1. -Mineral Processing Laboratory (an overview):

Mineral processing, also known as mineral dressing or ore dressing, is the process of separating commercially valuable minerals from their ores.

Unit Operations:

A mineral processing lab can consist of three sections:

1. Comminution – particle size reduction.2. Concentration by taking advantage of physical and surface chemical properties.3. Dewatering – solid/liquid separation.

Comminution:

Comminution is particle size reduction of materials. Comminution may be carried out on either dry materials or slurries. Crushing and grinding are the two primary comminution processes. Crushing is normally carried out on "run-of-mine"ore, while grinding (normally carried out after crushing) may be conducted on dry or slurried material.

1. Crushing:

A crusher is a machine designed to reduce large rocks into smaller rocks, gravel, or rock dust. Crushers may be used to reduce the size, or change the form, of waste materials so they can be more easily disposed of or recycled or to reduce the size of a solid mix of raw materials (as in rock ore), so that pieces of different composition can be differentiated.

Crushing is the process of transferring a force amplified by mechanical advantage through a material made of molecules that bond together more strongly, and resist deformation more, than those in the material being crushed do.

Crushing devices hold material between two parallel or tangent solid surfaces, and apply sufficient force to bring the surfaces together to generate enough energy within the material being crushed so that its molecules separate from (fracturing), or change alignment in relation to (deformation), each other.

Jaw Crusher:

A jaw or toggle crusher consists of a set of vertical jaws, one jaw being fixed and the other being moved back and forth relative to it by a cam or pitman mechanism. The jaws are farther apart at the top than at the bottom, forming a tapered chute so that the material is crushed progressively smaller and smaller as it travels downward until it is small enough to escape from the bottom opening. The movement of the jaw can be quite small, since complete crushing is not performed

in one stroke. The inertia required to crush the material is provided by a weighted flywheel that moves a shaft creating an eccentric motion that causes the closing of the gap.

Jaw Crusher

Single and double toggle jaw crushers are constructed of heavy duty fabricated plate frames with reinforcing ribs throughout. The crushers components are of high strength design to accept high power draw. Manganese steel is used for both fixed and movable jaw faces. Heavy flywheels allow crushing peaks on tough materials. Double Toggle jaw crushers may feature hydraulic toggle adjusting mechanisms.

Hammer Crusher:

The hammer crusher is one of the main equipment for intermediate and fine crushing the brittle materials with less than intermediate such as limestone coal and other used in metallurgy, building material, chemical and water - power industry, with a feature of big crushing ratio and even product graininess.

Hammer Crusher

2. Grinding

In this process stage, the crushed material can be further disintegrated in a cylinder mill, which is a cylindrical container built to varying length-to-diameter ratios, mounted with the axis substantially horizontal, and partially filled with grinding bodies (e.g., flint stones, iron or steel balls) that are caused to tumble, under the influence of gravity, by revolving the container.

Ball mill:

A ball mill, a type of grinder is a cylindrical device used in grinding (or mixing) materials like ores, chemicals, ceramic raw materials and paints. Ball mills rotate around a horizontal axis, partially filled with the material to be ground plus the grinding medium. Different materials are used as media, including ceramic balls, flint pebbles and stainless steel balls. An internal cascading effect reduces the material to a fine powder.

Ball mill

Ball mills are used extensively in the Mechanical alloying process[1] in which they are not only used for grinding but for cold welding as well, with the purpose of producing alloys from powders.

The ball mill is a key piece of equipment for grinding crushed materials, and it is widely used in production lines for powders such as including cement, silicates, refractory material, fertilizer, glass ceramics, etc. as well as for ore dressing of both ferrous non-ferrous metals. The ball mill can grind various ores and other materials either wet or dry. There are two kinds of ball mill, grate type and overfall type due to different ways of discharging material. There are many types of grinding media suitable for use in a ball mill, each material having its own specific properties and advantages. Key properties of grinding media are size, density, hardness, and composition.

Rod mill:

Rod mills are very similar to ball mills, except they use long rods for grinding media. The rods grind the ore by tumbling within the mill, similar to the grinding balls in a ball mill. To prevent the conditions leading to rod charge tangling, the length to diameter ratio is maintained at 1.4 to 1.6. Rod mills accept feed up to about 50 mm (2 in.) and produce a product in the size range of 3000 to 270 mm (–4 to –35 mesh). Grinding action is by line contact between the rods extending the length of the mill. Rods tumble and spin in roughly parallel alignment simulating a series of

roll crushers. This results in preferential grinding of coarse material and minimizes production of slimes.

