---
title: "Mineral Processing Technology"
tags : "SEM3"
---
# Mineral Processing Technology

## Introduction

Minerals are natural inorganic substances possessing definite chemical compositions and atomic structures.

Many minerals exhibit isomorphism – substitution without change in atomic structure

Polymorphism – Same chemical composition but different physical properties due to a difference in crystal structure

Mineral is often used in a more extended way – anything economic value – extracted from earth – Coal, Chalk, Clay, and granite.

Granite – Igneous rock – mineral components occur in ranging proportions – feldspar, quartz, mica
Coal – Various forms – peat, lignite, bituminous, sub-bituminous, anthracite

If minerals were uniformly distributed their extraction would be impossible
Natural agencies form clusters – making it affordable

Ores – Mixture of extractable minerals and extraneous rocky material described as gangue
Complex ore – contain multiple minerals
Sulphide ores – contain the metal as sulphides
Oxidized ore – valuable mineral may be present as oxide, sulphate, silicate, carbonate, or some hydrated form of these.
Ore – can be described as an accumulation of mineral in sufficient quantity as to be capable of economic extraction

Gold –> 5 PPM
Iron –> 15%

Customers and End users of mineral processing - Metalurgists, Cement Engineers, Steel Makers

Mineral Processing - To add value to mineral and consider it as ore deposite

Sequence of Operation -
- Liberation/ Breaking/ Comminution (make it smaller)
- Seperate
- Concentrate

### Extraction

Copper Ore - Low Grade - 1 to 1.2% metal content
In order to produce metals, the ore must be broken down by the action of heat (pyrometallurgy), solvents (hydometallurgy) or electricity (electrometallurgy), either alone or in combination, the most common method being the pyrometallurgical process of smelting. These methods consume vast quantities of energy.

#### 1. Transportation Cost - Minimizator Route

Smelters are often remote from mine site, where energy is relatively cheap

Essential purpose of MP - reduce the bulk of ore - transported to and processed by the smelter

MP is carried out at the mine site - mill/concentrator

Enrichment process - increases content value

#### 2. Improvement in Enrichment ratio

Cu ore - 1% Cu wanted, 99% unwanted
:arrow_right_hook: Cu ore - 20% Cu wanted, 80% unwanted

#### 3. Selection of Seperation methods

Usually physical process
Chemical Methods - problems related to chemical recycling

#### 4. Impurities

MP - reduced smelter energy costs and smelter metal losses due to less-metal bearing slag

The process also helps in removing deleterious impurities which makes the smelting operation sometimes inefficent.

Indian Iron ore has Alumina (4-5%) - increases input energy cost - to 1-2%

Duty of MP Engineer - Providing most economical viable route of separation

Remove arseno-pyrites

#### 5. Tailing and its Treatments

Tailing - loose wanted component from gangue

#### 6. Development of New Technology for lean ore processing

Froth floatation - allowed exploitation of vast low grade copper desposits and other low grade ores which were previously uneconomical to treat

#### 7. Separation of Complex Ore

Copper Sulphide ore - Copper, lead and zinc in economic amount

---
MP operation are often a compromise between improvements in metallurgical efficiency and milling cost

Less tonnage should be required

Apart from processing costs and losses, other costs which must be taken into account are indirect costs such as ancillary services
- Power Supply
- Water
- Transport
- Tailings handling
- Taxes
- Investments Requirements
- Research and Development
- Medical and Safety costs

---
### Mineral Beneficiation

Ore is aggregate of minerals and contains valuable and gangue minerals
The _mineral beneficiation_ involves *separation of gangue minerals from ore*
Mineral Beneficiation has 3 steps -
- Liberation
- Separation
- Concentration

##### How far do we break the ores?

Liberation - comminution
Liberation of valuable mineral - size reduction
Amount of gangue particle accepted - decided by metallurgist
Separation of coarse and fine particles
Tailing - Large amount of gangue compared to valuable mineral
Concentration to separate the gangue minerals to increase the metal grade.

- Liberation by size reduction
- Crushing
- Crystals in the ore are intimately joined to each other
- Minerals of equal abundance
- Cube is sectioned along a vertical plane
- Visualize that lattices with parameters 10mm and 5mm are superimposed
- Minerals of unequal abundance
- The less abundant mineral is not free at all unless the particles are finer that the grain size
- To free the less abundant mineral, the particles must be made much finer than the grain size
- The more abundant mineral is always freer than the less abundant mineral
- Liberation by detachment
- If the ore lump is made of mineral grains bonded loosely, fracturing to the grain size results in complete liberation

### Grade-Recovery curve

Compromise solution - economics and quality requirements
Ore deposit - Economical term
Mineral deposit - Geological term

Optimum grade we should target - which gives us maximum profit

The recovery is the percentage of the total metal contained in the ore that is recovered in concentrate.

A recovery of 90% means that 90% of the metal in the ore is recovered in the concentrate and 10% is lost in the tailings

Grade - content of the marketable end product in the material

Enrichment ratio is the ratio of the grade of the concentrate to the feed and it is related to the efficiency of the process

The ratio of concentration is the ratio of the weight of the feed to the weight

There is an approximately inverse relationship between the recovery and the grade of concentrate in all concentrating processes

The mineral processor's challenge is to move the whole curve to a higher point so that both grade and recovery are maximized.

NSR = Payment for contained metal - (smelter charges + transport costs)

Chnages in metal price, smelter terms, etc. obviously affect the NSR - concentrate grade curve, and value of the optimum concentrate grade
Metal prices increases - optimum grade will be lower - allowing higher recoveries to be attained

### Metallurgical Efficiency

Concentrate grade and recovery , used simultaneously, are the most widely accepted measures of assessing metallurgical (not economic) performance

Separation efficiency (S.E.) = R~m~ - R~g~

R~m~ - % recovery of valuable mineral
R~g~ - % recovery of the gangue into the concentrate

Feed - f% metal
Concentrate - c% metal
Tailing - t% metal
C - fraction of the total feed weight that reports to the concentrate

$R_m = \frac{100Cc}{f}$

Recovery of valuable mineral to the concentrate is equal metal recovery, assuming that all the valuable metal is contained in the same mineral

The Gangue content of the concentrate = 100 - (100c/m)%

where m is the percentage metal content of the valuable mineral

Similarly gangue content in feed = $100 (\frac {m-c}{m})$

$R_g = C \frac{\text{Gangue content of concentrate}}{\text{gangue content of feed}} = 100C \frac {(m-c)}{m-f}$

So Separation Efficiency,

$SE = R_m - R_g = 100 Cm \frac{(c-f)}{(m-f)f}$

# Particle Characterization

Particle technology is devoted to the understanding of particle-particle and particle-fluid interactions and using this knowledge to properly design processes and products

Particle Characterization presents special challenges that don't exist for the measurement of fluid properties
- The discrete nature of a particulate system means that it is heterogeneous
- Two particles in the same system dont have the same properties
- The properties of particulate systems can't be tabulated like the thermodynamic properties of fluid can
- The Properties of the system depend not only on the chemical composition, but also the particle morphology

## Particle Shape

- Affects flow ability, packing density and particle-fluid interactions
- Shape is very complicated to define and measure

Intrinsic Difficulties - Each non-spherical particle is unique in itself and requires more than one attribute to describe it

