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By F F. Pitard

The optimisation of a metallurgical plant requires two kinds of sampling systems. The first provides samples to follow process changes, so in due time actions to maintain key parameters within pre-established specifications can be applied. The second provides composite samples at the end of a working shift to demonstrate that valuable constituents sent to the plant went to either a final concentrate or to the tailings in a logical, expected proportion. Contrary to what many experts may claim, these two kinds of sampling requirements are incompatible and cannot be fulfilled using the same sampling systems; this is because the required samples have completely different objectives. A process control sample is an instantaneous sample with increments taken at short intervals, and the objective is to know where the process is at any given time. Excellent accuracy is not a must, however good precision is recommended since a possible process correction may need to be made. Online analysers fed with in-stream stationary cutters or other kinds of in-stream or by-stream probes can do well for such a mission. A composite sample for metallurgical accounting with increments collected over a long period of time, for which excellent accuracy and good precision are both required, must be generated by sophisticated and extremely well-maintained cross-stream sampling stations. The use of process control sampling systems to achieve good metallurgical accounting has been promoted by several manufacturers of sampling equipment around the world; it is a grave mistake that is misleading top management and a practice that should be scrutinised and preferably eliminated. Furthermore, bias tests used to prove otherwise are often based on insufficient data to draw valid conclusions; a guideline is provided.CITATION:Pitard, F F, 2014. Sampling systems for process control and metallurgical accounting, in Proceedings Sampling 2014 , pp 25–32 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 29, 2014

By George S. Barnett

The Equis and El Roble projects are located in the Cordillera Occidental of Colombia. The Equis vein deposits have sulfide ore reserves of 95,955 mt (105,770 st) grading 8.51 g/mt (0.248 oz/st) gold and 12.4 g/mt (0.36 oz/st) silver with 0.94 % copper, 1.10 % lead and 11.06 % zinc. Ore reserves at El Roble are estimated as 1.1 Mmt (1.21 million st) grading 4.89 % copper and 3.39 g/mt (0.099 oz/st) gold. Geologically possible reserves at Equis may total 1.6 Mmt (1.76 million st). El Roble has the potential to contain several tens of millions of metric tons. Exploration included diamond drilling, trenching, channel sampling, rock and soil geochemistry, geophysics and tunneling. Erratic high grade samples affect the weighting of channel and drill core samples. Secondary reconcentration of gold is also a factor. Sample maps and graphs show the distribution of values to be highly variable. Geostatistical treatment of some of these data gave important guidelines for parameters such as sampling densities, drill hole spacing and confidence limits.

Jan 1, 1985

By R. A. Metz, George S. Barnett

The Equis and El Roble projects are located in the Cordillera Occidental of Colombia. The Equis vein deposits have sulfide ore reserves of 95,955 mt (105,770 st) grading 8.51 g/mt (0.248 oz/st) gold and 12.4 g/mt (0.36 oz/st) silver with 0.94 % copper, 1.10% lead and 11.06% zinc. Ore reserves at El Roble are estimated as 1.1 Mmt (1.21 million st) grading 4.89 % copper and 3.39 g/mt (0.099 oz/st) gold. Geologically possible reserves at Equis may total 1.6 Mmt (1.76 million st). El Roble has the potential to contain several tens of millions of metric tons. Exploration included diamond drilling, trenching, channel sampling, rock and soil geochemistry, geophysics and tunneling. Erratic high grade samples affect the weighting of channel and drill core samples. Secondary reconcentration of gold is also a factor. Sample maps and graphs show the distribution of values to be highly variable. Geostatistical treatment of some of these data gave important guidelines for parameters such as sampling densities, drill hole spacing and confidence limits.