Rod mill

Rod mills normally carry 35 to 65% rod charge by volume. The limits on charge level are (1) keeping the feed end trunnion open so that feed will get into the mill, and (2) keeping the rod charge low so rods will not work their way into discharge openings where they can cause rod tangling.

Concentration:

Concentration involves the separation of valuable minerals from the other raw materials received from the grinding mill. In large-scale operations this is accomplished by taking advantage of the different properties of the minerals to be separated. These properties can be color (optical sorting), density (gravity separation), magnetic or electric (magnetic and electrostatic separation), and physicochemical (flotation separation).

1. Gravity and dense medium separation:

Historically the earliest method used, particles can be separated based on their specific gravity. Air is the main fluid medium used for the process.

Gravity separation methods fall into three broad categories: dense-medium separation, in which the particles are immersed in a bath containing a medium of intermediate density, so that some particles float and others sink; separation in vertical currents, such that advantage is taken of differing rates of settlement, as typified by jigging; and separation in streaming currents, or 'thin film sizing' as for example on a shaking table or spiral separator. A flat, rectangular surface that can be tilted and shaken about the long axis and has horizontal riffles for imposing restraint in removing minerals from classified sand. Also known as shaking table.

Gravity concentration on inclined planes is carried out on shaking tables, which can be smoothed or grooved and which are vibrated back and forth at right angles to the flow of water. As the pulp flows down the incline, the ground material is stratified into heavy and light layers in the water; in addition, under the influence of the vibration, the particles are separated in the impact direction. Shaking tables are often used for concentrating finely grained ores of tin, tungsten, niobium, and tantalum.

1. Flotation separation:

Flotation is the most widely used method for the concentration of fine-grained minerals. It takes advantage of the different physicochemical surface properties of minerals—in particular, their wettability, which can be a natural property or one artificially changed by chemical reagents.

By altering the hydrophobic (water-repelling) or hydrophilic (water-attracting) conditions of their surfaces, mineral particles suspended in water can be induced to adhere to air bubbles

Shaking table

passing through a flotation cell or to remain in the pulp. The air bubbles pass to the upper surface of the pulp and form a froth, which, together with the attached hydrophobic minerals, can be removed. The tailings, containing the hydrophilic minerals, can be removed from the bottom of the cell.

Flotation separation

Flotation makes possible the processing of complex intergrown ores containing copper, lead, zinc, and pyrite into separate concentrates and tailings—an impossible task with gravity, magnetic, or electric separation methods. In the past, these metals were recoverable only with expensive metallurgical processes.

3. Magnetic separation:

Minerals such as ilmenite and magnetite are naturally magnetic, and so can be separated from non-magnetic particles using strong magnets. There are a number of different processes that can be used. These include High Gradient Magnetic Separation (HGMS), High Intensity Magnetic Separator (HIMS) and Low Intensity Magnetic Separator (LIMS). The HIMS and HGMS are differentiated as the HGMS separators are a batch process while the HIMS are a continuous process. These two processes are typically used for paramagnetic particles while the LIMS are used for ferromagnetic particles.

Magnetic separation is based on the differing degrees of attraction exerted on various minerals by magnetic fields. Success requires that the feed particles fall within a special size spectrum (0.1 to 1 millimetre). With good results, strongly magnetic minerals such as magnetite, franklinite, and pyrrhotite can be removed from gangue minerals by low-intensity magnetic

separators. High-intensity devices can separate oxide iron ores such as limonite and siderite as well as iron-bearing manganese, titanium, and tungsten ores and iron-bearing silicates.

Dewatering:

Dewatering is an important process in mineral processing. The purpose of dewatering is to remove water contained in particles. This is done for a number of reasons, specifically, to enable ore handling and concentrates to be transported easily, allow further processing to occur and to dispose of the gangue. The water removed from dewatering can be recycled through a mineral processing plant. The main processes that are used in dewatering include dewatering screens, sedimentation, filtering, and thermal drying. These processes increase in difficulty and cost as the particle size decreases.

Filtration:

Filtration is the separation of a suspension into a solid filter cake and a liquid filtrate by passing it through a permeable filtering material. Important factors in this process are the properties of the suspension (e.g., size distribution, concentration), the properties of the filtering materials (e.g., the width and shape of pores), and the forces applied to the suspension. Filtration is carried out in gravity filters (screens, dewatering bins), in centrifugal filters (screen centrifuges), in vacuum filters (drum cell filters, disk filters), or in pressure filters (filter presses). Such devices make it possible to produce filter cakes containing 8 to 15 percent moisture.

