comminution may 21 final 2.0.pdf

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Bern Klein, Ph.D., P.Eng.Professor and Head

Norman B. KeevilInstitute of Mining Engineering

University of British Columbia

Vancouver CanadaMay 2013

ComminutionAndSize

Classification

Bern Klein Ph.D P.EngProfessor and Head, Norman B. Keevil Institute of Mining Engineering, University of British ColumbiaVancouver, Canada

[email protected] 822 3986

Process Design Engineer 2000-1998Professor Mineral Processing 1998-present

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Teaching:Comminution and Size ClassificationProcess DesignProcess MineralogyProcessing of Precious Metal Oes

Research Areas:Comminution - High Speed Stirred Milling, High Pressure Grinding RollsRheology – Hydraulic Transport, Paste and Thickened TailingsSensors and Sorting SystemsContinuous Centrifugal Gravity ConcentratorsWeathering of Waste Rock

Course Outline• UBC Norman B. Keevil Institute of Mining Engineering• Comminution Overview• Comminution Theory• Process Development and Plant Design

‒ Process Development‒ Metallurgical Testing‒ Sampling‒ Process Mineralogy‒ Physical Properties‒ Plant Design – 30 min

• Comminution Technologies• Sampling• Crushing• Screening

‒ Features and Design‒ Sizing and Selection

• Crushing and Screening Plant Design

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Course Outline• High Pressure Grinding Rolls

• Sensors and Sorting

• Introduction to Grinding• Grinding Circuits• Grinding and Classification – Ore Characterization• Grinding and Classification – Circuit Design

‒ – Mill Power‒ – Mill Sizing‒ Mill Sizing Example

• Ball and Rod Mill Sizing – Olav Meijo• Size Classification• Fine Grinding• Energy Efficiency in Mining• Statistical Experiment Design

Course Objectives

• To learn about the main unit operations that are used to process minerals including

• Introduce new comminution technologies and systems

• Describing the fundamental physical principles that are exploited/employed to achieve the purpose

• Demonstrating how to size and select the equipment

• Demonstrating the use of the equipment in mineral processing

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• List of Recommended Publications

‒Mineral Process Plant Design, A.L. Mular, D.N. Halbe, D.J. Barratt, SME, 2002

‒Mineral Comminution Circuits, T.J. Napier-Munn, S. Morrell, R.D. Morrison, T, Kojovic, JKMRC Mining and Mineral Processing, 2005

‒Advances in Comminution, S.K. Kawatra, SME, 2006

‒Mine to Mill Conference, A. Scott, S. Morrell, Aus IMM, 1998

‒Advances in Autogenous and Semiautogenous Grinding Technology, Proceedings, 1989, 1996, 2001, 2006, 2011 (2015)

‒Proceedings of the Annual General Meeting of the Canadian Mineral Processors, 1964 - present

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COMMINUTIONOVERVIEW

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Comminution at Face Coarse Breakage Fine Breakage

CHARACTERIZATION

Comminution Overview

Lithology Mineralogy Geometallurgy

Particle Weakening

Sensing and Sorting

Size Classification

- Mine to Mill

- Drill & blast optimization

- Continuous miners

- Caving methods

- Hydrofracturing

CHARACTERIZATION

Comminution at Face

Lithology MineralogyGeometallurgy

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- Sellfrag

- Electric Pulse Treatment

- Microwave

CHARACTERIZATION

Particle Weakening


- Crushers (gyratory, jaw, cone)

- Vertical roller mills (VRM)

- High Pressure Grinding Rolls (HPGR)

- Vibrocone

- SAG milling

CHARACTERIZATION

Coarse Breakage


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-Sorting

- High capacity sorting machines

- Sensors

-Other Sensing Applications

CHARACTERIZATION

Sensing and Sorting Systems


-Classification equipment

-Coarse classification

-Screening

-De-agglommeration

-Cyclones

CHARACTERIZATION

Classification


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-Ball milling

-Low speed stirred mills

-High speed stirred mills

CHARACTERIZATION

Fine Breakage (Grinding)


DefinitionsMineral Processing

– The technology of economically converting mineral bearing raw material into individual mineral constituents; the minerals remaining essentially unaltered in physical and chemical form throughout. The temperature of the system normally is less than the boiling point of water. Mineral processing is also known as mineral beneficiation, milling or concentration.

Unit Operation– An individual process with a specific function, which is a component or forms part of a complex process.

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Mineral Processing

Comminution

Mineral Separation

De-watering

Ore

Tailing

Concentrate

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Mine Primary Crushing

AutogenousGrinding

2nd/3rd Crushing

Screening

Rod Mill/Ball Mill

GravityCyclone

Flotation/ Leaching

Regrind

Thickening

Tailing

Filtering

Plant Design

Sampling

Material Transport

Unit Operations

Mineralogy & Process

Development

Primary Crushing

AutogenousGrinding

2nd/3rd Crushing

Screening

Rod Mill/Ball Mill

Cyclone

Regrind

Tailing

Filtering

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THEORIES OF COMMINUTION

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Theories of Comminution

• Large particle + Energy = Small Particles + Sound + Heat

• Energy dissipation (sound + heat) accounts for 99% of input energy

• Most expensive unit operation requiring 5 – 40 kWh/t

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Breakage Mechanisms

Properties of solids that influence breakage mechanisms:

• Elastic versus Plastic (stress-strain relationship linear or

nonlinear)

• Strain behavior (fracturing) depends on:

‒Microstructural differences in physical properties of

adjacent minerals e.g. hardness, brittleness, cleavage

‒Macrostructural weaknesses e.g. along joints, bedding

planes, grain boundary cementation/impurities

‒Microstructural weaknesses e.g. schistosity, number of

flaws/ number and type of defects including cracks,

crystal surfaces, impurities, minute inclusions

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Surface Properties

From fracture mechanics, for an isotropic material:

F’/A = 2Es/L

F’ - critical force to initiate fracture

A - cross sectional area

L - length of specimen

Es - surface energy

δ - Young’s modulus

Critical stress to initiate fracture is proportional to

surface energy which depends on the number of flaws

on surface.

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Breakage Energy

• ↑ cracks or flaws = ↓ energy required

• ↑ brittleness = ↓ energy required

• ↑ coarse grain crystals = ↓ energy required

• water = ↓ energy required

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1st Theory – Rittinger (1867)

• Constant energy per unit of surface area generated.

New surface area produced by crushing and grinding

is directly proportional to the useful work input.

where E - energy consumed

X2 - product size

X1 - feed size

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XXkE

Surface area is inversely proportional to the diameter of the particle

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2nd Theory – Kick (1885)• Constant energy per unit mass for similar relative reduction.

The work input required to deform a homogeneous rock to the yield point and to break it is proportional to the reduction in diameters of the particles concerned.

• Theory: Work required to reduce rock from 4 cm to 2 cm equals work required to reduce rock from 2 cm to 1 cm.

• Rock is not homogeneous due to flaws and breakage is controlled by number of flaws. Rock breaks at far below the stress required by its theoretical homogeneous elastic limit.

• Overestimates work input at coarse sizes and underestimates work input at fine sizes.

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2

1lnx

xkE

3rd Theory – Bond (1951)• Useful work input per ton is inversely proportional to the

square root of the new surface area produced. • Derived empirically from operating data and experimental test

results. • Compromise between Rittinger and Kick Theories and is still

used for most mill designs.

• Bond Equation gives us indices for Work Index and Operating Work Index for ores

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xxkE

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General theories of comminution

• Consider the incremental energy dE required to produce an incremental change in size dD. More energy is required to achieve a similar relative degree of size reduction as the product becomes finer:

• Where E’ = specific energy to introduce new surface energy; K = constant; D = particle size; n = value to describe behaviour in different size ranges.

• Rittinger: n=2; Kick: n=1; Bond: n= 1.5

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Particle Size (µm)

Kick slope=0

Rittingerslope=-1

BondSlope =-1/2

Log-Log plot of Energy Consumed vs Size

1cm+, Kick-1000μm, Rittinger

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Comminution Research

Main objectives:• Reduce unit operating cost ($/t)• Increase throughput• Improve downstream process performance as a result of

an improved size specification.• Improve energy efficiency.

• Two kinds of improvements• Fundamental change, novel technologies (e.g. ultrasonic,

microwave, impact and electricity)• Incremental (design, operating practice)

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Factors Affecting Fracturing

• Ability to fracture rocks depends on degree of internal strain which is influenced by:

‒ composition

‒ nature of chemical bonds

•grain boundary cementation/ impurities

•number of internal flaws

•number of surface flaws which decrease surface energy

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Breakage Mechanisms

Four breakage mechanisms

1. Impact

2. Compression

3. Abrasion

4. Chipping

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Impact/Compression BreakageParticle shatters into fragments with minimal secondary breakage (re-breakage)

Size distribution data often fits the Gaudin-SchuhmannSize Distribution Equation

Wp = cumulative fraction passing size X

K = size modulus

m = ln (Y1/Y2)/ln (X1/X2)

for impact/compression breakage n = 1

e.g. crushing

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Attrition Breakage - Rod and Ball Mills

• abrasion + chipping

• abrasion e.g. chalk on board

• chipping e.g. off center loading

Size SizeAbrasion Chipping

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Bond Work Index Power Draw vs. Product Particle Size & Throughput

Bond measured grindabilities of various ores using a batch mill in closed circuit with a screen. For ball mills he maintained a circulating load of 2.5 and for rod mills 1.0.

Bond conducted parallel tests using an 8 ft diameter ball mill and rod mill. Obtained ratio of net power to feed rate.

A plot of Work input vs F80 - P80 produced a straight line. The proportionality constant is the Work Index. The Work Index was obtained using an empirical equation for size reduction in a ball mill.

W = 10 Wi [1/P80 - 1/F80] (kWh/t)

P = W x TPH

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Therefore to estimate W:

1. Measure Rod/Ball Mill Grindability using the StandardProcedure.

2. Calculate Work Index using Bond’s empiricalequation.

3. Use the Work Index to calculate the Work Input, W.

4. Total Power Required = W x Feed Rate.

5. Estimate size of grinding mill using equation relatingnet power per mill versus mill geometry and operatingconditions.

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Typical Work Indices• Determined by:

‒ Crushability Test

‒ Rod Mill Grindability Test

‒ Ball Mill Grindability Test

• Typical Work Index Values (kWh/t)• Bauxite 11• Cement clinker 16• Corundum 33• Dolomite 14• Feldspar 13• Granite 12• Gypsum 8• Hematite 15• Limestone 15• Pyrite 11• Quartz 16

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Example P Calculation

What is the total power required for to reduce particle size from F80 = 1 mm to P80 = 50 µm for ore with Wi = 15 kWh/t at Capacity = 2500 tpd?

P = (2500/24)*10*15*(1/(50)1/2 -1/(1000)1/2)

P = 1716 kW

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Energy Efficiency

• Trommans and Meech

• Selective Comminution

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HVC: 0.3% CuIndustry Avg.: ~ 0.8%

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Process Development

Mine Life Cycle

All mining projects pass through a series of stages over the project life:

• Exploration

• Discovery

• Development

• Production

• Reclamation/Abandonment

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Pre-Feasibility & Feasibility Studies

Feasibility Study is conducted to determine the economic and environmental viability of a project and includes the following sections:

1. Geology and Geological Reserves2. Mineral Reserves, Mining Plan and Mining Methods

What is the difference between geological and mineable reserves?

1. Mineral Processing Plant Design2. Environmental Review3. Capital and Operating Costs4. Net Cash Flow5. Marketing Study

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Mineral Process Plant Design- including Plant Expansions and Retrofits

• Trade-off studies

• Process Selection:

‒ Process Design Criteria

‒ Flow Sheets

‒ Piping and Instrumentation Diagrams

• Process Equipment Specification/Selection

‒ Equipment Specifications

• Process Calculations

• Commissioning and Operations Support

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Steps of a Mineral Development

Project

Basic Engineering

Detailed Engineering

Implementation

company

Geological Exploration

Yes

No

Engineering Studies

Lab and Pilot Tests

Mineralogical Studies

Increasing ProjectCertainty

Mine Design

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Process Development

• Process Development is a blend of science, technology and economics.

• The objective is to develop a process which, when combined with all other aspects of the project, will optimize the overall economics of the project.

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Rocks or minerals

Ore or Valuable MineralsSaleable

Mineral Processing

1. Raw Material2. Technology3. Market4. Economic Aspects5. Environmental &

Social Issues

Transforming Rocks into Ores

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Process Development

• The Flow sheet is critical to establish:

‒Design Criteria

‒Mass balance

‒Water balance

‒Energy balance

‒Tailing disposal

‒Plant lay-out

‒Equipment sizing

‒COSTS

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Flow Sheet Development Objectives

• Determine processing parameters

• Determine mass/water/energy balance of each unit operation

• Evaluate processing alternatives

• Establish the list of main pieces of equipment required

• Create the foundation for the conceptual engineering (feasibility study)

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Flow Sheet Development Goals

• Create a procedure (process) to concentrate minerals with high recovery (hopefully >90%)

• Create a process to obtain concentrates with a high grade (saleable)

• Create an economically feasible process

• Create a safe & environmentally sound process

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Key Information for Process Flowsheet Definition

• Grades (chemical analysis of elements)• Ore-minerals• Gangue-minerals• Mineralogical Factors • Physical Properties• Chemical Properties• Liberation• Process Recovery

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Role of Metallurgical Testing in Project Development

‒ Is very project specific, however, like projects have like metallurgical requirements

‒Should be based on creating existing, saleable products, as well as using known technologies

‒ In most projects, early metallurgical testing is concerned with fatal flaw detection

‒Detailed project test work should ideally follow after ore reserve data is secure.

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Metallurgical Testing

Determine Processing Parameters• Lab Scale Testing‒Evaluate and Monitor Process Performance‒Evaluate Changes to Process Prior to Implementing‒Evaluate Reagents

• Equipment‒Size and Select Equipment‒Process Development

• Pilot Scale‒Confirm Process Selection‒Confirm Scale-Up & Test New Technologies

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Prefeasibility & Lab-Scale Feasibility

Testing

• Confirm flowsheet & identify reagents

• Establish recovery & concentrate quality

• Study variability (met mapping)

• Determine preliminary concentrator design criteria

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Steps to Define Process Flow Sheet

Lab Testing Pilot Testing MineralogicalStudies

Process Flow sheet ModelingMine Plan

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Sample

Rock (full of minerals)

Ore (with defined ore-minerals and gangue–minerals)

Crushing and Grinding Comminution

Mineral Separation Processing

ConcentrateTailing

1. Raw Material2. Technology3. Market4. Economic Aspects5. Environmental &

Social Issues

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• Most critical aspect of anymetallurgical test work.

• Needs rigorous planning

• Must link the knowledge of geologists, metallurgists mine planners and consultants

Sampling

Courtesy of SGS Lakefield Research

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Sample SelectionAll metallurgical test work is limited to the validity &

representativity of the sample(s) tested


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Representative Sample

• Representative sample (head sample): similar to the mineable material

• This sample must be used to define all process parameters, concentration routes and preliminary costs

• Many problems in the mining industry are caused by bad choice of the head sample for process development

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Sampling

• Sampling to Establish Geological Reserves‒Field samples‒Drill cores‒Bulk sampling (e.g. Trenches, Adits)

• Sampling to Develop/Evaluate Process Flow sheet‒Representative head samples (bulk samples:

trenches, adits, composite sample from drill holes, etc)‒Tailing (provide good information about what is wrong

in the plant)‒Concentrates

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Considerations for Composite Samples

Criteria for composites or met mapping matrix

• Rock types(s)• Alteration type(s)• Mineralogy• Head grade• Oxidation state• Mine plan• Unusual occurrences


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Composite samples are best, but…

Excessive compositing can mask valuable metallurgical response information and give misleading conclusions about actual plant performance.


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Head Sample Collection

• Particle size (too much fines cause problems in tests)

• Grade (if it’s too low, the lab tests are not representative)

• Ore oxidation (affects flotation testing)

• Contamination (oil could affect flotation)

• Different types of ore in the same mineral deposit (hard to make a representative composite sample; better test many different types separately)

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pyrite (Py) grain with inclusions of

galena (Ga)

sphalerite (Sp)

chalcopyrite (Cp)

Ref. MASc Thesis of Valerie Bertrand, DMMPE-UBC, Vancouver, 1998.

Micrography of back-scattered electrons

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Process Mineralogy

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• Mineralogy characterizes the physical and chemical characteristics of the ore-minerals and gangue-minerals

• Mineralogical analyses identify the particle size at which the ore-mineral is liberated from the gangue

• Properties of ore-minerals with respect to the gangue can be measured/evaluated

• These factors largely determine the mineral processes to be used in beneficiating the ore


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• Mineralogy: identification and quantification of minerals to establish concentration and/or leaching techniques

• Mineralogical factors: characteristics and properties of minerals determine the technological routes, mineral liberation, impurities, etc.

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• Which valuable minerals can be concentrated?

• Which contaminants will be in the concentrate (penalties)?

• Which technology is available and suitable?

• What are the environmental impacts?

• Which market the product is suitable for?

• How much will be spent to produce saleable mineral products?

Importance of Mineralogical Studies

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Mineralogical Factors

• Mineral types• Texture• Grain shape• Grain size• Mineral associations• Mineral surface• Inclusions• Crystal Structure• Alteration Products• Physical and Chemical Properties• Porosity

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Mineral Analysis Methods

• Hand Specimens (visual mineral identification)

• Rough Chemical Tests (e.g. fizz test)

• Physical Tests (e.g. scratch tests)

• Polarized Optical Microscopy

• X-ray Diffraction

• Electron Microscopy (Scanning & Transmission)

• Other Techniques: Thermal Analysis, Infrared Spectrometry, X-ray Photoelectron (XPS), Auger Spectroscopy

• Mineral Liberation Analysis

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Mineral TypesClasses Examples

Native Elements Gold, Au

Sulfides Pyrite, FeS2

Sulfosalts Enargite, Cu3AsS4

Oxides/Hydroxides Hematite, Fe2O3; Goethite, FeOOH

Halides Fluorite, CaF2

Carbonates Calcite, CaCO3

Nitrates Nitratite, NaNO3

Borates Borax, Na2B4O5(OH)4.8H2O

Phosphates Apatite, Ca5(PO4)3(F,Cl,OH)

Sulfates Barite, BaSO4

Tungstates Scheelite, CaWO4

Silicates Plagioclase, NaAlSi3O8-CaAl2Si2O8

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Impurities and Inclusions

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Penalty Elements

Typical limits for Cu Concentrate

Pb <6% Zn <5%As <0.5%Ni <0.3% Sb <0.2%F <0.1%Bi <0.05%Cd < 0.05%Hg < 0.01%

It’s important to know where are these elements in the ore:

- Forming minerals

- Structure of ore-minerals

- Structure of gangue-minerals

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Specification Cu-concentrate Escondida Mine, Chile

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Degree of Liberation

Mineral of interest not liberated

Assuming that the black particles are the mineral of interest (ore-mineral)

0.07 mm Mineral of interest liberated

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Gravity Separation

High degree ofliberation

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Liberation

• Reduce particle size to improve liberation

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Mineral Liberation and Separation

• Recovery and grade are two measures of separation performance.

• Recovery compares the quantity of valuable metal in the product stream with that in the feed stream.

• Grade usually refers to one stream, such as the grade of the concentrate.

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MLA

Source: Teck

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MLA

Source: Teck

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Grade – Recovery Relationship

Grade of the Concentrate (G)

Recovery (R%)

Mass of Concentrate

0 Low High

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Grade – Recovery Curve

• Trade-Off Between Grade and Recovery:

• Grade and recovery are interdependent for a given feed composition.

• Because liberation is usually incomplete, even in a well-run separation unit, there is a trade-off between grade and recovery.

• If the grade of a product increases, recovery drops. If the grade decreases, recovery rises.

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Physical Properties

• Specific Gravity (ore reserve estimation, gravity concentration)

• Moisture

• Magnetic and electrical properties

• Color/shape characteristics

• Specific surface area

• Degree of friability, hardness, toughness

• Particle Size

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Size Analysis

• Rotap with stack of sieves with largest sieve at the top.

• Mesh size is the number of openings per square inch (i.e. larger mesh number corresponds to smaller size).

