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By Graham G. W. Mustoe

Energy losses are important factors in a conveyor's performance and design. A significant energy loss due to belt sag within a conveyor system occurs when shearing motion between the bulk material particles occurs as the material moves along the belt. An initial analysis of these phenomena was performed using the discrete element method, which is a general-purpose numerical modeling technique for analyzing the mechanical behavior of particulate materials. The software used in this work was Overland Conveyor Company's, Chute Analyst Professional, a discrete element computer code designed specifically for analyzing bulk materials transportation and handling problems.

Jan 1, 2008

By B. K. Mishra, R. K. Rajamani

Discrete element is a numerical technique for describing the collision dynamics and motion of an assembly of particles. In particular, calculations are done on full three-dimensional space with a force-contact law for collisions and Newton’s law for subsequent motion. It may be said that there is no empiricism in this approach. The paper describes the full scale simulation of large diameter semiautogenous grinding mill of size 40X24 ft. It is shown that the simulation predicts the power draft of plant size mill extremely accurately. Also these simulations have been adapted uniquely to assess the motion of pebbles and slurry in pulp lifters. The passage of slurry from pulp lifters into trunnion is extremely important since flow-back and carryover must be avoided at all cost. The dynamics of slurry flow through pulp lifters is also described in this paper.

Jan 1, 2003

By Bill Dershowitz

Consider a deep gold orebody with grade of 4 g/t (0.11 oz/st). At the time of this writing, with gold prices at historic highs, it could be a good, but not great, prospect. But if it is a vein deposit, and those veins are 200 g/t (5.8 oz/st), it would be significantly more attractive if there was a way to produce directly from those veins, leaving the rest of the rock in place. [Figure 1 The red around each of the four injector wells shows areas of high pressure, where the lixiviant fluid is pumped into the rock mass, with orange and yellow indicating dissipated pressure. The black lines indicate some of the fracture pathways through which the lixiviant, with absorbed metal, flows toward the central recovery well where low pressure is indicated in blue. Lixiviant is pumped out through the recovery well. Image courtesy of Golder Associates.] There is a way to do this, in situ leach (ISL) or solution mining. It has been a viable commercial technology for more than five decades.

Jan 1, 2011

By K. J. Shelswell

This work describes the design, analysis, and comparison of discrete simulation and static spreadsheet models developed to compare the oreflow efficiency of two conveyor-based material handling systems; one approach with a conveyor stream in series and one with parallel conveyor streams. Analysis and comparison indicated that daily rates were significantly affected by random conveyor failures in both designs. The compound effect of random failures limited the effectiveness of long belt assemblies in series, while the parallel conveyor stream design partially alleviated this constraint. The static spreadsheet model predicted a lower average daily oreflow rate for the series conveyor stream design and a higher average daily oreflow rate for the design with parallel conveyor streams when compared to the discrete simulation results. These discrepancies were the product of model sensitivity to operational factors incorporated in the system and provided the opportunity to further use the discrete simulation models for trade-off comparisons and sensitivity breakdowns of mine operating practices and material handling system efficiencies in both the series and parallel belt stream designs

Feb 23, 2014

By Javad Sattarvand, Amin Moniri-Morad

Predicting equipment failure behavior plays a critical role in providing a safe operation. Although various reliability evaluation methods are available for estimating failure behavior profiles, these approaches are based on mathematical formulation, leading to actual operation simplification and improper estimation of failure trends. This study proposes a discrete-event simulation (DES) approach to model fleet failure behavior. This approach can model the maintenance strategies in multi-component systems with minimum simplifications. In this regard, the first step was to collect a historical failure time dataset (e.g., the time between failures). Then, the DES model is established to predict the severity of failure events and design maintenance strategy considering actual operation circumstances. Afterward, the maintainability analysis was performed to estimate equipment downtime and availability. The achieved results showed that the system availability was about 85%. Also, the findings demonstrated that the DES could efficiently predict the equipment failure behavior using various stochastic events.