Thickening:

In the process of thickening (also called sedimentation), the solids in a suspension settle under the influence of gravity in a tank and form a thick pulp. This pulp, and the clear liquid at the top of the tank, can be removed continuously or intermittently. In comparison with filtration, thickening offers the advantage of low operation costs; on the other hand, it has the disadvantage of leaving a higher moisture content in the pulp. For this reason, the dewatering of pulps containing fine particles often involves a combination of thickening and filtration. The thickening of finely grained pulps is often aided by the use of flocculating agents.

Drying

The removal of water from solid materials by thermal drying plays a significant role in modern mineral processing. A great number of dryer types are available. Convection dryers, employing a flow of hot combustion gases to remove moisture from a pulp stream, are the most common. To this type belong rotary drum, conveyor, and fluidized-bed dryers.

2. METALLURGICAL ACCOUNTING AND SAMPLING

Purpose of metallurgical accounting: To determine distribution of the various products of a mill, and the values contained in them. Metallurgical accounting is also used to control the operations since the values of recovery and grade indicate process efficiency. An efficient and representative sampling system is what ensures good accounting and control system. Sampling is is the process of generating a small amount of a material from the bulk material such that the small amount has properties that accurately represent those of the bulk material.

Weighing and sampling of ore is done when the ore is in its most finely divided. Ideally, weighing and sampling should be carried out before material is subject to losses e.g. Run-of-mine ore entering the primary crusher NOT after the material has been milled (at least for accurate weighing). For run-of mine sample to be of accurate analysis, at least 5% of the total weight of the ore must be taken as a sample, otherwise the results will be affected by segregation and variations in moisture content.

The percentage moisture in samples is determined using the following equation:

% moisture=wet weight−dry weightw et weight

* 100

The drying temperature should not be so high that there will be a breakdown of minerals either physically or mechanically e.g. sulphides are not dried above 105 °C.

In practice sampling is done more effectively when material has been reduced to the smallest size and will be in motion at a point of free fall discharge e.g end of a conveyor belt. A sample cutter that moves continuously across the stream at a uniform speed, is employed to generate a sample that represents the entire free-falling stream.

Gy devised a sampling method to calculate the size of a sample that ensures a satisfactory degree of accuracy. The method is based on the understanding that sampling depends on probability such that the more the samples taken then the more accurate will be the analysis.

Gy’s basic equation:

MLL−M

=K d3

σ2

Where:

M is the minimum weight of sample required (g), L is the gross weight of the material to be sampled (g), C is the sampling constant for the material to be sampled (g cm -3), d is the

dimension of the largest pieces in the material to be sampled (cm), and σ is the measure of the statistical error committed by sampling. Generally, M <<<< L, so Gy’s equation approximates to:

M= K d3

σ 2

During sampling with a collecting device that moves through the material as it falls from a conveyor, it is important that:

1. The face of the collecting device is at right angle to the stream2. The cutter covers the whole stream3. The cutter moves at constant speed4. The cutter is large enough to allow the sample to exit

Sampling is done in two stages whereby a primary sampling device passes material to a conveyor that will move the material to another location for crushing and further sample division.

Determining mass of sample when using a linear cutter

A schematic diagram of a linear cutter is shown in Figure 2.2.

Figure 2.2. Linear traversing sampler.

Operations depend on cutter opening, stroke length and cutter speed.

Correct cutter opening sizes ensure that there will be no blockages. Wider cutter openings allow for greater stroke speeds. The stroke length has to cover the width of the whole stream to be sampled.

The amount of sample, M, cut by a linear cutter is given by the following equation:

The amount of sample can be expressed in terms of volume, V i.e.

Example 2.1

Dolomite was carried to the bunkers of a blast fumace at the rate of 200 t/h using a 75 cm wide rubber conveyor belt. The rate of travel of the belt was 61 m/min. The size analysis of dolomite indicated 95 % smaller than 7 cm. The dolomite was sampled as it entered the bunkers using a linear traversing sampler capable of traversing at the rate of 60 cm/s and making 20 cuts per hour. Estimate the mass of sample collected in 10 minutes.