For Regular Shaped Objects - 3 aspects need to be quantified
- Size
- Equal Volume sphere diameter, d~s~
$\qquad d_s = \left( \frac{6V_p}{\pi} \right)^{\frac 13}$
- Shape
- Sphericity, $\psi$
$\qquad \psi = \frac {\text{Surface of equal volume sphere}}{\text{Syrface area of particle}}$
[Sphericity for Common Objects](https://en.wikipedia.org/wiki/Sphericity#:~:text=3%7D%7D%7D%7BA_%7Bp%7D%7D%7D%7D-,Sphericity%20of%20common%20objects,-%5Bedit%5D)
- Orientation
- Projected area or diameter qual area circle d~o~

## Paricle Size

Most Important property of particle - strongly influences other important particle properties

Size controls - Surface forces and body forces - surface forces dominant as size becomes small

### What Size is Measured?

- Laser Diffraction - Equivalent Spherical Diameter - 10mm to 50nm size range
- Dynamic Light Scattering - Hydrodynamic Radius
- Image Analysis - Length, Width, Equivalent Spherical
- Acoustic Spectroscopy - Equivalent Spherical Diameter - 100 µm to 10nm

### Particle Size Distribution Models

Some of the more common methods are -
- Sieve Analysis - 5-100,000 µm
- Sedimentation Methods - 1-40 µm
- Elutriation Techniques - 5-45 µm
- Microscopic Sizing and Image Analysis - 0.2-50 µm
- Electrical Impedance Method
- Laser Diffraction Methods - 0.1-2000 µm

| Method | Size |
| ----------------------- | ------------ |
| Electroformed Mesh | 38µm + |
| Sedimentaion | 0.5 - 5µm |
| Acostic Spectroscopy | 0.1 - 1000µm |
| Optical Microscopy | 0.8 - 150µm |
| Electron Microsopy | 0.001µm + |
| Electrical Conductivity | 0.4 - 1200µm |
| Laser Diffraction | 100nm - 1mm |
| Dynamic Light Scattering | 0.1nm - 10µm |

For analysis of particle size less than 40 µm - Sedimentation, Elutriation, Microscopy and Laser diffraction is used

#### Sieve Analysis

Passing a known weight of sample material successively through finer sieves and weighing the amount collected on each siece to determine the percentage weight in each size fraction

The machine used is called Ro-Tap or Sieve Shaker Screens with increasing mesh number from top to bottom

Selection on Sieve

- Compromise - accuracy, time, cost
- Select Sieves as close as possible
- Thumb Rule
- Top - 5% retained
- Bottom - 5% passed

Lab Screens are made of brass(dry) or stainless steel(wet)

200 mesh - 75 µm - Roughly

Test Sieves - designated by - Nominal aperture size - Nominal central separation of opposite sides of a square aperture or the nominal diameter of a round aperture.

Woven wire sieves - Mesh number

Mesh Number is the number of wires per inch, which is the same as the number of square apertures per square inch

D90: The portion of particles with diameters below this value is 90%

#### Rosin-Rammler Distribution

- Coal Particles - Coal Beneficiation
- Coals - Minerals and Naturals

$100 - P = 100 \text{ exp}(bd^n)$

P - Cumulative Undersize in percent
d - Particle size
b and n are constants

$\text{log}\left[\text{ln}\displaystyle\frac {100}{100-P}\right] = \text{log b} + \text{nlog d}$

#### Gaudin-Schuhmann Distribution

- Mineral Particles

$y = 100\left[\left(\displaystyle\frac xk\right)^a\right]$

y - cumulative mass % retained on size x
x - screen aperture size
a and k are constants

- This plot severely contracts the region above 50% and especially above 75% which is a major disadvantage of the method

#### Sub-Sieve Technique

- Sieveing is rarely carried out on a routine basis below $38 \mu m$
- Below this size the operation is refered to as sub-sieving
- Most widely used methods are **sedimentation, elutriation, microscopy, and laser diffraction**, although many other techniques are available

## Points to Remember

- Geting a representative sample is vital

- Use caution when comparing size distribution measured by different techniques - Very large errors can occur from converting from one form of size distribution to the other

- Microscopy is good technique for sizing paint pigment because projected area is the property of interest

- If fine dust is present in the sample - dry sizing and wet sizing will give give different size distribution

## Other Particle Properties

- Density - True, apparent (includes internal pres), Aerodynamic (includes internal pore) - Fluid Displacement
- Surface area - Caplillary pressure, permeability, nitrogen adsorption
- Shape - Image analysis
- Porosity - Mercury Porosimetry, nitrogen adsorbtion
- Surface Energy - Contact angle studies
- Friction - Surforce apparatus
- Hardness - Particle compression and breakage, Indentation (both micro and nano techniques)
- Defects - Micro caloriemetry
- Thermal Properties - Microcalorimetry
- Hygroscopicity
- Electrical and magnetic properties
- Refractive Index

| Particle Property | Characterization Technique |
| ----- | ----- |
| Density - True (Internal Pores), Aerodynamic (Internal and External Pores) | Fluid Displacement (Liquid or gas pyenometers) |
| Shape - Aspect ratio, shape factors, crystal habitm fourier series expanison, fractal dimensions | Image analysis, size distribution data |
| Surface area | Caplillary pressure, permeability, nitrogen adsorption, Size distribution data |
| Porosity | Mercury Porosimetry, nitrogen adsorbtion |
| | |

### Density

Bulk Density - Mass of many mineral particles of the meaterial divided by total volume they occupy

The total volume includes particle volume, inter-particle void volume and internal pore volume

Bulk Density is not an intrinsic property of a material
It can change depending on the material is handled

Skeletal Density
- $10 \mu m$ particle measure volume of gas or liquid displaced by the solids
- Use a liquid that completely wets the solid - Liquid pyncometer
- Use an inert gas, volume displaced calculated from measurements at two pressures assuming ideal gas equation

Particle (apparent density)
- Inportant for fluid particle interaction
- Most difficult density to measure
- Very difficult for small particles

### Angle of Repose

- The angle of repose or the critical angle of repose of a granular material is the steepest angle of descent or dip of the slope relative to the horizontal plane when material on the slope face is on the verge of sliding

- Used to design equipment for processing of particular solids

- Greater the angle of repose taller the cone

$\theta = \text{tan}^{-1}\left(\displaystyle\frac hr \right) \approx \text{tan}^{-1}(\mu_s)$

## Sampling

Procedure by which some members of a population are selected as representative of the entire population

Main aim - Minimize bias

Assay Analysis - Gold ore processing
Moisture Analysis - Coal processing
Size analysis - Laboratory/Industry
Flow Rates
Characterization - Properties
Process Control - On stream analyzer, Modeling, Simulation

### Fundamental Statistical Terminologies

A measurement is considered to be accurate if the difference between the measured value and the true value falls within an acceptable margin

Bias - Difference between the true value and the average of a number of experimental values and hence is the same as the systematic error

Variance - Measure of precision or reproducibility

Accuracy - Difference between mean and true value

Minimizing or preferably elminating biases is more important than improving precision for metallurgical accounting

Propagation of error

#### What would be the minimum mass of the sample?

Gy's basic sample equation can be written
$\qquad \displaystyle \frac {ML}{L-M} = \frac {Cd^3}{s^2}$

M - Minimum weight of sample required (g)
L - gross weight of material to be sampled (g)
C - sampling constant for the material to be sampled (g cm ^-3^)
d - dimension of the largest pieces in the material to be sampled (cm)
s - measure of statistical erroe committed by sampling

When M < L
$\qquad M = \displaystyle\frac{Cd^3}{s^2}$

The sampling constant "C" is specified to the material being sampled, taking into account the mineral content, and its degree of liberation.

