, leading to the selection of the best plan "of those tried," not "of all possible plans." This article, of course, is not the first mining paper to make this error. It seems that the word optimization is used more to impress people than to refer to any act of optimizing. It is used in a way that implies "try to optimize" or "come close to optimize," but not to really do it. It is usually appropriate to quietly ignore this error. But when Dr. Chatterjee, who has done so much good work in true optimization projects and whose work I have come to admire, makes such an error, it is time to publicly dispute it. Having discussed this very point with him in the past, I am sure that he will agree. If he can support this position in his response, perhaps people will start to listen and we can reduce the number of false claims of optimization. This should be easy for him in this case since the approach he used, simulation, is the more appropriate one anyway.

Jan 1, 1987

By M. J. McPherson, R. Venkataramani

R. Venkataramani (Assistant Professor of Mining Engineering, Dept. of Mining, The Pennsylvania State University, University Park, Pa.)-Y. J. Wang and L. W. Saperstein are to be congratulated for their paper on the computer solution of ventilation problems. The limitations on the problem size to be solved by the program (Appendix II) has been outlined in the paper. I would like to add the following additional limitations of this computer program: The dimensions of the variable J1and J2 should be changed to J, (550) and J2 (550) to handle problems containing more than 400 branches, and up to 550 branches. If there are a large number of branches common to the various meshes, another limitation on the problem size will be the dimension of the variable NA. While a higher-order polynomial fitting for the fan characteristic data points is more rigorous, a quadratic relation, if linear interpolation between the points is inadequate, will result in saving computing time without much loss of accuracy. Of course, this can be handled by minor modifications to the existing polynomial fitting routine in the program. M. J. McPherson (Dept. of Mining Engineering, University of Nottingham, Nottingham, England)-The

Jan 1, 1972

Jan 1, 1953

Jan 1, 1953

By M. Lonoff

G. Campbell The paper by M. Lonoff looks at the importance of byproduct prices on copper production. The paper develops several interesting points on this topic, but there are some points in the theoretical discussion that could use further development. A couple of these theoretical topics will be considered here using the paper's framework of assumptions without concern about how realistic the assumptions are for the copper industry. Lonoff's theoretical model is based on a static, homogenous world where all copper/byproduct deposits are identical, and these deposits are the main source of these metals. Due to the importance of the byproducts to the production decision, the term coproducts will be substituted for the term byproducts to reflect more accurately this condition. The conclusion is drawn that a rise in coproduct prices necessitates a decrease in copper prices because copper production is increased as a consequence of increased coproduct production. The observation that real world behavior does not always follow this pattern is dismissed as "speculation." However, it can be easily shown that within this simple framework market forces might create the observed behavior. The key question to be answered is what causes coproduct prices to rise. Three possible cases will be used as illustrations. The first case is the one implicity assumed by Lonoff. Here, the demand for coproducts increases at all prices (an outward parallel shift of the demand curve) with the demand for copper remaining constant. As reported in the paper, the results are higher coproduct prices, an increase in coproduct production, and lower copper prices due to the resulting increase in copper production. The second case is when the supply of coproducts are constrained-leading to higher market prices. Copper production, as required by the simple model, is also reduced which Reply by M. Lonoff Campbell's comments give me an opportunity to clarify a few points in "Copper and Its Byproducts." That paper examined the affect of byproducts on the copper market and considered the relative riskiness of multi-metal deposits from an investment standpoint. That brief note made no attempt to be exhaustive. Nevertheless, Campbell's comments miss the point of the paper and necessitate a response. My "theoretical model" was static and I freely conceded after introducing the assumption of identical deposits that "none of the assumptions hold." These simplifying assumptions allowed me to bound the possible effects of higher byproduct prices on the copper price by assuming identical deposits and computing average price effects. I took great pains to subsequently explain that since deposits are not identical the identity of the marginal deposit might change due to byproduct price changes. In this case, average price affects will overstate the affect of byproducts on copper prices. According to Campbell, I dismiss as speculation any "real world behavior that does not always follow this pattern" (of metals prices moving in opposite directions). In the byproducts paper I noted that gold, copper, and silver price movements often parallel each other on an intra-day or day-to-day basis. Such movements are largely due to market anticipation of or reaction to changes in interest rates that affect carrying costs of metals stocks. Other movements may be due to anticipated changes in available supply or physical requirements. I loosely grouped these effects as speculative. To distinguish this statement from the main thrust of the paper, I contined "In the long run if gold and silver prices remain high the equilibrium copper price will be lower." The paper set out long run equilibrium conditions rather than attempting to explain price movements on a daily basis or on a year-to-year basis.