Solution

Feed rate of stream = 200 t/h

Cutter opening = 3 x (0.07) = 0.21m

Cutter speed = (0.6 x 60 x 60) / 20 = 108 m/h

Therefore M/ h = (200x0.21)/ 108 = 0.388t = 388kg

In 10 minutes M = 388/60 x 10 = 64.8 kgs.

The following sample division methods are available:

1. Coning and quartering: Involves pouring material into a conical heap that is then flattened, divided into four equal segments, and discarding two opposite quarters: to remain with two opposite quarters that are combined and further coned and quartered if still too large, until the required sample size is obtained.

2. Table Sampling: Involves feeding material onto an inclined plane with a series of holes that cause material to leak and be discarded. Material that reaches the end of the plane is the sample.

3. The jones riffle: Involves feeding two opposite trays through a V-shaped box with chutes. The material in one tray is discarded and the material in the other tray is treated as the sample for assaying. However, the process can be repeated until the required sample size is required.

4. Online analysis: Uses X-ray fluorescence (XRF) analysis of flowing slurry systems enabling quick detection of quality variations.

5. On-stream ash analysis: Online monitoring of coal ash content by X-ray irradiation of flowing streams, leading to absorption and reflection of the radiation. The variation in absorption coefficient with atomic number leads to ash determination.

Rotary Arc Cutter

The rotary type of cutters (Figure 2.4) allows samples to be collected or passed through as indicated in the segments. For unbiased sampling, the edge of the cutters equals the radius of the circle forming the arc. The effective radius, R, swept out by the cutter at any point, in terms of the distance d from the center of rotation of the cutter to the stream to be sampled along the centerline is given by:

where θ is the angle between the radius of the cutter and the centerline of the solids stream.

The cutter opening changes as the cutter moves through the stream, then by simple geometry, the effective cutter opening, dcutter, at any point is approximately given by:

Figure 2.4. Continuous rotary arc sampler.

If ω is the rotational speed (rpm) of the cutter then the cutter speed, Scutter, parallel to the solid

stream, can be given by:

Use of statistical tools in sampling

An accurate measurement is the one with the difference between the measured value and the true

value that falls within an acceptable margin. When the true value of the assay is unknown then

the confidence we have in the accuracy of the measured value is also unknown. To increase our

confidence in the measured value, we use the statistical theory.

A random error (or variation) on average, over a period of time, tend to zero whereas integrated

systematic errors result in a net positive or negative value (Figure 2.5).

Figure 2.5. Random and systematic errors

The bias is the difference between the true value and the average of a number of experimental

values and hence is the same as the systematic error. The variance between repeated samples is a

measure of precision or reproducibility. The difference between the mean of a series of repeat

samples and the true value is a measure of accuracy (Figure 2.6).

Figure 2.6. Precision and accuracy

Precision does not necessarily imply accuracy. Accuracy is tested by calibration procedures and

precision is tested by repeating tests. If there is no bias in the sampling regime, the precision will

be the same as the accuracy. Normal test results show that assays differ from sample to sample.

For unbiased sampling procedures, these assay differences are not due to any procedural errors.

Rather, the term "random variations" more suitably describes the variability between primary

sample increments within each sampling campaign.

Random variations are an intrinsic characteristic of a random process whereas a systematic error

or bias is a statistically significant difference between a measurement, or the mean of a series of

measurements, and the unknown true value (Figure 2.5). Applied statistics plays an important

role in defining the difference between random variations and systematic errors and in

quantifying both.

The most important parameter for a population is its average value. In sampling and weighing

the arithmetic mean and the weighted mean are most often used. Other measures for the average

value of a series of measurements are the harmonic mean, and the geometric mean. Mode and

median are measures of the central value of a distribution. The mode forms the peak of the

frequency distribution, while the median divides the total number of measurements into two

equal sets of data. If the frequency distribution is symmetrical, then its mean, mode and median

coincide as shown in Figures 2.7 and 2.8.

Figure 2.7. Normal distribution.

Figure 2.8. Asymmetric distribution.

The Arithmetic Average x of a discrete set is defined as:

x= 1N

( x1+x2+x3+...+xn )

x= 1N∑i=1

N

x i

The weighted average xM of a discrete set is defined as

xM= 1

∑i=1

N

M i

∑i=1

N

M i x i

The weighted percentage is calculated, either from the total number of particles in each series, or

by multiplying each incremental percentage with the mass in each corresponding increment, and

by dividing the sum of all products by the total mass for each series. However, the small error

that is introduced by calculating the arithmetic mean rather than the weighted average is well

within the precision of this sampling regime. Due to random variations in the mass of each

primary increment the weighted average is a better estimate of v, the unknown true value, than

the arithmetic mean.