$C = fglm$

f - shape factor - 0.5 - except for gold ore - 0.2
g - factor dependent on the particle size range

If approximatelt 95% of the sample weight contains particles of size less than 'd' cm, and 95% of size greater than 'd''cm, then if

$\frac d{d'} > 4 \qquad g = 0.25$

$\frac d{d'} > 2 \qquad g = 0.5$

$\frac d{d'} < 2 \qquad g = 0.75$

$\frac d{d'} = 1 \qquad g = 1$

Gy's method of calculating "l"

$l=\left(\displaystyle\frac Ld\right)^{0.5}$

| d/L | <1 | 1-4 | 4-10 | 10-40 | 40-100 | 100 - 400 | >400 |
| --- | --- | --- | -----|------|-----|----|---|
| l | 1 | 0.8 | 0.4 | 0.2 | 0.1 | 0.05 | 0.02 |

"L" is the liberation size of the material to be sampled (cm)

"d" is the dimension of the largest pieces of the material to be sampled (cm)

"m" is a mineralogical composition factor which can be calculated from the expression

$m = \displaystyle\frac {1-a}a \{(1-a)r+at\}$

a - Fractional average mineral content
r - Mean density of valuable mineral
t - Mean density of gangue mineral

Sampling requirements
- Average assay/grade content
- Largest/Smallest particle size
- Mineralogical composition
- Adapt sampling techniques

#### Common Sample Preparation Errors

- Contamination
- Losses - Adsorption, condensation, precipitation
- Alteration of chemical composition (prevention)
- Alteration of physical composition - Agglomeration, breaking of particles, moisture
- Involuntary Mistakes - Mixed sample numbers, lack of knowledge, negligence
- Deliberate Faults - Deliberate error in increment delimitation, forgery

### Plant Sampling

#### Planning of Sampling

1. Gathering of information
- Analytes to be determined
- What kind of estimates are needed
- Frequency (hourly, daily, shift, batch, shipment, etc.)
- Distribution (heterogeneity) of the determinand in th e lot
- Highest or lowest values - Assay/tailing
- Priory information - Variance estimates, unit costs
- Necessary personnel and equipment available
- Maximum cost or uncertainty level of the investigation
2. Decisions to be made
- Manual vs Automatic Sampling
- Sampling Frequence
- Sample Sizes
- Sampling locations
- Individual vs Composite samples
- Sampling Strategy
- Random selction
- Stratified random selection
- Systematic stratified selection
- Training - Sampling with minimum bias

#### Moving Stream

- Best way - correctly designed sample cutter at right angle at te discharge point of a conveyor belt, chute, or slurry pipe
- Sampling devices which take only part of stream - likely to introduce serious bias
<br>
- Most automatic samplers operate by moving a collecting device through the material as it falls from a conveyor or a pipe
1. The face of the collecting device or cutter is present at right angles to the stream
2. The cutter covers the whole system
3. The cutter moves at constant speed
4. The cutter is large enough to pass the sample

# Comminution

- Fragmentation
- Disintegration

Size Reduction - Why?
- Liberation
- Transport
- Customer's Requirement

Size reduction in early stages is carried out in order to make freshly excavated material easier to handle by scrapers, conveyors and ore carriers
Expolsives in mining can be regarded as the first stage

Most minerals are finely disseminated and intimately associated with the gangue - liberated or unlocked - separation
This is achieved by comminution in which the particle size of the ore is pregressively reduced - clean particles of mineral can be separated

## The Size Reduction Process

Minerals being crystals have a tendency to break into endless numbers of sizes and shapes
The difficulty in size reduction - art of limiting the number of over and under sizes produced


When producing quality products from rocks and minerals - keep size reduction curves as steep as possible

We need to select the correct set of techniques for size reduction in a proper way

Different equipment have different reduction technique, reduction ratio, feed size,etc. and have to be combined in a optimum way to reach or come close to the requested size interval for the end product.

### Mechanism of size reduction

- Impact - Particle concussion by a single rigid force (hammer)
- Compression - particle disintegration by two rigid forces(nutcracker)
- Shear - produced when the particle is compressed between the edges of two hard surfaces moving tangentially
- Attrition - arising from particles scraping against one another or against a rigid surface (a file)


### Types of Impact

- Gravity Impact
- In gravity impact, the free falling material is momentarily stopped by the stationary object.

- Dynamic impact
- Most often used when it is necessary to separate two material which have relatively different friability
- The more friable material is broken first
- Preferential breakage

Compressive forces can be used when material is - hard, abrasive, not sticky - where the product is to be relatively coarse in size

### Factors affecting size reduction

Hardness
- It is a surface property of the material
- An arbitrary scale pf hardness has been devised known as Mohs Scale - scratch technique

Mohs Scale
=1 - Graphite
<3 - Soft Material
\>7 - Hard Material
=10 - Diamond

## Comminution Fundamentals

### Material Structure

- Homogeneous in character - easy to comminute
- Mineral substances may have lines of weakness along which the materials split to form flake-like particles

### Abrasiveness

- Wear Property
- Property of hard materials
- May limit the type of machiney that can be used
- During the grinding of some very abrasive substances the final powder may be contaminatied with more than 0.1 percent of metal worn from the grinding mill

### Moisture content

- It is found that materials do not flow well if they contain between about 5 and 50 percent of moisture
- Material tends to cake together in the form of balls
- Problem of agglomeration
- grinding can be carried out satisfactorily outside these limits

### Crushing Strength

The power required for crushing is almost directly proportional to the crushing strength of the material

### Friability

- Tendency to fracture during normal handling
- Crystalline material will break along well-defined planes and the power required for crushing will increase as the particle size is reduced

### Stickness

- A sticky material will tend to clog the grinding equipment
- Ground in a plant that can be cleaned easily

### Soapiness

- Measure of friction
- Low friction - crushing can be difficult

### Explosive

- Such materials must be wet or in an inert atmosphere
- Yielding dust could be harmful to health
- Dust should not escape

## Design of Size Reduction Processes

The process of size reduction is normally designed to take place in
- Single stage open circuit
- Single stage closed circuit
- Multiple stage open or closed circuit
- Combination of these methods

Single stage, single pass, open circuit size reduction operation, the product consists of range of particles sizes which seldom achieves the desired degree of liberation

- Second or third stages of size reducation are necessary to progressively reduce the remaining particle size to liberate mineral particles to an acceptable degree

| Open Circuit Crushing | Closed Circuit Crushing |
| -------- | -------- |
| Undersize material from the screen is combined with the crusher product and then routed to next operation | Undersize from the screen is the finished product and over size is recirculated |
| Often used in intermediate crushing stages or when the secondary crsuhing plant is producing ball-mill feed it is good practise to use closed | Closing the circuit gives the crushing plant flexibility |
| Not all ores can be crushed using this systems, the properties of the material should be known and material should be homogeneous | The properties of materials should not be know and it need not be homogeneous so awider variety of ores can be used
|  |  |

Two most commonly kused devices for size reduction are the crushers and grinding mills

Crushers - rocks 1m in size
Grinder - maximum rock size 50mm

In designing a plant for size reduction the two main features of interest are
- The power required for size reduction
- The choice of crushers and grinders

## Energy for size reduction - Work Index

It had been generally observed that in the process of size reduction, as the size of the particles diminishes the surface area of the particles increases

So a measure of size or surface areabefore and after size reduction would indicate the extent of energy expended in the comminution process

If E is the energy used for a desired size reduction, which resulted in a change in surface area S

$dE = k[S^ndS]$

k - constant and a function of the crushing strength of the rock

n = -2 (Rittinger)
n = -1 (Kick)
n = -1.5 (Bond)