Jan 1, 1992

By Stevenson I, Dickinson W, Taylor R. N

Despite flash smelting's widespread use little is known about the actual processes taking place in flash furnace shafts and comparatively few reports of sampling campaigns have appeared in the published literature. his paper reviews the previous reports of the use of horizontal trough samplers and analyses their expected collection efficiency. In the light of the deficiencies revealed by this analysis an isokinetic sampler was produced and a vertical sampling technique was also developed to obtain samples from directly below the burners in the shaft of the flash furnace at the Kalgoorlie nickel smelter. Comparison of the sizing of the samples obtained with the horizontal trough and isokinetic samplers confirmed the theoretical analyses and showed that the trough samplers were not collecting the fine particles. Besides providing data to validate mathematical models of the burners and shaft, chemical analyses of the shaft samples showed that the coal in the charge was reacting preferentially and that the plume of at least one of the burners was being deflected from its axial position. In the region directly below the burner there was evidence that the disperser on the burner was imparting more momentum to the coarser particles and that these were concentrating in the outer regions of the particle plumes issuing from the burners.

Jan 1, 1992

By R. Bruce Tippin

because of the mineral's high monetary value and the spotty occurrence of free gold in the deposit. Setting up a plant sampling procedure by simply applying the usual statistical sampling theory was questionable. Two sampling concepts were considered in the sampling study: o a sufficient number of assays can be taken such that the average determined from these individual samples represents a known quantity of ore. o a sufficient weight of sample can be taken such that when assayed it represents a known quantity of ore. The test program included evaluation of sampling techniques, sample preparation and analytical methods. The overall sampling program is depicted in Figure 2.

Jan 1, 1985

By P. E. Hand

Coal is a complex heterogeneous commodity that can be mined in a number of ways and needs to be processed to a homogeneous quality that satisfies the customer?s requirements, while attempting to maximize revenues. Only a small proportion of coal is suitable for metallurgical use. Export coals cover a wide range of qualities and some coals can be used optimally in the raw state for energy production. Critical quality parameters vary and can be a combination of heat value, ash, volatiles, sulphur, phosphorus, sizing, amongst others. The level of beneficiation is generally dictated by the washability of the coal, mining contamination, and the target product quality. The steps in the coal chain covered in this paper comprise exploration, mining selections, production, the washing process, and product delivery. Many points of sampling are needed to maximize yield at the correct quality, and some of these will be described in the paper. Keywords coal chain, coal beneficiation, sampling.

Jan 1, 2014

Discovery of a hitherto unsuspected extension of the Vermilion range iron formation in Northern St. Louis County, Minn., has been announced by the director of the State's geological survey, Dr. George M. Schwartz. USGS aeromagnetic maps show that the Vermilion range curves southeast from the Tower-Soudan area into the wilderness between Embarrass and Bear Head Lake. Dr. Schwartz believes that this new information justifies considerable exploration and drilling for iron ore in an area of about 20 sq miles southeast of Soudan. The aerial maps were a result of a three year USGS-Minnesota Geological Survey aerial search for iron formations in a 30,000 sq mile area in northern Minnesota.

Jan 12, 1950

Discovery of a deposit of magnetite ore estimated at 3 million tons and of quality sufficient to warrant mining has been located near Reading, Pa. by the Bethlehem Steel Corp. Last January; the company spent nearly $400,000 for about 1750 acres of farm land which had been valued at only about $50 per acre. It is expected that a pilot shaft 18 in. in diam will be sunk some time this spring. The ore body, delimited by diamond-drilling by Sprague Henwood, is said to measure roughly 2000 sq ft and 1000 ft thick, beginning 1500 ft below the earth's surface. In a continuing search for strategic minerals, the Atomic Energy Commission expects to put eight to ten diamond drilling rigs into the area 11 miles southwest of Blanding, San Juan Co., Utah early this year. The Commission's primary objective is the Salt Wash member of the Morrison formation. Holes 140 ft deep are expected to be drilled, with solid bit drilling through overburden, mudstone, shale and sandstone overlying the area.