• Tyler Sieves, US Mesh Number, Canadian Mesh Number

• Convention is 2 series (successive meshes vary by 2)

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OpeningUS SieveSize

Tyler Equivalentmm in

- 2½ Mesh 8.00 0.312- 3 Mesh 6.73 0.265

No. 3½ 3½ Mesh 5.66 0.233No. 4 4 Mesh 4.76 0.187No. 5 5 Mesh 4.00 0.157No. 6 6 Mesh 3.36 0.132No. 7 7 Mesh 2.83 0.111No. 8 8 Mesh 2.38 0.0937No.10 9 Mesh 2.00 0.0787No. 12 10 Mesh 1.68 0.0661No. 14 12 Mesh 1.41 0.0555No. 16 14 Mesh 1.19 0.0469No. 18 16 Mesh 1.00 0.0394No. 20 20 Mesh 0.841 0.0331No. 25 24 Mesh 0.707 0.0278No. 30 28 Mesh 0.595 0.0234No. 35 32 Mesh 0.500 0.0197No. 40 35 Mesh 0.420 0.0165No. 45 42 Mesh 0.354 0.0139No. 50 48 Mesh 0.297 0.0117No. 60 60 Mesh 0.250 0.0098No. 70 65 Mesh 0.210 0.0083No. 80 80 Mesh 0.177 0.0070No.100 100 Mesh 0.149 0.0059No. 120 115 Mesh 0.125 0.0049No. 140 150 Mesh 0.105 0.0041No. 170 170 Mesh 0.088 0.0035No. 200 200 Mesh 0.074 0.0029No. 230 250 Mesh 0.063 0.0025No. 270 270 Mesh 0.053 0.0021No. 325 325 Mesh 0.044 0.0017No. 400 400 Mesh 0.037 0.0015 * 1.0 mm = 1000 microns (µm

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Sieve Analysis ReportSieve Size Individual

% RetainedCumulative% Retained

Cumulative % Passing

Sieve fraction(µm)

Weight(g)

Aperture size(µm)

+210 0.75 210 0.3 0.3 99.7

-210 + 149 6.25 149 2.5 2.8 97.2

-149 + 105 45.51 105 18.2 21 79.0

-105 + 74 63.01 74 25.2 46.2 53.8

-74 + 53 41.80 53 16.7 62.9 37.1

- 53 + 44 13.01 44 5.2 68.1 31.9

-44 + 37 12.50 37 5.0 73.1 26.9

- 37 67.25 26.9

Total 250.08 100.0

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Cummulative % passing vs. particle size

0

10

20

30

40

50

60

70

80

90

100

20 100 500

Cu

mu

lati

ve %

pas

sin

g

Particle size [microns]

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Particle Size Distributions Equations• Determining PSD is laborious and repetitive

• Typical particle size distributions belong to families of curves, with normal, or log-normal distributions

• You can represent data with mathematical functions, using a small number of parameters.

• The coefficients of the mathematical equation can be used to monitor operations or can be used in models for process simulation.

• The two mathematical functions used most commonly in mineral processing are the Gaudin-Schuhmann and the Rosin-Rammler equations.

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Gaudin-Schuhmann Equation

where, Wp = Cumulative percent passingX = size in micronsK = size modulus (size at Wp = 100)

(measure of top size)m = distribution modulus (slope of

log-log plot of Wp vs X)

The coefficients can be determined graphically or from linear regression. The function is most appropriate for coarse, crushed material, which has been screened at some top size.

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Rosin-Rammler Function

where, Wr = cumulative weight percent retained on XX = size in micronsa = size at which (100/exp) = 36.8% of

particles are retainedb = constant

(slope of plot of ln ln(100/Wr) vs ln x)

Special graph paper available to plot cum. % retained values directly on the Y-axis. A line at cum.% retained = 36.8 is included for estimation of “a”

Originally developed for coal, but fits many mineral size distributions very well, especially finely ground material (e.g. ball mill product)

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Generated using Matlab, 2010

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Particle Size Analysis Methods

• Sieving (wet/dry)

• Cyclosizer

• Coulter Counter (Elzone PSA)

• Laser beam diffraction methods (Malvern)

• Sedimentation Methods -Andreassen Pipette

The resultant particle size depends on method used

• particle size that passes through a sieve

• equivalent spherical diameter of a settling particle

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Gupta et al, 2006

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Particle Size Analysis Methods

Assay / Chemical Analysis Methods

• Wet chemical assays

• Fire assays

• Atomic Absorption

• Inductively Coupled Argon Plasma Emission Spectroscopy (ICP)

• X-ray Fluorescence Analysis

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Size-Assay Analysis – Grain SizeSieve size Wt retained Au DAu

(mesh) (%) (ppm) (%)+6 3.31 8.60 10.87

-6 +8 4.50 7.00 12.02-8 +10 7.80 4.09 12.18

-10 +14 6.70 3.45 8.82-14 +20 6.75 4.01 10.33-20 +28 8.90 2.70 9.17-28 +35 9.80 2.93 10.96-35 +48 8.90 2.54 8.63-48 +65 6.02 0.81 1.86

-65 +100 6.20 1.36 3.22-100 +150 7.55 0.98 2.82-150 +200 6.30 0.82 1.97-200 +270 5.97 1.12 2.55-270 +400 6.30 1.13 2.72

-400 5.00 0.98 1.87Total 100.00 2.62 100.00

83% of gold + 48 mesh

Not necessarily coarse: Au can be fine but notliberated

Mineralogical Factors (grain size) 93


• The behavior of a sample under a well-defined set of chemical and physical conditions

• The technically and economically optimum conditions for concentration or separation to specific project requirements, and

• The ultimate plant design incorporating well-informed selections of processing unit operations, equipment types and sizes, materials of construction and physical arrangements

McNulty, T.P., Mineral Processing Plant Design, Practice and Control, SME 2002

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• Grain Size Analysis

• Assays (grades)

• Geotechnical properties

• Bond Work Index Determinations

• Abrasion Tests

• Concentration Tests (Flotation, Gravity, etc)

• Leaching Tests

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• In Bench Scale‒ Evaluate and Monitor Process Performance‒ Evaluate Changes to Process Prior to

Implementing‒ Reagents (quality and quantity)

• Equipment Selection Based on Parameters Obtained in the Bench Scale and Mineralogical Studies

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Pilot Testing - Purpose

• Verify processes in a continuous operation• Identify differences between batch bench and full scale

continuous‒batch versus continuous grinding‒circuit stability

• Provide scale-up information‒Bench Pilot Full Scale

• Evaluate and test equipment designs and processes• To test conditions on large scale• To evaluate new equipment• Confirmation of material and energy balances, equipment

selection and plant design • Produce adequate sample size for downstream testing

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Cerro Verde

Simplified Process

Flowsheet

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Process Development - Overview

• Review pertinent background information• Sampling (representative sample)• Obtain good mineralogical information• Evaluate concentration possibilities/ alternatives (lab

tests) • Determine important process information• Economic evaluation of process alternatives• Process optimization• Pilot testing?• Process plant design and feasibility study

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Process Plant Design -Objectives

• Review the major steps in process development.

• Introduce the key documents a process design engineer must be familiar with.

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Project Phases

101

STUDIES

FRONT-END ENGINEERING

DETAILED ENGINEERING

STARTUP

CONSTRUCTION

TYPICAL PROJECT PHASES

Typical Total Project Duration About 2-3 Years

PROCUREMENT

Actual Project Phases

STUDIES

FRONT-END ENGINEERING

DETAILED ENGINEERING

STARTUP

CONSTRUCTION

Project Duration: ASAP

PROCUREMENT

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Project Definition

Pro

babl

e A

ccu

racy

W/O

con

ting

ency

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Project Definition

0

10

20

40

50

Order of magnitude estimate

Preliminary Feasibility Estimate

Bankable Standard

Definitive Estimate

Mechanical Completion

Project Completion

% P

rogr

ess

30

% Engineering & Design Duration

3020100

0

A B

10

20

C

8070605040

D

Preparation period

C Bankable standardB Preliminary FeasibilityA Order of magnitude

D Definitive

40

50

70

60

80

100

90

100 90

103

Studies / Conceptual Engineering

Developing project requirements, proposing & optimizing solutions, estimating the costs, and evaluating the economics of a project

Conceptual work such as developing configurations and material balances.

Conceptual engineering work such as developing preliminary material balances and process flow diagrams.

104

53

Project Phases – Front End Engineering

Preliminary Engineering

Completing first-pass process, control systems, and mechanical engineering design activities.

Developing cost estimates for the project.

Supporting environmental studies and permitting.

What documents would typically be prepared for Front-End Engineering?

Design Basis and Scope, PFDs, Material Balance,

Material Selection Diagrams, Plot Plan (layout), P&IDs

Equipment Data Sheets, Instrument Data Sheets, Utility Balances

105

Project Phases – Detailed Engineering

Completing the process, control systems, piping, structural, and electrical design. Incorporating vendor information. Procurement of equipment and bulk items.

What additional documents would typically be prepared for Detailed Engineering?

Isometrics (piping design), Structural Drawings, Electrical Drawings.

106

54

Project Phases - Construction

Building and testing

Engineering responsibilities include:

Supporting construction questions and changes.

Completing field checkout and developing punch lists.

Supporting testing of equipment and systems (Pre-operations).

107

Project Phases - Startup

Commissioning and starting unit operation

Engineering responsibilities include:

Operator training

Supporting operations during startup

Monitoring startup and unit operation

Supporting performance tests.

108

55

Typical Engineering Documents• Process flow diagrams

• P&IDs

• Process data sheets

• Plot Plan/Layout

• Equipment list

• Design criteria

• Piping Line list

• Equipment specifications and vessel sketches

• Utility requirements

• Soils data

• Design specifications (all accounts)

• Sewer and paving layouts

• Concrete, steel & building drawings/sketches

• Piping drawings/sketches: alloy large dia. C.S., special fabrication

• Motor list

• Single-line wiring diagrams

• Area classification (electrical)

• Electrical equipment specifications

• Conduit/cable schedules

• Electrical design drawings/layouts

• Instrument list

• Insulation schedules (equipment and piping)

109

Design Criteria• Set basis for all design and calculations

• Criteria cover ‒ life of mine ‒ throughputs ‒wastes ‒operating parameters ‒maintenance schedules ‒ feed properties ‒product qualities‒+++

110

56

Design Criteria - Example111

Equipment Specifications - Example112

57

P&IDs

Diagram which shows the piping of the process flow together with the installed equipment and instrumentation

Process and Instrumentation Diagrams (P&IDs):

- Schematic representation of the equipment, piping, and instrumentation of a plant

- Formal documentation of a plant engineering design.

P&IDs are required by authorities in many areas of the world.

113

P&ID Development

• Input

‒Process Flow Diagrams

‒Process Description

‒Design Criteria

‒Equipment Datasheet

‒ Instrument Datasheet

‒Line sizing

‒Piping Spec

114

58

P&ID Development - Basic Steps

Conduct The Joint P&id Review

Issue For Hazop Review

Issue For Design

Issue For Construction

Issue P&IDs For Record

115

Flow Sheet - Ball Mill Circuit

116

59

P&ID Ball Mill

117

Process Design - Summary

• Different project stages include:‒Studies‒Front-end engineering (feasibility)‒Detailed Engineering‒Construction‒Commissioning

• At each stage metallurgists create and provide definition for the project, including the following key documents:‒Process flow diagrams (Flow sheets)‒Material Balances (Mass Balances)‒Design criteria‒Equipment specifications‒P&IDs

118

60

COMMINUTIONTECHNOLOGIES

119

Objectives

• Understand basic principles of comminution

• Review common comminution equipment

• Review common comminution circuits

120

61

Introduction

Def: Comminution is the size reduction of solid materials through the application of energy, usually by means of mechanical forces.

Objectives:• To liberate valuable minerals from waste prior to concentration

• To increase surface area available for chemical reaction (e.g. lime, leaching processes)

•

• To produce minerals particles of required size and shape (e.g. industrial mineral products)

1st stage of comminution: Blasting

121

Comminution – Process Significance

‒Power Requirements•Typically accounts for 30% - 50% of total plant•For hard ores, up to 70%

‒Operating costs – typically 50%

‒Capital costs – 20-50%

‒Only a small percentage of power actually used for comminution:•Grinding efficiency may be as low as 1%•Most energy is used transferring heat to the ore.

122

62

Breakage Mechanisms

1. Impact

2. Compression

3. Abrasion

4. Chipping

Crushing – Impact/Compression

Grinding – Abrasion/Chipping

123

Crushing Circuits

Crushing:• Relatively Coarse Sizes• Usually include screening equipment• Usually dry process

Three classes:• Primary• Secondary• Tertiary

124

63

Primary Crushers

• Jaw Crusher• Gyratory Crusher• Roll Crushers• Impact Crushers

125

Jaw Crusher

126

64

Gyratory Crusher

127

Impact Crusher

128

65

Roll Crusher -MMD Sizer

129

Secondary Crushers

• Jaw• Reduction Gyratory Crusher• Cone Crusher• Hammer Mil• Impact Crushersl

130

66

Cone Crusher

131

Hammer Mill

132

67

Impact Crusher

133

Tertiary Crushers

• Roll Crusher

• Short Head Cone Crusher

• High Pressure Roll Crusher

• Impact Crusher

• Hammer Mill

• Finer Reduction Gyratory Crusher

134

68

High Pressure Grinding Roll - HPGR

135

HPGR Roll

136

69

Grinding Equipment

Producing relatively Fine Product Sizes - Usually include size classification equipment – typically hydrocyclones

Tumbling Mills• Autogenous (AG) Mills• Semi-autogenous (SAG) Mills• Rod Mills• Ball Mills• Stirred Mills‒Tower Mills‒Vertical Pin Mills‒Horizontal Pin Mills

137

Ball Mills138

70

Horizontal Stirred (Bead) Mills - ISA

139

Circulating Load• Open Circuit

• Closed Circuit

Circulating load expressed as a percentage of new feed :CL = 100 x O/F

140

Feed ProductComminution Size

Classification

Oversize

Feed Product

Comminution

71

Sizing Classificaton Technologies

Screens‒ Static grizzlys

‒ Inclined vibrating

‒ Sieve Bends

Size Classifiers

‒ Cyclones

‒ Hydraulic

‒ Rake/spiral

141

Plant Availability

• Plant availability is the percentage amount of time the plant is actually running.

• If a plant is designed to produce a set tonnage, a certain amount of downtime for maintenance must be planned.

• Example: 100,000 tpd design at:

‒90% availability; tph = 100,000 tpd/24 h/0.90 = 4,629 tph

‒100% availability: tph = 100,000/24 = 4,167 tph

142

72

Availability Example – Ball Mill Screens

Plant Availability 93%

Circulating Load 90%

Ore S.G. 2.75Screen Operating Density (wt % solids) 50%Ball Mill Screen Feed % Solids 94%Ball Mill Screen O/S % Solids 90%Ball Mill Screen

Undersize (t/d) 13,500Screen Deck Sprays (m3/h) 200

Feed Grade (%Cu) 0.64

Mass Balance

Solids (dry basis) Water Wet basis Copper

t/d Avg t/h S.G. t/h % Solids S.G. m3/h % Cu

143

Myra Fals- Crushing

Circuit

144

73

145

Myra Falls- Grinding Circuit

Highland Valley Copper146

74

Highland Valley Copper AG Mills

147

Highland Valley Copper SAG Mills

148

75

Cerro Verde –Crushing Circuit

149

150

Cerro Verde –HPGR

Grinding Circuit

76

151

Sampling

152

77

Definition

Sampling is the process of securing, in either weight or a sample, a representative fraction / lot for some purpose such as assaying.

Basic Rule for Correct Sampling

Each particle of ore or concentrate must have an equal probability of being collected and becoming part of the final sample for analysis

153

Sampling

154

• Sampling for feasibility– Field samples– Drill core– Bulk sampling

• Trenching• Mined sample

• Plant /Operations sampling― ROM samples― Head samples― Mill feed― Crusher, mill, cons & tailings samples

78

• Determine material characteristics hardness, abrasivity, BWI, angle of repose

• Assess size distributions

• Obtain samples for assay- Determine Feed, Concentrate Grade- Mass Balances- Assess Process Performance (Recovery)- Estimate Metal Production- Identify deleterious elements

Why do we want to sample a plant?

155

Representative Sample – precision, accuracy and confidence

156

True Value

Mean

Accuracy

PrecisionRepeat 2

Repeat 1

Sample

AS

SA

Y

79

Accuracy and Precision

157

From Statistics, recall that for a set of values y1, y2…yn, the mean value is:

and the variance of x is:Var(Y) = s2 = (Yi – Y)2/(n-1)Where, s is the standard deviation.

n-1 = the degrees of freedom

For several sets of results, the variance of the mean value is:

Var(Y)= s2/n (1)

n - number of sample increments

s - standard deviation associated with determining Y

n

yy

n

ii

1

158

Sample Variance

80

The true mean can be expressed as the estimated mean plus/minus a confidence interval as indicated in the following expression.

µ = Y ± t,1-V(Y)1/2 (2)

µ - true mean valueY- estimated mean valuet,1- - t-statistic at

degrees of freedom, and probability(see statistic reference)

Equations (1) and (2), can be used to determine number of increments for a desired precision

n = [t,1-s/(µ-Y)]2 (3)

159

Confidence Interval

Example 1- Precision and Accuracy

160

Determine the standard deviation and the 95% confidence interval for the following Au grades.

Assay Au (g/t)1 5.452 4.733 4.664 5.395 4.71Mean 4.99

81

V(Y) = S2 = (Yi - Y)2/(n-1)S = 0.396

Y = Y ± t,1-V(Y)1/2 [Eq. 2] = n-1 = 4 = 0.95

from table of t-statisticst,1- = t4,0.05 = 2.776

therefore,Y = 4.99 ± 2.776x0.396Y = 4.99 ± 1.099 g/t Au

161

Example – Confidence Interval

Example 2 - Confidence

162

Estimate the number of samples required, at 95% confidence, to obtain a difference of not more than 0.1 g/t Au between the true mean assay estimate and the estimated mean. Assume infinite degrees of freedom.

n = [t,1-S/(µ-Y)]2 [Eq. 3]

(µ-Y) < 0.1 g/t Au

from t-statistic tablet, 0,0.95 = 1.96

use calculated S,S = 0.396

82

Therefore, the number of increments required is:

n = (1.96x0.396/0.1)2

n = 60.2 increments or cuts of a stream.

Similarly,Max. Difference Number of Samples

0.2 g/t 15.1 (15)0.3 g/t 6.7 (7)0.4 g/t 3.8 (4)

163

Example 2 - Confidence

Sample Size for Desired Precision, Accuracy and Confidence – Gy’s Method

W = C x [d3/σ2]

Sampling Error Variance determined by Pierre Gy, 1982σ2 = Cd3/W

Where,

σ2 - sampling error variance

C - sampling constant which is a function of material characteristics.

d - nominal top size, cm

W - sample mass, g

164

83

Sampling Constant, CC = fgmL

f - shape factorg - size distribution factorm - mineral composition factorL - liberation factor

Re-arranging the equation, provides an expression for sample size.

W= fgmLd3/S2

165

Gy’s Method

f – Shape factor

f = 1 f = 0.5 f = 0.1 f = 0.2

g – size distribution factor

Wide range in size (d0.95/d0.05 >4); g = 0.25Medium range in size (2 < d0.95/d0.05 <4); g = 0.50Small range in size (1 < d0.95/d0.05 <2); g = 0.75Uniform size - pulverized (d0.95/d0.05 = 1); g = 1.0

166

84

m – mineralogical composition factor

m = (1-a) [(1-a)m + ag]/a (units – g/cm3)

where a = fractional average mineral contentm = specific gravity of the mineralg = specific gravity of the gangue

167

l – liberation factor

l = (dL/d)0.5

dL= Liberation size d = 95% passing size

Francois-Bongarcon and Gy (2002) proposed general form of l=(dL/d)b

- where in the case of gold mineralization, the value of bis almost always experimentally found close to 1.5

168

85

Example

Information is given for a copper/gold process.

If W= fgmLd3/S2

What size sample should be obtained for assay?

a. Mill discharge

b. Flotation feed

169

Mill details

Ore typeFeed RateMill DischargeFlotation Feed SizeFlotation Pulp DensityLiberation size, d1m (CuFeS2)g (gangue)Sampling error

Massive sulphide copper2500 tpd95%-0.1 cm95% -48 mesh (0.0297 cm)40% solids.200 mesh (0.0074 cm)4.2 g /cm3

2.7g /cm3

<0.01% Cu (0.0289%CuFeS2)

%Cu ore = Atomic weight of Cu x % Chalcopyrite in oreMol. Wt. Chalcopyrite

170

86

a. Find f - Particle Shape Factorf = 0.5 for most ores, f= 0.2 for Au ores

b.Find g - Size Distribution Factorselect according to ratio d/d’ d - top size; d’ - lower size (5% passing size)d/d’ g>4 0.2524 0.5<2 0.751 1.00

Mill discharge d = 1000 µm d’ = 100 µmFlotation feed d = 300 µm d’ = 20 µmg = 0.25

171

c. Find m-Mineralogical Factorm = (1-a) [(1-a)m + ag]/a

From mineralogical analysis, chalcopyrite grade estimated to be 1%

for a = 0.01m = 414.3

d. Find L – Liberation Factor: L = (dL/d)0.5

Mill Discharge: L = (0.0074/0.1)0.5= 0.272

Flotation Feed: L= (0.0074/0.0297)0.5 = 0.50

172

87

e. Calculate W – sample mass

W = fgmLd3/ S2

Gy recommends a factor of 2 to 3 times larger thancalculated

f. Calculate pulp volume

Flotation Feed @ 40% solids

Volume ore = 24,366/2.7 = 9,024 mL

Volume water = 1.5 x 24,366/1.0 = 36,549 mL

Total Volume = 45.57 L

173

Comparison od Sample Sizes

174

Parameter Mill Discharge Flotation Feed

d (cm) 0.1 0.0297

S2 8.35 x 10-8 8.35 x 10-8

f 0.5 0.5

g 0.25 0.25

m 414.3 414.3

L 0.272 0.499

W (kg) 168.6 8.12

Gy x factor of 3 505.8 24.4

88

If the desired copper assay to be within +/- X% Cu, how do you calculate desired value of s?

a) Select desired sampling accuracy e.g. +/- 0.05% Cu, 95 out of 100 times

b) For a probability of 95%, the number of standard deviations needed to give the above confidence level is1.96 (For 99%, it is 2.576)

c) Then 1.96s = ao/a

where ao is desired sampling accuracy (0.05% Cu)

a is the Cu assay in the ore

175

Coning and Quartering

176

89

Jones Riffle splitter

177

Jones Riffle splitter178

90

Jones Riffle splitter for -1 cm

179

Rotary splitter

180

91

Sampling system

• Regular increment

• Uniform speed

• Normal direction

• Proper cutter

• Minimize error

181

182

92

Crushing

183

Overview - Crushing

• Applications

• Crusher features & terminology

• Primary crushing

• Secondary and tertiary crushing

• Crusher selection

184

93

Crushing & Screening – Part 1

185

Introduction

Terminology

Crushing Principles

Crusher Types

I

Introduction– why do we crush?

