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By R. K. Steinhorst

Multivariate cluster analysis, MANOVA, canonical analysis, and discriminant analysis of hydrochemistry data were used to investigate the directions of ground water movement in basalts in the vicinity of the Hanford Reservation, Washington. The statistical analyses indicate that the hydrochemistry of the ground waters in these basalt formations is distinctly different on each side of the Columbia River. This suggests that the river is a ground water divide or that the river is roughly coincident with a hydrogeologic barrier boundary. The statistical procedures used in this study constitute a quantitative means for differentiating ground waters according to hydrochemistry.

Jan 1, 1990

By C. Flores, L. G. Twidwell, T. S. Jordan

It is well known that manguniferous silver ores containing manganese intimate) associated with silver are not amenable to conventional extraction methods. The segregation process has been applied primarily to the recovery of copper from oxidized and oxide-sulfide ores. A new alternative process, consisting of segregation roasting followed by flotation to recover the silver from refractory manganiferous silver ores, was studied using a 23-factorial experimental design. Laboratory investigations were conducted on a manganiferous silver ore analyzing 0.02% copper, 0.09% lead, 0.33% zinc, 12.55% manganese and 187 g/t silver. The investigation was designed to study the effects of the addition of salts, coke and copper (11) oxide on silver recovery. The results indicated that 79.3% of the silver can be recovered in the absence of copper oxide and 88.4% of the silver can be recovered with a copper oxide content of 1.5% at 750°C, 2% salt (NaCI). 1 % coke and 30 min of roasting. It was concluded that the addition of copper oxide improves silver recovery.

Jan 1, 1996

By Ross W. Smith, D. L. Taylor, K. A. Altman

Traditional sensitivity analysis of metallurgical data has the potential to overestimate the value of mining projects. Such analyses provide no information about the probability of the results. Simulations that rely on the input of statistical information provide more realistic predictions of the value of future projects and offer additional information regarding the probability of the outcome.

Jan 1, 2003

By K. Kim, T. M. Yegulalp

A new explanation of the scale dependency of rock strength is presented based on the theory of extremes. A brief review of past work on specimen size and strength relationship is followed by an introduction to the fundamentals of the underlying theory of extremes and its relationship to the scale effect. It is shown that the weakest link theory is directly related to extremal statistics and that parameters of strength distributions of rock can be derived as a function of the specimen size. Three sets of Brazilian test data are used to demonstrate the use of this approach.

Jan 1, 1994

By T. M. Yegulalp

A new explanation of the scale dependency of the strength properties of rock is presented based on the theory of extremes. A review of past work on specimen size strength relationship is followed by an introduction to the fundamentals of the underlying theory of extremes and its relationship to the scale effect on the statistical properties of the strength distribution. It is shown that the weakest link theory is directly related to extremal statistics and properties of strength distributions of rock can be derived as a function of the specimen size. Three sets of Brazilian test data are used to demonstrate the use of this approach.