Rittinger - coarse size reduction
Kick - finer size
Bond - almost covers entire range of particles

Substituting n = -1.5 and integrating we get

$E = 2k \displaystyle\left[\frac{1}{\sqrt P} - \frac{1}{\sqrt F}\right]$

F - Feed particle size
P - Product Particle size
k - constant and function of ore characteristics

For size distribution we use passing size

Bond's Work Index (Closed Circuit grinding)

$W = 10 WI\displaystyle\left[\frac 1{\sqrt P_{80}} - \frac 1{\sqrt F_{80}}\right]M_f \,\text{ kWh}$

W - work energy input per tonne/hour

WI - Operating work - A constant for the ore

WI is known as Bond work index and represents the work required to reduce the ore from an infinite size to $100\mu m$

P~80~,F~80~ - 80% passing size of Product and Feed respectively ($\mu m$)

Rittinger's Theory
- Energy α new surface area formed
- n = -2

Bond's Theory
- Energy used in cracking α Crack length produced
- n = -1.5

Rittinger's Theory
- Energy α Ratio of change in size
- n = -1

### Energy Utilization

Distribution of the energy fed into a crusher was carried out by OWENS who concluded that energy was utilized as follows
- Elastic deformation before fracture
- Inelastic deformation - size reduction
- Elastic distortion of equipment
- Friction between particles and between particles and machine
- Noise, heat and vibration
- Friction losses in plant itself

Owens estimated only about 10 per cent of total power is usefully employed

### Estimation of Work Index for crushers and grinding mills

The standard laboratory procedures for estimating work index can be divided into two categories

- Involves tests on individual particles of rock
- Bulk rock material

Standard laboratory procedures adopted in industry to get an idea of the rock strength
- Bond Pendulum test
- Narayanan and Whitens rebound pendulum test
- JKMRC drop Test - Julius Kruttschnitt Mineral Research Centre
- Bond ball mill grinding test
- Bond rod mill grinding test


### What exactly is the "Work Index"?

"Work Index" is the unit used to measure the energy in size reduction

It is a standard measure that brings all size reduction circuits onto a common basis for comparison

Estimating the new production rate by changing one of the variables is just one of the ways you can use this equation

Work Index Efficiency
- The ratio betweeen the test work index and the operating work index

w~lo~ < w~lt~ - circuit is more efficient than the average
w~lo~ > w~lt~ - less efficient

## Crushers

### Comminution and Sizes


Crushing - 24hr job
Mining - 16hr job

Crushing is the first mechanical stage in the process of comminution in which the main objective is the liberation of the valuable minerals from the gangue

It is generally a dry operation and is usually performed in two or three stages

Crushers capacity should match with the rate of production of mining actvities - synchronization

Lumps of run of mine ore can be as large as 1.5m across and these are reduced in the primary crushing stage to 10-20cm in heavy-duty machines

### Primary crushers

Heavy-duty machines - run-of-mine ore down to a size suitable for transport and for feeding the secondary crushers or AG/SAG mills

Crushers are operated in open circuit, with or without heavy-duty scalping screens (grizzlies)

Mainly two types
- Jaw Crushers
- Gyratory Crushers

#### Jaw Crusher

The distinctive feature of this class of crusher is the two plates which open and shut like animal jaws

The jaws are set at an acute angle to each other and on jaw is pivoted so that it swings relative to the other fixed jaw

The mechanism of crushing is either by applying impact force, pressure or a combination of both

The jaw crusher is primarily a compression crusher while the others operate primarily by the application of impact

Soft - Compressive Forces
Hard - Impact forces

Jaw Crusher Type
- Blake
- Pivot at Gape (top)
- Control Feed Size
- Industrial Application
- Dodge
- Pivot at the Set (bottom)
- Control product size
- Laboratory Application
- Universal
- Pivot at the center

Jaw crushers are rated according to their receiving areas - Width of plates and gape

Single Toggle vs Double Toggle Jaw Crusher
- Single-toggle jaw crushers - the swing jaw is suspended on the eccentric shaft which allows a lighter, more compact design than double-toggle
- ST - high capacity for the same size of gape
- Direct attachment of the swing jaw to the eccetric imposes a high degree of strain on the dirve shaft, and so maintenance costs tends to be higher than with the DT machine
- DT cost 50% more - usually used on tough, hard, abrasive materials
<br>
At crushing rates above 545t/h the economic afvantage of the jaw crusher over the gyratory diminishes; and above 725t/h jaw crushers cannot compete with gyratory crushers

#### Gyratory Crushers

- Used in surface crushing plants, a frew currently operate underground

- The gyratory crusher consists essentially of a long spindle, carrying a hard steel conical grinding element, the head, seated in an eccentric sleeve

#### Selection - Crusher

In mines with crushing rates above 900t/h, gyratory crushers are always selected

Gyratory crushers range in size up to gapes of 1830mm and can crush ores with top size of 1370mm at a rate of up to 5000 t/h with a 200 mm set

Gyrator crushers have high power consumption - 750 kW

If t/h < 161.7(gape in meters)^2^, use a jaw crusher

##### Crushing Capacity

Crushing capacity depends on - angle of nip, stroke, spped, the liner material as well as feed material, inital particle size

Capacity problems do not usually occur in the upper and middle sections of the crushing cavity, providing the angle of nip is not too great

Discharge zone determines the crushing capacity

The Type of material being crushed may also determine the crusher used - Jaw crushers perform better than gyratory crushers on clayey, plastic material, due to their greater throw

Gyratory Crusher have been found to be particularly suitable for hard, abrasive material, and they tend to give a more cubic product than jaw crusher if the feed is laminated or "slabby"

### Secondary Crushers

Secondary Crushers are much lighter than the heavy-duty, rugged primary

Since they take the primary crushed ore as feed - less than 15cm in diameter - most harmful constituents in the ore, such as tramp metal, wood, clays, ans slimes have already been removed - easier to handle

Similarly, the transportion and feeding arrangements serving the cushers do not need to be as rugged as in the primary stage

Scondary Crushers prefer closed circuit crushing

Secondary also operate on dry feed - reduce ore to size suitable to grinding

In those cases where size reduction can be more efficiently carried out by crushing - there may be a tertiary stage before grinding

Tertiary crushers are to all intents and purposes of the same design as secondaries, except that they have a closer set

#### Cone Crushers

- Cone crusher is a modified gyratory crusher
- The essential difference is that the shorter spindle of the cone crusher is not suspended, as in the gyratory, but is supported in a curved, universal beating below the gyratory head or cone
- The throw of cone crusher can be up to five times that of primary crushers, which must withstand heavier working stresses
- Operated at much higher speeds
- Material Passing through the crusher is subjected to a series of hammer-like blows rather than bring gradually compressed as by the slowly moving head of the gyratory
- High-speed action allows particles to flow freely through the crusherm and the wide travel of the head creates a large openeing betweem it and the bowl when in the fully open position
- This permits the crushed fines to be rapidly discharged, making room for additional feed

#### Impact Crushers

Sharp blows - high speed free falling rock

- Moving parts - beater
- Internal stresses created in the particles are often large enough to cause them to shatter
- These forces are increased by causing the particles to impact upon an anvil or breaker plate

Hammer Mill
- Used in small-scale operations
- Coarse liberation sizes
- hammer velocities (50mps)
- Small capacity
- High wear rates of hammers and screen
- Screen hole - controls size

#### Roll Crushers

Roll crushers, or crushting rolls are still used in some mills, although they have been replaced in most installations by cone crushers