• Improve material handling characteristics

• Generate products of a particular size fraction – e.g. aggregates

• Prepare for downstream processes – increase surface area, reaction rate, match feed properties

186

94

Applications

187

Preparation of heap leach dumps

Open Pit(oxides)

Primary Gyratory Crusher

Conveyor

Heap Leach HeapTo leach orPressure OX

U/S

O/S

Screen

188

95

Prepare mill feed product

Mill Feed Bin

Secondary Crushers

Primary Crusher

ROM/Overland conveyor

189

TerminologyTerms

F80 – 80% passing size fraction in feedP80 – 80% passing size fraction in

productGape – feed opening dimensionOSS – maximum jaw gap at dischargeCSS- minimum jaw gap at dischargeThrow = OSS - CSSMechanical reduction ratio = Gape/OSS

(jaw) or Gape/CSS (cone/gyratory)Particle reduction ratio = f80/p80

OSS

Gape

CSS

F80

P80 P80

190

96

Terminology

Frame

Pitman

Jaw

Bowl

Mantle

Toggle

Eccentric

Liners

191

Types of Crushers

• Jaw Crusher• Gyratory crusher• Cone crusher‒Standard‒Short-head

• Roll crushers‒Single roll‒Double roll

• Impact Crusher (interparticle crusher)• Hammer mills

192

97

Jaw CrusherFeatures‒Spec by throat dimensions

eg 80x60in‒Sized by max particle size

in feed‒Gape 440-1200mm‒Feed ~ 80% gape‒OSS > P80 > CSS ‒Reduction ratio ~ 5:1 max‒45-250 kW‒10-1600 tph‒Prefer blocky, coarse

material, can be wet‒Robust, simple, compact

design‒Manual or semi-auto

operation

193

Jaw Crusher

194

98

Gyratory CrusherFeatures‒Specify by Gape/Mantle

dimension e.g. 60x102in‒Sized by throughput‒Gape 0.7-2,5m‒Max feed size 80% of

gape‒P80 ~ OSS‒Reduction ratio ~ 8:1 max‒500 – 7000 tph‒200 – 1000 kW+, mantle ~

100rpm‒Can accept wide range of

feed types‒Expensive and complex

vs. jaw, but higher throughput

‒Manual or auto operation

195

Gyrato

ry Cru

sher

196

99

Gyratory Crusher

197

Cone CrusherFeatures‒ Spec by mantle diameter, e.g. 6ft

‒ Sized by product spec & throughput

‒ F80 - 50% of mean gape

‒ P80~CSS (fine)

- Theoretical reduction ratio can be 13:1 max, prefer 3:1

- 90-650 tph typical

- 45-350kW , up to 750kW

- Compact but complex, higher shaft speeds, finer applications only

- Automatic operation only

198

100

Roll Crushers – MMD SizerFeatures‒Softer materials (coal and

chrome)‒ In-pit and underground sizing

for material handling‒High throughputs in soft

material‒Single- or double rolls‒Allows fines to fall through‒F80 0,3 – 2m‒ ‘Coarse’ product profile, low

reduction ratio

199

Impact Crushers and Hammer Mills

• Interparticle crushing

• Softer materials

• Lower throughput, 5 – 100 tph

• Low wear / unit throughput

• Require dry, regular sized feed

200

101

Crushing – Part 2

201

Primary Crusher selection‒ Duty & Capacity

‒ Feed characteristics

‒ Product requirements

Worked examples

Primary Crusher Duties

• Primary crusher feed – variable tonnage, topsize, size distribution

• Product requirements not usually strict• Typically prepare feed for conveying, stockpiling, or feed

preparation for secondary crush• Capacity dependent on feed size, Work index, crusher size,

speed, throw, CSS

202

102

Selection parameters

• Duty

• Feed arrangement

• Location

• Topsize

• F80

• Fines/Clay

• Throughput

• P80

• Work Index

• Abrasion Index

• Hardness

• Product size distribution –preferred sizes

• Discharge arrangement

203

Crushing Principles

• Understand feed characteristics

‒Throughput (tons per hour)

‒Size distribution (f80)

‒Work Index (kWh/ton)

‒Abrasion & Hardness (Mohs or or mass-loss test)

‒Moisture content (%H2O by mass)

• Understand desired product properties

‒Number of products (separate size fractions)

‒Size distribution – p80 = f80 to next process

• Crushing is a route from one state to the other

204

103

Crushing Principles Power Estimate

From Comminution Theory:

Wi = 10BWi(1/√p80-1/√f80)Where Wi = specific work index

BWi = Bond Work Index for material

Power = k (Q x Wi )Where k = 0,75 (primary), 1 (secondary)Q = throughput

Apply safety factors for surge, feed size variation, environment ~ maybe 25-30%

205

Crusher Selection206

104

Typical Crusher Ranges

207

Preliminary Crushing Sizing

1. Estimate Free Run in Feed (if screened prior to crushing)

2. Estimate Crusher Capacity

3. Estimate F80 and P80

4. Estimate Power Requirements

5. Determine top size

6. Select crusher

208

105

Jaw Crusher Selection

• Example:Quartzite – BWI ~ 12 kWh/tThroughput = 200 tphf80 = 300 mm, topsize

450mmFeed – decline conveyor

• Discharge to secondary cone ~ f80 = 80mm

• See Metso Handbook:

Gape = Topsize/80%

CSS < p80 < OSS

Choose crusher

Check capacity

Size motor

209

Jaw Crusher Section

Jaw

F80 300000um

P80 80000um

Q 200t/h

BWi 12kWh/t

Wi 0.205kWh/t

k 0.75

SF 1.3

P 40.0kW

CSS ~ P80 ~ 80 mmTop size, 450 mmTop size = 80% gapeGape = 563 mm

Metso C-Series Jaw Crusher:C106

210

106

Typical arrangement211

Gyratory CrusherFeatures‒Specify by Gape/Mantle

dimension e.g. 60x102in‒Sized by throughput‒Gape 0.7-2,5m‒Max feed size 80% of gape‒P80 ~ OSS‒Reduction ratio ~ 8:1 max‒500 – 7000 tph‒200 – 1000 kW+, mantle ~

100rpm‒Can accept wide range of

feed types‒Expensive and complex vs.

jaw, but higher throughput‒Manual or auto operation

212

107

Preliminary Crushing Sizing

1. Estimate Free Run in Feed (if screened prior to crushing)

2. Estimate Crusher Capacity

3. Estimate F80 and P80

4. Estimate Power Requirements

5. Determine top size

6. Select crusher

213

Gyratory Crusher Selection

Example:

Copper Porphyry Ore – BWI ~ 15 kWh/t

Plant design throughput = 50,000 tpd

Crusher operating time = 7 x 2 x 8 hr shifts/week.

F80 = 420mm, top size 1200mm

Feed = haul truck

Discharge – overland conveyor ~ 150mm

214

108

Gyratory Selection - Example

F80 420000umP80 150000umQ 3125t/hBWi 15kWh/tWi 0.156kWh/tk 0.75SF 1.3P 475kWTop Size 1200mmGape 1500mm

215

Gyratory Crusher Capacities

216

Source: Metso Crushing Handbook

109

Gyratory Selection - Example

F80 420000umP80 150000umQ 3125t/hBWi 15kWh/tWi 0.156kWh/tk 0.75SF 1.3P 475kWTop Size 1200mmGape 1500mm

Metso: 62-75 Gyratory, increase availability or move to 165 OSS.

217

Typical Arrangement

218

110

Summary: Jaw vs Gyratory

Jaw• Lower max capacity, f80

than gyratory• Compact, robust, cheap• Must screen out fines• Prefer reduction ratio ~ 3:1• Limited by feed

arrangement

219

Gyratory

• Highest capacity, f80

• Complex, robust, expensive, but low cost/tph

• Can accept high fines ratio

• Better reduction ratio

• Accepts all feed methods

• Discharge arrangement needs care – high tph

Screening:Features, Design

220

111

Objective

• Understand principles of screening

• Review screening equipment

• Learn how to size a screen.

221

Purpose of Screening

Definition:

- Screening is a mechanical process which accomplishes a separation of particles on the basis of size and their acceptance or rejection by a screening surface.

• Prepares products of appropriate sizes for downstream process or final sale.

• Efficiency is determined by the perfection of separation based on the aperture size.

222

112

Screening

• Effective from 300mm to 40μm

• Less efficient at finer sizes

• Typically:

‒Dry screening >5 mm

‒Wet screening <250μm

223

Screening Applications

Metso

224

113

Screening Applications

• Scalping (oversize rejection)

• Sizing

‒Oversize / recycle

‒ Intermediate sizes, feed splitting

‒Final sizing (mill product screens)

• Feed preparation

• Dense media recovery screens (Drain and Rinse Screens)

• Dewatering/desliming

• Trash removal

225

Screening Theory

• Screen Bed

226

114

Screening Principles

ABC

A - feed zoneB - stratificationC - separation

UndersizeOversize

Saturated zone

v

f, a

L

227

Particle flow rate through deck related to screen length

228

Zonesa. Feedb. Stratificationc. Separation

115

Screening Mass Balances

F=200 t/hfx = 0.7ox = 0.2O?U?

229

Mass Balance Example

• F = O + U

• Ffx = Oox + U

• If F = 200 t/h, fx = 0.7, ox = 0.2, determine O, U.

‒O = F(1-fx)/(1-ox)

‒O = 200(1-0.7)/(1-0.2)

‒O = 75 t/h

‒Solve for U

‒U = 125 t/h

230

116

Screen Efficiency

• Undersize Removal Efficiency in Oversize

• Efficiency of Undersize Recovery

)1()1(

xx

u oO

fFE

)1( xx

xx

xu of

of

Ff

UR

(1)

(2)

Example. Eu = 80%

Ex. Ru = 89%

231

Types of Screens

• Vibrating Screens

‒ Inclined,

‒Grizzly,

‒Horizontal,

‒Dewatering,

‒Banana screens

• Static

‒Self cleaning grizzly

‒Trommel

‒Linear

232

117

Screen Types233

Multi-deck screenScalping screen

TrommelLinear Screen

Features

234

Frame

Top deck

2nd deck

3rd deck

Feed plate Side plates

Drive

Flow

118

Screen Surfaces/Medium

Surface Characteristics:

• Must withstand stress and loads, and be abrasion and corrosion resistant.

Materials:

• Monel, stainless steel, abrasion resistant high carbon steels, rubber, and reinforced polyurethane.

Best surfaces provide:

• -Required opening size and capacity

• -Wear resistances

• -Minimum replacement cost per unit of throughput

235

Media SelectionWoven wire cloth -all sizes:

Rail grizzly bars

- coarse sizes:

Wedge wire

- fine and difficult screening duty

Poly panels – wear and corrosion resistant, medium fine to medium coarse

236

119

Screen Aperture Shapes

• Square: coarse applications, accurate sizing

• Rectangular / Parallel: - higher capacity (higher area), less susceptible to blinding, suited to needle shape particles, good for high moisture ores with clay.

• Rectangular / Perpendicular - less blinding for dry screening, longer screen life, higher efficiency.

237

Screen Surfaces

Woven Wire - Traditional

Profile Wire/Bar

• Parallel to flow used for coarse screening

• Perpendicular to flow used for wet fine screening, desliming and dewatering.

Perforated plate

• Pros: high wear resistance, less blinding, higher efficiency, higher accuracy.

• Cons: more expensive, less open area

• Polyurethane/rubber screens now standard:

‒ less expensive, robust

238

120

Influence of Variables on Screen Performance

• Screen Area/Open Area‒Effective Area < Actual Area‒Capacity ∝ screen area

• For a given area‒Capacity ∝ width‒Efficiency ∝ length

• Length is usually 2 to 3 times width

• Best capacity and efficiency when solids 1 particle layer in depth at end of screen

239


• Aperture Size/Shape

‒ aperture size, capacity

‒ aperture size, efficiency

‒ aperture size, blinding

• Slope

‒ slope, capacity

‒ slope, effective aperture size

‒ slope, Constant Efficiency up to Critical Slope, then .

‒Typical Slopes: 20 - 25

240

121


• Deck Motion (Speed/Throw)

‒Purpose: To lift material causing stratification and conveying of particles.

‒Vibration: Inflow vs. Counter Flow, circular/elliptical motion

‒Amplitudes: Typical 3-15 mm

‒Frequency: Normal 700-1000 cycles/min

‒Frequency: High Speed 3600 cycles/min

241


• Amplitude:

‒Too small allows blinding

‒Too large reduces efficiency

‒Too large reduces bearing life

• Elliptical Circular Motion

‒ In flow increases capacity

‒ In flow may decrease efficiency

‒Counter flow decreases capacity

‒Counter flow increases efficiency

‒Counter flow may increase blinding

242

122


• Speed:

‒High speed used with small throws, small particles

‒Low speeds used with large throws, large particles

243

Properties of Feed Material• Particle Size/Shape/Distribution

‒At fixed screen opening particle size, Capacity

• Near size particles = 0.5 to 1.5 of screen size.

‒Amount of near size is rate determining

‒ near size, capacity, blinding, efficiency

‒To maximize capacity, exposure of fines and near size to screen

• Use upper screen deck to reduce oversize, ensure good stratification, optimize throw

244

123

Properties of Feed Material

• Moisture Content

‒Moisture + Clay leads to agglomeration and blinding

‒ In severe cases:

• can heat wire screen,

•Switch to wet screen

•Add rubber ball tray under screen

245

Properties of Feed Material

• Feed Rate/Bed Depth

‒Bed depth = function of (Feed rate, slope, size distribution, circulation direction)

‒Bed depth increases with increasing feed rate

‒Screen width selected to maintain bed depth at discharge, therefore screen width determines capacity.

246

124

Screen Sizing and Selection

Two methods presented (many more exist):

1. VSMA Screening Surface Area Calculation,Developed collaboratively by VSMA, screen manufacturers to ensure consistency and compatibility of screening equipment. Based on theoretical surface area of a ‘perfect’ screen in an application.

2. Metso Handbook

247

Screen Sizing and Selection

Screening Area = USA x B x C x D x E x F x d x SF

• Where:US = undersize tonnage (t/h)A = basic capacity (m3/h/m2)B = oversize percentage factor (of the deck concerned)C = efficiency screening factorD = halfsize percentage factor (of the deck concerned)E = efficiency screening factor for wet screeningF = deck factord = bulk density (t/m3)SF = free area factor

• In calculating SA, other factors are important:M = split (mm)OS = oversize tonnage (t/h)HS = half size tonnage (t/h)

248

125

Screening Unit Efficiency and CapacitySelect:

Factor A = basic capacity for woven wire cloth

Factor E = efficiency screening factor for wet screening

Factor C = screening efficiency factor

normal screening C = 1

high efficiency screening C = 0.8

light screening C = 1.2

Factor F = deck factor

1st deck F = 1

2nd deck F = 0.9

3rd deck F = 0.8

4th deck F = 0.7

249

Oversize and Undersize

Factors

250

126

Free Screening Area and Efficiency

251

SF –Surface Factor

252

127

Check Bed DepthIf the motion is with

flow:

s = 1100 m/h = 0,3 m/s

If the motion is counterflow:

s = 800 m/h = 0,22 m/s

Average screen

Dry process, we must have D < 4 x aperture

Wet process, we must have D < 6 x

Bed depth at end of deck :

D = OSlds

WhereD = bed depth (m)OS = oversize tonnage (t/h)l = screen width (m)d = bulk density (t/m3)s = material travel speed (m/h)

253

Choosing media aperture and material for applicationRelief deck• can be required for 2 reasons :• to have a smaller bed depth at the split

considered• because of the excessive feed size falling on

the deck considered (see table).Important :• Data based on observations of field life of

screen deck• Increase of in size 20% is suitable for gravels• Coarser feed at smaller apertures requires

poly decks• Coarser feed at larger apertures requires

perforated plate or grizzly decks

254

128

Correcting for MoistureMoisture = H20%This factor influences the efficiency of fine screening. When the split (M) is

less than 10mm, we consider :If H20% < M Use conventional woven mesh

8If M < H20% < M Use stainless or wedge wire cloths

8 4

If M < H20% < M Use anti-blinding stainless cloths4 2

If M < H20% < M Use ani-blinding or self cleaning deck2

If M < H20% Wet process is required

*Note - if there is clay content, screening capability must be checked in laboratory.

255

Screening:Sizing and Selection

Primary Source: AJ Gunson

256

129

Objective

• To review the Metso screen sizing method.

• To size a screen through an example problem.

257

Reference: Screen

Conversions

258

130

Screen Sizing Data

a) Features of material to be screened:

• Density

• Maximum feed size

• Product granulometry

• Particle shape

• Moisture content

• Presence or lack of clayey material

• Temperature etc.

b) Capacity

c) Product separation ranges

d) Desired efficiency

e) Type of job:

• Washing

• Final classification

• Intermediate classification etc.

f ) Any room and weight limitations

g) Degree of knowledge of the material and desired product

259

Screen Area

• Screen area determination (Metso):

• Qu = t/h undersize in the feed

• S = Safety factor (1 to 1.4)

• A = Screen capacity for required size (t/h/m2)

• B to L = Screen Area Modifying Factors

LKJIHGFEDCBA

SQArea u

260

131

Screen Sizing Factors: A – Screen Capacity

Metso

261

Screen Sizing Factors: A – Screen Capacity

Metso

262

132

Screen Sizing Factors: B – Oversize Fraction Factor

Metso

263

Screen Sizing Factors: C

Metso

264

133

Screen Sizing Factors• D: Position of screen deck (from top) factor

• E: Wet screening factor, desired separation size.

(1 if dry screening)

• F: Material weight factor (can be graded)

Metso

265

Screen Sizing Factors

• G: Open surface factor

• H: Shape of screen surface opening factor

• I: Particle shape factor

• J: Screen efficiency factor (%)

%50

%__ areaopenActualG

Metso

266

134

Desired separation size vs. actual required

screen size

• Due to screen slope, actual screen size must be larger than the desired separation size.

• 3% to 5% of the screen undersize may be slightly greater than the specified size – this difference is taken into account in the sizing factors and does not need to be separately calculated.

267

Screen Free Open Area: A

268

135

Screen Free Open Area: B

269

Screen efficiency, based on screen loading

Metso

270

136

Screen Sizing Factors

• K: Screen type factor

• L: Feed moisture factor (% moisture by mass)

Metso

271

Screen Sizing –Width & Bed Depth

• Width:

• Where,

B = nominal screen width (m)

Q = oversize (discharge) capacity (m3/h)

Not (t/h): Typical bulk density, 1.6 t/m3

d = material layer thickness (mm)

V = material transport speed (m/s)

• Dry process, d should be < 4 x separation size

• Wet process, d should be < 6 x separation size

dv

QB

6.3

272

137

Screen SizingMaterial Transport Speed

Metso

273

Screen SizingRecommended Feed Bed Depth

Metso

274

138

Screen Sizing:Recommended Discharge Bed Depth

Metso

275

Typical Screen Models

Metso

276

139

Screen Sizing Example

a) Features of feed material:

• Density: 2.7 t/m3

• Max. feed size: 100mm

• Product granulometry

• Particle shape: flaky

• Moisture content: 3%

• Presence or lack of clayey material

b) Capacity: 380 t/h

Mesh (mm) 100 25 13 10 5

% Passing 100 75 45 30 22

277

Screen Sizing Example

c) Product separation ranges

+25mm, 10 to 25mm, -10mm

d) Desired efficiency: 90%

e) Type of job:

• Dry screening

• Dual sloped, variable elliptical screen

• Inclined screen at 20 degrees, circular motion (coarse)

f ) No room/weight limitations

g) Degree of knowledge of the material and desired product

278

140

Problem Solution

• Set up mass balance

1st Screen:

• Qu =285 t/h; Assume Safety Factor S=1.0

• A = 54 t/h/m2 (Either Factor A chart)

Mesh (mm) % Passing (Cumm.)

t/h (Cumm.) Size Fraction t/h (fraction)

100 100 380 +25 95

25 75 285 -25+13 114

13 45 171 -13+10 57

10 30 114 -10+5 30.4

5 22 83.6 -5 83.6

380 t/h

285 t/h

95 t/h

114 t/h

171 t/h

279

Problem Solution

• B = 1.35, from Factor B chart.

%O/S in feed = 100% - 75% = 25% @ +25 mm.

• C = 1.1, from Factor C chart.

%U/S ½ the opening size: Opening size: 25mm

% passing 25/2 ~ 13mm: 45%

• D = 1, first deck.

• E = 1, dry screening.

• F = 1, solids density = 2.7 t/m3

280

141

Problem Solution

• G = Open Surface factor

‒Assume a heavy square hole, which is appropriate for the size range and the flaky material.

‒From the “Desired separation size vs. actual required screen size” table, for at 25mm product size, the screen size must be between 27-30mm, or 28.5mm, or around 1 1/8". For a 1 1/8" heavy screen, the actual screen free open area is 61%.

G = actual open area/50% or 61%/50% = 1.22

• H = Screen surface opening factor, or 1.0 for square openings.

281

Problem Solution

• I = Particle shape factor, or 0.9 for flaky particles (from table).

