COMMINUTION THEORY
CH 3120
INTRODUCTION
Minerals are finely disseminated and intimately
associated with the gangue, they must be initially
"unlocked" or "liberated" before separation can be
undertaken.
Each particulate process needs a certain size of feed
to operate
What is comminution?
Comminution in which the particle size of the ore/solid
is progressively reduced using external forces until the
required size/clean particles of mineral ore can be
separated by such methods as are available.
OBJECTIVES OF COMMINUTION/SIZE REDUCTION
Size reduction of solids is carried out in almost all the
process industries for a number of reasons
To increase the surface area (to increase reaction/transfer rate)
To produce solid particles of desired size distribution, shape
and density
To separate unwanted particles effectively
To dispose solid waste easily
To mix solids more intimately
To improve the handling characteristics
SIZE REDUCTION METHODS
Various comminution devices employ different actions
to solid particles for size reduction, which is customer
tailored
There are four basic ways to reduce the size of solid
material
Impact
Compression
Attrition
Shear (sometimes it is referred as chipping/cutting too)
Most of the size-reduction equipments employ a
combination of all these size reduction methods.
PRINCIPAL FORMS OF EFFECTS IN THE
COMMINUTION OF MATERIALS
SIZE REDUCTION METHODS …
Compression is used for coarse reduction of hard solids, to
give relatively few fines
Impact gives coarse, medium, or fine products
Attrition yields very fine products from soft, nonabrasive
materials.
Sometimes size reduction results from the attrition of a
particle by one or more other particles or from intense shear
in the supporting fluid.
Cutting gives a definite particle size and sometimes a
definite shape, with few or no fines.
CRITERIA FOR COMMINUTION.
Crushers and grinders are types of comminuting equipment
An ideal crusher or grinder would
(1) have a large capacity,
(2) require a small power input per unit of product, and
(3) yield a product of the single size or the size distribution desired.
The usual method of studying the performance of process
equipment is to set up an ideal operation as a standard, compare
the characteristics of the actual equipment with those of the ideal
unit, and account for the difference between the two.
When this method is applied to crushing and grinding equipment,
the differences between the ideal and the actual are very great,
and despite extensive study the gaps have not been completely
accounted for.
On the other hand, useful empirical equations for predicting
equipment performance have been developed from the incomplete
theory now at hand.
CRUSHING VS GRINDING
Comminution in the mineral processing plant takes place
as a sequence of crushing and grinding processes.
Crushing reduces the particle size of run-of-mine ore to
such a level that grinding can be carried out until the
mineral and gangue are substantially produced as
separate particles.
Crushing is accomplished by compression of the ore
against rigid surfaces, or by impact against surfaces in a
rigidly constrained motion path.
This is contrasted with grinding which is accomplished
by abrasion and impact of the ore by the free motion of
unconnected media such as rods, balls, or pebbles.
CRUSHING VS GRINDING
Crushing is usually a dry process, and is performed in several
stages, reduction ratios being small, ranging from 3 to 6 in each
stage.
The reduction ratio = maximum particle size entering the crusher
--------------------------------------------------------------
maximum particle size leaving the crusher
Tumbling mills with either steel rods or balls, or sized ore as the
grinding media, are used in the last stages of comminution.
Grinding is usually performed "wet" to provide a slurry feed to
the concentration process, although dry grinding has limited
applications.
There is an overlapping size area where it is possible to crush or
grind the ore.
CALCULATION OF REDUCTION RATIO
Example
Let us say Feed material: F80=400mm
80% smaller than 400mm
Product size required: P80=16mm
80% smaller than 16mm
Total reduction ratio required is F80/P80
400/16 = 25
SIZE REDUCTION BEHAVIOR OF MINERALS
SIZE REDUCTION RATIOS-CRUSHERS
SIZE REDUCTION RATIOS-COMMINUTION DEVICES
CHARACTERISTICS OF NATURAL SOLIDS IN
COMMINUTION
For a particular size-reduction operation, the choice of machine to
be used mainly depends on
Size and quantity of material to be handled, and
Nature of the product required
One of important properties of solids is Hardness
The hardness of the material affects the power consumption and
the wear on the machine.