- Handles - Friablem sticky, frozen and less abrasive feed - limestone, coal, chalk, gypsum, phosphate, and soft iron ores
- Jaw and gyratory crushers have a tendency to choke near the dischrge when crushing friable rock with a large proportion of maximum size pieces in the feed
- Compression

Angle of Nip
- The angle between the the two tangents drawn on the rolls at the point fo contact of the particles with rolls


The coefficent of friction between steel and most ore particles is in the range 0.2-0.3, so that the value of the angle if nip should never exceed about 30°, or the particle will slip

- Coefficent of friction decreases with speed, so that the speed of the rolls depends on the angle of nip, and the type of material being crushed

##### High Pressure Grinding Rolls (HPGR)

The utilization of specific energyof breakage as a result of impact was much less than with compressive forces.
Thus during high pressure grinding where large compressive forces were applied to the bed of ore, the total energy required would be relatively less compared to comminution where impact forces

- Roll - Partile nnipped and the forces of compression andfriction between the rolls and particles are responsible fo rsize reduction provided the combined forces exceed the compressive strength of particles
- HPGR - Comminution could take place by compressive forces as well as by inter-particle breakage, provided again that the total applied pressure was greater than the crushing strength of the rock pieces
<br>
- Decreasing particle size the energy utilization increased

Theses observations resulted into the development of HPGR - cement, iron ore and diamond industries

- Fine product sizes - HPGR has been used for both crushing and grinding - it can replace tertiary crushing - intalled before a ball mill - Kudramukh

#### Crusher Selection

There is an important difference between the states of materials crushed by pressure and by impact

There are internal stresses in material broken by pressure which can later cause cracking - Impact causes immediate fracture with no residual stresses

This stress-free condition is particularly valuable in stone used for brick, road

Impact crushers, therefore have a wider use in the quarrying industry than in the metal-mining industry

They may give trouble-free crushing on ores that tend to be plastic and pack when the crushing forces are applied slowly, as in the case in jaw and gyratory crushers

These types of ore tend to be brittle when the crushing force is applied instantaneously by impact crushers

Cone crusher tend to produce more elongated particles because of their reduction ratio and abilitu of such particles to pass through the chamber unbroken

### Crushing - Calculation of Reduction Ratio

- Crushers have limited reduction - The number of stages is guided by the size of the feed and the requested product

## Grinding

Size reduction of particles by a combination of impact, shear and abrasion either dry or wet

It is performed in rotating cylindrical steel vessels known as Tunbling Mills

### Types of Grinding

Ore - Soft or Hard
Quantity of ore to be ground
Use of the ground product - Wet or dry condition

Methods
- Batch or continous grinding
- Differential ginding
- Dry and wet grinding
- Open circuit or Closed circuit grinding
- Primary and Secondary grinding (stage grinding)

Minimize fine generation

#### Batch Grinding

A definite quantity of the feed is ground for a pre determined time

The ground material is removed from the mill

The grinding media will remain in the mill

Second batch is loaded for grinding and the operation continues

Useful in laboratory - not in MPT

Tumbling mills are used for batch grinding

Any shape of particle can be used in feed
Inefficient, more product is over ground

#### Continuous Grinding

- Ore is fed into the mill continuously at a fixed rate
- Product is discharrged after a suitable dwelling time
- Meanwhile new feed is charged

Mass Balance - Resident time of materials in mill - Volume of mill

Harder Materials - More resient time

#### Differential Grinding

Ores and mierals vary in their relative grind abilities

Softer material may be ground finer and harder material coarser, ifthey co-exist

This differential action is increased in close circuit grinding

Capacity decreases in Differential Grinding

#### Dry and Wet Grinding

Depends on subsequent concentation process

Material is ground either in totally dry or wet (slurry condition)

Grinding in moist/sticky state consumes lot of energy - grinding should not be done in this state

Inhibit grinding surfaces, resident time, flow ability

Dry grinding - when subsequent concentration process is dry

Wet Grinding - Normally used in mineral dressing (subsequent concentration processes - flotation, leaching etc. are wet processes)

Dry Grinding
- Feed material should have low (<1%) moisture content
- The Feed should be in less contact with air (it may abosrb moisture)
- The grinding media and the liner inside the mill should not wear off
- Costly filtering equipment are not required
- Dust control during frinding is needed
- Cement Industry (limestone), pharmaceuticals

Wet Grinding
- Consumes less power
- Neeeds less spcae
- Minimum dist control only needed
- Required large quantities of water and reliable pumping system
- Generally cheaper than than a dry grinding installation
- Recycling of water

#### Primary and Secondary Grinding

Grinding can be done in stages - primary and secondary

Primary mills work faster and shatter the feed

Secondary mills work gently and uniformly finer products are formed

#### Open Circuit Grinding

The mill grinds the feed to desired size in one pass and removes the product to recieve the next feed

It needs more pwer - needs skilled operator - flow rate, feed rate, rpm, water

Used normally - for coarse grinding, when closed circuit grinding becomes very costly

#### Closed Circuit Grinding

The mill discharge is sized

Oversize particles are reground

This cycle repeats till all particles are of same size

During regrinding of oversize, new material is also fed to the grinder

Need of less skilled operators - reduced cost

#### Ball mills

They are rotating cylinders with liner and grinding balls inside

Grinding medium - steel, iron, wc balls

They are continous machines (4-20 rpm)

Crushed ore is fed in one end through a feeder

The balls fall back onto the feed during rotation of the shell

Ground ore is discharged at the other end or through the periphery

They are used in closed system for maximum efficiency

#### Autogenous Grinding Mill

The Coarse particles are the medium

Self-grinding of the ore

A rotating drum throws larger rocks of ore in a cascading motion

Larger Rocks - Impact Break
Finer Particles - Compressive Grinding

#### Semi Autogenous Grinding Mill

SAG mills utilize grinding balls in grinding like in a ball mill

Used as primary or first stage grinding solution

SAG mills use a ball charge of 8 to 21%

Attrition between grinding balls and ore particles causes grinding of finer particles

# Movement of Solids in Fluid

Majority of Processes involve water - we need to know how particles behave in water - Grinding/Industrial screning/Separation units

To improve the understanding the models

To develope schemes to predict the settling velocity of a particle of known shape, size and density in a stagnant liquid of known properties

Most cases the fluid is in flowing conditions

- Spherical Particles
- Non-Spherical Particles
- Concentrated Systems
- Particles concentration in Fluids

## Free settling

### Assumptions

- Volume fration of solids in <5% (some times >2%)
- Interaction of particles and fluid, ignore particle-particle collision
- Spherical particles only
- Stagnant Fluid
- Free settling condition

### Forces on Particles
- Gravitational forces
- Buoyancy Force (Archimedean Principle)
- Drag force due to the relative movement of the particles and the fluid

F = ma = F~g~ - F~b~ - F~d~

Equation of Particle Motion

$\displaystyle m\frac{dv}{dt} = mg - mg\frac{\rho_f}{\rho_p} - C_d\rho_fv^2\frac A2$

At terminal sttling condition acceleration is zero

$v^2_t = \displaystyle\frac{2mg(\rho_p - \rho_f)}{C_d\rho_p\rho_f A}$

$v_t = \left\{\displaystyle\frac{4D_p g(\rho_p-\rho_f)}{3C_d\rho_f}\right\}^{0.5}$

Drag coefficient depends on flow conditions around the particle i.e. Reynolds Number

$R_e = \displaystyle \frac {v_t\rho_f D_p}{\mu_f}$

- For R~e~ < 0.1, C~d~ = 24/R~e (Stokes or Laminar Region)
$\qquad v_t = \displaystyle \frac{gD^2_p(\rho_p-\rho_f)}{18\mu_f}$