Jan 1, 1992

By C. Widham

Introduction It is generally accepted as dogma that sampling contributes most of the error in gold fire assays. Differences in assay results on pulps from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" of relatively coarse gold particles. It is true that coarse gold particles can contribute to substantial sampling fluctuations. But, while the process of sampling is probably the major source of error, the analytical process cannot be completely ignored as a possible contributor to erratic assay results. To maintain a stable assay process, the analytic part of the system must also be kept in control. One method of monitoring the performance of the analytic system is to systematically assay standard materials, whose sampling characteristics are carefully controlled. Gold assay standards are not prepared, nor can they be prepared, to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for both preparation (i.e., comminution and splitting) and fire assaying and then come to conclusions only about the fire-assay process. Because most gold ores are very heterogeneous, sampling errors would, in most cases, completely mask the contribution of the analytical errors. Assay-standard material is prepared only to assess the accuracy and variability in the fire assay process. Because the objective of the assay standard is to provide information about the fire assaying, it is necessary to control the sampling error of the standard material, so that it is only a minor constituent of the discrepancies observed in any assay results. To do this requires that the particle size of the standard material be reduced to a point where the relative standard deviation of the sampling error (i.e... the standard deviation of the errors divided by the average gold content of the material) is 2% or less. For all but very homogeneous mineralization, this means that the material must be reduced to 100% -150 mesh before the sampling errors are adequately controlled. However, even reducing the particle size can contribute to sampling problems. The liberation of gold may cause segregation that can cause large sampling fluctuations that are not easily controlled while maintaining the desired grade. Because, in most cases, the standard material would already be in the "pulp" state when it is submitted to a lab for assay, it is not possible to entirely conceal the nature of the sample from the lab. This is a problem inherent in using assay standard material. Because of the contribution of sampling to error generation in the assay process, the use of "coarse" material does not solve the problem of submitting a totally "blind" standard to the lab. In the sections that follow, the selection, preparation, testing and use of gold fire assay standard material is discussed. While some may dismiss the production of standard material as folly, it is possible to produce and utilize standard material to stabilize and improve the fire-assay process to produce more reliable assay results. Material selection It is desirable to use material that has as nearly the same metallurgical characteristics as the samples with which the standards will be included. However, this is usually difficult. For many reasons, including the particle size at which a significant amount of the gold mineral is liberated, the sampling characteristics of even -150-mesh material may preclude the use of geologically and metallurgically similar ore as a standard. It is usually easier to get material having desirable grade characteristics with the necessary sampling properties than it is to find geologically and metallurgically similar material with the required sampling characteristics. High-grade standards are especially difficult to find and prepare. This is because, as grade increases, the size of the gold particles usually increases. Larger gold particles are liberated and tend to segregate during comminution, and the homogeneity of the material cannot be maintained. For grades much above 3 g/t (0.088 oz/ton), it is very difficult to find material that has the proper sampling properties. Old mill tailings are likely candidates for assay standards. Some of these have sufficiently homogeneous mineral contents, so that the sampling errors can be effectively controlled. Where mill tailings are either not available or are not acceptable, mineralization that has exhibited homogeneous results in reassays of the pulp material is also a good candidate for the standard. Finally, the mineralized rock being sampled may (and should) be used if adequate homogeneity in the -150mesh material exists. "Adequate" ("acceptable") homogeneity is defined below.) It is important to use standards having a wide range of grades. This alone may preclude the material being

Jan 1, 1997

By S. Davis

It has been accepted almost as dogma that sampling contributes most of the error to fluctuations in gold fire assays. Differences in assay results on pulp material from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" or relatively coarse gold particles. It is true that if coarse gold particles are present they contribute to substantial sampling fluctuations, but while the process of sampling is probably the major source, the analytical process cannot -be completely ignored as a possible contributor to erratic assay results. In order to maintain a stable assay process, the analytic part of the system must be kept in control as well as the sampling and preparation part. One way of monitoring the performance of the analytic system is to systematically assay standard material whose sampling characteristics are carefully controlled. Gold assay standards are not prepared nor can they be prepared to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for preparation (which includes both the processes of comminution and splitting) followed by fire assay, to make inferences only about the fire assay process. Because most gold ores are very heterogeneous, sampling errors would in most cases completely mask the contribution of the analytical errors. Assay standard material is prepared only to assess the accuracy and variability in the fire assay process.

Jan 1, 1995

By John A. Wolfe

Applications of mathematical statistics to the field of exploration are still relatively new. There are two primary reasons why little has been published in this field. First, if one discovers an effective technique for exploration, he does not like to disclose it. Second, the geologist needs to work closely with a mathematical statistician, and the communications barrier between the disciplines is formidable. The authors of this paper, one a geologist and the other a statistician, were interested in the economic benefit which appeared to be possible in the interdisciplinary area which they have called "geostatistics." An actual example has been selected to illustrate this benefit.