Jun 25, 2023

By Nora M. Hutt, Kevin A. Morin

There is currently some pessimism over mixing of net-acid-neutralizing (NAN) and net-acid-generating (NAG) rock to obtain indefinite near-neutral seepage from mined-rock piles. This is due in large part to the lack of well- documented, successful cases of blending and layering, and to the knowledge of unsuccessful attempts. Past work often defined a potentially successful mix in terms of the ratio of net-acid-neutralizing rock to net-acid-generating rock. For example, one case study indicated the bulk pile-wide ratio was approximately 3: 1. Since this exceeded a common ratio used in acid-base accounting, no acidic drainage was predicted. However, acidic drainage appeared within two years. A large part of the ambiguity in mixing arises from attempts to predict success based on a ratio. This paper looks in detail at simple discrete-zone mixing, where at least one truckload of NAG rock is placed in a particular location with no further rehandling or dozing. The lack of acidic drainage in this scenario is dependent on the intervening distance between the discrete NAG zones, along flowpaths occupied by NAN rock. Calculations show that the bulk mixing ratio of a mined-rock pile is not an accurate indication of whether near-neutral drainage can be maintained. For example, a pile with a bulk ratio around 300: 1 could still release some acidic drainage. Calculations also show that the minimum separation distance of the NAG zones (L) can be so great, even with typical NAG and NAN rock, that the mixed pile could safely contain only a few percent of NAG rock, which would not be sufficient for many minesites with NAG rock. The comparison to a more elaborate, computer-based statistical model shows that the simple discrete-zone approach will provide a reliable yes-no indication of whether any acidic drainage will leave a pile. However, predictions of whether combined downstream drainages will be acidic depend on numerous site-specific physical and geochemical factors within and below a pile that cannot be modelled in a general way, like the number of flowpaths and the nature of their intersections.

Jan 1, 2000

By Cindi Byrns, Andy Davis, Amy Tisdale

The Robinson district, Ely, Nevada is a hydrogeologically complex system with several distinguishable geologic blocks, each with a distinct background groundwater chemistry. To discriminate between background and mine-impacted groundwater, background wells, monitoring wells, pit lakes, waste rock seeps, and surface water samples were analyzed for a suite of major cations and anions, together with trace and precious metals, rare earth elements, 2H-deuterium and 18O/16O. The data allowed identification of groundwater flow paths, verification of hydrochemical source areas and characterization of natural attenuation mechanisms (e.g., mixing, dilution and mineral precipitation) that control the concentration and migration of metals at the site.

Jan 1, 2000

By Andrea Koschinsky, Akira Usui, Michael Bau, Katja Schmidt, James Hein, Thomas Kuhn

Marine ferro-manganese (Fe-Mn) crusts and nodules are metal-rich chemical sediments that are archives of paleoceanographic proxies and potential metal resources and targets of deep-sea mining. Traditionally, crusts and nodules are subdivided into hydrogenetic, diagenetic, and hydrothermal types. While hydrogenetic Fe-Mn crusts are a potential resource for Co, Te, Pt, and REY, nodules are enriched in Cu, Ni, Mo, and Li, and hydrothermal deposits may be enriched in individual metals such as Mo, Ba, and Li, depending on the temperature and composition of the hydrothermal fluid. The different types of marine oxidic Fe-Mn precipitates, therefore, have different economic potential. Hence, a robust classification is not only helpful in the general geochemical characterization of such precipitates (and as such is a useful teaching tool, for example), but may also simplify the evaluation of their importance as a potential metal resource, which helps to prioritize exploration targets for deep-sea mining.

Sep 1, 2014

By Guangyao Si, Ismet Canbulat, Xun Luo, Yi Duan

Routine analyses of seismicity and event locations are essential for coal burst risk management, especially in the presence of unfavorable and complex geology. In an Australian longwall coal mine, a small-scale seismic monitoring network was installed to monitor a section of a major dyke intersected by the roadway, which was classified as a coal burst prone zone. The Deep Convolutional Neural Network (DCNN) technique was adopted for automatically discriminating seismic events to assess seismicity in this zone. The discriminated seismic events were located with the Shortest Path Method based on the Boundary Discretization Scheme (BDS-SPM) for temporal-spatial seismic event distribution analysis. The results demonstrate that the seismic events are discriminated with an average accuracy of 94%. Moreover, the seismic events are more accurately located using the BDS-SPM with a 3D heterogeneous velocity model compared with results obtained with a homogeneous velocity model. The temporal and spatial variances in seismic activities identify that the rock fractures in the dyke zone are closely related to the longwall mining process and a local dyke has a controlling influence on the stress concentration in its vicinity.