Jan 11, 1983

By G. Campbell

The paper by M. Lonoff looks at the importance of byproduct prices on copper production. The paper develops several interesting points on this topic, but there are some points in the theoretical discussion that could use further development. A couple of these theoretical topics will be considered here using the paper's framework of assumptions without concern about how realistic the assumptions are for the copper industry. Lonoff’s theoretical model is based on a static, homogenous world where all copper/byproduct deposits are identical, and these deposits are the main source of these metals. Due to the importance of the byproducts to the production decision, the term coproducts will be substituted for the term byproducts to reflect more accurately this condition. The conclusion is drawn that a rise in coproduct prices necessitates a decrease in copper prices because copper production is increased as a consequence of increased coproduct production. The observation that real world behavior does not always follow this pattern is dismissed as "speculation." However, it can be easily shown that within this simple framework market forces might create the observed behavior. The key question to be answered is what causes coproduct prices to rise. Three possible cases will be used as illustrations. The first case is the one implicity assumed by Lonoff. Here, the demand for coproducts increases at all prices (an outward parallel shift of the demand curve) with the demand for copper remaining constant. As reported in the paper, the results are higher coproduct prices, an increase in coproduct production, and lower copper prices due to the resulting increase in copper production. The second case is when the supply of coproducts are constrained-leading to higher market prices. Copper production, as required by the simple model, is also reduced which

Jan 1, 1984

By Shiou-Chuan Sun

SHIOU-CHUAN SUN (author's reply).-Thanks are extended to Professor Hassialis for his recognition of the usefulness of a new tool, the cataphoretic cell, as an adjunct to the bubble machine and the abstraction test. His questions concerning adsorption, dielectric constant, floatability, activation, and depression are interesting and worthy of discussion. I According to Mueller,28 it is questionable that any of the present formulas gives absolute values of zeta potentials which are completely accurate. The problem is further complicated by the question" of whether the "dielectric constant" has any meaning at all for such a microscopically thin layer. With these in mind, the results in this paper should be considered in the relative sense as a first approximation and not as absolute quantities. Adsorption Referring to item a of Fig. 8, the dielectric constant and the viscosity of the xanthate solutions are the same for galena, sphalerite and quartz. If dielectric constant and viscosity (but not the adsorption) were the first-order variable of the cataphoretic system, as claimed by Professor Hassialis, then the magnitudes of zeta coefficient of galena, spha)erite and quartz would have been similar to each other. These are not. The big difference of zeta coefficient of these three minerals in the same xanthate solutions is not altogether unjustified to be attributed to their difference in adsorption of xanthate ions. This is supported by the results of chemical abstraction tests reported by Ince.14 Again, the big difference of zeta coefficient between wollastonite, calcite, and fluorite in the same laurylamine hydrochloride solutions (p. 118, Figs. 58, 59, and 60 of ref. r5) also indicates that the cataphoretic system is not governed chiefly by the dielectric constant. Beside the data shown in Fig. 8, other experimental evidences15 which support the idea of correlation between adsorption and zeta coefficient are: (I) there is a qualitative parallelism between the zeta coefficient curve and the chemical abstraction curve of sphalerite in solutions of various concentrations of sodium cyanide, (2) there is a qualitative parallelism between the zeta coefficient curve and the chemical abstraction curve of sphalerite in solutions of constant concentration of copper sulphate at different pH values, and (3) there is a qualitative parallelism between zeta coefficient curve and chemical abstraction curve of quartz in solutions with constant concentration of barium chloride at different pH values. The above mentioned experimental results are generally in agreement with Gouy's double layer theory,1-5 and support this idea that the concentration and the kind of ions adsorbed at the mineral surface and in the adjacent surrounding liquid chiefly govern the electrokinetic phenomena. Dielectric constant and viscosity of the liquid medium may be of somewhat lesser importance. It follows that the correlation between the coefficient and adsorption as claimed in this paper is justified. Dielectric Constant The term "dielectric constant " was first introduced into the electrokinetic equations by Perrin.30 In a footnote of his publication he states that Holmheltz has forgotten to include the dielectric constant. The conversion of the moment29 to the zeta potential involves an additional difficulty and confusion not involved for the moment, namely, assigning a value to the dielectric coefficient. This is conventionally assumed to be constant and equal to the dielectric constant of the bulk liquid. 21 The published literature 10, 12 indicates that the values of dielectric constant for dilute chemical solutions have been assumed as those of pure water.