- For R~e~ > 760 C_d = 0.445 (Newtonian or turbulent region)
$\qquad v_t \approx \left[\displaystyle\frac{3D_p g(\rho_p-\rho_f)}{\rho_f}\right]^{0.5}$

- 0.1 < R~e~ < 750
- Transition region
- Single equation not available - No equation can describe Standard Drag Curve
- Lapple and Shepard (1940) proposed drag curve
- Various Models - Kleeman 1975, **Concha and Almenda 1979** Zigrang and Sylvester 1981, Turton and Clark 1987, Haider and Levenspiel 1989 proposed single equations based on drag curve but predictions from one another

Best fitted Curve - Cliff et. al

C~d~, R~e~, V~t~

- We have two unknowns and one equation
- Use iterative techniques to sort out
- Use **various convergence criteria**

The Best number,
$\qquad N_D = \displaystyle \frac{4\rho_f(\rho_s - \rho_f)gD^3_p}{3\mu^2} = C_D\times R_e^2$


### Non-Spherical Particles in Newtonian Liquids

Commonly used measures
- Size - Equal cvolume sphere diameter, d~s~
$\qquad d_s = \displaystyle\left(\frac{6V_p}{\pi}\right)^{\frac 13}$
- Shape - Sphericity, $\psi$
$\qquad \psi = \displaystyle\frac{\text{Surface area of equal volume sphere}}{\text{ Surface area of particle}}$

Popular Correlations
- Haider and Levenspiel 1989
- Ganser 1993
- Chein 1994
- Chhabra et al. 1999

## Hindrance Settling

Hindrance - Resistance
- A decrease in the available cross section for the upward flow of the fluid which results in an increased fluid approach velocity
- An increase in the apparent viscosity of the pulp
- A decrease in the gravitation driving force due to decrease in the difference in apparent specific gravity between the particles and the pulp
- An increase in the wall hindrance

To evaluate hindered terminal settling velocity V~th~
We need - Free settling velocity - V~t~ and correction factor (1-C)^n^

C - Volumetric concentration of particles
n - constant

### Richardson and Zaki model

$\qquad V_{th} = V_t(1-C)^n$

$n = (n|2.33\leq n\leq 4.65|n\in\Bbb R)$ (Maude and Whitmore)

$n = 4.6 - R_e\left[\displaystyle\frac{10+2.3R_e}{(1.5+R_e)(105+R_e)}\right]$ (Holland - Batt)

Limitation of the model - Applicable only to uniform density and monodisperse - rare because of heterogeneity of mined ores

Models for Ploydisperse and Polydense suspensions
- Lee's model (extension of Concha and Almendra
- Brauer and Thiele's Model

### Conclusions

Richardson and Zaki model may be used for uniform density and monodisperse suspension

For Polydense and Polydisperse suspension Brauer and Tiele's model seems realistic; however, the model has to be validated well with reliable data set

Reliable hindered settling model is yet to be develope for practical use

Issues
- Inadequate measures of shape, size and orientation
- Irregular shapes $\rightarrow\psi$
- Viscoplastic and Viscoelastic liquids
- Wall effects
- Settling under dynamic consitions
- Hindered Settling

### Effect of centrifugal force

Centrifugal force in radial direction
$\quad F_c = m \omega^2r$

$G = \displaystyle\frac {F_c}{F_g} = \frac{\omega^2r}g$

The sedimentation of a spherical particle in an incompressible fluid in a centrifugal field may be written from the equation of motion as
$\qquad\displaystyle\frac{dv}{dt}+\frac{18\mu}{\rho_p D_p^2}v = \frac{\omega^2r}{\rho_p}[\rho_p-\rho_f]$

For a very small particle settling in the Stokes region (10^-4^ < R~e~ < 0.2)
$\qquad v=\displaystyle\frac{(\rho_p-\rho_f)D_p^2\omega^2r}{18\mu}$
$\qquad v = Gv_g$

Similarly we can also prove that

$\qquad v = G^{1/2}v_g\qquad0.2<R_e<500$
$\qquad v = G^{1/3}v_g\qquad500<R_e<2\times10^5$

Applications
- Design Problems
- Classifiers
- Optimization and design

# Classifiers

Very dine particles - more surface areas

Industrial screen - technically difficult - Econmically not viable

Separation based on size - Movement of solids in fluids

## Classification

Classification is a method of separating mixtures of minerals into two, or more products on the basis of the velocity with whcih the particles fall through a fluid medium

The carrying fluid can be a liquid or gas - usually water

Wet classification is applied to particles which are considered too fine to be sorted efficiently by screening

Classifiers are nearly always used in closed circuit grinding operation, and so strongly influence the performance of these circuits

### Princple of Operation

Velocity of particles in fluid medium dependent on
- size
- specific gravity
- shape

Classification involves the balancing of the accelerating, and opposing forces action upon particles

Coarser, Heavier, and spherical - settle faster
Emphasis of separation is based on size difference

Stokes' law and Newton's law for a particular fluid can be simplified to

$\qquad V = K_1 D_p^2(\rho_p-\rho_f) \qquad R_e < 0.1$

$\qquad V = K_2[D_p(\rho_p-\rho_f)]^{\frac 12}\quad R_e > 750$

Both laws show that the terminal velocity of a particle in a particular fluid is a function only of the **particle size and density**

Same density - Larger diameter higher terminal velocity

Same diameter - Heavier particle higher terminal velocity

Consider two mineral particles - $(\rho_a,d_a), \,(\rho_b,d_b)$ falling in fluid $\rho_f$ falling at exactly same settling rate

Their terminal velocities mkust be tkhe same, hence from Stokes' law
$\qquad d_a^2(\rho_a - \rho_f) = d_b^2(\rho_b - \rho_f)$

$\qquad\displaystyle\frac{d_a}{d_b}=\left(\frac{\rho_a - \rho_f}{\rho_b - \rho_f}\right)^{\frac12}$

Free Settling Ratio of two minerals

Similarly from Newton's Law, the free settling ratio of large particles is

$\qquad\displaystyle\frac{d_a}{d_b}=\left(\frac{\rho_a - \rho_f}{\rho_b - \rho_f}\right)$

Density difference between the particles has a more pronounced effect on classification at coarser size ranges

Classifier - Sorting Column
- Fluid is rising at a uniform rate
- Particles are introduced
- Particles sink or rise accroding to whether their terminal velocities, a result of the net force, are greater or smaller than the upward velocity of the fluid

## Types of Classifiers

Although they can be categorized by many features, the most important is the force field applied to the unit - gravitational or centrifugal

Centrifugal classifiers have gained widespread use as classiying equipment for many different types of ore

In comparision - gravitational classifiers, due to their low efficiencies at small particle size (<70µm) - only found in older plants

A comparision of key parameters for Centrifugal and Gravitational Classifiers

| Item | Centrifugal Classifiers | Gravitational Classifier |
| -------- | ----------------------- | --- |
| Capacity | High | Low |
| Cut-Size | Fine-Coarse | Coarse |
| Capacity/cut-size dependency | Yes | No |
| Energy Consumption | High (feed pressure) | Low |
| Initial Investment | Low | High |
| Footprint | Small | Large |

### Gravitations Classifier

- Best suited for coarser classification and are often used as dewatering and washing equipment
- They are simple to operate and have low energy requirements, but capital outlay is relatively high compared to cyclones
- Gravitational Classfiers can be further categorized into two broad groups, depending on the direction of flow of the carrying current
- Fluid Movement - horizontal and forms an angle with the particle trajectory the classification is called sedimentation classification
- Fluid Movement and particle settling directions are opposite, the classification is called hydraulic or counter flow