The Median, x́

It is the value of a characteristic that splits the probability distribution into two sets of equal proportion or frequency.

The mode, x̂

It is the value of a characteristic where the probability reaches global or local maximum (i.e. the most probable result). A probability distribution may have several modes.

The double poisson distribution

Basic dispersion parameters

Consider a binary mixture of quartz and hematite particles with approximately 10% hematite.

Samples are taken and the number of hematite particles is counted to obtain the percentage of

hematite in the sample. Table 2.1 gives the result often samples. For a binomial sampling unit the

range is (maximum value - minimum value) = 12.6 - 5.7 = 6.9%.

Table 2.1. Sampling with a binomial population

If each series of measurements is placed in ascending order, then the range is numerically equal

to xn – x1 so that the range does not include information in increments x2, x3….,xn-1. For a series

of three or more measurements the range becomes progressively less efficient as a measure for

variability as indicated in Figure. 2.7. For two samples, the range is the only measure for

precision but this is not sufficient to estimate the precision of a measurement process. The

precision of a measurement process requires the mean of absolute values of a set of ranges

calculated from a series of four or more simultaneous duplicates.

The easiest way to measure the dispersion of values xi is to compare them to their arithmetic average x, which can be done by measuring all these differences xi - x. Because the average of all these differences equals zero it is convenient to work with square of the differences (x i - x)2. Thus, we can define the experimental estimate of the sample variances as follows:

s2= 1N∑i=1

N

( xi−x)2

In practice we use the variance for calculation because only the variance has additive properties. In practice the square root of the averages of all the squared differences (i.e. the variance) is defined as the experimental estimate, s of the true standard deviation σ .

σ=√ 1N ∑

i=1

N

( x i−x )2

It is important to note that standard deviations cannot be added; only variances can be added.

The variance, and its derived parameters such as the standard deviation and the coefficient of

variation, is the most important measures for variability between test results. The standard

deviation is the square root of the variance. The coefficient of variation (CV) is a measure of

precision and is numerically equal to:

Variance values from a sampling procedure with a binary mixture of mineral particles are given

in Table 2.2. The physical appearance of a sample that consists of fifty primary increments of 5

kg each is similar to that of a sample containing five increments of 50 kg, or to that of 250 kg of

a bulk solid. However, the difference in intrinsic precision (as indicated by the variance) may be

dramatic, particularly if the variability within the sampling unit is high. In practical applications

of sampling bulk solids we compromise by collecting and measuring unknown parameters on

gross samples, and by reporting x, the sample mean as the best estimate for v, the unknown true

value. If all increments are contained in a single gross sample, we have no information to

estimate the precision of this sampling regime. If we want to know more about the precision of

samples, systems and procedures, it is essential that duplicate or replicate measurements be

made, from time to time, to determine the coefficient of variation for each step in the chain of

measurement procedures.

Table 2.2. Variance values from the sampling example with a mixture of quartz and hematite

Other convenient measures for precision are confidence intervals (CI) and confidence ranges

(CR). 95 % confidence intervals and 95 % confidence ranges may be used, although if concern

over sampling precision is high, then 99% or 99.9% confidence limits must be considered. That

is, if we repeat a particular experiment 100 times, then 95 times out of 100 the results would fall

within a certain bound about the mean and this bound is the 95 % confidence interval. Similarly,

confidence limits of 99 % and 99.9 % mean that 99 times out of 100, or 999 times out of 1000

measurements would fall within a specified or known range. In the draft Australian Standard,

DR00223, for estimating the sampling precision in sampling of particulate materials, a

confidence interval of 68% is chosen.

Fortunately, we don't need to repeat a measurement one-hundred times if we want to determine

its 95% confidence interval, either for individual measurements or for their mean. Applied

statistics provides techniques for the calculation of confidence intervals from a limited number of

experiments. The variance between increments, or between measurements, is the essential

parameter.

The most reliable estimate of σ 2 is var(x), the variance of the sample. The reliability of this

estimate for σ 2 can be improved by collecting, preparing and measuring more primary

increments, or by repeating a series of limited experiments on the same sampling unit. The 95 %

confidence interval for a normal distribution is equal to ±1.96σ from the distribution mean. In

practice, we often use the factor 2 instead of 1.96, to simplify calculations and precision

statements. The 68 % confidence interval is equal to ±0.99σ , for infinite degrees of freedom and

if the number of replicate results exceeds 8 then a factor of 1.0 is an acceptable approximation.