Apr 26, 2022

By Katzer R. Klimpel, J. Sewell

Dr. Roussey Roussev The use of chemical additives on grinding is of significant importance considering the high energy consumption of grinding processes. My research indicates that the dispersant approach explains the effects, in this particular case of wet grinding. Further, the dispersant approach combined with torque measurements give the possibility of clarifying the mechanisms involved when using grinding aids. I find the conclusions derived from the data obtained to be correct and useful for grinding. In general, I agree with the explanations. However, I would like to discuss several additional points that I consider to be important, and in the same time to mention some of my own results from investigations similar to those presented in the study under discussion. The "bed volume concept" and the change of slurry viscosity explain adequately the data plotted on fig. 3, in conjunction with Figs. 1 and 2. However, the significant increase of the average torque in the case of 83% solid with XFS-4272 introduces the necessity of establishing the optimum of percent solid when dispersant is used. For example, the optimum percent of solid for different materials varies. One of the reasons is the material's mass density. On the other hand, it is necessary to determine the concentration of the chemical used. Because of this, it would be interesting to know how the cited concentration was selected. The supportive discussion and verification by Dr. Roussev, with results similar to that of the paper, is appreciated. I will try to answer the additional questions he has raised. To begin with, the mill was fitted with six lifters of approximately one-quarter inch height. There has been extensive lab and plant level work to understand downstream influences of using dispersants like XFS-4272*. In sulfide ore processing, which is the area in which most industrial scale testing has been performed with this approach, neutral to positive influences have been observed. For example, positive effects (e.g., increased recovery) have been noticed in flotation operations involving ores that have a tendency to produce excessive slimes upon grinding. (1) Also, the use of a dispersant has been shown to demonstrate a positive influence on classification by improving the sharpness of separation and preventing a decrease in d50 value that usually accompanies increasing flow rates to classifiers.(2) The biggest potential downstream problem is in thickening, which at the dosages involved, has not been a problem in plant scale usage. The commercial price of dispersants like XFS-4272 is quite variable depending on source, concentration, etc, but a typical cost of XFS-4272 to achieve a 10% increase in throughput in industrial mills has been between 20 and 35- US per ton of feed ore (1981).

Jan 12, 1982

By K. Hanumantha Rao, A. Nayak, K. S. Narasimhan, S. N. Mahapatra

B.A. Hancock It is not at all surprising that causticized potato and potato derived amylopectin starch solutions performed much better than their parent starches. Some preparation is required to rupture the starch granules to effect the polymeric adsorption and interparticle bridging necessary for selective flocculation. In laboratory work comparing the deslime performance of causticized and autoclave cooked laboratory corn starch solution preparations, it was found that higher deslime weight rejections, with attendant proportionally greater iron unit losses, occurred with the causticized starch. These results may be specific to the ore involved but they do suggest that cooking and causticizing cause different starch granule rupture and/or starch breakdown, which have an effect on desliming response. I calculated from the data in the article that the slimes product grades were high - 24.3% and 20.3% Fe when 53.7% and 54.5% Fe concentrate products were obtained, respectively, in Table 4, and 21% Fe with a 62.6% Fe concentrate in Table 5 - using the natural tailings sample, which had a head of 34.3% Fe. It may be advisable for the authors to consider different starch preparations in future investigations. The combination of upgrading and selectivity results presented in Table 4 are not as good as the authors suggest. The authors' claim that a system has been developed to produce saleable concentrates from the Kudremukh tailings is quite disconcerting. There are many hurdles yet to be crossed before commercial application of selective flocculation becomes possible because differences between the very small-scale laboratory tests conducted and commercial application are rather large. Among the many differences are varying circuit feed grades that will occur from use of tailings, the apparent face that much lower tailings grades will be encountered in practice (it is much easier to achieve a high concentrate grade with reasonable recoveries using 34.3% Fe tailings as in the study rather than 25.3% Fe tailings grades that the plant apparently averages), the hydraulic nature of the thickeners used in operations compared to the static system used in laboratory tests, the different size distributions that will be obtained from a plant closed grinding-classification circuit, and differences in water used in a plant operation and the laboratory. The authors wrote that it was necessary to overgrind to be sure that the coarse gangue would not settle with the iron oxide floccules. This situation is likely to be exaggerated in commercial operations where it is assumed cyclones would be used for classification. Because cyclone classification is greatly influenced by particle densities, there will probably be an even greater difference in size between the iron and gangue particles in the plant, which would make the gangue slightly coarser still in relation to the iron. This would make the selective flocculation-desliming separations using the procedure employed by the authors even more difficult and, using the dispersant system the authors employed, greater overgrinding would be required. To grind finer to minimize the coarse gangue in the flocculated iron oxides is quite inefficient and appears not to broach the problem. The actual problem appears to be insufficient dispersion of the ground pulp. In this situation, addition of a dispersant would likely be required to attain a sufficiently high pulp dispersion level to efficiently effect a selective flocculation-desliming separation. Although the very coarse particles would still have a tendency to settle with the floccules, it probably would be found unnecessary to overgrind as much as indicated. Use of an optimum combination of dispersant and pH modifying reagents may also significantly improve the selectivity of desliming. Additionally, although it is possible that sufficient dispersion may be obtained by pH control alone in some situations, it is quite probable that added dispersity was obtained in the reported work from using distilled water. It is research experience that distilled water enhances dispersion. In commercial operations it may not be expected that sufficient dispersion will be obtained by pH control alone, unless the water used in the process is by nature quite dispersive. Overall, a change in the Kudremukh tailings dispersant scheme appears necessary where a dispersant is used in conjunction with a pH modifying reagent. With this change, different dispersion-flocculation responses will result that would have to be further evaluated. Therefore, it is still an open question whether an efficient and effective selective flocculation separation using Kudremukh tailings may be obtained that will produce saleable concentrates.