Jan 1, 1947

By J. Gross

G. H. Clevenger, Chairman of the Milling Methods Committee of the Institute, made the following introductory remarks: "Several years ago, a number of us felt that the time was ripe for a fundamental investigation of crushing and grinding. At the outset, it appeared that the first thing we needed was a yardstick whereby grinding efficiency could be measured. "The U. S. Bureau of Mines has been most generous in cooperating with the Milling Methods Committee in getting this work well under way. John Gross, who served the committee for a year as secretary, was placed in charge of the investigation and has been ably assisted by S. R. Zimmerley. "Messrs. Gross and Zimmerley will now present the Progress Report covering their work to date." PROGRESS REPORT J. Gross, Salt Lake City, Utah. -This has not been a simple problem, and when I tell you that we can give you a verbal report of what we have done during three years in five or ten minutes you will realize that we have necessarily done a great deal of work that does not appear in the final results. We have been in a virtually new field. Therefore, we have had to feel our way at each step so as to be fairly sure we were correct. The first thing that was realized in this problem was that unless we had some method of measuring what happened when we crushed an ore, we might as well quit and not go further. We realized that if we tried to measure the results of crushing or grinding by the ordinary sizing test we would not get anywhere. We could sieve down to say 200 mesh fairly accurately; we could even go one sieve size further with a little less accuracy, and then we were absolutely lost, unless we went into microscopic measurement. Even this latter method would not have been satisfactory. The question was: what were we going to measure? If we were going to measure size, we might measure one particular dimension of a particle and be off 200 per cent. or more. If we tried to measure surface, we would have something tangible; the surface of a particle, no matter how irregular, is something definite, far more definite than any linear dimension would be. Moreover, if we could measure surface, we would immediately have a method of checking the Rittinger law as to whether it was or was not correct. So the first thing that we sought was a method whereby we could measure surface on crushed particles or, we will say, on particles; it would not make any difference whether crushed or not. It then became a question of what kind of particles we were going to use in obtaining a method for surface measurement. We realized that it would be rather a com-

Jan 1, 1928

Mr. Raden has described the practical problems associated with fines in phosphate rock beneficiation. In this discussion, a colloid chemical viewpoint is given to the problem of separating phosphate values from phosphatic clay slurries. The phosphatic clays are predominantly colloids of a complex mixture of many minerals (1). The constituents are typically 25% apatite, 40-50% clays, and various amounts of wavellite, quartz, dolomite, fluorite, and other minerals. The clays are montmorillonite, attapulgite, and illite, with some kaolinite. The various mineral colloids in the slurry are heterogeneously coagulated in the as-produced state. Dispersion of the coagulated state is evident from the fact that dispersing agents (certain polyelectrolytes) cause a large reduction in the viscosity of the slurry (2). The as-produced slurry settles from 4 to 8% solids within a week, but thereafter settles much more slowly in the form of a sediment of flocs. The supernatant liquid is often clear because of the cooperative action of the mutual interaction of particles during settling. Mineral segregation during settling has not been observed for the same reason. The initial slow settling rates indicate that the coagulated assemblies are very small. Efforts to separate apatite from the other minerals would be complicated by the heterogeneous coagulation state. Somehow the apatite must be "liberated" from its association with the other minerals before it can be physically separated. One approach for liberating apatite is to disperse the entire suspension. While this is feasible technically, for example by using certain polyelectrolytes (2), the reagent costs based on present