• J = Screen efficiency factor, or 1 assuming standard 90% efficiency (from table)

• K = Screen type factor, or 1.3 assuming a dual slope variable elipitical screen (from table)

• L = Feed moisture factor, or 1.0 assuming 3% moisture (from table)

282

142

Problem Solution

• A1 = (2851)/(541.351.11111.210.911.31)

• A, deck 1 = 2.5 m2

• A2 = (1141)/(330.90.790.9111.0410.911.31)

• A, deck 2 = 4.4 m2

LKJIHGFEDCBA

SQArea u

283

Problem Solution –Width & Bed Depth

• Reviewing the typical screen sizes, the Metso 5 x 12 model meets the minimum area required for the 2nd deck (25mm & 10 mm). Bed depth.

Variable Deck 1 Deck 2

B (m) 1.5 1.5

O/F (t/h) 95 175

Bulk Den (t/m3)

1.6 1.6

Q (m3/h) 59 107

v (m/s)* 0.58 0.58

d (mm) 19 34

dv

QB

6.3

*Inclined Screen at 20, circular motion, coarse classification

D is less than 4 x separation size for both decks, 5 x 12 model passes depth test, screen size is adequate.

284

143

Crushing & Screening:Plant Design

Primary Sources: AJ Gunson, B Klein

285

Outline

• Screen Efficiency and Circulating Loads

• Factors Affecting Crusher Design

• Crushing Plant Design Procedure

• Flow Sheet Examples

• Design and Layout

• Design Criteria, Operability & Cost

• Operation & Control

• SAG vs. HPGR

286

144

Screen Efficiency

• Undersize Removal Efficiency in Oversize

• Efficiency of Undersize Recovery

)1()1(

xx

u oO

fFE

)1( xx

xx

xu of

of

Ff

UR

(1)

(2)

287

Crushing Circuits

• Closed Circuit A

• Closed Circuit B

288

D, dx ProductCrusher Size

Classification

Oversize

Circulating load expressed as a percentage of new feedCL = 100 x O/D

FeedSize Classification

CrusherOversize

Product

cx=% passing x in CD = tph fresh feeddx = % passing x in DF = t/h screen feedfx = % passing x in FO = tph screen oversizeox = % passing x in OU = tph screen undersizeC = tph crusher discharge

D, dx

U

U

F, fx

F, fx

O, ox

O, ox

C, cx

C, cx

C=O

C=F

D = U at steady state

145

Screen Efficiency and Circulating Loads

• Circuit A

As F = O + D, substitute in efficiency eqn 1 & solve for O/D

As D = U, substitute in equation 2 and solve for O/D

1

1

1

x

u

fED

O

1)(

1

xu fRD

O

289

Screen Efficiency and Circulating Loads

• Circuit B: As D = U, C = O

F(1-fx) = D(1-dx)+O(1-cx)

Substitute in equation 1 & solve for O/D

• Similarly: Ffx = Ddx+Ocx

)1(

)1(

xu

x

cE

d

D

O

xu

xu

cR

dR

D

O

1

290

146

Factors Affecting Crusher Design

• Plant throughput / availability

• Desired product size for downstream process

• Ore Characteristics

‒Size distribution

‒Moisture content

‒Density

‒Crushability

‒Abrasiveness

• Climatic Conditions

291

Crushing Circuit Planning

• Choose flow sheet and select equipment sizes for efficient metallurgical performance at designed capacity

• Ensure good access for maintenance and that future expansion or modification can be carried out without difficulty

• Plan for minimum capital and operating costs, while allowing for efficient metallurgical and mechanical performance.

292

147

Crushing Plant Design Procedure• Know the feed size and tonnage, product size req’d

• Choose # of stages of crushing (reduction ratios!)

‒ Decide open or closed circuit at each stage

‒ Draw flow sheet. Check your logic!

• Select crushers

‒ Optimum crusher open/close side settings

‒ Estimate product stream characteristics (tph, P80)

• Select screens

‒ Estimate product stream characteristics (tph, P80)

• Determine if parallel circuits are required

• Determine capacity of surge bins and conveyors

• Size motors

‒ Draw up equipment list

Remember – it’s an iterative exercise….

293

Crushing Reduction Ratio

294

148

295

Metso

Crushing Reduction Ratio

Circuit Design & Layout

• Feed method and orientation• Material handling criteria set chute/bin angles and opening

sizes (angle of repose & 3 x max size)

• Conveyor length ~ feed height

• For bins, feed height ~ bin capacity

• Check recycle streams, conveyor or structural clashes

• Check centre – centre distances

• Review maintenance access (personnel, cranes & hoists)

296

149

Design Criteria, Operability and Cost

• Multi stage crushing usually required

• Open circuit means less size control

• Closed circuit usually means larger capacity units

• Scalping prior to a crusher reduces unit size

• Crusher, chutes, feeders & conveyor size ~ particle size

• Surge capacity > cost, increases availability

• Unit capacities must account for tonnage, size, grade, moistureand operational variabilities

• Good maintenance facilities >cost, but < downtime

• Design last crusher circuit running @ 100% load.

297

Crusher Circuit Design Basics -1

• Multi-stage crushing usually required – more efficient and typically a single crusher cannot provide required reduction ratio.

• Closed circuit of final stage necessary, of earlier stages may not improve efficiency

• Crushers, feeders & surge bins need to be able to handle largest rock to stop bridging (3-5 x top size)

• Capital & power costs per ton at same closed side setting does not decrease significantly with crusher size – feed size and capacity more important than capital and power costs – oversize equipment.

298

150

Crusher Circuit Design Basics -2

• For a given crusher, power draw increases linearly with feed rate.

• At a given power draw, product size with throughput.

• fines leads to throughput, power

• Steady feed leads to throughput – surge capacity important

• Primary crushers have intermittent feed, so need to be oversized.

299

Crusher Cavity Operation

300

151

Operation and Control

• Maintain product size and throughput targets, maximisethroughput or optimise size

• Equipment health!

‒Electrical status (on/off/trip/emergency stop)

‒Temperatures and pressures

• Interlocks – startup, shutdown and safety

• Monitor system variables vs. design criteria (throughputs, levels, densities etc.)

301

Operation and Control Variables 302

1

23

4

5

6

7

8

9

10

11

12

13

14

SCALPING GRIZZLY-on/off-New feed rate

STOCKPILE/BIN-Level-Feed in-Feed out

-Feeders on/off-Feed rate (v/s)

(

SIZING SCREEN-Motor on/off

SECONDARY CRUSH-Motor on/off/power-Cavity level-CSS-Hydraulic status-temperatures

TERTIARY CRUSH-motor on/off-Cavity level-CSS-hydraulic status-temperatures

SECONDARYSCREEN-Motor on/off

PRIMARY CRUSH-Motor on/off + power-If hydraulic then hydraulic healthy, CSS,Tramp warning

CONVEYORS GENERAL-motor on/off-belt condition-maybe variable speed-pull cord

152

Flow Sheet Examples

• High capacity crushing (iron ore)

• Coal plant feed preparation

• Hard rock crushing circuit

• HPGR vs SAGB

303

1

2 3

4

5 6

7

8

9

10

11

IN-PITGYRATORY

SECONDARYCRUSHING(P80 – 80mm)

SIZING SCREEN(-30mm)

FEED BINSTERTIARY CRUSH(P80- 25mm)

OVERLAND CONVEYOR

-1000mm

MID – SOUTH IRON ORE, SA: 10 000 TPH304

153

1

2

3

4

5

6

7

8

9

10

11

12

STATICGRIZZLY(-400mm)

SIZINGSCREEN(-80+20;-20+3)

PRIMARYJAW(P80 = 80mm)

FEED PREPSCREENS(-1mm)

WASH WATER

OVERSIZE DUMP

RECYCLE CONVEYOR

DMSCYCLONE

DMSDRUM

U

U

U

U = -1mm UNDERSIZE & FINES TO MILL & SPRIALS

SECONDARY SCREEN (-80)

ROM PIT FEED-? @ 500 TPH

-80 + 20

-20 + 3

TAVISTOCK COLLIERY, SA: 500 tph

305

1

23

4

5

6

7

8

9

10

11

12

13

14

SCALPING GRIZZLY(-120mm)

STOCKPILE(12000 T)

SIZING SCREEN(-12mm)

SECONDARY CRUSH(P80 – 40mm)

TERTIARY CRUSH(P80 – 12mm)

SECONDARYSCREEN (-40)

PRIMARY CRUSH(P80 – 100mm)

RECYCLE CONVEYOR

-400mm @350 TPHFROMU/G)

MESSINA PLATINUM, SA – 2000 tpd

306

154

High Pressure Grinding Roll Technology

HPGR at Boddington Gold(http://www.womp-int.com/images/story/2009vol10/13a.jpg)

1. HPGR Intro & History

2. Main Components and Wear Items

3. Testing and Sizing Factors

4. Flowsheets and Applications

Presentation Outline

155

Typical HPGR Comminution Duty

HPGRHPGR

History of HPGR Technology

• Comminution method was patented by Dr. Schönert in 1979

• First HPGR installed in a cement application in 1985

• HPGRs became established in the cement industry due to

recognized energy benefits

• 1987 - HPGRs first applied in the diamond industry

• ~1995 Unsuccessful trials in hard rock applications (eg.

Cyprus Sierrita)

156

History of HPGR Technology

• 1995 till present- HPGRs installed in hard rock applications

due to Improvements in roll wear linings and gaining

momentum (more than five vendors participating in the

market)

• 2012, Expiration of studded lining patent. Increase in HPGR

vendors, now including CITIC/KHD, Polysius,

Koeppern/Outotec, Metso & FLSmidth

HPGR - Function

157

313

314

158

HPGR – Main Components

HPGR –Edge Effect

159

317

318

160

HPGR Wear Components

from Weir Minerals Brochure

courtesy of Koeppern Machinery Aus.

Studded Lining (~2000 to ~10,000 hours)

Cheek Plates (~1500 hours)

ROLL SURFACE - STUD LINING Wear Parts – Roller Changeout

Hart et al (SAG2011)

Newmont roll changeoutHart et al (SAG2011)Koski et al (SAG2011)

161

321

HPGR Test Work and SizingTest Work Carried out to Determine:

HPGR Sizing Parameters

‒ Suitable specific pressing force

‒ Specific throughput Mdot

‒ Net specific energy consumption (kWh/t)

‒ HPGR operating gap / Feed top size

‒ Flake density

Process Flowsheet Parameters

‒ Size reduction

‒ Influence of feed parameters

on HPGR comminution

‒ Influence of transfer size

and circuit configuration

162

HPGR Test Work and Sizing

Agglomerated HPGR product (Flake)

324

163

325

326

164

327

328

165

329

330

166

331

332

167

333

334

168

335

336

169

Existing & Upcoming Operations

Project Company Location HPGRs

TPD Ore Type

Op. Since

Cerro Verde Freeport Mc. Peru 4->12 120 ->360 ktpd

CopperPorphyry

2006

Grasberg Freeport Mc. Indonesia 2 ~70ktpd Copper,Gold

2007

Mogalakwena Anglo Platinum S. Africa 1 ~25ktpd Platinum 2008

BoddingtonGold

Newmont Australia 4 ~100ktpd Gold,Copper

2009

Penasquito Goldcorp Mexico 1 ~+100 ktpd(peb.crushercirc.)

Poly-metallic

2010

Salobo Vale Brazil 2 ~33ktpd Copper, Gold

2012

Sierra Gorda KGHM/Sumitomo Chile 4 ~110ktpd Copper -Moly

2014?

Morenci Freeport Mc. USA 1 -> 115ktpd CopperPorphyry

2014

Reported Benefits of Using HPGR

• Energy efficiency

• Reduced steel consumption (in comparison to SAG milling)

• Not sensitive to ore variability (in comparison to alternative comminution equipment)

• Breakage along grain boundaries (promoting liberation)

Courtesy of Koeppern Machinery Aus.

170

Reported Disadvantages of Using HPGR

• Relatively small number of operations and experienced engineers

• Maximum HPGR throughput is approximately 2500 tph(increasing in near future to ~3000+ tph)

• Sensitive to feed moisture

• Assessment of HPGR is expensive (no lab scale test)

Approach to Application• Feed Size: Top size related to roll diameter and gap.

Typically a maximum of 50 mm top size

• Feed Moisture: less than 8%

• Circuit Configuration: Typically tertiary application with closing screen. Quartenary (Grasberg) and pebble crusher duty (Penasquito and Empire Mine)

• Material Handling: Choke fed feed hopper located directly above HPGR. Product is typically wet screened

171

Approach to Application

METSO HRC (METSO Catalogue, 2013)

• Tramp Metal: Needs to be removed to protect roll lining

• Wear Linings: Spare roller set needed toreduce downtime during liner changes

Machine Control:Product Size: Controlled by changes in pressing force

(hydraulic setpoint) – not roll gap!

Throughput: Controlled through changes in roll speed (VFD)

Roller Skew: control depends on vendor and can be

mechanical or hydraulic (adjusted via control loop).

HPGR Operation

‘Machine response to changes in roll speed or pressing force setpoints is almost instantaneous’

172

HPGR Operation

Influences on Roll Wear:

Feed Moisture: Wear generally increases with moisture

Roll Speed: Wear increases with higher roll speeds

Pressing Force: Wear increases when greater pressing forces are used

Feed Size: An HPGR feed top size that exceeds the width of the operating roll gap is particularly detrimental to roll wear

344

173

345

Typical Flowsheet: Tertiary Application

Cerro Verde Flowsheet (Vanderbeek 2006)

174

Villanueva et al (SAG2011)

HPGR – QuartenaryRole (Grasberg)

HPGR – Pebble Crusher Role

Peñasquito(Mexico)Palmer et al (SAG2011)

175

HPGR & The Future

2 stage HPGR & Stirred Milling

Wang et al (CMP2013)

Novel Flowsheet for Ores with Clays

Rosario (2010)

176

COMPARISON OF HPGR - BALL MILL AND HPGR - STIRRED MILL

CIRCUITS TO THE EXISTING AG/SAG MILL - BALL MILL

CIRCUITS

Chengtie (Fisher) Wang

Presented at CMP Conference, Ottawa, 2013

352

177

353

Outline Introduction

Objectives

Experiment program

Results and discussion

Conclusions and recommendations

354

178

Introduction

• Comminution is energy intensive and energy inefficient process

• Low-grade fine-grained deposit increases energy consumption and carbon emission

• Energy efficient comminution technologies include high pressure grinding rolls and stirred mills

*US Department of Energy, Industrial technologies program, June 2007

-61％

355

High pressure grinding rolls

(Napier-Munn et al., 1996)

356

179

Horizontal stirred mill

(Arburo & Smith, 2009)

357

Objectives

HPGR-ball mill circuit

HPGR-stirred mill circuit

358

180

Experimental programExisting Operation

Plant Survey and Sampling

Bulk Sample

Characterization:JK DW parameterBond work indexSize distributionSpecific gravity

Density

Pilot HPGR Testing

Pilot Stirred Mill Testing

Identification of Key Parameters

Circuit Modelling and Simulation

Circuit Identification

Comparison AnalysisComminution equipment energy

Complete circuit energyOperating and capital costs

Plant DCS dataEquipment data

359

Test flowsheet

360

181

JK SimMet simulation

JK DW TestBBWiPSD%S……

Mill DimensionBall Charge……

(Napier-Munn et al, 1996)

361

Case A - SAB circuit

Copper-Molybdenum porphyry

889 tph

JK DW A x b = 65, Ta = 0.45

BBWi = 13.8

F80 = 108 mm

P80 = 0.19 mm

362

182

Case C - SAB circuit


1332 tph

JK DW A x b = 64.9, Ta = 0.31

BBWi = 13.6

F80 = 92 mm

P80 = 0.27 mm

363

Case D - AGBC circuit


765 tph

JK DW A x b = 74.2, Ta = 0.58

BBWi = 13.8

F80 = 95 mm

P80 = 0.24 mm

364

183

Case H - SABC circuit


766 tph

JK DW A x b = 31.3, Ta = 0.59

BBWi = 18.0

F80 = 66 mm

P80 = 0.16 mm

365

Sample

366

184

HPGR testing results

367

Test No. Specific FSP M-dot ESP net

Scaled HPGR product

(90% Center, 10% Edge)

[N/mm2] [ts/hm3] [kWh/t] P80 [mm] P50 [mm]

A1 3.0 257 1.37 6.30 1.91

A2 4.0 191 2.22 1.67 0.54

C1 3.0 266 1.23 6.54 1.58

C2 4.0 208 1.87 1.88 0.76

D1 3.0 244 1.55 4.70 1.17

D2 4.0 142 2.90** 1.71 0.55

H1 3.0 184 1.89 6.50 3.00

H2 3.0 222 1.25 3.83 1.75

Bond ball mill work indices

368

Circuit RoM

[kWh/t]

HPGR product

[kWh/t]

Difference

[%]

A 13.8 12.1 -12.3

C 13.6 12.6 -7.4

D 13.8 12.8 -7.2

H 15.4 15.4 -14.4

185

IsaMillTM testing results

369

Test Description Units ISA A1 ISA C1 ISA D1 ISA H1

Feed top size [µm] 710 710 1000 710

F80 [µm] 310 326 420 343

Target P80 [µm] 100 100 100 75

Specific Energy [kWh/t] 3.8 4.4 5.0 4.8

Media Consumption [g/kWh] 6 7 5 3

Pure comminution energy

Note: A power factor of 120% and 95% of net specific energy was used to determine the total motor power draw of the HPGR and IsaMill for the process capacity, respectively.

370

HPGR-BM @ 160 um, 24%

HPGR-BM @ 75 um, 10%

HPGR-IsaMill @ 75 um, 37%

186

HPGR - ball mill circuit

371

HPGRs - stirred mill circuit

372

187

Complete comminution energy

Note: A power factor of 120% and 95% of net specific energy was used to determine the total motor power draw of the HPGR and IsaMill for the process capacity, respectively.

373

HPGR-BM @ 160um, 21%

HPGR-IsaMill @ 75 um, 34%

Comparison breakdown

SAG mill

HPGR

374

188

Comparison breakdown (cont’d)

375

Capital cost

*determined from vendor quotes and installation costs

376

189

Operating cost

377

NPV and IRR*

F80 P80 HPGR/ball mill to SABC HPGR/stirred mill to SABC

[mm] [um] NPV, M$ IRR, % NPV, M$ IRR, %

66 160 33 22 n/a

66 75 22 23 5 7

*@5%, 15 years

378

190

Conclusions• The combination of HPGR and stirred mill in a single flowsheet,

without tumbling mills, has been demonstrated to be technically feasible, with the implementation of two passes of HPGRs in the flowsheet, and large-diameter ceramic media in IsaMill™ for coarse stirred milling.

• The work has demonstrated that the HPGR - ball mill circuit and HPGR – stirred mill as alternatives to existing SAB/AGBC/SABC comminution circuits has significant potential in energy saving.

• Economics of HPGR - ball mill option and HPGR - stirred mill option are more favourable compared to existing SABC circuit

‒ larger operation and long mine life

‒more expensive energy supply area

379

Recommendations

• Evaluation of the influence of ore hardness variability

• Further evaluation of size classification for HPGR product

• Further evaluation of coarser stirred milling

380

191

Acknowledgements

381

Questions?

192

Towards Tomorrow’s ‘‘Smart Mine’’: Embedded Sensor Telemetry and Sensor-Based Sorting

Sensors and Sorting

Acknowledgements

Andrew Bamber, CEOMineSense Technologies Ltd, Vancouver, Canada.

N. Emre Altun, Associate ProfessorMuğla University, Mining Engineering Department, Muğla,

Turkey.

Malcolm Scoble, ProfessorNorman B. Keevil Institute of Mining, UBC, Vancouver,

Canada.