Jan 1, 1962

By A. L. Boerner

Off-highway tire costs represent a significant portion of the total mining costs in openpit, truck-shovel operations. To extend the lives of tires, the site-specific factors influencing tire life should be investigated Valuable data can be obtained by combining historical operational data captured by a mine dispatch system with detailed tire and maintenance histories. Assuming that failure counts satisfy a Poisson distribution, F-tests can be applied to determine significant deviations from desired or target counts. The methodology developed in this paper can be used to identify the haul routes and loading and dumping zones that have significantly higher incidences of tire failure. Corrective action can then be targeted at these zones by modifying the shovel or truck operator practices; changing the haul route maintenance and clean up practices; or altering the bench, ramp or waste dump design parameters. An example is given of the correlation of tire separation and tire impact failures with haul routes for a fleet of nine Caterpillar 793C trucks in operation at the Chuquicamata Mine in northern Chile. A high incidence of impact failures was observed for the ex pit ore crusher and for tires installed in the left outer rear position on the trucks. The latter was postulated to be due to a preference for drivers to execute right-hand turns prior to dumping. Recommendations were made to revise crusher and dump cleanup practices and investigate the feasibility of super-elevating the surface of dumping zones to reduce ground pressure on the left rear tires.

Jan 1, 2002

By Daniel Hodouin, Antoine Berton

Mineral processing plants are monitored and controlled using measurements that are usually processed by on-line material balance calculation techniques. However, gross errors, due to sensor biases or failures, may corrupt all the process variable estimates. On-line gross error detection methods are required to ensure efficient mass balance evaluation. In the proposed approach, material imbalances and raw measurement corrections are tested by statistical techniques designed to detect and isolate sensor problems.

Jan 1, 2000

By Scott D. Thayer, George H. Milly

INTRODUCTION Ambient concentrations of radon and its daughter products have been measured and analyzed by a number of investigators for a variety of purposes. Principal among these purposes have been: (1) descriptive, to characterize the distribution and changes in concentrations under various conditions; (2) research in the use of radon as a tracer gas in the study of atmospheric characteristics and motions, such as eddy mass transfer, diffusivity profiles, large scale circulations, and the like; and (3) the use of radon as an atmospheric tracer in exploration for uranium deposits.* This information forms the basic data for this paper and for its placing the ambient natural, or non-anthropogenic, radon concentrations into the perspective of ambient radon health standards and lung cancer risk calculations. To enable better understanding of some aspects of the ambient radon data, review and analysis is also performed on selected measurements of radon emanation or flux from the surface of the earth into the atmosphere. These measurements have generally been made for purposes similar to those for ambient radon, i.e., (1) description of radon emanation characteristics; or (2) to support and justify the use of ambient concentration measurements in atmospheric research; or (3) in exploration for uranium. Interest is also developing in the use of such measurements for earthquake prediction. In addition, to complete the perspective, brief examination is given to anthropogenic ambient and flux radon measurements related to the mining and milling of uranium, so that comparison can he made with the values from natural sources. As a frame of reference we cite here previous summaries of studies which have presented representative values and ranges of ambient concentrations and emanation rates. H. Israel, in the Compendium of Meterorology (1951), cites eight studies of ambient radon concentrations which we have selected as representative of non-anomalous continental values. Their means generally range from [0.06 to 0.15 pCi lit-1 with the smallest reported minimum of zero and the largest maximum 0.53 pCi lit-1. The overall mean is 0.10 with a standard deviation of 0.03 pCi lit-1. Means over oceans are much smaller, and the data scarcer, with only three values ranging from 0.0004 to 0.003 pCi lit-1 and a mean of 0.0016 pCi lit-1.] Thirteen studies from Israel's list were selected as representative of mountainous terrain. These data, except for the cases of higher elevations, frequently show significantly higher values than the average cases in non-mountainous terrain described-above. The averages range from 0.10 to 0.59 pCi lit-l; the smallest minimum is zero and the largest maximum is 9.2 pCi lit-1. The overall mean is 0.30 with a standard deviation of 0.17 pCi lit-1. Israel also cites five studies of radon emanation (flux) from the earth's surface. These show a mean of 0.40 pCi-2m-2 sec-1 and a range of from 0.21 to 0.74 pCi m-2 sec-1. Data on flux are naturally scarcer in the literature than data on ambient concentrations, because of the greater interest in and utility of the ambient information. In this paper we also give special consideration to observations of the variability in time and space of radon flux rates, and to the impact of these phenomena on the use of such data for a variety of purposes. NATURAL(NON-ANTHROPOGENIC)AMBIENT RADON CONCENTRATIONS We have examined the following reports for the data selected for this category; these studies were generally intended to describe radon characteristics in the atmosphere. Jonassen and Wilkening (1970); Bradley and Pearson (1970); Wilkening (1970); Lambert, et al (1970); Pearson and Moses (1966); and DickPeddie, et al (1974). Another set of studies which was reviewed was selected because the investigators made ambient radon measurements in the course of examining the use of radon as a tracer in atmospheric research. This set consists of: Israel and Horbert (1970); Carlson and Prospero (1972); Subramanian, et al (1977); Larson (1978); Cohen, et al (1972); Hosler (1966); and Shaffer and Cohen (1972). Finally, unpublished data from uranium exploration activities (Milly and Thayer, 1976) was analyzed. [Treating the ocean cases first, the mean values are generally consistent with those quoted earlier from Israel (0.0004 to 0.003 pCi lit-1); they range from 0.001 to 0.011 pCi lit-1, with 0.003 the most frequently reported value. Continental values, from eight studies, range in means from 0.07 to 0.41 pCi lit-1 (not including mineralized areas, or "uranium country", discussed later), with maxima as high as 2.4 pCi lit -l. For comparison, the means from Israel are 0.06 to 0.15 pCi lit-1, with a maximum of 0.53 pCi lit-1. Some of these studies also present the typical decrease of-1 concentration with height to 0.01 to 0.04 pCi lit at 5 to 7 km. The vast numbers of uranium prospecting radon data of]