With hard and abrasive materials it is necessary to use a low-speed
machine and to protect the bearings from the abrasive dusts that
are produced.
Materials are arranged in order of increasing hardness in the Mohr
scale in which the first four items rank as soft and the remainder
as hard.
HARDNESS
Hardness Substance or mineral
0.2–0.3 caesium, rubidium
0.5–0.6 lithium, sodium, potassium
The Mohs scale of mineral 1 talc
gallium, strontium, indium, tin, barium, thallium,
hardness characterizes the 1.5
lead, graphite
scratch resistance of various hexagonal boron nitride,[10] calcium, selenium,
2
minerals through the ability of cadmium, sulfur, tellurium, bismuth
magnesium, gold, silver, aluminium, zinc,
a harder material to scratch a 2.5 to 3
lanthanum, cerium, Jet (lignite)
softer material. 3 calcite, copper, arsenic, antimony, thorium, dentin
4 fluorite, iron, nickel
4 to 4.5 platinum, steel
apatite, cobalt, zirconium, palladium, tooth enamel,
5
obsidian (volcanic glass)
5.5 beryllium, molybdenum, hafnium
orthoclase, titanium, manganese, germanium,
6
niobium, rhodium, uranium
glass, fused quartz, iron pyrite, silicon, ruthenium,
6 to 7
iridium, tantalum, opal
7 osmium, quartz, rhenium, vanadium
7.5 to 8 emerald, hardened steel, tungsten, spinel
8 topaz, cubic zirconia
chrysoberyl, chromium, silicon nitride, tantalum
8.5
carbide
corundum, silicon carbide (carborundum), tungsten
9–9.5
carbide, titanium carbide
boron, boron nitride, rhenium diboride, stishovite,
9.5–10
titanium diboride,
10 diamond
nanocrystalline diamond (hyperdiamond, ultrahard
>10
fullerite)
CHARACTERISTICS OF NATURAL SOLIDS IN
COMMINUTION…
Structure
Normal granular materials such as coal, ores and rocks
can be effectively crushed employing the normal forces of
compression, impact, and so on.
With fibrous materials a tearing action is required.
Moisture content
It is found that materials do not flow well if they contain
between about 5 and 50 percent of moisture.
Under these conditions the material tends to cake together
in the form of balls.
In general, 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.
CHARACTERISTICS OF NATURAL SOLIDS IN
COMMINUTION…
Friability
The friability of the material is its tendency to fracture during
normal handling.
In general, a crystalline material will break along well-defined
planes and the power required for crushing will increase as the
particle size is reduced.
Stickiness.
A sticky material will tend to clog the grinding equipment and it
should therefore be ground in a plant that can be cleaned easily.
Soapiness.
This is a measure of the coefficient of friction of the surface of the
material. If the coefficient of friction is low, the crushing may be
more difficult.
Explosive materials must be ground wet or in the presence
of an inert atmosphere.
Materials yielding dusts that are harmful to the health
must be ground under conditions where the dust is not
allowed to escape.
CHARACTERISTICS OF COMMINUTED
PRODUCTS
One measure of the efficiency of the operation is based on the energy
required to create new surface, usually the surface area of a unit
mass of particles increases greatly as the particle size is reduced.
The product always consists of a mixture of particles, ranging from a
definite maximum size to very small particles.
Some machines are designed to control the magnitude of the largest
particles in their products, but the fine sizes are not under control.
In some types of grinders fines are minimized, but they are not
eliminated.
The ratio of the diameters of the largest and smallest particles in a
comminuted product is of the order of 104• Because of this extreme
variation in the sizes of the individual particles, relationships
adequate for uniform sizes must be modified when applied to such
mixtures.