193

Mines of the Future

Low grade, complex geology, deep and remote

Clean - less waste, improved waste management

Healthy and Safe

Energy efficient

Invisible - underground mining and processing

Smart – best use of information eg sensors

Sensing and Sorting Technologies Hand sorting - pre-Roman times

Automated sorting

Uranium radiometric sorting Ontario 1958

Diamonds X-Ray fluorescence W. Australia 1985

Recent large scale examples (est. 300 sortersinstallations)

Nickel, Kambalda W. Australia

Platinum, Amplats, Rustenburg UG2 Section

Sensors - Surface versus Bulk Properties

Challenges – Better sensors, higher throughput machines

194

Sensor Technologies

Method Analysis Application

Photometric (reflection, brightness, grey level, RGB, IR, UV, texture)

Surface Coal, sulphides, phosphates, oxides

Radiometric Bulk Uranium, gold

Conductivity, magnetic susceptibility

Bulk Metal sulphides, native metals, iron oxides

X-Ray Fluorescence Surface Diamonds, metal sulphides, limestone, iron

X-Ray Transmission Bulk Coal, sulphides

Conductivity Testing at UBC

Balancing Coil 1 Balancing Coil 2 Balancing Coil 3

Sensing Coil 1 Sensing Coil 2 Sensing Coil 3

PC

A/D Converter: Signal generation

and analysis

Sort Signal

Amplifier Bridge/

Power Supply

Conductivity Sorting

CommoDas ‘‘ROM Secondary EM’’

Conductivity Sorter

195

Courtesy C. BergmanMintek, 2009

390

196

391

392

197

393

394

198

395

396

199

397

398

200

399

400

201

401

Sorting Economics

Mining Value Chain (after Porter, 1980)

202

Sorting Economics

Value Chain (with sorting)

Sudbury Ni-Cu Operations – Energy Assessment

203

Sudbury Operations - Conductivity Sorting

Deposit Conc. Mass (%) Conc. Grade (%) Recovery (%)Ni Cu Mg Ni Cu Mg Ni Cu Mg

0.83 11.42

0.81 0.36

0.43

1.40

1.29 9.08

0.87

Montcalm West

1.16 0.47

2.10 0.35

0.32 0.15

1.66 0.56

0.68

TL Footwall

TL Zone 2

TL Zone 1

Montcalm East

Craig 8112

Craig LGBX

Fraser Ni

Fraser Cu

5.54 72 1.50 0.57 5.16 93.49 87.40 67.46

2.57 83 2.43 0.37 2.39 95.85 86.70 77.07

4.21 80 0.94 0.40 3.73 92.73 89.43 70.67

1.81 41 1.65 20.92 0.68 81.12 74.89 15.42

1.90 66 1.85 12.05 1.08 94.66 87.88 37.51

3.41 62 2.03 0.87 3.41 90.35 83.84 59.11

40.476.00 44 0.98 0.48

68.224.61 75 2.06 0.63

29.935.97 30 0.64 0.30

Feed Grade (%)

6.05 59.23 57.50

4.17 93.60 85.48

5.58 63.07 48.43

McCreedy East Mine - U/G Sorting

204

McCreedy East Mine – U/G Sorting

Operation MontcalmThayer

LindsleyFraser Copper Fraser Nickel Craig Onaping Depth Ni Rim S

Hoisting $399,995 $1,319,625 $505,001 $684,364 $2,391,748 $1,891,163

Haul $786,583 $302,422 $884,600

Pre-con -$1,342,180 -$843,569 -$615,687 -$979,603 -$1,285,380 -$1,285,380 -$1,167,864

Grinding $560,607 $273,248 $236,058 $320,410 $476,930 $476,770 $418,730

Processing $1,397,813 $698,906 $436,817 $873,633 $1,310,450 $1,310,450 $1,135,723

Overall Savings $1,402,823 $831,002 $1,376,812 $719,440 $1,186,364 $2,893,589 $3,162,352

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

9000.00

10000.00

Power (kW)

Montcalm ThayerLindsley

FraserCopper

FraserNickel

Craig OnapingDepth

Ni Rim S Ni Rim SF/W

Base

Precon

Sudbury Operations – SortingOverall reduction in energy consumption 20%

205

Sorting Past – Present - Future? Proven Technology

Sorting machines exist

Metallurgy proven

Concepts for mine designs developed

Economics demonstrated

Challenges of implementation

Better sensors

Higher capacity sorters

Technology transfer - Risk averse industry

How can we make better use of sensors? Sensors – organic part of mining system

Apply to all aspects from exploration (geophysical, borehole) to mining to processing

Embedded sensors in material handling systems (ore passes, scoops, shovels, bins, chutes, conveyors)

Transmission, recording, analysis technologies

Wireless data transmission (WiFi)

Data available to GEMCOM, MineSight, process control

Intelligent connected mines with active online telemetry

206

Innovative Use of Sensors

• Core logging equipment

• Boreholes

• Blast hole drill rigs

• Face shovel

• Belts

• Sorter

Multi-Sensor Product Platform

ConductOreXTM – Desktop Evaluation System

BeltSense™ - Multi-modal Mineral Telemetry System (completed

Pilot SortOre – HFEMS or HSXRF @ 10 tph (on demand)

ShovelSense™ - Scoop/Shovel HFEMS System (in progress)

SortOre™ – High Capacity Sorting System (in progress)

412BeltSenseTMShovelSenseTMSortOre40TM

207

Sensor Based Systems in Surface Mining

Sensor-based technologies and U/G Mining

208

Conventional vs Sensor Based Mining Conventional mining:

- people-orientated, plan-based, subjective, time consuming

Future mining:

Application of on-line telemetry from in-mine sensors: Production scheduling, grade control,plant process control settings:

- flexible- objective - real-time- simultaneous

Conclusions

The outcomes of sensor-based technologies and sorting are significant

in economic and environmental measures

Challenges to the application of these technologies relates primarilly to aspects of technology transfer and mining culture

rather than technical issues

209

NBK Research Centre

Introduction to Grinding

418

210

Grinding & Classification Outline

1. Types of Mill Equipment and Circuits 2. Factors In Grinding Circuit Selection3. Ore Properties and Grinding Testwork4. Mill Power and Sizing Grinding Mills 5. Importance of Grinding Media6. Ultrafine Grinding7. Classification Principles and Equipment

419

Types of Mill Equipment and Circuits

• Introduction• Grinding Fundamentals Recap

‒ Why Grind? Breakage vs. Enrichment and Upgrading‒ Grinding Economics‒ Grinding Mechanism Characteristics‒

• Types and Characteristics of Grinding Equipment‒ Overview of Ball Mill Feed Preparation Systems‒ Grinding Mill Equipment Types‒ Characteristics of Grinding Mills

420

211

Introduction

• Course covers grinding equipment typically used in the ferrous and non-ferrous mineral industry.

• Internationally the technology is fundamentally similar with minor variations to local conditions.

• Over past 100 + years ball mills remain the central component and workhorse of most grinding circuits.

• Circuit differences are mainly in feed preparation.

421

Introduction• Technology is specialized because of the need to grind

mostly siliceous, highly abrasive ores.

• Some adaptation of cement industry equipment has resulted in power savings with harder rock (High Pressure Grinding Rolls).

• Wet grinding is almost universally practiced.

• The notable exception of dry-grinding, air-swept, double compartment ball mills (also adapted from cement industry) that grind refractory gold ores prior to roasting.

422

212

Grinding FundamentalsWhy Grind? Breakage vs. Enrichment and UpgradingIn the size reduction stages of grinding we are creating the necessary mineral liberation conditions, or surface area, for subsequent separation and enrichment, upgrading and recovery.

423

Grinding Economics

• Rule of Thumb. Mills consume about two-thirds of the entire process plant power, or about 20-25 kWh/t (65% of 35-40 kWh/t).

• Mills consume about 1-2 kg/t (C$1-2) of grinding media & liner steel.

• Assuming 10c/kWh/t overall grinding costs (power+media) are about $3-$5/t, or about 40-50% of overall mill consumable costs.

424

213

Grinding Economics

• Lost performance in separation due to miss-grinding represents a major problem for many operations, eroding the process economics.

• An economic balance is required between the marginal cost of grinding and revenue to maximize net revenue.

425

Grinding Mechanism Characteristics

c) Energy Efficiency

b) Dominant Grinding Action

Impact / Compression Attrition/ Chipping Abrasion

Tumbling/Impact Cataracting Cascading

Lowest (-) Improving Highest (+)

a) Breakage Mechanism

426

214

Tumbling Mill Ball & Energy Distribution

427

Ball Mill Feed Preparation Systems

1. Crushing the ROM feed by primary crusher to a top size of about 300 mm at crusher settings of 150 to 200 mm to permit conveyor transport.

2. Further size reduction by either:

‒ 2 + stages of crushing by cone crushers to a ball mill feed size of 10 to 15mm.

‒ 2 + stages of crushing & rod milling to a ball mill feed size of 1.5 to 2mm.

‒ Semi-autogenous (SAG) or autogenous (AG) grinding to a ball mill feed size of 1 to 4 mm.

‒ Cerro Verde Crusher/HPGR: 2.8 mm.

428

215


• As concentrator capacities have increased, SAG mills have become the standard method of preparing ball mill feed.

• The capacity of secondary and tertiary crushers has not kept pace with increasing plant capacity, as well as limitations in rod mill capacity.

• Currently the largest cone crusher commonly in service is the MP1250 driven by a 1,250 hp motor.

429


• A 50k tpd+ secondary and tertiary crushing plant is complex – with many lines, screens, conveyors, bins, etc.

• SAG mills were the only practical way to prepare ball feed at medium and high tonnage rates.

• SAG (or AG) mills have been installed in most mineral processing grinding circuits in the last 20 years.

• Now HPGRs have been shown to be viable alternatives.

430

216

Types of Grinding Equipment

SAG/AG

Ball

Rod

Pebble

Vibrating BallVertimill

Isamill

Stirred Media

Detritor (SMD)

431

Common Mill Components

1 – Shell2 – Mill Heads3 – Trunnion Bearings4 – Grinding gear & pinion5 – Grinding Mill Reduction Unit6 – Mill Motor

7 – Frame8 – Feed spout9 – Discharge Trommel10 – Discharge Chute11 – Mill Liners

432

217


433

Ball Mill (Grate Discharge)

Rod Mill

Insides of rod and ball mills

434

Rod mill

Ball mill

218


435

Vertimill Vibrating Ball

Regrind Mills

436

219

Grinding Circuits

437

Outline

• Grinding Equipment Selection

• Types of Grinding Mills

• Evolution of Grinding Equipment

• Grinding Circuit Arrangements

• Mongolian ASM Circuit

438

220

Source: Mt Polley

439

Reduction Ratio: Grinding vs. Crushing• Crushers have a limited reduction ratio - due to the design,

there is a limit to the residence time for the material passing through.

• Grinding in a mill takes place in more open space, thus the retention time is much longer and can easily be adjusted during operation.

• In practice size reduction by grinding is done in optimized stages.

440

221

Grinding Equipment Selection

441

Grinding Equipment Selection

442

Mill Type Grinding Media Feed Size Product Size Diameter / Length

a) Autogenous Coarse Ore 2 feet -100 mesh 3 to 1

b) Semi-autogenous

Coarse Ore / Balls

2 feet -10 mesh 2 or 3 to 1

c) Rod Steel Rods 2 inch -10 mesh 0.5 to 1

d) Ball Steel Balls 1 inch to 4 mesh

-200 mesh 0.5 up to 1 to 1

e) Pebble -8” + 4” Pebbles -1 inch -200 mesh 0.8 to 1

f) Verti-Mill Sand/Ceramic - 2mm 25-10 microns

Vertical

222

Autogenous (AG) and Semi-Autogenous Mills (SAG)

443

Autogenous (AG) Mill (D:L is about 3:1 US and 1:1 Europe/RSA)

• Wet or dry grate discharge

• Product: ~ -100 mesh (149 micron)

• Primary, coarse grinding (up to 2’ feed)

• Grinding media is the feed material (min load of 15% > 6 in)

• High capacity (short retention time)

• Sensitive to feed size & material composition (critical size)

444

223

Semi-Autogenous (SAG) mill (D:L is about 2-3:1 US and 1:1 Europe/RSA)

• Wet or dry• Product: ~ 10 mesh (2 mm)• Higher capacity than AG mill• Primary, coarse grinding (up to 2 ft feed size)• Grinding media is feed plus 4-12% ball charge (4-5

inches)• High capacity (short retention time)• Less Sensitive to feed composition (critical size material)

445

Gibraltar’s New SAG (28’)446

224

© Metso Minerals, Inc. 2003Fully Assembled 40 ft. x 22 ft. SAG Mill @ Cadia

447

HVC Line C: 43'x16‘, 2 x 4700 kW motors

448

225

Rod Mills (D:L is about 0.5:1)

• Overflow is wet only• Mostly open circuit (secondary)• Grinding media is rods• Primary grinding secondary/tertiary

crushed • product (19-50 mm)• Coarse grind 600-2500 micron

• End & Center are mainly dry• Special Applications• Capacity < 200 t/h limited by rod

length (22 ft max)• Power < 1,500 kW

449

Rod Mill Dimensions

• Rod length to mill diameter – 1.4 to 1.6

• 6.8 m is practical limit on rod length

• Mill length should be 0.1 to 0.16 meters (4” to 6”) longer than the rods.

450

226

Rod mill @ Mount Polley

451

Overflow Ball Mills (D:L is about 0.5-1: 1)

452

- Wet only, Robust & Simple- Primary on 1 in. to 4 mesh crushed feed- Mostly closed circuit (secondary) on AG/SAG/Rod/HPGR product

- Finer Grind (longer retention time) to > 20 microns- Higher risk of over grinding- Ball charge 35-45%.

227

Grate Discharge Ball Mills (D:L is 0.5-1:1)

453

- Wet or dry- Discharge grate more complex- Primary on 10-19 mm crushed feed- Mostly closed circuit (secondary) on rod product- Coarser grind (short retention time) > 74 microns- Lower risk of over grinding- Can take 5-10% more balls

22 ft x 36.5 ft Ball Mills @ Cadia

454

228

24 ft x 36 ft Ball Mills @ Cerro Verde, 13 MW

455

Pebble Mill (D:L is about 0.8:1)

456

- Wet or dry grate discharge (product –200 mesh)- Secondary grinding (AG/SAG/Rod/Ball Product) of –1 inch feed- Grinding media pebbles (-8 + 4 inch) screened from feed, flint

pebbles, porcelain balls- Larger than ball mills at same power draw

229

Grinding @ Mount Polley

457

Vertimills

458

• Vertical stirred

• From 10 HP through 1500 HP.

• For wet application 2 mm feed to as fine as 10 microns.

• Secondary/Regrind/Lime Slaking

230

VTM-1250-WB Vertimills at Chino

459

Main Grinding Mill Suppliers (Sales 1990 –2002)

460

Metso

FFE

Bradkin

Krupp

Outo.

Others

Metso – MetsoMinerals

FFE – Fuller-Vecor

Outo- Outokumpu(purchased Nordberg/Morgardshammar)

231

AG/SAG Mill Evolution

461

1959 - 1st 18 ft/5.49m. diameter AG Mill @ 600 HP/448 kW

1959 - 1st 22 ft./6.71m diameter AG Mill at 1,250 HP/933 kW

1962 - 1st 24 ft./7.32m diameter AG Mill @ 1,750 HP/1,306 kW


1965 - 1st 20 ft./6.10m diameter AG Mill @ 500 HP/373 kW




1973 - 1st 36 ft./11.0m diameter AG Mill @ 12,000 HP/8,955kW


1986 - 1st Gearless SAG Mill @ 11,000 HP/8,209 kW

1996 - 1st 38 ft./11.6m diameter SAG Mill @ 26,800 HP/20,000 kW

1996 - 1st 40 ft./12.2m diameter SAG Mill @ 26,800 HP/20,000 kW

Proposed – 42 ft./12.8m diameter SAG Mill @ 37,500 HP/28,000 kW

Ball Mill Evolution

• 1965 - 1st 14’ (4.27m) dia. Ball Mills @ 1,306 kW

• 1966 - 1st 15.5’ (4.73m) dia. Ball Mills @ 1,493 kW

• 1967 - 1st 16.5’ (5.03m) dia. Ball Mills @ 2,612 kW

• 1970 - 1st 18’ (5.49m) dia. Ball Mills @ 3,172 kW

• Following poor performance of 18 ft mills at Bougainville, there was speculation that the limit of ball mill size had been reached. It was subsequently proved that operating conditions were the cause of observed lower grinding efficiency and not size.

462

232

Ball Mill Evolution

•1980 - 1st 21’ (6.4m) dia. Ball Mill @ 8,060 kW

•1990 - 1st 20’ (6.1m) dia. Ball Mill @ 5,597 kW

•1996 - 1st 22’ (6.71m) dia. Ball Mills @ 8.955 kW

•1996 - 1st 24’ (7.32m) dia. Ball Mills @ 10,448 kW



•Current – 22 MW+

463

Ball Mill Evolution

• Ball mill sizes have continued to increase and there is currently no evidence to suggest that efficiency drops as diameter increases.

• Economics is driving selection of the fewest number of mills lines.

•

• A large SAG mill followed by a large ball mill could enable a single mill line to mill up to 150,000 tpd of ore.

464

233

Ball Mill Evolution465

34 ft. SAG & 20 ft. Ball Mills @ Fairbanks Gold

Grinding Circuit ArrangementsSecondary and Tertiary Crushing plus Single-stage Ball Mill Grinding•This circuit and the following rod/ball mill circuit were almost universal pre-1975.

•Variations such as pebble or tube mills and deleting tertiary crushing for softer ores or low tonnage operations.

•The 3-stage and single-stage ball remains one of the most energy efficient compared to AS/SAG but crusher/rod mill sizes did not keep pace to industry leading to its demise.

466

234

SECONDARY CRUSHING

SCREEN

TERTIARY CRUSHING

SCREEN

BALLMILL

CYCLONE

PRIMARY CRUSHER FEED PRODUCT

Secondary and Tertiary Crushing plus Single-stage Ball Mill

467

Primary, Secondary and Tertiary Crushing plus Rod Mill and One or Two-Stage Ball Mills

CYCLONE

SCREEN

SECONDARY CRUSHING

TERTIARY CRUSHING

RODMILL

BALLMILL

PRODUCTPRIMARY CRUSHER FEED

468

235

SAG/AG Mill ± (Pebble Crushing) + Ball Mill

• These circuits have been the workhorse of the industry for the last 20 years.

• External pebble crushing improves power efficiency and is necessary for competent ores that exhibit a propensity to form critical size material.

• Early AG installations in the iron industry have operated well for many years.

469

SAG/AG Mill ± (Pebble Crushing) + Ball Mill

• Similar installations in the copper industry were not so successful, typically grinding too fine at low tonnage rates. Some circuits were modified to SAG operation.

• There are a few single stage SAG mills operating successfully. This type of circuit is well suited to uranium sandstone deposits (Colorado Plateau Ores) in which uranium coatings are released for leaching.

470

236

PRODUCT

CYCLONE

PRIMARY CRUSHER FEED

BALLMILL

SCREEN

SAG/AG Mill + Ball Mill471


SCREENBALLMILL

CYCLONE

PEBBLE CRUSHER

MAGNETIC SEPARATOR PRODUCT

SAG/AG Mill + Ball Mill + Pebble Crushing

472

237

Double Rotator Dry Grinding

• This circuit has been adopted by two gold roasting operations in Nevada. The circuit was adapted from cement industry practice and combines drying with two stages of grinding.

• The handling and classification circuit is relatively complex –airslides, bucket elevators, dynamic and static classifiers and product recovery baghouses.

473

PRODUCT

DRYING

CYCLONE

COARSEGRIND

FINEGRIND

HOT GAS


Double Rotator Dry Grinding

474

238

Mongolian ASM Circuit

475

476

239

477

478

240

479

480

241

481

482

242

Grinding & Classification – Ore Characterization

483

Introduction – Ore Testing

• Grinding Ore Testing - To quantify what type and size of grinding circuit is best suited to the ore.

• Test work can range from simple tests, based on a small sample of rock or core, to comprehensive pilot testing requiring hundreds of tonnes.

• Objective – to become familiar with commonly used ore tests for grinding.

484

243

Common Ore Tests

• Bond grinding indices (rod, ball and abrasion)

• Unconfined compressive strength (UCS)

• Impact crushing tests

• Autogenous Media Competency (Tumble Test)

• JK drop weight tests

• McPherson

• SPI Minnovex (Starsky)

• Pilot scale milling

• Circuit Surveys

485

Standard Bond Ore Testing

Four Most Relevant Indices:

a) Bond Ball Mill Work Index (BMWI)

b) Bond Rod Mill Work Index (RMWI)

c) Bond Abrasion Work Index

d) Standard Bond Crushing Work Index (see Impact Crushing Tests)

486

244

a) Bond Ball Mill Work Index• BMWI standard test was developed by Fred Bond in the

1920s, published in 1952 and modified in 1961.

• Test enables basic grinding power requirements to be determined, from the feed 80% passing size (F80) to the circuit 80% passing size (P80).

• BMWI test determines the standard Wi of a sample of ore, or the specific power (kWh/t) required to reduce the P80 of a sample of material from ‘infinite’ size to 100µm.

• BMWI is used in designing new equipment and in simulating existing equipment to improve performance.

487

What is a Ball Mill Wi Test?

• The BMWI is a measure of the resistance of the material to crushing and grinding.

• It is a 'locked cycle' test conducted in closed circuit with a laboratory screen.

• Requires 10 kg of drill core or rock, crushed to –3.35mm (6# Tyler)

• The closing screen size is selected so that the product P80

from the test is as close as possible to the product P80

expected from the circuit under design.

• Note: Wi is linked to the tested closing sieve size.

For full details, refer to the original Bond paper (Ref: Bond, F.C. 1961. “Crushing and Grinding Calculations Part I and II”, British Chemical Engineering, Vol 6., Nos 6 and 8).

488

245

When would a BMWI Test be required?

• A BMWI is required for the design of a new mineral processing plant. Tests should be on a samples of ore that are typical of the proposed feed to the plant.

• A BMWI may also be used in the simulation and subsequent optimization of existing mill(s) and the associated grinding circuit.

• The Bond Equation can be used to calculate:

‒The specific energy requirement for a given grinding duty, and

‒The feed size and required product size.

• It is then possible to determine the size of mill required based on throughput, and therefore motor power.

489

Detailed Ball Mill Work Index Test Procedure

1.Stage crush the feed to ≤ 3.35mm (- 6 mesh) and take a representative sample.

2.Undertake a series of batch grinds in a standard Bond mill. A Bond mill is 0.305m x 0.305m (12”), with rounded corners, smooth lining, running at 70rpm. The charge consists of 285 balls, weighing a total of 20.125kg.

3.Initially, a 700ml sub-sample of feed is prepared for use in the first batch grind. It is ground in the mill for 100 revolutions. All grinding is dry.

4.After each batch grind, the contents of the mill are sieved on the selected 'closing' screen to remove the undersize. This is replaced by an equal weight of fresh feed to bring the weight back to that of the original charge.

490

246


5. This sample is then ground in the mill for a predetermined number of revolutions calculated to produce a 250% circulating load. The number of revolutions required is calculated from the results of the previous period to produce sieve undersize equal to 1/3.5 of the total mill charge.