Jan 1, 1981

By S. Al-Thyabat

Conditioning of flotation feed is an important prerequisite for efficient flotation. This process depends on parameters such as conditioning time, slurry concentration and slurry pH. The objective of this paper is to optimize the conditioning process for the flotation feed. This was achieved by first conducting preliminary experiments at constant slurry pH to determine the significant ranges of slurry concentration and conditioning time. Then, factorial experimental design (32 experiments) was used to investigate the significance of the above parameters and their interactions on flotation recovery and grade. Statistical analyses using ANOVA approach showed that flotation recovery (R) and concentrate grade (g) were affected by feed conditioning. It was found that concentrate grade was linearly proportional to the slurry concentration and conditioning time, while flotation recovery was exponentially proportional to the conditioning parameters. A contour plot of the flotation response (recovery and grade) against conditioning parameters showed that the optimum operating parameters for flotation feed conditioning was a conditioning time of 1.5 to 2 minutes and a slurry conentration of 55% to 60%.

Jan 1, 2008

By John A. Patterson

There are certain data handling techniques used by statisticans that can help one to calculate the size of an orebody and to develop some of the relationships between size, cutoff grade, average grade, mining cost, and profit. Knowing the relationships amongst these factors can help determine the most desirable operating conditions. A statistical technique that we will use is data grouping. This allows us to work with relatively few groups instead of many samples, If we were able to segregate the ore in an orebody into grade groups, add the amounts in each group, and plot the sums as a curve, we would get something like Figure 1. A smooth curve develops when the grade classes are small enough, otherwise a "stair step? histogram results. The area under the curve, being the sum of the tonnages in all of the grade classes, is proportional to the total number of tons in the orebody. If we take the data of a distribution such as Figure 1 and add the tonnages above a specific grade we have in effect a cutoff grade

Jan 1, 1958

By K. R. Long

Until it was defunded in 1995, the U.S. Bureau of Mines maintained a Cost Estimating System (CES) for prefeasibility-type economic evaluations of mineral deposits and estimating costs at producing and non-producing mines. This system had a significant role in mineral resource assessments to estimate costs of developing and operating known mineral deposits and predicted undiscovered deposits. For legal reasons, the U.S. Geological Survey cannot update and maintain CES. Instead, statistical tools are under development to estimate mining costs from basic properties of mineral deposits such as tonnage, grade, mineralogy, depth, strip ratio, distance from infrastructure, rock strength, and work index. The first step was to re-estimate ?Taylor?s Rule? which relates operating rate to available ore tonnage. The second step was to estimate statistical models of capital and operating costs for open pit porphyry copper mines with flotation concentrators. For a sample of 27 proposed porphyry copper projects, capital costs can be estimated from three variables: mineral processing rate, strip ratio, and distance from nearest railroad before mine construction began. Of all the variables tested, operating costs were found to be significantly correlated only with strip ratio.