Sedimentation - Free settling type and accentuate the sizing function

Hydraulic - hindered-settling types and so increase the effect of density on the separation

#### Sedimentation classifier

Non-mechanical sedimentation classifiers

As the simplest form of clssifier, there is little attempt to do more than separate the solid from the liquid, and as such they are sometimes used as dewatering units in small-scale operations

Therefore, they are not suitable for fine classification or if a high separation effeciency is required

They are often used in the aggregate industry to de-slime coarse sand products

Main difficulty - Balancing of the sand discharge and deposition rates; it is virtually impossible to maintain a regular discharge of sand through an open pipe under the influence of gravity


### Mechanical Sedimentation Classifiers

Lower settling velocity - carried away in a liquid overflow
Higher settling velocity - deposited on the bottom of the unit and is transported upwards against the flow of liquid by some mechanical means

Used in closed-circuit grinding operations and in the classification of products from ore-washing plants - act as sizing device - as particles are unliberated and so are of similar density

In closed-circuit grinding they have a tendency to return small dense particales to the mill (same as cyclones)

#### Rake Classifier

- Uses rakes actuated by an eccentric motion, which causes them to dip into the settled material and to move it up the incline for a short distance
- Rakes are then withdrawn, and returnto the starting-point where the cycle is repeated
- Settled material is thus slowly moved up the incline to the discharge


#### Spiral Classifier

- A continuously revolving spiral movers the sands up the slope
- They can be operated at steeper slopes than the rake classifiers, in which the sands tend to slip back when the rakes are removed
- Steeper slipes aid the drainage of sands, giving a cleaner, drier product
- Agitation in the pool is less than in the rake classifer, which is important in separations of very fine material


SC 90 ST 1 - Spiral Classifier, 90cm spiral diameter, straight tank, 1 pitch

- Tank options and adjustable weir for full flexibility in pool area and classification cut point(cp)
- The size at whcih the separation is made and the qualit of the separation depend on a number of factors
- Feed Rate - increasing the feed reate increases the horizontal carrying velocity and thus increases the size of particle leaving in the overflow
- Feed should not be introduced directly - causes agitation - releases coarse material from the hindered-settling zone - slowed using apron, partially submerged in the pool - sloped toward the sand discharge end - kinetic energy away from overflow
- The speed of the rakes or spiral determines the degree
- For coarse separation, a high degree of agitation may be necessary to keep them in suspension
- It is essential that the speed is high enough to transport the sands up the slope
- The height of the overflow weir is an operating variable in some mechanical claasifiers
- Increasing the weir height increases the pool volume, and hence allows more settling time and decreases the surface agitation - reduces the pulp density at overflow level where final separation is made
- High weirs - fine separation

Dilution of the pulp is the most important variable in the operation og mechanical classifiers

Closed-circuit grinding operation
Ball Mills - discharge at more than 65% weight usually
Mechanical classifiers number operate with more than 50%

Increased dilution
- Reduces the density of the weir overflow product
- Increases free settling - allowing finer particles to settle out of the influence of the horizontal current

Therefore finer separations are produced, provided that overflow pulp density is above a value known as the critical dilution, which is normally about 10% solids

Below this density - effect of increasing rising velocity with dilution becomes more important than the increase in particle settling rates produced be decrease of pulp density

The overflow therefore becomes coarse with increasing dilution


Disadvantage of Mechanical Classifier
- Inability to produce overflows of fine particles size at reasonable pulp densities - Too dilute for subsequent operations - May require thickening before concentration - capital cost and floor space of the thickener, oxidation of sulphide may occur in the thickener - affect froth flotation

Spiral Classifer - Applications
- Closed circuit grinding
- Dewatering
- Sand recovery
- De-s;iming
- Heavy media densifying

### Centrifugal Classifier

### Hydraulic Classifier

Hydraulic classifiers are characterized by the use of water additional to that of the feed pulp, introduced so that its direction of flow opposes that of the settling particles

They consist of a series of sorting columns - with a vertical current of water

The rising currents - high in first corting column - lowest in the last sorting

A series of underflow(spigot) products can be obtained

Hydraulic classifiers may be free-settling or hindered settling types

Free-settling types
- rare, simple, high capacity but inefficient in sorting and sizing
- They are characterized by the fact that each column is of the same cross sectional area throughout its length

Hindered-settling classifier
- Uses much less water than the free-settling type
- More selective in its action
- Due to the scouring action in the teeter chamber, and the buoyancy effect of the pulp, as a whole, on those particles which are to be rejected

### Hydro-Cyclone

Extremely versatile in application - clarification, dewatering, washing, separation of two immiscible liquids, degassing etc

Simple, cheap, easy installation, little maintenance and support structures, easy operation

Less space requirement and high throughput

#### Heart of any mineral processing plant
- Effective linkage between Comminution and downstream Processes
- Reduces Regrinding


#### Working
- Under pressure the feed is tangially introduced - swirling motion to the pulp
- A vortex is generated - low pressure zone along the verical axis
- An air cone develops along the axis, normally connected through the apex opening - in part created bt dissolved air
- The outer region of downward flow - inner region upward flow implies a postion at which there is no vertical verlocity
- Particles thrown outside the envelope of zero vertical velocity by the greater centrifugal force leave in the overflow - particles swept to the centre by greater drag force leave in the overflow
- Particles lying on the envelope may report to the underflow or overflow with equal probability

Renner and Cohen
- Four regions
- Unlassified Feed - Narrow region A adjacent to the cylinder wall and roof of the cyclone
- Fully Classified Coarse material - Region B occupies a very large part of the cone of the cyclone and contains fully classified coarse material - the size distribution is practically uniform and resembles that of the coarse underflow product
- Fully classified fine material - A narrow region C surrounding the vortex finder and extending below the latter along the cyclone axis
- Classification Region - Toroid shaped region D - Across this region, size fractions are radially distributed, so that decreasing sizes show maxima at decreasing radial distances from the axis

#### Cyclone efficiency

Represented by performance or partition curve
- Relates the weight fraction or percentageof particle size in the feed which reports to the apex or underflow to the particle size
- The cut point, or separation size of the cyclone - size at which particle reports to underflow and overflow equally - d~50~ size
- The sharpness of cut depends on the slope of the central section of the partition curve for hydrocyclone - It is expressed by taking the points at which 75 and 25% of the feed particles report to the underflow
- The effeciency of separation or imperfection, I
$\qquad I = \displaystyle\frac{d_{75} - d_{25}}{2d_{50}}$
- Many mathematical models of hydrocycones include the term "corrected d~50~"
- The uncorrected partition curve can be corrected by
$y' = \displaystyle\frac{y-R}{1-R}$
y' - Corrected mass fraction of a particular size reporting to underflow
y - The actual mass fraction of a particular size reporting to the underflow
R - fraction of feed liquid which is recovered in the coarse product stream

# Froth Flotation

Flotation is the most important and versatile mineral separation technique, and both its use and application are continually being expanded to treat greater tonnages and to cover new areas

Flotation has permitted the mining of low-grade ore and complex ore bodies, which would otherwise been regared as uneconomic

Earlier practice, the tailing of many gravity plants were of a higher grade than ore treated in many modern flotation

Liberation size, gravity concentration, tailings

Initially developed to treat sulphide minerals of Copper, Lead, Zinc - expanded to nickel, platinum and gold hosting sulphides - non sulphide minerals including hematite and cassiterite
Non-metallic minerals such as flurite, talc, phosphates, potash and energy (fuel) minerals, fine coal and bitumen