Jan 1, 1951

Sixteen executives, technicians and operative personnel from the French mining industry, now touring mining operations in the U.S., will wind up their visit to this country at the AIME Annual Meeting. Traveling under ECA auspices, they will be in Denver on Feb. 5, Salt Lake City, Feb. 8 to 13, Bonne Terre on Feb. 16. Four of the group are engaged in bauxite mining, nine in lead and zinc, two in pyrites mining. All are interested in American mining equipment and methods, and hope to contact manufacturers' representatives in the various areas they visit. A $600,000 manganese pilot plant is expected to be put into operation by Sept. 1, by the Bureau of Mines at Boulder City, Nev. S. R. Zimmerly, chief of the Bureau's metallurgical div. for the region, recently completed the mill design and flow sheet; and the Bureau is awaiting steel priorities before building. Ore from the Artillery Peak area, 60 miles south-west of Kingman, Ariz., will be used in the mill. Construction will be handled by Rex Lloyd of Boulder City.

Jan 2, 1951

By Reed M. E, Cloutt B

Particulate samples were taken from the gas space in the settler of the Kalgoorlie nickel smelter using a vertical sampling probe and a specially designed isokinetic sampling probe which also quenched the samples. The vertical sampler was found to give unrepresentative samples. Suction thermocouple measurements of the gas temperature were also made. Using the isokinetic probe samples were taken at four points ranging from near the base of the reaction shaft to the base of the uptake at depths up to 1.5 m into the settler. Dust loadings and the sizing of the samples were determined. These parameters were found to be most affected by sample position and depth. The dust loading decreased along the settler but increased with depth. The loadings varied from zero near the roof to several hundred g Nm 3 near the slag. The dust also became coarser with increasing depth into the settler. Examination of the samples showed them to consist of spherical particles the largest of which were about 500 microns in diameter. The dust was mainly composed of mixed iron/nickel oxides with a little sulphide.

Jan 1, 1991

By D. N. Collins

A sampling program was conducted in which both spoon and isokinetic sampling techniques were used to collect samples from the reaction shaft. The samples were then characterised by chemical, XRD and mineralogical analysis. Further information was acquired by measuring the oxygen potential and temperature at the bottom of the shaft using disposable probes. Comparison of the results of the two sampling methods showed that the spoon samples were devoid of material less than 25 m. Sulfur analyses on the samples provided information on the extent of reaction, plume shape and recirculation patterns. Disposable probe measurements showed the measurable particle temperatures ranged from 1150 to 1700 °C and that the material falling into the bath had a normalised oxygen potential similar to the slag. These latter measurements combined with the sulphur elimination and mineralogical analyses provided further information on the extent of reaction and enabled the reaction sequence to be ascertained.

Jan 1, 1999

By F F. Pitard, K J. Ehrig

The Olympic Dam iron-oxide copper-gold (IOCG) uranium-silver deposit is second in size only to Norilsk, the gigantic metalliferous deposit. Olympic Dam is the largest publicly declared uranium, fifth largest copper and third largest gold resource. The deposit is typified by texturally destructive brecciation and intense iron metasomatism of the Roxby Downs Granite, bedded clastic facies rocks and mafic-ultramafic dykes. The deposit contains over 100 minerals. Copper mineralisation consists of chalcopyrite, bornite and chalcocite. Uraninite, coffinite and brannerite are the dominant uranium-bearing minerals. Gold mineralisation consists of electrum, tellurides and Au-Cu alloys. Hessite is the major silver-bearing mineral. The economic minerals are disseminated throughout the breccia matrix where the average grain sizes of the Cu-sulfide, uranium, gold and silver minerals are ~50, 20, <5, <5 microns, respectively.A significant number of sampling theory-based test programs have been completed since the mid-1990s to establish sampling nomographs, select appropriate sampling (ie split versus chip and interval lengths) and sample preparation protocols, quantify the errors associated with each subsampling stage, determine the practical uncertainty limits of Olympic Dam matrix-matched standards, and identify improvement opportunities related to the ongoing assaying quality assurance / quality control (QA/QC) program. Invaluable knowledge and unexpected insights gained from sampling studies at Olympic Dam have helped to improve our understanding of the distribution of economic and deleterious elements within the Olympic Dam deposit.CITATION:Ehrig, K J and Pitard, F F, 2017. Underground bulk sampling, uniform conditioning and conditional simulation – unrealistic expectations?, in Proceedings Eighth World Conference on Sampling and Blending , pp 21–28 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2017