Jan 1, 2011

By F. Romero, L. Yacher, M. Orchard

Specific software tools for Statistical Multivariate Analysis combined with real time process data were applied to Concentrator Plant at Compañía Minera Doña Inés de Collahuasi SCM in Chile, basically to two Mill Lines, each one with one SAG mill (32’x15’8MW)and one Ball mill (22’x36’9.7MW). The main objective was to empower the operator actions using process patterns references instead of process variable set-points. Pattern clustering and the analysis of pattern deviations regarding normal or desired pattern, allows for improvements in process control and the further implementation of soft sensors for those variables not included in the initial model.

Jan 1, 2003

By G. Reed Marchant

The control systems engineer is often faced with the problem of designing tests or experiments where the cost of obtaining information is expensive. This is true in aerospace as well as in process industries. In these situations the details of test design should be carefully evaluated before any test is executed so that the maximum amount of information is obtained for the effort expended. In recent years there has been a steady trend towards increased automation, In the process industries this has resulted in extensive review of process variables and, instrumentation techniques, development of more accurate system mathematical models, and extensive investments in complex control system as well as completely automated plants. When planning and developing these systems, where each measure of a process variable is usually expensive, it behooves the design engineer to give considerable thought to the details of test design before instrumentation is procured and installed so that the maximum amount of information can be obtained for the expense incurred.

Jan 1, 1968

By E. L. Schrader

Statistical Process Control (SPC) is a cooperative arrangement between a component or raw materials supplier and a manufacturing customer. The supplier must analyze his own manufacturing process and determine, predict, and control those variable elements in the circuit which affect finished product characteristics according to the customer's specifications. The results include: control of fluctuations in product characteristics to a narrow range, close communication between supplier and customer, and an increased responsibility for quality control placed on the supplier. In the mining and. processing of airfloated kaolin some unique problems arise with the SPC concept: 1) The SPC system was designed for manufacturing facilities that did not have to deal with natural variations in their raw material; 2) The airfloat process is relatively simple and offers limited opportunity to change processing steps or "fine tune" a circuit for special product needs; 3) Determining adequate sampling frequency for a plant which processes hundreds to thousands of tons per day is statistically difficult; and, 4) Due to the variety of customer industries served, different SPC programs must be set up to deal with widely varying specifications. For airfloated kaolin, SPC is "in line" process control, not after the fact "quality" control. The emphasis must be on statistically valid sampling of the kaolin ore and complete monitoring of its path through the beneficiation circuit.

Jan 1, 1987

By Richard M. Crowell

"As thorough sampling is usually expensive, the cost of a complete job is often unwarranted, and a cheaper approximation must be substituted. The engineer should, however, weigh the situation thoroughly before subscribing to an alternative other than an accurate assay basis on which to build his conclusion." Examination and Valuation of Mineral Property. R. Parks, 1949

Jan 1, 1994

By A. M. Elmahdy

An amphoteric collector was tested for dolomite removal from phosphate ore. The effects of some operating parameters and their significance on the flotation of dolomite were studied using statistically designed experiments. The parameters studied were impeller speed, pH and collector dosage. Analysis of the results showed that pH is the most significant parameter. Moreover, a concentrate containing 0.53% MgO and ~31.1% P2O5 with a recovery of ~ 90% can be achieved at optimum values of studied parameters, i.e., a pH of 12, an impeller speed of 1,000 rpm and a collector dosage of 2.5 kg/t.

Jan 1, 2007

By Silvia H. M. Grimaldi, Afonso H. Martins

The scope of this experimental work was to study the yttrium extraction and stripping behaviour in a solvent extraction system with mono(2-ethylhexyl)2-ethylhexylphosphonic acid (IONQUEST 801) in a chloride system The study was performed for only one contact between organic and aqueous phases The experiments were carried out according to a factorial design. Due to the statistical analysis and its experimental proof, the optimum conditions for maximum yttrium loading into the organic phase of the extraction stage were 16 minutes for time of contact between phases, 980 rpm of stirring intensity and pH=2.3 for the aqueous phase of the sovent extraction system. The optimized experimental conditions by the statistical approach for the stripping stage were: time of contact between phases equal to 20 minutes, 1050 rpm of stirring intensity and 1.75 M HCI into the stripping aqueous solution.

Jan 1, 1995