Deinking recycled paper pulp, deoiling refinery effluents

Flotation is a physico-chemical seprartion process that utilizes the difference in the surface properties of the valuable and gangue minerals

Froth Flotation involves three different phases- solid (fine ore powder), liquid(water) and froth

The process of separation of mineral includes three important mechanism
- True Flotation - selective attachment to air bubbles - aerophilic
- Entrainment - in water which passes through the froth
- Aggeration - Physical entrapment between the particles in froth

Need for Impeller with Air
- Turbulent
- Suspension
- Homogeneous Mixture

True flotaion dominates the recovery of the valuable minerals and the other two decide the separation efficienct between the valuable and the gange

Entrainment - mechanical mass transfer process - particals suspended in the water between bubbles enter the flotation froth from the top pulp region and are transferred to the concentrate

Hydrophovic and hydrophilic mineral particles suspended in water can experience entrainment

Attment of valuable minerals to air bubbles - most important - represents majority of the particles that are recovered to the concentrate

Degree of liberation increases for low grade ore

Flotation - can be applied to relatively fine particles
If particles are coarse and heavy - their weight will be greater than the adhesion between the particle and the air bubble and the particle will detach from the bubble

There are two ways of flotation -
1) Direct Flotation - Mineral attached to the froth
2) Reverse Flotation - Mineral remains in tailing

Applications
- Sulfide minerals from silica gangue
- CuFeS~2~, ZnS, PbS
- KCl from NaCl
- removing silicate from iron ores
- Phosphate minerals from silicates
- Even non-mineral applications such as deinking
- Fine-grained ores that are not amenable to conventionalgravity concentration

## Flotation Mechanism

The essential mechanism of flotation involves the attachment of mineral particles to air bubbles in such manner that the particles are carried to the surface of the ore pulp, where they can be removed

- Grinding the ore to a size sufficiently fine to liberate the valuable minerals from one another and from the adhering gangue minerals
- Making conditions favourable frot the adherence of the desired minerals to air bubles
- Creating a rising current of air bubbles in the ore pulp
- Forming a mineral-laden froth on the surface of the ore pulp
- Removing the mineral-laden froth

This process commences with comminuition(to increase the surface are of the ore)

The ore is ground to fine powder and wetted with water to form a Slurry

A surfactant chemical - collector - mixed with slurry to render the desired mineral hydrophobic

This slurry is then placed in the water bath containing Frother - areated to create bubbles

The desired mineral escape water by getting attached to the air bubbles, which rise to the surface and form froth

Froth is removed and concentrated mineral is refined

## Basic Principle of Flotation

The basis of froth flotation is the difference in wettabilities of different minerals

Particles can be naturally hydrophobic or the hydrophobicity can be induced by chemical treatments

Naturally hydrophobic - Hydrocarbons, non-polar solids - elemental sulfur

The stability of the froth depends on the strength of the attachment of the bubble to the mineral surface

This strength can be estimated with the help of Young-Dupre Equation - relates strength of attachment to the interfacial energies

Young-Dupre equation

$\Gamma_{W/A}\text{ cos}(\theta) = \Gamma_{S/A} - \Gamma_{S/W}$

Where
$\Gamma_{W/A}, \Gamma_{S/A}, \Gamma_{S/W}$ - Surface enegries between water-air, solid-air, solid-water
$\theta$ - Contact angle

Work of adhesion - force required to break the particle-bubble interface

$W_{S/A} = \Gamma_{W/A} - \Gamma_{S/A} + \Gamma_{S/W}$
$W_{S/A} = \Gamma(1-\text{ cos }\theta)$

Greater contact angle - grater work of adhesion - resilient to disruptive forces

If bubbles are larger in size relative to the particles - decreasing the surface area of the bubble - more fluid to enter into the froth- leads to entrainment

Bubble diameter must be comparable to the particle diamenter - good contact between them

Stability of the froth must not be too high - persistent foam - difficult to convey and pump through the plants

Common Ores

Specific ore application

## Floatation System

1) Chemistry Components
- Collectors
- Frothers
- Activators
- Depressants
- pH
2) Equipment Components
- Cell Design
- Agitation
- Air Flow
- Cell Band Configuration
- Cell Bank Control
3) Operation Components
- Feed rate
- Mineralogy
- Particle Size
- Pulp Density
- Temperature

## Chemicals of floatation

Required for
- To maintain relative Hydrophobicity between the particles
- To maintain proper froth characteristics

Types of chemicals
- Collectors
- Frothers
- Regulators
- Activators
- Depressants
- pH modifiers

### Collectors

Collectors are reagents that are used to selectively absorb onto the surface of particles

Form a monolayer on the particle surface that essentially makes a thin film of non-polar hydrophobic hydrocarbons

The collectors greatly increase contact angle - adhere to bubble - effective

Collectors can be
- Nonionic - simple hydrocarbon oil
- Anioic
- Cationic

Ionic - a polar part that selectively attaches to the mineral and a non polar part that projects out into the solution and makes the surface hydrophobic

Collectors cna be chemically bonded to mineral surface or be held on the surface by physical forces


#### Adsorption of collectors

- Chemisorption
- Ions or molecules form irreversible bonds with the surface, through chemical reaction
- Highly specific process - more selective
- Physisorption
- Ions or molecules from solutions reversibly attach to the surface, either by electrostatic attraction or van der Waals bonding
- Less selective

Collectors should be used in very small concentration
- adversly affects the recovery of the valuables
- due to development of multi-collector layers on the surface, thereby reducing the proportion of hydrocarbon part oriented toward the bulk solution, which reduces the hydrophobicity
- Increases the cost
- tends to float other minerals thus reducing selectivity
- Reduce capacity

Non-ionic
- Required to enhance hydrophobicities of the partially hydrophobic minerals surfaces by selectively absorbing
- Fuel and Kerosene oil

Ionic Collectors
- Complex molecules
- Asymmetric in nature
- Heteropolar - molecules have a non-polar hydrocarbon group (water repellant in nature) and polar group (reacts with water)

#### Anionic Collectors

These collectors possess non-polar and a polar group in the Anionic part, cationic has no significant role

##### Carboxylates

- Oxyhydryl
- Fatty Acis or soap
- Oleic acid and Linoleic acid - Examples
- Soaps have an advantage over other ionic collectors that though theyk have long carbon chains they are soluable in water
- strong in nature and low selectivity
- Used for flotation of Ca, Ba, Sr, Mg and salts of alkali and alkaline earth metals


##### Sulphonates and Sulphates

- Oxyhydrl
- Lower power
- greater selectivity
- Used for Barite, Celestite, Fluorite, Apatite, Chromite, Cassiterite, Mica, Kyanite andScheelite

##### Xanthates

- Sulphydryl
- They are most widely used THIOL collectors
- Xanthogenates
- Formed by reacting Alkali Hydroxides (eh KOH), Carbon Disulphide (CS~2~) and Alcohol(ROH)
- - Normally contain 1 to 6 Carbon Atoms
- Sodium Alkyl Xanthates decreases in efficacy with age


- Abosrb chemically on sulfide mineral surface and form insoluble metal Xanthates
- Used for collection of oxidised ore like malachite, cerrusite, anglesite and native minerals like gold and sliver

##### Dithiophosphates

- Sulphyhydryl
- Comparatively weak collectors
- possess Pentavalent phosphorus in the polar group
- Also called - Aerofloat Collector - effective selective collectos for copper silfide minerals