INTRODUCTION TO SAMPLING THEORY Before specifically discussing mineral sampling and sampling procedures, let us briefly consider broader and more universal concepts of modem sampling theory. A sample is de- fined as a representative part or a single item from a larger whole, being drawn for purpose of inspection or shown as evidence of quality. In modem theory the sample is a part of a statistical population whose properties are studied to gain information about the whole. The theory of sampling is built around the concept that if enough representative units of a larger overall population are selected without bias, the average value of the units will approximate that of the total population. Modem theory attempts to answer the question of how many samples are enough, given certain limits and constraints, and seeks to apply methods of sample selection and of estimation that provide, at the lowest possible cost, estimates that are precise enough for the purposes at issue. In order to meet these objectives the designer of a sample survey must rely heavily upon statistical theory. Statistics has been defined as the collection, presentation, analysis, and interpretation of numerical data. Statistical methods are primarily concerned with making valid inferences about a population based upon samples taken from the population. For most statistical applications, the total sample is in terms of number of items, attributes, or things; whereas mineral samples are usually in terms of weight or volume of mineral particles. Certain steps are involved in a well designed sample survey without regard to the particular field of application. Because the desired characteristics of an unmined mineral deposit can- not be known other than by sampling, we will consider these principle steps in terms of a mineral sample survey: 1) Clear definition of the objectives of the survey. In the case of mineral sampling this step is so apparent as to be almost ridiculous. However, it is surprising how often the overall objective of a sampling program is overlooked when decisions are made on a day-today basis. 2) Definition of the population to be sampled. The word population is used to designate the aggregate from which the sample is chosen. A sampling program may be designed to determine the grade of a single stope within a mine, the grade of a particular zone within a complex ore body, or the total value and extent of a mineral deposit. Since mineral sampling is usually done in phases, it is well to

Jan 1, 1980

Sampling criteria and practical implementation of these criteria are discussed with a view of achieving and maintaining a high level of quality for minerals at their various stages of production through to their utilisation. From this it will be shown the advantages that can be gained by producers who undertake stringent quality control programmes for their ores, thus ensuring they have a competitive edge over other producers.

Jan 1, 1985

By R. J. Howarth, P. L. Llowenstein

The errors resulting from field sampling, sample preparation and analysis are investigated for drainage sediments derived from homogeneous sandstone, shale, limestone, basic igneous and granite lithologies as a background to a primary reconnaissance survey of England and Wales. Emission spectrographic analyses of approximately 350 samples for Al, Ca, Fe, K, Si, Ba, Co, Cr, Cu, Ga, Li, Mn, Ni, Pb, Sc, Sn, Sr and V and atomic absorption analyses for Cu, Ni, Mn, Co, Zn and Pb have been treated statistically. For routine broad-scale surveys analysis of the unground -80-mesh sediment fraction proves satisfactory. Sampling error between localities in a stream is shown to be less than spectrographic analytical error for many of the elements considered here, except where mineralisation (contamination) occurs, but exceeds the atomic absorption analytical errors in most cases. Unless it it critical to reduce the amount of between-site variability (having regard to analytical errors) in the regional survey, there appears to be no advantage in the use of a more sophisticated sampling technique. The utility of moving-average maps in reducing the width of the confidence belt around the regional 'geochemical surface', and thus compensating to some extent for the sampling errors, is also demonstrated.