Jan 1, 1979

The problems associated with the processing of the Tilden ore are very much representative of the problems encountered in plants processing fine grained magnetic and nonmagnetic iron ores. I would like to comment on some of the problems mentioned in Dr. Nummela'spaper and add to his list of research opportunities in the processing of iron ores. Grinding, the most important step in the processing of fine grained iron ores, is synonymous with liberation. One grinds to separate discrete grains of minerals from the gangue. By convention- al grinding in tumbling mills, mostly random size reduction is achieved with relatively little preferential liberation of minerals. Not only are discrete particles broken that should not be broken, but damage is done to the mineral surfaces. The combination of over- grinding and surface damage shows up in lower recovery figures and higher grinding costs. What is obviously needed is a better comminution process that is more discriminating and that would permit liberating mineral particles at the coarsest possible size with a minimum production of fines. Laboratory attempts at such preferential grinding have been quite successful, but technological difficulties have unfortunately prevented its use. Impact grinding is a good example of a new comminution process that has not been accepted because of equipment problems. Either these problems have to be solved or new comminution systems have to be developed to reduce grinding costs and improve liberation. In his paper Dr. Nummela mentions the change in the primary mill throughput that occurs during the winter months. Seasonal changes in the operation of the grinding circuit and other unit operations have been observed in many plants, and many explanations for this phenomenon have been advanced. The fact is that we do not fully

Jan 1, 1979

As far as rapid determination of oxygen in liquid steel by means of a galvanic cell is concerned, I should like to summarize in a few words the activities of Centre de Recherches Metallurgigues (CRM) in Belgium. This work has been conducted both in a laboratory (Tammann and Induction furnaces) as well as on an industrial scale (converter and ladle). The galvanic cells developed by CRM are of two kinds: one with an air reference and one with a solid reference. As far as galvanic cells with air reference are concerned, we have tested numerous solid electrolytes (zirconia, spinel, and alumina). We finally chose zirconia sheathed with quartz. In order to be in a position to accurately determine the time when thermal equilibrium is reached, it was deemed useful to fit the galvanic cell with a Pt/Pt, Rh thermocouple, so as to follow the temperature variations at the interface of the solid electrolyte, until the temperature becomes equal to that of the bath. In actual fact the solution is highly interesting since it is possible to determine both the oxygen activity and the temperature of the bath with a single cell.