Jan 9, 1986

By J. D. Patsey, G. T. Lineberry

A.E. Hall The authors are to be commended for their attempt to provide a convenient piece of software for preliminary drum hoist specification. This field has received little attention in recent years and is eminently suited to calculation by computer. Unfortunately, there appears to be an error in the calculation of the required rope diameter. The 66-mm (2 5/8-in.) rope selected is oversized for this application. Wire rope weight and breaking strength are related to the rope diameter. For a round strand rope

Jan 8, 1987

By J. Hanna, H. R. Gonzalez

Discussion by N.L. Hargett Dear Dr. Hanna: As discussed in our phone conversation, we are enclosing a suggested revision to the paper, "Application of Bentonitic Clays in Suspension Fertilizer Formulations," published in MINERAL & METALLURGICAL PROCESSING, May 1990. The revision will replace the second paragraph in the article. The reason for the revision is that suspensions have decreased in market share since 1984 and at present comprise an estimated 25% to 30% of fluid mixtures. This represents 6% to 7% of all fluids and only 2% to 3% percent of all fertilizers. Based on national surveys conducted by the Association of American Plant Food Control Officials (AAPFCO), suspensions comprised an estimated 25% of all fluid mixtures in 1974, 33% in 1976, 35% in 1980, 40% in 1984, and 36% in 1988. Revision to "Application of Bentonitic Clays in Suspension Fertilizer Formulations." Suspension fertilizers are an important segment of the fertilizer industry in the United States. Suspensions allow higher concentrations of nutrients (N, P2O5, K2O) than clear liquid solution fertilizers. K20 content of solutions is limited to about 10%, while suspensions can contain more than 30% K2O. Suspensions can tolerate greater variations in temperature than solutions. In suspensions, if crystallization occurs, the crystals can remain suspended in a clay jell instead of settling as they would in solutions. Solubility is not a limiting factor in suspensions, since complete solubility of phosphate is not required. This allows a wider range of phosphate materials to be used. Also, materials commonly used in formulating suspensions are less expensive and more widely available than those for clear liquids (Getsiner et al., 1984).

Jan 1, 1992

By Adrian C. Dorenfeld, John T. Oleksy

John D. Maefadyen Subject paper unfortunately has some serious flaws negating the usefulness of the paper. The authors claim that sulfur is the major source of production problems in cement kilns. This is not the case. Sulfur is not a problem as long as the mole ratio of sulfur to alkali oxides is less than, or equal to, 1. This is attributed to the sulfur preferentially combining with the alkali oxides and not acting as a clogging agent due to the nature of the pre-heater vessels. Where the mole ratio exceeds 1, many methods are available to eliminate or reduce the clogging problems such as using the preheater bypass or a precalciner with up to 100% kiln gas bypass. In non-preheater kilns, the presence of sulfates is hardly ever a problem anyhow. Thus, the level of sulfur in the fuel and raw material that might cause problems is not a fixed amount, but is predictable. The purpose of the paper is to discuss the economics of conversion of kilns in the Indonesian and Phillippine cement industries from oil firing to coal firing. This economic analysis has very little to do with the sulfur levels. Thus, the section of the paper on sulfates is actually rather meaningless. The economic analysis is also rather meaningless because the authors have failed to follow accepted economic analysis procedures by including interest charges. They have fallen into the trap of confusing financing with economic evaluation. When the accepted methods of economic evaluation are used, the return on investment increases to about 35%. In conclusion, the paper is not a meaningful contribution, and sadly, quite erroneous.

Jan 11, 1982

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The au thors claim that their proposed jackknife method, which is a rekriging of each block by eliminating, in turn, one sample from the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors' selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn't the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner's toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper consist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data valuebased measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text. ?

Jan 1, 1998

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 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 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 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