Application of Gy’s Method - Mineral Particles Differing in Size

The Gy’s formula can be written as:

Where:

dmax – is the dimension of the largest particle

Mmin – minimum mass of sample required

σ2 – variance allowable sampling error in an assay (equals standard deviation for a normal

distribution)

K – sampling constant (kg/m3)\

dmax is taken as the screen aperture through which 90-95% of the material passes. Since the

probability of events when 95 out of 100 assays would be within the true assay value is

represented by 2σ, 2σ is the acceptable probability value of the sample. K is a function of

material characteristics:

K = PsPDPL.m

See Table 2.3

PL is related to the largest particle size dmax and to the liberation size dL of the mineral in the

sample space. Table 2.3 is used to determine PL. In practice, PL is rarely below 1.0 and if the

liberation size is not known, it is safe to assume that PL is 1.0.

Table 2.3. Liberation factor as a function of largest particle size and liberation size.

The total variance of a sample σ T is the sum statistical errors during sampling, σ S and the

statistical error of the assay, σ A, i.e. σ T2=σ S

2+σ A2

σ T2=σ S

2+σ A2

The standard deviation, σp, of mineral particles in an infinite lot where the mineral has been

mixed with gangue and the particles are large enough to be counted is determined using the

formula:

Where:

Example 2.2

Regular samples were required of the feed to a copper processing plant, having a copper content

of about 9%. The confidence level of estimation was required to be 0.1 % Cu at 2σ standard

deviation. The liberation size of the Cu mineral (chalcocite) in the ore was determined to be 75

µm. The top size of the ore from the sampler was 2.5 cm. Determine the minimum mass of

sample required to represent the ore. Given; the density of chalcocite is 5600 kg/m3 and the

density of the gangue is 2500 kg/m3.

Example 2.3

A composite sample of galena and quartz was to be sampled such that the assay would be within 0.20% of the true assay, of say 5.5 %, with a probability of 0.99, ie. the sample assay would be 5.5 % ± 0.20 %, 99 times out of 100 . Given that the densities of galena and quartz were 7400

kg/m3 and 2600 kg/m3 respectively and the average particle size was 12.5 mm with a mass of 3.07g, determine the size of the sample that would represent the composite. Use Table 2.4 for your answer.

Table 2.4. Probability P vs deviation X, relative to unit standard deviation.

Peculiarities about the Sampling of Precious Metals

They can be divided into three categories: Financial, Theoretical and Practical.

Financial Peculiarities

The sampling is very challenging yet small amounts of material can involve very large amounts of money. Due to the financial implications, the achievement of sampling precision and accuracy is very critical.

Theoretical Peculiarities

Precious metals are economic at very low levels and their sampling therefore involves traces.

Practical Peculiarities

Practically, there are a lot of difficulties involved in sampling precious metals. Gold is a classic example of a mineral that is not very easy to sample, for the following reasons:

1. The gold content of a sample and the gold content of the surrounding ore can be very different.

2. The gold content of a tiny analytical subsample and the gold content of the sample from which it was selected can also be very different.

3. The density of gold is enormous (λAu = 19.3), promoting strong segregation phenomenon as soon as gold is liberated.

4. Gold nuggets do not commune very well, therefore gold smears and easily coats sampling equipment.

The above problems increase as the grade of ore decreases, as gold deposits become marginal and as the distribution of gold in rocks becomes erratic.

Practical Examples:

1. Determination of sample weight to be collected:

Method 1: Using allocated variance, S2FE – Applies when the metal is liberated

We assume that the weight ML of the lot is larger than MS by several orders of magnitude.

1. The first step is to calculate the allotted variance S2FE:

2. We then calculate the constant factor of constitution of heterogeinty IHL:

IHL = 0.8aL

d3; aL = element content and d is the largest particles of element

3. Calculation of minimum sample weight, Ms, using the formula:

M s=I H L

s FE2

Method 2: Using sampling constant, C – Applies when metal is not liberated

C = 1

2 SFE( amax

aL

−1) density of metal xdensity of ganguedensity of gangue ( amax )+density of gold (1−amax)

amax = maximum grade

aL = expected average grade at the same size as amax

then IHL = Cd3;

therefore

M s=I H L

s FE2