Jan 1, 1972

By M. G. Ayat, B. C. Scott

J. Dasher Having an interest in coal slurry pipelines from a decade of arguments with Ed Wasp and crew at Bechtel about pumping thicker slurries slower, I immediately read this article and found nothing in it pertinant to the title. Ayat and Scott pumped five unidentified coals at 9% solids (50%-60% is the area of interest) in a 25-mm (1-in.) pipe around two square elbows through a 76-mm (3-in.) cyclone for up to 60 minutes and sized a large number of samples of unstated size on an unidentified wet screening device. They did not measure power consumption, discharge pressure, flow rate, or give pump tip speed or impeller diameter. They siad the cyclone had a "high" pressure drop (unmeasured) and did much of the degradation (measured) but more or less per unit of energy expended? Hargrove was not measured, so there are no data as to whether it would correlate with degradation. The authors conclude, with no attempt, correlation is "hard to establish." Please experiment before concluding. I am at a loss to know what "increasingly smaller size" means, much less what theory says such particles take "exponentially larger quantities of energy," which the authors neglected to measure. If such experiments without pertinent data or justified conclusions must be published, please attach a pertinant title. reply by M. G. Ayat The first and the last criticism of this paper is that the work is not pertinent to the title. Anybody who reads this article will immediately realize that the work describes the breakage of coal particles to finer sizes in coal slurry pipes and pumps. If this is so, why not title the work "Degradation process in coal slurry pipelines"? What could be more pertinent to this title than the investigation concerning the degradation phenomenon of coal particles in a pipe carrying a coal slurry? Mr. Dasher complains that he does not understand the meaning of the term "increasingly smaller size." The first sentence of this article defines the degradation process as "the breakage of coal particles to increasingly finer sizes." The term "increasingly finer sizes" here means successive breakage of a fine particle to finer and finer sizes. According to Hukki (Hukki, 1975), the probability of breakage is high for large particles and rapidly diminished for fine sizes. We apologize for being brief about some of these definitions. The degradation process, breakage of particles to increasingly finer sizes, is so widespread in the mineral industry that we did not feel it necessary to bore the reader with lengthy definitions of some simple terms. Mr. Dasher states that the coals examined and their original size consist are unidentified. Please look at Table I and Table 2 in the paper again where you will find the original size consist of the coals examined and their full specifications. We only named the coals A, B, C, D, and E to avoid identifying the coal seams that were more susceptible to degradation. Not identifying the name of the wet screening device used in this work has also been criticized. In our opinion, wet screening operation is such a routine and standard procedure that naming the device by which the screening is performed would serve no purpose but to promote a sales approach. This was not our intention. We did not conclude that the correlation between the degradation process and Hardgrove Grindability Index is hard to establish as Mr. Dasher writes in his letter. We stated, not concluded, that "It is reasonable to assume that some relationship between the extent of degradation and its physical properties, such as Hardgrove Grindability Index, does exist. However, any definite correlation is difficult to establish." This statement is based on other researchers work, which are clearly referenced in the article. The conclusions of this paper were based solely on the findings of the experimental work. As for the theory of comminution that Mr. Dasher asks, we would like to refer him to some basic comminution books and articles where various theories are clearly described. For example, Hukki (Hukki, R.T.,"The Principles of Comminution; An Analytical Summary," Eng. Min. 176, 106, 1975) suggests that the relationship between energy and particle size is a composite form of three laws (Bond's law, Kick's law, and Rittinger's law). A comprehensive analysis of coal breakage processes is also performed by Broadbent and Callcott (S.R. Broadbent, and T.G. Callcott, "Coal Breakage Processes, I. - A New Analysis of Coal Breakage Processes;" and "Coal Breakage Processes, II. - A Matrix Representation of Breakage," Journal of the Institute of Fuel, pp. 524-539, December 1956). These and many other relevant publications explain the relationship between the particle size and energy much better that what can be said in this short reply. We will, however, agree with Mr. Dasher on one particular point. We, too, believe that if the investigation concerning the degradation process in coal slurry pipeline were to be pursued further, one could choose to determine one or more of the variables available in the process, such as discharge pressure, power consumption, percent solid, pipe diameter, etc.

Jan 1, 1989

By M. G. Ayat, B. C. Scott

H. P. Ferri I refer to the article "Degradation Process in Coal Slurry Pipelines" by M.G. Ayat and B.C. Scott in the September 1988 issue of Mining Engineering. I would like to congratulate Dr. Ayat and his colleague on a very interesting and valuable piece of work. This article is an excellent one, describing a real phenomenon that has been ignored for so long. I do, however, have an objection. The article fails to address the degradation process when coal is processed or transported in other ways than slurry form, particularly those employed in this work. Could, for example, screening (wet or dry) have contributed to the extent of degradation? Perhaps scanning electron micrographs of the samples examined and after screening would have helped to clarify this. I would like to point out that degradation is also observed in pneumatic conveying systems, mechanical conveying, and other means of transportations employed by the mineral industry. Reply by M. G. Ayat We gratefully acknowledge Dr. Fern's comments on the subject paper. As he so rightly points out, the degradation process is a real problem, not only in coal slurry pipelines, but also in many handling and processing equipment employed by the coal and mineral industry. Scanning Electron Microscopic examination of samples may offer very little information about the extent of degradation for several reasons. One is that preparing a representative sample that has undergone degradation will be extremely difficult if not impossible. This problem is exacerbated by the fact that SEM requires only very small amounts of material for testing. Secondly, there is a sample preparation step involved in the SEM examination and, as such, it would be very difficult to associate the extent of degradation to either sample preparation or handling and processing operations. Finally, it is probably worth mentioning that degradation is a multi-faceted phenomenon involving many natural and man-made factors. The logical approach to this problem would, therefore, seem to be a "one-step-at-a-time" approach.