6. Repeat at least 7 times until the weight of undersize produced per mill revolution reaches equilibrium.

7. The average of net mass per revolution from the last three cycles is taken as the ball mill grindability (Gbp) in g/revolution.

8. A representative sample of product is sized to determine the P80.

491


9. Calculate the BMWI using the Bond equation:

Wi = 44.5 / [(P1)0.23 x Gbp0.82 x 10 (1/P80 - 1/F80)]

Where:Wi = Ball mill work indexP1 = opening in microns of the sieve size testedGbp = the average of the last three net grams per revolution, or grindability.

492

247

How are BMWI results reported and what do they mean?

• The standard report details the Bond test procedure method, and presents the results including F80, P80, Grindability and Work Index.

• The Bond BMWI provides a measure of how much energy is required to grind a sample of ore in a ball mill.

• Typical BMWI results and their relative measure include:

Property Soft Medium Hard Very Hard

Bond WI (kWh/t) 7 – 9 9 –14 14 –20 > 20

493

Additional Bond BMWI Comments• A typical BMWI test takes 1 week.

• As a rule of thumb, for a given closing sieve size, the resulting product P80 will be ~ one root 2 series sieve size smaller. For example, if the required product P80 is ~ 106 µm then use a 150 µm closing sieve size.

• Wet sieving is only used if the material is likely to agglomerate or if the closing sieve size is ≤ 45µm.

• Wet sieving significantly increases the test time, as the test must be carried out on dry material. The sample must be oven-dried after each wet sieving process.

• There may also be issues of material degradation either in water or at the high drying temperatures, which needs to be considered before the test is carried out.

494

248

b) Bond Rod Mill Work Index

• BRWI test requires 20 kg of material, which is crushed to -12.7mm (-1/2”) and is tested in a standard Bond Rod mill.

• The sample is ground to -1.18 mm (14# Tyler) to emulate the duty of a primary rod mill in front of a secondary ball mill.

• The rod mill index derived from this test is used in conjunction with the ball mill work index to determine the rod mill power demand, again using the Bond power equation.

495

Rod Mill Grindability Test Procedure

1. Weigh 1250 cc of crushed –1/2 inch rock2. Conduct sieve analysis and determine, F803. Grind dry in closed circuit with 100% circulating load in 12

inch diameter x 24 inch long rod mill4. Screen and weigh undersize of product5. Add fresh feed to original 1250 cc weight6. Calculate number of revolutions to produce 100% circulating

load7. Repeat cycle until the net grams of undersize produced per

revolution is constant8. Conduct Sieve Analysis on product and determine P809. Calculate Wi:

Wi = 62 / [(P1)0.23 x Gbp0.625 x 10 (1/P80 - 1/F80)]

496

249

c) Bond Abrasion Index

• The abrasion index test requires only 5 kg of material, which is crushed and screened to an exacting size range of +12.7 –19.0 mm (+½” – ¾”).

• The test uses a small laboratory scale mill with a test paddle that is weighed before and after being rotated in contact with the dry test sample.

• The difference in weight is designated as the abrasion index, and is used in conjunction with Bond formulae to predict liner wear and media consumption in rod and ball mills, as well as in crusher liners.

497

d) Impact Crushing Tests: Standard Bond Method

• These tests can take two forms. The first is the Standard Bond Crushing Test, which has a requirement of twenty pieces of rock or core of size +50 – 75 mm (+2” – 3”). Pieces are placed in a twin pendulum device and impacted to failure to produce an impact crushing strength, measured in kWh per tonne of ore.

• Twenty specimens are tested to provide a measure of variability of results, as there is a tendency towards heterogeneity in rocks of larger sizes. The standard index is used primarily by crusher manufacturers to assign down rating factors for ore toughness in crusher selection.

498

250

Impact Crushing Tests: Standard Bond Method

499

Impact Crushing Tests: Standard Bond Crushability Method

Crushability Test Procedure

1. –3 + 2 inch rock mounted between two-30 lb weights on wheels

2. Weights strike rock simultaneously on smallest dimension

3. Increase height until rock breaks4. Calculate impact crushing strength, C

(ft. – lb/inch)5. Determine rock SG6. Calculate Wi from average of 10

breaks

Wi = 2.59 x C / SG

500

251

Impact Crushing Tests: Modified Bond Method

• Test uses a larger sample of rock or drill core.

• 120 kg of material is tumbled in the standard 1.83 m diameter x 0.3 m wide Bond autogenous media competency test mill for 500 revolutions at 26 rpm, to eliminate imperfections in rocks and to mimic seasoned pebbles in a mill charge.

• The product is screened to remove –19 mm material. The oversize are sorted into 4 or 5 classes, depending on the feed size. The size classes are 19 x 25 mm, 25 x 38 mm, 38 x 51 mm, 50 x 75 mm, and 75 x 100 mm.

• Select 20 rocks in each size class and subject to standard Bond Impact Crushing Work Index Test.

501

a) Bond Impact Test Method: Barratt Approach

Barratt (1986) proposed a method for predicting SAG power involving the use of a combination of Bond Work Indices over a range of sizes from F80 to a defined P80, applying a correction factor to resultant power, and deducting the ball milling component of the power:

E (SAG) = [10Wic(Sp) + 10Wir(Sr)*Kr + 10Wib(Sb)*Kb] * 1.25 - 10Wib(Ssb)

where: E (SAG) is the specific SAG mill power in kWh/tWic,r,b are the Crushing, Rod and Ball mill Work IndicesSc,r,b are [1/P - 1/F] for the equivalent stage size ranges

It was noticed that the method can be used unless the Wic and Wir are significantly higher than the Wib, in which case SABC is indicated and E (SAG) can be discounted by 10% to arrive at a power efficient SABC design.

Single Particle Methods (AG and SAG)

502

252

b) Bond Impact Test Method: Siddall ApproachSiddall, et al., (1996) classified the responses obtained from impact testing the products of a tumbling drum and related them to a correction factor, designated f(SAG) which is applied to the Bond Ball Mill Work Index to predict the total power required to grind from F80 = 150 mm to P80

= 75 micron. The equation takes the form:

P(TOT) = 10 WI * f(SAG) [1/75 - 1/150000]

By subtracting the ball mill power requirement and correcting for feed size, the SAG mill power can be predicted.

P(SAG) = P(TOT) – P(cr) – P(bm)

P(TOT ) is the total circuit powerP(cr) is the correction for feed F80 sizeP(bm) is the correction for ball mill power

Single Particle Methods (AG and SAG)

503

The Barratt Approach and Siddall Approach methods have been found to predict the single stage grinding power required in a AG/SAG mill.

In both methods, there is a reliance on either pilot plant data or database correlations in order to establish T80 (SAG transfer size), and hence the SAG mill power in a two-stage grinding circuit.

SINGLE PARTICLE METHODS - AG AND SAG

504

253

Impact Crushing Tests: Results

• The test provides the raw data required to derive an impact crushing profile, used to identify the type of comminution circuit is best suited to the ore.

505

Additional Ore Characterization Tests

• Unconfined compressive strength (UCS)

• Autogenous Media Competence Test

• JKDrop Weight Test

• McPherson Test

• SPI Minovex

• Pilot Scale Testing

• Plant Circuit Surveys

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254

Ore characterization test requirements -SAG/AG mills

• Must test particles over the entire size range of SAG mill feed for both impact and abrasion breakage, to determine energy levels expected in commercial mills

• Must determine media competency;

• Must allow examination of steady-state mill load characteristics (critical sized material);

• Must generate a breakage vs. energy level map for simulation

• Must be reproducible (need representative samples);

• Must determine total grinding power required; and,

• Must use a small sample mass.

507

Unconfined Compressive Strength Test

• This test determines the strength of a rock sample under compression by a single vertical force.

• The test requires the use of a specialized compression device which applies an evenly controlled force to the rock until failure.

• Unfortunately, the test is undertaken in many different types of devices, with widely varying sample specifications, which makes cross-comparison of results difficult at times.

508

255

Unconfined Compressive Strength Test

• One international standard that is used widely is the ASTM2938-86.

• A sample specimen is machined into a cylinder featuring a length twice that of the specimen’s diameter, ideally 50 mm (2”).

• The test produces two outputs:

‒The mode of breakage, providing insight into the nature of the rock.

‒The actual UCS value, usually quoted in MPa.

• The UCS value is used to guide crusher manufacturers in selecting the appropriate equipment, and to assist the grinding consultant in assessing an ore’s competency.

509

Autogenous Media Competency Test• When a sample is available in the form of lump rock, the standard Autogenous Tumbling Test can be carried out using 10 rocks in five size ranges between 102 and 165 mm.

• The rock is normally tumbled for 500 revolutions in a 6 ft x 1 ft drum and the product sized.

• The product provides data to enable evaluation of the following:‒ Interpretation of the product distribution against generic curves.‒ Production of media in AG and SAG mills.‒ The amount of critical size build-up.‒ The tendency for ore to generate fines (-6 mm material).‒ Overall amenability to autogenous milling.

510

256

Autogenous Media Competency Test

• The test provides excellent insight into impact breakage and auto abrasion characteristics of ores, but is currently only performed in a few laboratories around the world.

511

JK Drop Weight Test

• This test has been devised by the Julius Kruttschnitt Mineral Research Centre (JKMRC), and is used to derive impact breakage and abrasion parameters for use in their simulation package, JKSimMet.

•

• The method involves dropping a metal weight from a set height onto a test specimen and sizing the “daughter” products from the resultant rock failure.

512

257

JK Drop Weight Test

• JK Tech introduced a Drop Weight Test to replace the Pendulum Test.

• A number of specimens of varying sizes are tested to generate breakage curves from which the JKSimMetsimulation parameters are calculated.

• The test is a useful adjunct to the other media competency tests: once the type of circuit that is best suited to the ore is identified, JKSimMet can be used to verifying initial mill sizes.

513

JK Rotary Breakage Tester

514

258

JK Rotary Breakage Tester

Minerals Engineering 22 (2009) 602–612

515

McPherson Test

• The most notable method in use in the Americas is the test developed by Art MacPherson.

• It uses dry grinding on material typically crushed to –38 mm to ascertain the ore’s autogenous characteristics in a 450 mm diameter mill.

• The results are compared to a standard Bond test, and an empirically scaled value for the amount of power that is theoretically required to grind the ore is determined.

• The test is normally used as a precursor to pilot scale AG/SAG milling.

516

259

McPherson Test

• The main area of concern with the test is the underlying assumption that ore at large lump sizes behaves in a similar manner to the small sizes used in the test at –38 mm, which is not consistently correct.

• This is particularly so with tough siliceous ores (typical of the greenstone belts in Australia and parts of Africa).

• However, the test can serve as a useful adjunct to the other testes discussed above in providing some insight into the autogenous characteristics when whole ore is not available for testing.

• It generates an estimate of the product size from an AG/SAG mill.

517

SPI Minnovex Test (Starkey)

• This test has been devised by Minnovex in Canada to predict SAG mill specific power requirements using only –12.7 mm material.

• The test uses a small 300 mm dia. x 100 mm long laboratory scale mill with a small ball charge of 25 mm balls to grind a 2 kg test sample.

• The objective is to establish the grinding time required to grind the ore to 80% passing 1.7 mm (10#), the closing screen size.

• This test claims to demonstrate a strong correlation between grinding time for ores and their corresponding SAG mill specific power draw. It provides an attractive alternative to tests requiring large sample size.

• Like the McPherson test it draws on a large database for comparison with actual operations, which also provides the basis for calibration of the model against laboratory results.

518

260

Pilot Scale Testing

• Most “greenfields” projects can not access whole ore in the early stages of the study; hence, the focus on drill core testing.

• If whole ore is available from a current operation or from a development audit or shaft it is possible to undertake pilot scale SAG mill testing.

• For circuits of less than 2 MTPA capacity, piloting is usually not justifiable, with the cost of such a venture usually incorporated into extra mill length and/or motor rating.

• For simple AG or SAG mill piloting without online downstream piloting of other unit processes (such as flotation or solvent extraction) 100 – 150 tonnes of ore are required, with campaign duration being 10 to 15 working days in a test facility.

• For more complex arrangements, campaigns have been known to run over two months, with corresponding escalating costs.

519

Plant Circuit Surveys

• When the mill selection being considered is the result of an intended plant upgrade, obtain plant survey data in the form of mass balances and sizing data.

• Supplement with process information such as milling rate, power draw and equipment configurations (operating ball charge, total mill charge volume, milling speed, cyclone parameters, etc.).

• This data can be used to provide input information for power based modeling, or for more sophisticated breakage rate based on stimulators.

520

261

Grinding & Classification Circuit Design – Mill Power

521

Sessions Outline

1. Types of Mill Equipment and Circuits 2. Factors In Grinding Circuit Selection3. Ore Testing4. Mill Power 5. Sizing Grinding Mills 6. Grinding Mill Design and Operation

522

262

Milling Power

1. Introduction

2. Power Method Considerations

3. Bond Grindability Method

4. Mill Speed

5. Liner Profile and Speed Effects

6. Classification and Circulating Loads

523

Reference Papers“Bench-Scale and Pilot Plant Tests for Comminution Circuit Design,” Mosher & Bigg & “Selection of Rod Mills, Ball Mills and Regrind Mills” Rowland. SME, 2002.

Introduction

• In 1951 Mr. Fred C. Bond of the AllisChalmers Co. proposed his third theory of comminution.

• Mr. Bond developed his work index (Wi), which is used extensively to determine power input.

• This session describes methods of determining mill power (used as the basis of mill sizing) and ore testing.

524

263

Introduction

• Ore characterization for comminution is to provide parameters to design circuits that economically achieve the throughput and grind that is suited to the balance of the plant’s equipment and capabilities.

• Circuit design is a balance between:

‒ Finding the minimum operating cost to attain the desired final grind (consumables and power) &

‒Efficiently using installed capital.

‒The most efficient circuit is the one that allows the greatest rate of return to a project.

525

Introduction

• Certain circuit configurations require more ore characterization that others.

• A conventional crusher-rod mill-ball mill circuit requires less characterization than an AG or SAG circuit.

• AG/SAG circuits power draw is dynamic and greatly affected by changes in operating conditions.

526

264

Mill Power

• Around half the energy used in most mineral processing plant is consumed in grinding. Usually, it is the single biggest operating cost item, and good energy utilization is critical to project economics.

• Sizing of grinding mills is mostly carried out by determining the energy required for the duty and selecting an appropriate unit to deliver that energy.

• Determining the energy required can often be done by laboratory testing. Two forms of testing are common:

‒The Bond grindability tests

‒Single particle tests e.g. the Impact test or the Drop Weight Test.

527

Power Method Considerations: Testing

• Bond grindability (ball and rod mills)‒The Bond Grinding Indices are for predicting rod and ball

mill power requirements. They can also be used by operators to assess the power efficiency of an existing circuit, as explained below. However, the Bond BWI is not a good predictor of AG/SAG mills unless adapted using empirical factors.

• Single particle (AG and SAG mills)‒ In order to assess AG/SAG behavior, single particle tests

have been devised which look at the energy required to break the particle under impact conditions, and the relationship between the energy applied and the size distribution of the “daughter” products.

528

265

Bond Grindability Method (Ball and Rod)Work Input Determination

• Ball mill circulating load 2.5: Rod mills CL 1.0.

• Bond derived a formula for the calculation of the required energy to reduce particles from a feed 80% passing size (F80) to a product 80% (P80).

Where: W = work input in kWh/tWi = Bond Work Index in kWh/tMultiplying the new feed (t/h) by W gives the power requirement (kW).

8080

1110

FPWW i

529

Bond Efficiency Factors

Efficiency Factors are applied to W to derive the corrected power requirement, based on empirical experience:

W Corrected = WBond* EF1 *EF2 *EF3 *EF4 *EF5 *EF6 *EF7 *EF8 *EF9

EF1 – Dry GrindingEF2 – Open Circuit GrindingEF3 – Diameter Efficiency FactorEF4 – Oversized Feed FactorEF5 – Fineness of GrindEF6 – High/Low Ratio of Reduction Rod MillingEF7 – Low Ratio of Reduction Ball Milling FactorEF8 – Rod Mill FeedEF9 – Rubber Liners Factor

530

266


• EF1 (Dry Grinding)

With most materials, for the same range of work, dry grinding requires 1.3 times as much power as wet grinding. In some special cases, this correction factor can be as low as 1.1 or great as 2.0.

531

Product SizeControl Reference

% Passing

EF2

50 1.035

60 1.05

70 1.10

80 1.20

90 1.40

92 1.46

95 1.57

98 1.70

Bond Efficiency Factors• EF2 (Open Circuit

Grinding)

• For ball milling, EF2 is a function of the degree of control required on the circuit product. Open circuit inefficiency factors are as follows:

532

267


• EF3 (Diameter Efficiency Factor)

Using a base diameter of 2.44 m (8’) inside liners the correction for other diameters (in meters) is given by:

• The minimum value applied for EF3 is 0.914 for practical design purposes.

2.044.2

3

DEF

533

Bond Efficiency Factors• EF4 (Oversized Feed Factor)

• Rr = Reduction Ratio, F80/P80Wi = Rod Mill or Ball Mill Work Index in kWh/stFo = Optimum feed size = Zf * (13/RWi)0.5

Zf = A constant, where: rod milling = 16,000ball milling = 4,000

RWi = Rod Mill Work Index in kWh/st• The influence of Rr should be assessed with caution in the

first stage of a two-stage circuit.• Do not use EF4 for rod mill prepared feed to a ball mill and

do not apply if EF4 < 1.0• In two-stage ball milling, use EF4 = 1.2

r

o

oir

R

F

FFWR

EF

)7(

4

534

268


• EF5 (Fineness of Grind)

• Apply this factor only when P80 < 75μm (200 mesh).

80

80

145.1

3.105

P

PEF

535

Bond Efficiency Factors• EF6 (High/Low Ratio of Reduction - Rod Milling)

Do not use EF6 if (Rr-Ro) is between -2 and +2:

• Where:

D = inside liner diameter of rod mill (meters)L = length of rods (meters) = Rod Mill Inside L – 0.15

150

162

or RREF

D

LRo

58

536

269


• EF7 (Low Ratio of Reduction Ball Milling Factor)

• If the Rr ,or reduction ratio, of the ball feed to product drops below 6, use the EF7 correction factor. The lower the Rr the more power required.

• Note: Do not apply an EF7 factor greater than 2.0 without conducting continuous test work.

)35.1(2

26.0)35.1(27

r

r

R

REF

537


EF8 (Rod Mill Feed)

• When calculating rod mill power for rod milling only, an EF8 value of 1.4 is used when the feed is prepared by open circuit crushing and 1.2 in closed circuit.

• For Rod/Ball circuits 1.2 is used for the rod milling stage only, if the feed is prepared in open circuit.

• Do not use with Rod/Ball circuits with closed crushing circuits.

538

270

Bond Efficiency FactorsEF9 (Rubber Liners Factor)

• With respect to wear resistance, rubber liners are best suited for ball diameters up to 80 mm.

• Steel liners are best suited to primary ball milling applications requiring larger than 80 mm balls and rod mills, and ball mills larger than 16.5 ft in diameter.

• EF9 is applied to mills with rubber lifters, as they tend to be somewhat bulkier than the equivalent steel configuration, reducing the available grinding space.

• Rubber liners also absorb a portion of the impact energy of the steel media, reducing efficiency.

• An EF9 of about 1.07 is typically assigned for rubber lined mills.

539

Fines Correction

• The product from the first stage of grinding (AG, SAG, or rod mill) typically has a higher fines content than a crushing circuit product.

• To predict the ball mill size required in a secondary milling application, the mill feed size is modified by removing finished product from it.

• The next slide shows the size distributions for a crushed vs. ground feed, with different fines but the same P80.

• A partition curve is typically applied to the SAG product at the final product separation size.

• The result is that only a fraction of the SAG product requires secondary grinding, and this daughter product exhibits a coarser size distribution than its parent.

540

271

Fines Correction

541

The product from the first stage of grinding i.e. an AG mill, SAG mill, or rod mill, usually has a different size distribution than that produced by crushing to prepare ball mill feed.

Bond Method Limitations• The method is designed to predict power in a wet grinding

circuit at a 250% circulating load. Moving away from this condition reduces the accuracy of the test.

• It does not predict the behavior of large rocks in grinding circuit where the mode of breakage is impact dominated versus attrition and abrasion in ball mills (SAG/AG Mills).

• The Bond Work Index is based on the energy per unit mass required to reduce a particle from “infinite” size to 80% passing 100 μm. If the P80 is less than 100 μm, serious discrepancies can occur. The closing screen in the Bond test must reflect the size to which the particle is to be ground.

• If P80 ≤ 10 μm, do not apply Bond predicators of power.

542

272

Bond Method Limitations

• The shape of the size distribution generated by a two-stage grinding operation may differ significantly from the shape obtained by crushing.

• The F80 may be the same, but the amount of fines at say F30 or F20 may be markedly different.

• A size distribution correction may be necessary to better predict 2nd stage power requirements for:

‒SAG/Ball milling and 2-stage ball milling

‒Other ‘unnatural’ or scalped feed distributions.

• These conditions require additional grinding energy based upon the variation from a more standard feed distribution.

543

Mill Speed - Critical Speed• Grinding mill is usually shown as a percentage of critical

speed, Nc.

(D in meters) (D in feet)

• Normal mill speeds range from 60 to 90% of Nc, dictated by operational and economic considerations.

• Power drawn is proportional to mill speed, suggesting that mills should be run as fast as possible.

• However, the useful work done by the grinding charge is related to the mode of breakage induced, which is in turn influenced by the liner design and charge level.