Dec 1, 1971

Early in 1940 the development and sampling programmes in hand on the North and British Sections of North Broken Hill Limited were such as to necessitate the drilling of a large number of drill holes ranging up to about thirty feet in length. On the British Section, one purpose was to test the existence, width, and value of narrow lodes believed, for geological reasons, to occur in the walls of the existing workings. Another object was to definitely disprove the existence of payable shoots of ore in certain largerhodonite and quartz-garnet ("garnet sandstone") pillars which had been formerly left as unpayable.On the North Section, the main purpose of the short holes was to delineate the ore-body boundaries by drilling laterally from drives in ore, and thus enable level layout to be planned in advance of sill stoping. It was also desired to test the walls of stopes in those portions of the mine where the economic limit of mining is not rendered obvious by a clear-cut wall, but should be determined by assay. In these latter cases it was hoped to eliminate "prospecting by stoping," a procedure by which any doubts as to the existence of further good ore behind the low-grade walls were settled by continuing to stope laterally until all chance of such an occurrence was removed.LONG HOLE ROCK DRILLINGFollowing an investigation of recorded instances of similar practice elsewhere it was decided to use the rock drill for a series of trial sample holes. A 3-in. drifter was used. This was selected from those in use underground, and was given a special overhaul; had a new machine been purchased, a 4-in. type would probably have been obtained as being more suited to the work. The rods were H in. hollow round steel with a type "1" Jackrod thread. Couplings were of chrome steel, and were H in. in diameter, and 2 in. long. Jackbits (type "1" thread) in sizes from 2 in. to 4 in., with 1-in. gauge changes, gave a range of nine bit sizes. They were resharpened by hot milling, and were not milled to a definite gauge size.After sharpening, bits were sent underground without sorting into sizes, the drillers selecting the next bit with callipers. In view of the small scale of operations, it was not considered worth while to adopt special measures, such as the cold grinding of bits, which might have given a better product. Later, however, new bits were used exclusively, the idea being to accumulate enough blunt Jackbits to warrant a thorough treatment of the sharpening...

Jan 1, 1941

There are many different challenges when sampling mineral commodities. Sampling is part of many decision-making processes, from control of the number of drops of a reagent to all aspects involved in determining how much to pay for a mineral consignment. However, if all decisions must be supported by correct assumptions, or at least agreed terms, how can this be guaranteed? The main approach is to emphasise the importance of continuous surveying of sampling practices. If they are based on non-recommended protocols, this raises concerns. In addition, safety failures and lack of appropriate behaviour from the technical perspective can lead to disasters, both from the human and business perspectives. Impacts on safety and health are clearly unacceptable. It should be noted that imperfect safety and health practices in sampling operations have a strange correlation with incorrect sampling techniques. The commercial interface can also be affected. Companies have studied extensively the various aspects of measuring quality parameters for mineral commodities to understand the risks for investors and owners, and they take decisions that fundamentally respect the interests of parties in contracts and not result in losses. Every result should be obtained in defensible ways, and neither losses nor profits taken in indefensible ways. Most of such situations are related to bias; a significant systematic difference between a measured value and a reference value for a contractual quality parameter. Bias is always undesirable, because it always implies an incorrect advantage for one party and without doubt an undesired disadvantage for the other party. These situations are solved financially through a third-party arbitrator becoming involved in delicate situations, such as a commercial claim, but the outcome is always tangibly or intangibly bad for one of the parties. Another possibility is a permanent or temporary loss of precision. Poor precision, due its nature, generates reasonably balanced losses and profits, but it may hide out-of-control situations, generate instability and induce financial losses due to actions taken towards clearing commercial disputes involving interlaboratory programs, sample exchanges and duplicated sampling and sample preparation procedures, in the end wasting time and resources and creating a permanent source of commercial tension. While bias situations demand immediate adjustments for correctness, poor precision has to be understood as something that cannot be just calibrated out and is a situation that demands investment of time and effort. Precision optimisation has to take into account best practice for obtaining the required precision as well as cost/benefit analysis studies. Purchasers, engineers, salesmen and all personnel need to recognise that sampling is a major area to understand when taking decisions. The aim is to spread concepts that can really help, such as simple in-house actions to improve productivity and completion of surveys on commercial sampling operations, in order to ensure correct results are obtained and assertively take corrective actions, thereby establishing a healthy relationship with investors, suppliers and purchasers and in the process optimising the business.