CHARACTERISTICS OF COMMINUTED
PRODUCTS…
The term average size, for example, is meaningless until the
method of averaging is defined, and several different average
sizes can be calculated.
Unless they are smoothed by abrasion after crushing,
comminuted particles resemble polyhedrons with nearly plane
faces and sharp edges and corners.
The particles may be compact, with length, breadth, and
thickness nearly equal, or they may be platelike or needlelike.
For compact grains, the largest dimension or apparent diameter
is generally taken as the particle size.
For particles that are platelike or needlelike, two dimensions
should be given to characterize their size.
PRINCIPLES OF COMMINUTION
• Most minerals are crystalline materials in 3-D arrays.
• The configuration of atoms is determined by the size and types of
physical and chemical bonds holding them together.
• In the crystalline lattice of minerals, these inter-atomic bonds are
effective only over small distances, and can be broken if extended by a
tensile stress
Strain of a crystal lattice resulting
from tensile or compressive stresses Stress concentration at a crack tip
The increase in stress at a active crack site is proportional to the
square root of the crack length perpendicular to the stress
direction.
Therefore, there is a critical value for the crack length at any
particular level of stress at which the increased stress level at the
crack tip is sufficient to break the atomic bond at that point.
Such rupture of the bond will increase the crack length, thus
increasing the stress concentration and causing a rapid
propagation of the crack through the matrix, thus causing
fracture.
Although the theories of comminution assume that the material is
brittle, crystals can, in fact, store energy without breaking, and
release this energy when the stress is removed. Such behaviour is
known as elastic.
When fracture does occur, some of the stored energy is transformed
into free surface energy, which is the potential energy of atoms at
the newly produced surfaces. Due to this increase in surface
energy, newly formed surfaces are often more chemically active,
and are more amenable to the action of flotation reagents, etc., as
well as oxidising more readily.
Griffith (1921) showed that materials fail by crack propagation
when this is energetically feasible, i.e. when the energy released by
relaxing the strain energy is greater than the energy of the new
surface produced.
Brittle materials relieve the strain energy mainly by crack
propagation, whereas "tough" materials can relax strain energy
without crack propagation by the mechanism of plastic flow, where
the atoms or molecules slide over each other and energy is
consumed in distorting the shape of the material.
Crack propagation can also be inhibited by encounters with other
cracks or by meeting crystal boundaries.
Fine-grained rocks, such as taconites, are therefore usually tougher
than coarse-grained rocks.
The energy required for comminution is reduced in the presence of
water, and can be further reduced by chemical additives which
adsorb onto the solid.
This may be due to the lowering of the surface energy on
adsorption providing that the surfactant can penetrate into a crack
and reduce the bond strength at the crack tip before rupture.
Real particles are irregularly shaped, and loading is not
uniform but is achieved through points, or small areas, of
contact.
Breakage is achieved mainly by crushing, impact, and
attrition, and all three modes of fracture (compressive, tensile,
and shear) can be discerned depending on the rock mechanics
and the type of loading.
o When an irregular particle is broken
by compression, or crushing, the
products fall into two distinct size
ranges- coarse particles resulting from
the induced tensile failure, and fines
from compressive failure near the points
of loading, or by shear at projections
IMPACT & ATTRITION BREAKAGE
In impact breaking, due to the rapid loading, a particle
experiences a higher average stress while undergoing
strain than is necessary to achieve simple fracture, and
tends to break apart rapidly, mainly by tensile failure. The
products are often very similar in size and shape.
Attrition (shear failure) produces much fine material, and
may be undesirable depending on the comminution stage
and industry sector.
Attrition occurs mainly in practice due to particle-particle
interaction (inter-particle comminution), which may occur
if a crusher is fed too fast, contacting particles thus
increasing the degree of compressive stress and hence
shear failure.