Jan 2, 1989

By P. L. Webster, S. D. Thompson

Sevim and Wang (1988a) have presented a model for designing haulage systems in underground coal mines. The authors contend that their model uses a heuristic algorithm to optimize various haulage system parameters. In reality, it would be nearly impossible to optimize a haulage system, because mining plans are uncertain and often change with respect to time. Therefore, haulage system design poses both a stochastic and a dynamic design problem, and its optimization appears to be well beyond the scope of heuristic algorithms. In regard to the authors' design model and its practical significance, a number of additional issues warrant further discussion and clarification. These issues include: l) their model's alleged advantage over simulation models, 2) the correctness of their belt network design, 3) the correctness of their bunker design, 4) the necessity of their proposed bunker clearance policies, 5) the correctness of their shaft-bottom bin design, and 6) the

Jan 1, 1991

Dunn has written an excellent paper providing a wealth of advice on what is often the most costly consumable in the mineral processing plant. As he pointed out, grinding media selection and quality control can play a major role in successful plant operation. Owing to the economic importance of this topic, there are some important factors related to media sizing that I believe merit further comment. Dunn made reference to a slightly simplified version of the Azzaroni (1981) equation and pointed out its successful use for the Henderson SAG and Climax ball mills.

Jan 1, 1991

Contribution by F.S.A. de Frey The authors are to be congratulated on a job well done by making, in their paper, such a pool of information available to mining engineers. I would like to comment on the following statement: 'As an alternative to the commonly used deep-level mining methods, consideration should also be given to pillar mining at great depths as a logical extension of the current methods. For example, a 75 per cent extraction Or Ryder's discussion The moderate levels if average pillar stress (APS) (320 MPa) are consistent with pillar stability. Squat 10:1 pillars should never 'fail' in themselves, and foundation strengths are also not exceeded (the stresses are well below the 2 ½ x UCS rule-of-thumb provided the foundations comprise normal strong 200 MPa quartzites). Authors' reply We thank Dr de Frey for his contribution to our paper on shallow hard-rock pillar systems. To considerable extent, we share his enthusiasm the potential role of squat pillars in deep-level mining, although we harbour reservations concerning strata control, mining economics, other issues. We agree wholeheartedly that further research, together with carefully planned field trials, is warranted in pursuit of this potentially highly rewarding concept. .

Jan 1, 1995

By P. Malozemoff

Discussion by P. Malozemoff I have no objection to using mathematics in the value appraisal of properties. The factor that is not emphasized in the paper is that very few important properties have a lifetime that reflects the initial ore reserves of the property divided by the rate of production adopted. In the majority of cases, major properties mine out several times the initial reserves. How much more will be mined out is not known, and only exceptionally gifted geologists can predict that additional reserves will be found. There is the further factor of metals price, which, over the long term, is not predictable. Another factor vitiating making calculations on initially established ore reserves is the speculative nature of exploration success. In my judgment, the life of a property, in addition to an established ore reserve, should include ample time for exploration to find additional reserves. The likelihood of additional reserves is based on the geological promise of the general area where the mine is established. This is especially important because of various risk factors associated with small orebodies, the economic life of which is about five to seven years. In underground mines, it is not economic to develop reserves beyond a certain depth, so the life of initially established reserves must be limited. In these cases, it is especially important to have a good geological understanding of the orebody and its continuity. To accommodate these concepts and present proof of economic soundness for a mining enterprise, a mathematical analysis should yield a life long enough to allow exploration and the development of additional reserves that would ensure a longer mine life and a more profitable result.

Jan 1, 1994