Jan 1, 2008

By G J. Lyman, F S. Bourgeois

As the prices of metals slide, financial control of mineral processing operations becomes more and more important. Control of a mineral processing operation implies measurement of grades, recoveries and losses, with every effort being made to recover more product from the same feed. Shareholders become more concerned with the transparency of the operations and the corporate governance.There is only one way to achieve this and this is by sampling and making good use of the results of that sampling. Sampling systems that provide only 'rough' figures are not good enough. Similarly, a competitive position in the marketplace demands close control of product quality. Maximisation of product output demands that the product just meet the specification so that product yield is maximised. Decisions based on precise sampling results carry less risk that those based on imprecise results.This paper reports some recent advances in sampling theory that permit full quantification of sampling distributions, not just the sampling variance as has been possible in the past. These advances can be used together with simulation methods to tie down sampling precisions and develop calculations that quantify decision making risk when using the sampling results. A number of examples illustrate the use of the new advances and a final example indicates the development of risk analysis curves in the coupling of sampling precision to sale of a commodity.CITATION:Lyman, G J and Bourgeois, F S, 2015. Sampling, corporate governance and risk analysis, in Proceedings MetPlant 2015, pp 27–34 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 7, 2015

By C. Alan Tapp

Introduction Mine sampling determines the practicality of any mining operation. Improper sampling can result in an incorrect appraisal of present production and future potential. Therefore, the mine department in charge of ore-reserve calculations and mine sampling should be overseen by competent and experienced professionals with technical backgrounds qualifying them to produce accurate results. Sampling is a process by which portions of an ore body are collected and analyzed to estimate the average mineral content of the entire ore body. It is incorrect to assume that a large number of samples eliminates any errors in the sampling method. To obtain unbiased samples, proper sample location with respect to rock type and mineralization is just as important. The sampling procedure must yield correct results for the type of mineral deposit, and careful consideration should be given to whether or not the sampling technique has been developed to an extent sufficient to eliminate as much human error and bias as possible. Only after the ore has been mined and milled is the sampling accuracy known. Sampling also provides information about the bulk composition of the ore for mineralogical and metallurgical tests that determine the economic ore-waste boundaries and the geologic trends for exploration. Actual mining plans can be developed from this information to maximize profits. Accurate sampling is critical, and thus must be approached in a scientific manner. Sampling Techniques Sampling practices and techniques are as varied as the mines in which they are used. The method(s) chosen must be tailored to suit the company and mining needs. For instance, tabular uranium deposits, vein gold deposits, and porphyry copper deposits pose special problems in conducting unbiased sampling. The mine geologist or engineer in charge must develop a sampling method, test it in a sample area, and then critically evaluate the results. If the results from the test area are accurate within the economic limits established by the company, they then may be adopted for general use in the mine. Four routine sampling methods are suitable for specific sampling objectives in the daily mine routine: (1) channel sampling, (2) chip sampling, (3) grab sampling, and (4) bulk sampling. The final sampling results depend upon how the four methods are combined to accurately determine the grade of the ore body. When used in conjunction with each other during different stages of mine development, the channel, chip, grab, and bulk sampling methods provide an in-house check or a comparison by which mining methods and sampling procedures can be evaluated. However, the most valid check is based upon the daily mill production. Channel Sampling Channel samples consist of cuttings collected from a groove cut into the rock about 102 mm (4 in.) wide and 19 mm (0.75 in.) deep. Various tools ranging from a 1.8-kg (4-lb) hammer and moil to a pneumatic chisel can be used to cut the sample. Accessibility and rock hardness determine the applicable sampling tools. Before attempting to take a sample, the