• Higher speeds lead to higher rod, ball and liner wear.

DNc

31.42

DNc

63.76

544

273

Mill Speed545

Effect of Mill Speed on Load TrajectoryFigure 1 illustrates the effect on the trajectory of the outer envelope of the charge at increasing speeds for the same ball size with two lifter designs.

Mill Speed

Speed Guidelines

• Studies such as on the previous slide have produced the following general guidelines:

• AG Mills - An impact mode of breakage is usually sought, and with no steel media in the mill it is possible to run at speeds in the range 80-90% Nc.

• SAG Mills - Typical operating speeds are around 75% Nc. Liner damage will occur if the balls are allowed to impact them directly, and SAG mills usually have variable speed drives.

546

274

Rod Mill Speed

547

Rod Mills operate at a lower speed than ball mills to ensure that there is no cataracting of the rods. Typical speeds related to the inside shell diameter are:

Diameter

(m)

% Nc

Inside Shell

2 68.0

3 65.0

4 64.0

4.57* 62.6

* max. recommended diameter

Ball Mill Speed

• Smaller mills can be run at high speeds up to 85% Nc, medium diameter mills at lower speed – 70-72% Nc. There is an emerging trend of operating very large mills (>5 m dia.) at higher speeds – typically 76% Nc – in an attempt to overcome an “inactive kidney problem.”

• Typically for Ball Mills D < 5m:

% Nc = 83.5 [D] –0.108

548

275

Liner Profile and Speed Effects

• Figure 1 also shows the effect of differing lifters on the trajectory of balls in the ball mill.

549

Liner Profile and Speed Effects

• Fine Grinding:For fine grinding, it is desirable to have the charge cascading rather than cataracting. This is achieved by selecting a lower mill speed and/or using a wave liner profile.

• Impact BreakageFor breakage of larger feed particles, the grinding balls should strike the charge close to the toe. Higher lifter bars and mill speeds will assist.

550

276

Classification and Circulating Load• Efficient classification is key to any closed grinding circuit.

• Typical equipment include screens, classifiers or hydrocyclones.

• Typical SAG Circulating Load Ratio (CLR): 50-150%

• Typical CLR for Ball Mills 250-350%.

• Ensure that the classifier is performing well by analyzing its behavior on a regular basis.

• CLR is best measured by mass flow to the cyclones.

• There is also a standard method which uses the size distributions of the streams to derive a mass balance.

• Use these techniques to check that the mill is grinding the optimum tonnage by maintaining the target CLR.

551

Summary

• A key aspect for sizing and selecting grinding mills is to determine the power required.

• Bond's equation works well, but must be modified with efficiency factors.

• Mill Power is also influenced by mill speed and liner profiles.

• Efficient classification is critical to an effective circuit.

552

277

553

Grinding & Classification Circuit Design – Mill Sizing

554

278

Sessions Outline

1. Types of Mill Equipment and Circuits 2. Factors In Grinding Circuit Selection3. Ore Testing4. Mill Power 5. Sizing Grinding Mills 6. Grinding Mill Design and Operation

555

Grinding Mill Sizing and Design• Introduction

• Mill Sizing ‒ Factors influencing mill power‒ Tumbling Mill Power Calculation and Sizing‒ Calculating Grinding Media Size and Consumption

• General Mill Design Considerations‒ Drive Selection‒ Motor Selection‒ Mill Discharge and Feed System SelectionReference Paper

“Selection of Rod Mills, Ball Mills and Regrind Mills,” Chester Rowland

556

279

Introduction

Objective: to describe methods of sizing ball and rod mills once the grinding power requirements for these have been determined.

The approach to sizing SAG mills is fundamentally similar to ball mills with modification for the effect of grates on the charge, aspect ratio and pebble crushing.

557

Factors Influencing Mill Sizing

a) Mill Speed

b) Mill Diameter and Length

c) Mill Discharge Opening Size

d) Type of Discharge Mill Head

e) Amount/Size of Grinding Media

f) Feed Size

g) Feed SG

h) Ore Hardness

i) Feed Rate

j) Water addition (viscosity)

558

280

Mill Power Factors: Mill Speed

Ps = KTωWhere:• Ps = Power transmitted

through shaft from motor • K = Constant• T = Torque• ω = RPM

% of Critical SpeedN

et H

P

HP approximately proportional to speed over wide range

100

559

Mill Power Factors: Mill Dimensions

• Mill Diameter & Length

Average Slope = 2.5

Small mills ~ 2.4Large mills ~ 2.6

P D2.5 P L

Log (Mill Diameter)Log

(net

HP

per

uni

t len

gth)

Mill Length

Net

HP

HP proportional to length

560

281

Mill Power Factors:Discharge Opening Size

Mill Discharge Opening Size Distance Between Load Centroid & Mill Center

% of Critical Speed

Discharge Opening Increases

Spread in curves is exaggerated

As the discharge opening becomes smaller, the distance from mill center to the centroid of the load becomes smaller, due to shift in center of gravity of load. So, HP goes down (despite small increase in load).

Ne

t HP

Discharge Opening Rotation Direction

Distance from mill center to centroid of load

561

Mill Power Factors: Discharge Head Type

• Grate Discharge draw more power than Overflow due to the distance from Centroid to Mill Center

Distance X Along Mill Length

Area under curve is proportional to mass of load

Mas

s of

Sol

ids

at P

ositi

on X

= center of gravity of load for high discharge mill

= center of gravity of load for diaphragm (grate) discharge mill

Load centroid is closer to mill center than Load centroid

P

N

N

N

Load

Load N

Discharge EndFeed End

P

P

P

562

282

Mill Power Factors:Discharge Head Type

Grate Discharge

Spout Feeder

Overflow Discharge

Drum Feeder

563

Mill Power Factors: Amount/Size Grinding Media

Critical Speed is the speed at which a ballor rod will be centrifuged in the mill.From force balance, Wc (rpm):

% Media Load, by volume

Ne

t HP

Due to change in mass Due to shift in centroid of load and mass

60 8070

% of Critical Speed

Ne

t HP

r

Radius R

mg

(m(R-r)w)w

Angularvelocity, w

D = 2Rd = 2r dDcW

63.76

564

283

Mill Power Factors

Feed Size and RateFrom Bond Equation

P = KT[k – 1F80]K, k are constant and T is feed rateAs feed rate increases, P will increase and then level off

Feed Specific GravityThe higher the specific gravity, the higher the power draw

SG = Power Draw

565

Mill Power Factors: Ore HardnessFrom Bond Equation

• P = KWi

Log P80

Log

(HP

/T)

Work Index Increases

Slope of about –1/2

566

284

Mill Power Factors: Feed Rate- Startup

Time

Ne

t HP

Due to build up of rock in the mill

Centroid Shift causes less HP draw

0

Power drawn with steel ballsand water only.

At time = 0, cut in fresh feed solids

Less power from slippage

Steady State Reached

-Steady State

Rod Mills and Ball Mills

Feed Rate

Ne

t H

P

Feed Rate

Ne

t H

PAutogenous Mills

567

Mill Power Factors: Water Addition Rate, Pulp Viscosity

Overflow Discharge: - Rod Mills : 80% solids- Ball Mills – 76% solids

Water Addition Rate Viscosity, Flow and Power Draw

Water Addition Rate Flushing Fines, Power Draw and Wear

Ore containing clays can be excessively viscous. The viscosity can be reduced by adding:1. Water2. Polyacrylic acids3. Calgon (phosphate dispersant) Pulp Density, gm per cc

Pul

p V

isco

sity

, cp

“Ice Cream” Discharge

“Sausage” Discharge

568

285

Mill Grinding Power and Sizing Calculation: Work Input

• The mill work input to grind a tonne of feed of 80 % passing size (F80) to a product passing size of 80 % (P80) is calculated by the Bond equation:

W = 10 Wi [1/P80 - 1/F80] where: W = work input in kWh/tWi = Bond Work Index in kWh/t

• Efficiency factors EF are applied to W to derive the corrected power requirement WCOR

• WCOR is multiplied by the new mill feed tonnage T to give the mill power requirement P = T * WCOR

• This is the power that must be applied at the mill drive in order to grind the feed tonnage T from one size distribution F80 to a finer product size distribution P80.

569

Mill Grinding Power and Sizing Calculation: Matching Mill Size to Power Requirement

• Once the mill power is determined the mill size to draw the required power must be calculated.

• Power draw theory is based upon a charge load in equilibrium, and relates to its center of gravity.

• The centroid of the charge is maintained in dynamic equilibrium at an angle of repose A to the vertical by a mechanical lever arm force balance between the mill drive and charge weight.

570

286

Mill Grinding Power and Sizing Calculation: Matching Mill Size to Power Requirement

• The figure below shows a section of a mill charge load in equilibrium in relation to its center of gravity.

W = weight of chargeD = DiameterC = distance of center of gravity of charge from center of mill in feetA = dynamic angle of repose of the chargeN = mill speed in rpm

A

D

C

N

W

571

Matching Mill Size to Power Requirement:DuPont Power Model

An early theoretical power model of DuPont (1900’s) shows the effect of charge weight, mill diameter and mill speed on the power draw per unit of mill length (P/L) :

1. Charge Weight: P/L ∝ Mass W ∝ D2

2. Mill Diameter: P/L ∝ Lever Arm Length C (Centroid to Mill Center) ∝ D3. Speed: P/L ∝ Speed ∝ 1/ D 2

Therefore P/L ∝ D2 * D * 1/ D = D 2.5

or P ∝ D2.5 * L

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287


P ∝ D2.5 *L

This illustrates that: - mill power is more sensitive to diameter than length- the relationship between length and power is linear - diameter affects power draw exponentially- incremental changes in diameter provide step changes in power draw

Therefore the selection of larger diameter (and fewer) mills can significantly reduce the number of mills required in an application.

573


• Capital cost climbs steeply with diameter due to:‒ manufacturing methods‒ greater load on mill structure‒ more expensive drive systems

• Therefore the number of mills required becomes a trade-off between capacity and capital. In general, the larger the mill selected the lower the overall installed capital.

There are practical limitations. Currently the largest mills are about:

Rod Mill – 15 ft diameter by 24 ft long ( 2,625 hp)Ball Mill – 26 ft diameter by 38 ft long (20,770 hp) SAG Mill – 42 ft diameter by 26 ft long (22,000 hp)

574

288

Matching Mill Size to Power Requirement:Nordberg Power Model- Theoretical Approach

Nordberg used a mechanical torque arm force balance analysis to show that the theoretical power input (hp) required to maintain the centroid of a mill charge in equilibrium at an angle of repose A to the vertical is:

hp = K * (W) * (C) * Sin A * 2π * N where:K =1/33,000 W= weight of chargeC = distance of center of gravity of charge from center of mill in feetA = dynamic angle of repose of the chargeN = mill speed in rpm

575

Matching Mill Size to Power Requirement:Nordberg Power Model

hp = K * (W) * (C) * Sin A * 2 π * N

The model is based on the availability of data from similar installations. If the value of the angle A can be found then the power demand of mills with various diameters at the same speed can be calculated.

However the value of angle A varies with:• the type of discharge• percent of critical speed• grinding condition.

Thus direct comparison can only be made between mills with a similar type of discharge.

576

289

Matching Mill Size to Power Requirement:Nordberg Power Model

If various types of discharge are to be used, the following factors must be applied for mills of the same size and speed:

• Dry diaphragm = 1.0

• Wet diaphragm = 0.9

• Wet overflow = 0.8

In order to use the preceding Nordberg Equation, it is necessary to have considerable data on existing installations. Therefore, this approach has been simplified.

577

Matching Mill Size to Power Requirement:Simplified Nordberg Power Model

The five basic conditions that determine the horsepower drawn by a mill are:

1. Diameter2. Length3. Charge (% Loading)4. Speed5. Mill type

Nordberg incorporated these conditions into four factors A,B,C & L to allow the calculation of the approximate horsepower of a mill at the pinion drive shaft as follows:HP = A * B * C * L

578

290

Matching Mill Size to Power Requirement:Simplified Nordberg Power Model

• The Nordberg power factors for calculating rod and ball mill power are on charts on pg 9 of the Nordberg Grinding Catalog, where:A = factor for diameter inside the shell liners = D^2.5/5.6442 B = factor for mill type and charge volume (% loading) – steel grinding media C = factor for mill speed expressed as a percentage of mill critical speedL = length in feet of grinding chamber measured between head liners at the junction of the shell and head liners (Equivalent Grinding Length EGL) – in most cases subtract 6” from the length inside the mill shell.

B factor is based on steel grinding media at 315 lbs per cubic ft. The B factor must be adjusted by the ratio of the actual charge density or, Factor =B x charge density/315.

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Summary

• Tumbling mills are sized to deliver the power required to achieve the desired grind size.

• Several factors influence power draw, including mill speed, dimensions, type, feed size, type and rate.

• Power draw theory is based upon a charge load in equilibrium, and relates to its center of gravity

• Mill power is more sensitive to diameter than length

• Mill size can be estimated by the simplified Nordberg Power Model.

580

291

Grinding & Classification Circuit Design – Mill Sizing

Example

581

Nordberg Mill Sizing Example- Calculation

Exercise: Size a single stage ball mill (overflow) in closed circuit with a cyclone with the following parameters:

Feedrate = 500 tonne/hF80 = 9,400 micrometersP80 = 175 micrometersRWI = 13.2 kWh/stBWI = 11.7 kWh/stCL = 250% Circulating LoadCdensity = 340 lb per cubic ftSG = 2.7Ai = 0.25

582

292

Nordberg Mill Sizing Example –Calculation

• The feed to a standard Bond ball mill grindability test is minus 6 mesh (3360μm)

• However the coarser fraction of a minus ½” single-stage ball mill feed is not included in the feed to the grindability test mill

• If RWI is different than BWI, then particularly if the former is higher, a two step calculation should be used to determine the grinding power input, using 2100 μm to divide the calculations.

583

Nordberg Mill Sizing Example – Calculation

Calculate Uncorrected Grinding Power Input

Step 1:W = 10 * (13.2 - 13.2 )= 1.52 kWh/st

2,100 9,400

Step 2:W = 10 *(11.7 - 11.7) = 6.29 kWh/st

175 2,100

584

293

Nordberg Mill Sizing Example – CalculationCalculate Uncorrected Grinding Power Input

Step 3:Total = 1.52 + 6.29 = 7.81 kWh/st

= 7.81 * 1.102* 1.341* 500= 5766 HP, uncorrected

Where:

Power (HP) = Power (kW) x 1.341

1 tonne = 1.102 short ton

585

Nordberg Mill Sizing Example - Calculation

• Step 4: Apply Efficiency Factors

HPcorrected = HPuncorrected*Relevant EF1 to EF8 factors

• EF1: Dry grinding. Does not apply.

EF2: Open circuit grinding. Does not apply.

EF3: Diameter Efficiency = (2.44/D)0.2 .

Mill will be larger than 3.81 m (12.5’) in diameter so use 0.914.

586

294


EF4: Oversize Feed =

Rr = Reduction Ratio = F80/P80 = 9400/175 = 53.7

Fo = Optimum feed size = Zf*(13/RWI)0.5

Zf = 4000 (ball milling)

Fo = 4000 * (13/13.2)0.5 = 3970

EF4 = 53.7 + (11.7-7) * [9400-3970)/3970] = 1.1253.7

r

o

oir

R

FFF

WR

EF

)7(

4

587


EF5: Fineness of Grind – P80 > 75μm, Does not apply.

EF6: High/Low Rr - Rod Milling, Does not apply.

EF7: Low Rr Ball Milling Factor, Does not apply.

EF8: Rod milling factor, Does not apply.

EF9: Rubber Liners Factor, Does not apply.

HP,corrected = 5,766 * 0.914 * 1.12 = 5903 HP

588

295


• Step 5: Select # of MillsAssume use 1 mill: 5,903/1 = 5,903 HP Mill

• Step 6: Size Mill ShellHP = A * B * C * L

We don’t know D so substitute factor A with D^2.5/5.6442

Charge density is 340 lb/cubic ft so multiply B by ratio of 340/315

5,903 = D2.5/5.6442 * B * (340/315) * C * L

589


• Step 7: Determine factor B:

Most overflow discharge ball mills operate with a charge volume that occupies 35% to 45% of the mill volume.

> 20 ft use 35%< 20 ft > 16.5 ft use 40%< 16.5 ft use 45%

An average value would be 40%. From tables,Wet Overflow Ball Mills @ 40% Loading B = 5.02The B Factor must be adjusted to the steel density of the balls (340/315).5,903 = D2.5/5.6442 * 5.02 * (340/315) * C * L

590

296

591


• Step 8: Determine factor C:

• Critical Speed

The percent of critical speed (peripheral speed at which charge centrifuges) is one of the major factors in determining the power that a grinding mill draws.

To relate critical speed and peripheral speed as mill diameter increases, the average recommended speed as % of critical speed is shown in the table on the following slide.

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297


• Step 8: -cont-Through an iterative process, you can find the mill diameter will be >15 ft, therefore use a speed of 68% of .

From Nordberg tables Factor C will be = 0.1583AND by substitution

Mill Diameter Inside Liners

% of Critical Speed

Meters Feet Rod Mills

Ball Mills

0.91-1.83 3-6 76-73 80-78

1.83-2.74 6-9 73-70 78-75

2.74-3.66 9-12 70-67 75-72

3.66-4.57 12-15 67-64 72-70

> 4.57 >15 - 70-68

5,903 = D2.5/5.6442 * 5.02 * (340/315) * 0.1583 * L

593

Factor C – Ball Mill Sizing

594

298

Nordberg Mill Sizing Example -Calculation

• Step 9: Estimate Mill L/D Ratio.

Recommended rod mill length to diameter inside liners is 1.4 to 1.6.

Being free from the limits imposed on rod mills, ball mills have more variation in length to diameter ratios, ranging from 1:1 to 2:1. The ratio used varies with- the circuit type (type of grinding)- size of the feed- the ratio of reduction and specified fineness of grind

• In general, as desired fineness of grind L/D

595


Type of Grinding

Feed F80

Microns

Top Ball Size

mm in.

L/D Ratio

Wet 5,000 – 10,000 60 –90 2.5 –3.5 1:1 to 1.25:1

Wet 900 – 4,000 40 –50 1.8 –2.0 1.25:1 to 1.75:1

Wet or Dry Fine Feed –Regrind 20 –30 ¾ - 1¼ 1.5:1 to 2.5:1

Wet or Dry Fine Feed- Open 20 –50 ¾ - 2.0 2.0:1 to 3.0:1

Dry 5,000 – 10,000 60 –90 2.5 –3.5 1.3:1 to 2:1

Dry 900 – 4,000 40 -50 1.8 –2.0 1.5:1 to 2:1

Ball Mill L/D Ratio – General Application Guidelines

596

299


• Step 9: -cont-

Based on the preceding table, wet milling and a F80 of 9,400 mm and P80 of 175 microns (not fine regrind) a L/D ratio of 1.25 is selected.

By substitution into equation:

5,903 = D2.5/5.6442 * 5.02 * (340/315) * 0.1583 * 1.25D

597


• Step 10:Calculate Mill Diameter (Inside liners):Power Equation

Rearranging:31,075 = D3.5

D = 19.2 feet (inside liners)

L = 1.25 * 19.2L = 24.0 feet

5,903 = D2.5/5.6442 * 5.02 * (340/315) * 0.1583 * 1.25D

598

300


• Step 11:Select Mill Shell Size:Add new shell steel liner thickness (0.6 ft) to calculated diameter = 0.6ft + 19.2 ft = 19.8 ft (Closest standard is 20.0 ft)

Select a 20.0 ft inside shell diameter by 24.0 ft long overflow ball mill @ 40% ball charge and running at 5,903 hp.

599

Nordberg Mill Sizing Example - Calculation• Step 12:

Calculate Maximum Ball Size for Mill Charge:

The equations for selecting the largest diameter (in inches) rod (R) or ball (B) in the initial mill charge, or make-up charge, for a mill of diameter D is:

R = (F800.75 /160) * [(SG * RWI) / (100 * Cs * D 0.5)]0.5

B = (F80 /K)0.5 * [( SG * BWI)/ (100 * Cs * D 0.5)]0.34

Ball Mill K Factor: Mill Type Steel or C.I. Balls K

Wet Overflow 350

Wet-Diaphragm 330

Dry- Diaphragm 335

600

301


• Step 12: (cont.)F80 = 9.4 mm, convert to microns K = 350SG = 2.7Cs = 68%BWI = 11.7D = 19.8 ft by substitution:

B = (9400/350)0.5*[( 2.7* 11.7)/(100*0.68*19.80.5)]0.34

B = 2.4 in. Closest standard is 2.5 in.

601


• Step 13: Calculate rod/ball and shell liner consumption:

• The following empirical equations use the abrasion index Ai

to estimate rod, ball, and liner wear rates.

Wet Rod Mills:Rods kg/kw-hr = 0.1590 * (Ai – 0.020)0.2

Liners kg/kw-hr = 0.0159 * (Ai – 0.015)0.3

Wet Ball Mills:Balls kg/kw-hr = 0.1590 * (Ai – 0.015)0.34

Liners kg/kw-hr = 0.0118 * (Ai – 0.015)0.3

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302


• Step 13: (cont.)