rock surface must be cleaned thoroughly; the method of cleaning depends upon the amount of mine dust accumulated on the surface or the degree of alteration of the rock surface. Typical cleaning methods 'employ a wire brush, water, or chipping a fresh surface. Next, the sample outline is marked on the prepared surface, taking care to choose appropriate sample loca- tions. After determining the proper sample outline and length, the sample can be chiseled out, catching the rock fragments on a canvas tarpaulin on the floor, in a powder box, in a canvas bag to avoid contamination, or by some other suitable means to capture all of the sample. Vertical veins present a special problem because the drift's back usually is arched, not square. For example, Fig. 1 shows that if sample intervals are measured from A' to D', the length of the sample interval is greater than the true vein width, resulting in an incorrect calculation of the ore reserves. The correct method would collect three samples at A'-B', B'-C', and C'-D', using either actual measurements in the mine represented by A-B, B-C, and C-D or trigonometric calculations to determine the true ore thickness. Then, each sample can be weighted by grade and true thickness for the vein. Channel lengths usually are a maximum of 1.5 m (5 ft), and it is good practice to divide longer samples into smaller intervals according to structures, changes in rock types, or differences in rock hardnesses. The influence of those features on the mineralization then can be determined. Chip Sampling Chip sampling is a variation of channel sampling used when the rock is too hard to channel sample economically or when little variation in the mineral content indicates that this sampling method will yield results similar to those of channel sampling. Rather than cutting a channel in the rock, small chips are flaked off at regular intervals over the entire face or area being the mine. sampled. Care must be taken to assure that the sample is representative of variations in the rock hardness and type. hi^ method is fast and useful in preliminary evaluations, but it should not be used for quantitative ore-reserve calculations. Grab Sampling Grab sampling is a fast method for double checking either channel or chip-sampling procedures, and, in some instances, mine production can be estimated from carefully taken grab samples. Grab sampling takes equal amounts of material at selected intervals over a mine dump, a muck pile, or from an ore car to estimate its Channel Sampling mineral content. Generally, this method is not considered reliable. Many independent variables can affect this type of sampling process. Thus, if the ore occurs in the softer fraction and a proportional amount of the result-

Jan 1, 1982

A metallurgical balance drawn around a mineral processing plant or smelter must involve all process streams crossing the plant boundary. Modern sampling theory, as formulated by Gy, and sound statistical method can be used to determine the uncertainties in the observed assays for the set of balance analytes and in the mass flow rates of the process streams for the balance period. These uncertainties can then be used together with the material balance equations to arrive at adjusted component mass flows that satisfy the material balances exactly. To determine whether or not the data is consistent with the level of uncertainty in the data and with the material balance equations, a goodness of fit test is applied. This goodness of fit criterion is the principal tool to quantify the quality of the material balances. The mathematical structure of the statistical material balance problem poses a number of challenges. For example, while the variances of the adjusted component mass flows do not vanish, the variances of the sums of the adjusted component mass flows about each balance node do vanish, simply because the balancing computation demands that the balances close exactly. Even though it can be shown that the variances of the adjusted component mass flows are always lower than the estimates for the corresponding unadjusted component flows, it is still not possible to construct a confidence interval on the component mass flow into (and out of) a balance node using the adjusted component flows. On the face of it, such a confidence interval is exactly what is most desired from the balance calculations. The problem arises because the balance problem is a data adjustment rather than a parameter estimation problem. It is possible, however, to calculate the recovery of a component to a product stream and determine a confidence interval for the recovery value. It is also possible to calculate an uncertainty in the mass flow of any balance species in any process stream, before and after balancing.

Jan 1, 2005