Importance of Mill Liners

- Shell Liner Protect the Mill Shell- Lifters attached to Liners which help distribute load for grinding- Lifter wear leads to loss of power- SAG/AG Mills have white metal liners- Ball Mill > 18 ft have white metal liners- Ball Mill< 18 ft can have rubber liners (but note EF8)

603

Various liner materials and arrangements

604

303

Typical Abrasion Index Values

Material Abrasion g Ai

Dolomite 0.0160

Schist-biotite 0.1116

Copper Ore 0.1472

Hematite 0.1647

Heavy Sulphides 0.1284

Magnetite 0.2517

Gravel 0.3051

Granite 0.3937

Quartzite 0.7751

605


• Step 13: (cont.)Substitute Ai = 0.25 into ball mill equationsBalls = 0.1590 * (0.25– 0.015)0.34 = 0.0972 kg/kw-hr Liners = 0.0118 * (0.25– 0.015)0.3 = 0.0072 kg/kw-hr

Liner consumption typically ~10% of media consumption.

Multiply by the power draw (kw) and divide by feed rate of 500 t/h to give consumption in kg/t.

Balls = 0.0972 * (5903 *0.75) / 500 = 0.86 kg/tLiners = 0.0072 * (5903 *0.75) / 500 = 0.064 kg/t

606

304

Mill Discharge and Feed Type Selection (Ball Mill)

Overflow Discharge:

• Suitable for almost all applications

• Simple and trouble-free.

• The discharge trunnioncan be furnished with a trommel screen.

Grate Discharge:

• 15-20% higher capacity per unit volume

• Coarser product with high circulating load producing little extreme fines.

• Can have a trommelscreen as well.

607

Mill Discharge and Feed Type Selection (Rod Mill)

• Overflow: Common for wet mill rod milling. Diameter of discharge trunnion is larger than feed to promote flow.

• End Peripheral Discharge: Used when a coarse product is required.

• Center Peripheral Discharge: Suitable for dry grinding at extremely high capacities and coarse grinding, wet or dry. Also applicable for viscous material and moisture content 3-15% by mass.

608

305

Example of Grate Discharge with Spout Feeder – Rod Mill

Spout Feeder

609

Nordberg Mill Sizing Example -Calculation

• Spout feeders normally feed rod mills

• Spout feeders require at least 5 ft head between mill center line and feed hopper for proper flow

• Spout feeders are normally fed from ball mill cyclone underflow box, requiring higher pumping heads relative to a scoop or drum feeder.

• There is a trade-off with scoop/drum drive power and higher maintenance, such that in modern large mills the scoop/drum feeder is rarely used.

• Based on the exercise:Select an overflow ball mill with a spout feeder.

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306

Summary

Mill sizing led to the selection of:

• A 20.0 ft inside shell diameter by 24.0 ft long overflow ball mill @ 40% ball charge and running at 5,903 hp.

• Ball size: 2.5 in.

• Ball wear estimate: 0.86 kg/t

• Liner wear estimate: 0.064 kg/t

• Feeder/Discharge Arrangement:

‒Overflow mill with a spout feeder

611

Motor Selection

612

Drive and Motor Types and Efficiencies

Motor Fixed Variable Speed

Drive LSS WR LCI CCV WR PWM

Single Pinion 4.5-10MW 0.950 0.932 0.922 0.916 0.899 0.924

Dual Pinion 9-20MW 0.950 0.912 0.922 0.916 0.899 0.924

Gearless 9-30MW NA NA NA 0.915 NA 0.923

LSS Low Speed Synchronous

WR Wound Rotor

LCI Load Commutated Inverter

CCV Cycloconverter

PWM Pulse Width Modulated

Motor Key:

307

Motor Selection - Summary

In general the mills should be driven by a large enough motor to allow the mill:

1) to operate with a 45% by mill volume charge with new liners and to 2) to overcome the drive train and motor efficiency

Based on the example calculation in the last section:

Select a single-pinion fixed speed drive with a low speed synchronous motor.

Power required = 5903 hp at the mill pinion at 40% mill volume charge.

Based on previous Table: Drive efficiency = 0.95

Select motor size of 5903 * 45/40 * 1/ 0.95 = 6,990 HP = 5250 KW

613

BALL & ROD MILL SIZING

OLAV MEIJO

HATCH ENGINEERING

May 2013

308

615

Presentation Outline

1. Brief introduction to Bond’s theory

2. Lab Work index‐ Equipment – Procedure

3. Work index calculation

4. Correction Factors applied to the Lab work index

5. Calculation of the power required for grinding

6. Calculation of the mill power draw

7. All calculations together

8. FAQs

9. SAG design test methods

616

• In 1930 Allis-Chalmers hired Fred Bond to carry out research on size reduction of ores and grains.

• Bond first task was to determine if the two existing theories of comminution were right.

• Bond found that Kick and Rittinger theories were wrong and he proposed the third theory of comminution.

Introduction

309

617

• Bond’s second task was to develop a relationship between ball mill operating data and grindability test data.

• Bond developed a grindability method to determine the work index Wi test.

Introduction

618

The Bond Work Index Wi

The equation shown below is used to determine the value of the work index Wi based on the standard Bond grindability lab test.

310

619


• The feed for the Ball mill grindability test is 100% - 3350 microns and 80% -2100 microns

• The feed for the rod mill grindability test is 100% -13200 microns.

• The Wi Test corresponds to the motor output power Bond correlated to an overflow discharge ball mill of 2.44 m(8 foot) internal diameter in wet grinding conditions, closed circuit at 250% circulating load.

620


Does it really work ?

311

621

Validity of the Bond theory

Relationship between Energy consumption and particle size, R.T. Hukky 1961 ( Taken from the history of grinding by Alban J. Lynch

and Chester A. Rowland)

622

Factors affecting the Bond work index

• There are eight efficiency factors to be applied to the lab test work index. The result obtained is the corrected work index:

Wi corrected = Wi test x EF1 x EF2 x….EF8

• These factors are applied to take into account conditions observed in real applications that differ from the bond lab test conditions.

The efficiency factors are:

312

623

Factors affecting the Bond work index

• EF1 Dry grinding

• EF2 Open circuit ball mill

• EF3 Diameter efficiency factor

• EF4 Oversized feed

• EF5 Fine grinding in ball mill – product P80 less than 75 microns

• EF6 High or low ratio of reduction rod mill

• EF7 Low ratio of reduction ball milling

• EF8 Rod milling

624

• EF1 : This factor is applied for dry grinding. The value is 1.3

• EF2 : Open circuit grinding requires more energy than closed circuit grinding and is a function of the product size. The table below shows the values

Efficiency Factors

(Chester A. Rowland and David M. Kjos)

313

625

Efficiency Factors

• EF3 Diameter efficiency factor is calculated based on the ball mil inside diameter used by Bond.

EF3 = (2.44/D)0.2 and EF3=0.914 when D>3.81 meters (12.5’)

• EF4 Optimun feed size is applied when the feed size to a ball/rod mill is coarser that the optimun size “Fo”.

EF4=( R + (Wi‐7) (F‐Fo)/Fo ) / R

Ratio of reduction R= F80/P80 ,

Fo= 4000 (13/Wi)0.5 For ball mills

Fo= 16000 (13/Wi)0.5 For Rod mills

626

Efficiency Factors

• EF5: This factor is apply when the P80 is finer than 75 microns. This factor is calculated using the equation:

EF5=(P80 + 10.3)/(1.145xP80)

• EF6: This factor is applied for rod mills when the ratio of reduction R is high or low outside the range Ro =+/‐ 2 :

EF6=1 + ( R –Ro)2/150

Ro= 8 + 5 L/D,

L: Rod length D: intern mill diameter

• EF7:The low ratio of reduction factor is applied when “R” is less than 6

EF7=(2(R‐1.35)+0.26 )/(2(R‐1.35)

314

627

Efficiency Factors

• EF8: This factor is apply to rod milling only. There are only recommended values:

EF8=1.4 for open circuit crushing, rod milling only

EF8=1.2 for closed circuit crushing, rod milling only

EF8=1.2 for open circuit crushing and Rod mill-ball mill circuit

EF8=1.0 for closed circuit crushing and Rod mill-ball mill circuit and rod mill F80 is less than 12 mm

628

Bond developed an empirical correlation between power and ball charge to determine power required for a wet grinding overflow ball mill. The correlation was later modified by Rowland and Kjos. The final equations is:

kW/st = 3.1 D0.3 (3.2 -3Vp) Cfs (1-(0.1/2(9-10Cfs)) + Ss

D = Mill diameter Inside liners in ft.

Vp = Mill volume fraction of balls

Cfs = Fraction of critical speed

Ss = Ball size factor

*For low level grate discharge mills applied a factor of 1.16 to the above calculation.

Mill Power Draw

315

629

Mill Power Draw

Ss= (B‐3D/20)/2

B = Ball size in inches

D= Mill diameter inside liners in feet

Ss = Power per short ton of ball

Mill Power Draw

630

316

631

Ball Mill Sizing – All together

632

Ball Mill Sizing – All together

317

633

Ball Mill Sizing – FAQs

• Can I use the Bond ball mill work index for sizing crushers ?

No.

The Bond work index is not the same as the bond crusher work index.

Bond equation is inappropriate to determine the energy required for crushing.

Bond crushing index underestimates the power required for crushing.

634


• I’m sizing a ball mill, why do I need the “rod mill work index” ?

Energy required for grinding from 13200 microns to a P80 ‐2100 microns is calculated by using the rod mill work index and then added to the ball mill energy required from 2100 microns to the target P80. All ball mill efficiency factors should also be applied.

318

635


• Why don’t use big Rod Mills ?

Rod mills are limited in capacity by the maximum rod length.

636


• What’s the relationship between Rod mill work index (RWi), Bond mill work index (BWi) and the amount of pebbles produced in a SAG mill ?

RWi > BWi Specific energy requirement is higher in the large fraction than the specific energy in the small fraction thus the probability of producing pebbles is higher ( ¼” to 2” pebbles).

BWi > RWi Specific energy to grind coarse particles is lower than the specific energy require to grind fine particles thus the likelihood of forming pebbles is low.

319

637


• I’m using the Bond equation to calculate the mill power but it’s no even close to what the vendors proposed. What’s wrong ?\

Double check that the correction factors you are using are right. If still It’s not close to vendor’s calculation, the vendor is wrong !

JK drop weight test-JKSimMet

638

320


639

• The JK Method uses two methods to characterize ore breakage at different energy levels.

1. High energy levels are characterized by an impact breakage test using a drop weight device

2. Low energy levels are characterized an abrasion test using a tumbling test. The abrasion parameter is “Ta” determined by the abrasion test.

3. “T10” is the percentage passing 1/10 of the original size.” Ecs” is the specific comminution energy


• To use the results of testing, the ore type parameters A and b and ta are entered into the SAG/autogenous mill model in JKSimMet,

• The simulation predicts product size and mill load using appropriate breakage rates. The simulator can then also be used to predict mill performance with variations in screen and classifier configurations or even with recycle crushing.

Phantom Cyclone in JKSimMet

• The “phantom overflow” represents the finished product produced by the SAG mill which will require no work by the ball mill circuit, as it will report directly to the actual ball mill cyclone overflow. The “phantom underflow” however, represents the actual tonnage and f80 of material on which the ball mill will perform work

640

321

SMC Test:Steve Morrell’s Approach to Mill Sizing (1)

• The SMC Test® generates a relationship between specific input energy (kWh/t) and the percent of broken product passing a specified sieve size.

• The results are used to determine the drop‐weight index (DWi), which is a measure of the strength of the rock when broken under impact conditions.

• The DWi is directly related to the JK rockbreakage parameters A and b and hence can be used to estimate the values of these parameters

641


642

322


643

Steve Morrell’ Approach to Mill Sizing (1)

644

size.screen closing

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crusher. pebble a have do circuits where0.95 andcrusher pebble recycle a without circuits coarse all and circuits fine allfor 1

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isequation reduction size general The

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particles coarse grind energy to specific

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323


645

Coarse particle breakage work index (Mia):

Mia = 19.5 kWh/t (from SMC test)

Fine particle breakage work index (Mib)

From the BBWI test results the ff values were obtained:

Gbps = 1.3 gr/revF80(um) = 2250P80(um) = 78P1(um) = 106

f(p80) = -0.2951

f(f80) = -0.2973

Mib (kWh/t)= = 20.1136

)1000000/x(0.295- f(xj) j

))((

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646

Primary crusher product P80 (um) = 1500000Final Product P80 (um) = 75

Coarse and fine particle comminution specific energy

K 1Coarse particle comminution specific energy

x1(um) 100000 Crusher Productx2(um) 750 Definitionfx1 -0.395fx2 -0.2958

Wa (kWh/t) = 10.184

Fine particle comminution specific energy

x1(um) 750x2(um) 75fx1 -0.2958fx2 -0.2951

Wb (kWh/t) = 11.1477

Total comminution specific energy

WT (kWh/t) = 21.3317

)(1

)(2i

12(4W xfxfi xxKM

324

SAG design Test(1)

• The SAGDesign test measures the pinion energy to grind ore from 80% passing 152mm to 80% passing 1.7 mm (WSAG).

• The 2nd stage of the test measures the Bond Ball Mill Work Index on SAG ground ore, Sd‐BWI.

• SAGDesign ore feed is prepared from a minimum of 10 kg per sample of split or whole diamond drill core pieces by stage crushing the ore in a jaw crusher to 80% product passing 19 mm.

• The crushed ore is then ground in a SAGDesign SAG mill (489 mm inside diameter x 163 mm EGL), seen here, that operates with parameters similar to commercial SAG mills (26% total charge; 11% steel load, 15% ore load; and rotation at 76% of critical speed)

(1) http://sagdesign.com/home/products‐and‐services/sagdesign‐test

.

647

SAG design Test(1)

648

325

SAG design Test(1)

649

Plant Survey

• The objective of a plant survey can be: 1. to increase throughput

2. to increase the finess of grind

3. reducing the costs associated to energy expenditure

4. replacement of grinding media

5. replacement of lifter

650

326

Plant Survey

• The final recommendations made to the client will be the optimum conditions proposed for: 1. Mill feed size

2. Feed rate

3. Ball load and size

4. Percentage solids

5. Discharge mechanism

6. Recycle crushing

7. Mill circulating load

8. Operation of cyclones

9. Mill liner type and profile

10. Throughput

651

Plant Survey

• Streams to be sampled

1. ROM feed (belt cut) TPH, PSD, %Sol

2. Cycl. Feed % Sol, PSD

3. Cycl. OF

4. Cycl. UF

652

327

Application of Bond’s Correction Factors in Trade-off studies

653

Alternative 1 Alternative 2 Alternative 3 Alternative 4

Qty 2 new + 1 future 1 new + 1 future 2 new 1 new + 1 future

Equipment Dimensions 13’x19’ 16.5’x21’ 15’x19’ 16.5x21’ Equipment Arrangement Parallel Parallel Parallel Series

Project current capacity Project future capacity Required power @ current capacity [kW]

2640 2520 3680 2520

Required power @ future capacity [kW]

3960 2520 N/A 4180

Immediate Equipment Installation Cost @ Project current capacity

R$ 42.9 M R$ 32.2 M R$ 53.8 M R$ 32.2 M

Additional Equipment Installation Cost for future capacity

R$ 23.0 M R$ 22.9 M N/A R$ 32.2 M

Final Equipment Installation Cost after future expansion

R$ 65.9 M R$ 55.1 M R$ 53.8 M R$ 64.4 M


654

328


655

SAG Mill Power Draw

656

Primary SAG Mill

Mill Operating Parameters and Power Required:

Daily Feed Tonnage 35000 tpdMill Availability 92 %Mill Feed Rate 1585 tphFeed Size F80 150000 umProduct Size P80 2500 umSAG Mill Work Index 15.5 kWh/tSAG Efficiency Factor 1.5Transmission Loss Factor 1.05Unit Power Consumption 4.25 kWh/tMill Power Required 6740 kWMill Power Required 9039 HPSAG Mill Power Installed 10000 HP

Fit of Mill Size to Motor Size:

Number of SAG Mills 1Power Installed per SAG Mill 10000 HPMill Outside Diameter 32 ftMill Length-EGL 16 ftPercent of Critical Speed (VS) 76 %Mill Speed, rpm 10.38Percent Volume Total Charge 28 %Percent Volume Steel Charge 8 %Tons of Steel Charge 149.27Ore Specific Gravity 2.8Slurry Pulp Density 70 % solSlurry Specific Gravity 1.82Charge Specific Gravity 3.40Charge Density, lb/ft³ 212.03Mill Power Draw 7920 kWMill Power Draw 10621 HP

329

SAG Mill Power Draw

657

SAG Mill Power Draw

658

SAG MILL PARAMETERSLiner thickness m 0.10-0.15 m

Fraction of crit. speed 0.72 to 0.75

Ball volume nominal design % 10-15%

Ball volume max operating % Max operating

Ball volume structural design % 2-5% above max operating

Total filling nominal design % 26% for SAG mill, 28% for AG mill

Total filling max operating % 30-35%

Discharge slurry % solids % solids 65% to 78%, typically 72%

Discharge mechanism Grate discharge for SAG or AG mill

BALL MILL PARAMETERSLiner thickness m 0.075 m

Fraction of crit. speed 0.72 to 0.76

Ball volume nominal design % 38% to 40%

Ball volume max operating % 38% to 40%

Ball volume structural design % 40%

Discharge slurry % solids % solids 65% to 78%, typically 70%

Discharge mechanism Overflow for ball mill

Discharge screen Trommel

330

659

Size Classification

Primary Sources: B Klein, AJ Gunson

660

331

Classification - Outline1. Introduction

2. Wet Size Classification

‒ Principles

‒ Types of classifiers

‒ Factors affecting performance

‒ Separation efficiencies

3. Hydrocyclone Classifiers

‒ Hydrocyclone description

‒ Geometry variables

‒ Process variables

‒ Cyclone sizing & selection criteria

‒ Example calculation

4. Maintenance and Optimization

661

Reference Paper“Hydrocyclone Selection for Plant Design”Timothy Olson and Patrick Turner

Size Classification – Introduction

• Size classifiers (water or air) separate particles of various sizes, shapes and specific gravities under the influence of gravitational or centrifugal forces.

• Size classifiers enhance the effect of particle size over other properties to produce a size split.

• Size classification is critical to achieving the target particle size in order to ensure efficient valuable mineral recovery.

662

332

Size Classification – IntroductionFactors that influence size separation:

• Small particles settle slower than large particles.

• In free vortex motion, centrifugal forces affect movement of large particles more than small ones.

• Small particles have less inertia and therefore flow with liquid or suspending medium.

• Large particles require higher conveying velocity.

• Collision Frequency Increases with particle size.

663

Size Classifier Categories

• Physical - Screens

• Wet Classifiers (Water)

‒Mechanical

•Spiral Classifiers

•Rake Classifiers

‒Non-Mechanical

•Cones

•Hydraulic Classifiers - jigs

•Hydrocyclones

• Pneumatic (Dry) Classifiers

‒Cyclones

664

333

2. Classification Principles

• Cut Size (separation size) has many definitions

‒Size which passes 95% of the overflow

‒Size at which cumulative percent passing in the overflow equals the cumulative percent coarse in the underflow

‒X50 as determined from fractional recovery curve.

‒X50C as determined from corrected fractional recovery curve

665

2. Classification Principles

• Fractional Recovery to the underflow stream

Ri = Uui/Ffi‒Where U = tph of dry solids in underflow

‒Ui = weight fraction retained in size interval i in underflow

‒F = tph of dry solids in feed

‒Fi = weight fraction retained in size interval i in feed

666

334

Classifier Performance

667


• Classifier efficiency is measured by imperfection of separation, I

• d75 = Size at which 75% passes to U/F



668

50

2575

2d

ddI

I = 0 means perfect separation

335


669

Classifier PerformanceTo correct a partition curve

Where:

yi’ = Corrected recovery of i

yi = Uncorrected recovery of i

Rf = Recovery of water to coarse fraction

f

fii R

Ryy

1'

670

336

Do I have the correct curve?

671

Rake & Spiral Classifiers

Classification variables:

-Feed rate

-Particle size, shape, SG

-Tank geometry (length, slope freeboard)

- Rake/spiral velocity (2-10 rpm)

length

Wierheight

Coarsematerial

Finematerial

feed

Fluid velocity

Bottomslope Rake or

Spiral

672

337

Rake & Spiral Classifiers• Adjust rake travel and frequency, spiral rpm‒Balance transport velocity against turbulent environment

• Adjust weir height to achieve correct cut point• Can use wash water sprays to clean coarse fraction• Don’t feed into pool agitation

673

Rake & Spiral Classifiers• Longer spiral for dewatering applications

• Spirals classifiers can be

steeper than rake classifiers

• 100 – 1000 um

674

338

Settling Cones

• Used in desliming or dewatering applications

675

Jig Classifiers

• Finer material shorter strokes, greater frequency• Coarser material longer strokes, lower frequency• Better suited to density classification

676

339

3. Hydrocyclones

677

Hydrocyclones - Introduction

Hydrocyclones are mainly used in mineral processing classification flowsheets.

1.Hydrocyclone Description

2.Process and Geometry Variables

3.Efficiency and Performance

4.Cyclone Selection Criteria

5.Example Calculation

678

340

Why use hydrocyclones?

‒Small footprint

‒Low capital expenditure

‒No moving parts

‒Reliable

‒Efficient

‒Can achieve fairly dense underflow

Often abused in mineral processing plants!

Typically a good place to begin optimisation

679

i) Hydrocyclone Description

680

341

Hydrocyclone Description

681

Geometry Variables:Inlet Area• Determines entrance

velocity and affects tangential velocity profile. Rectangular are most common.

• Increased area requires increased flowrate to maintain tangential velocity.

• Inlet Area is typically 6 to 8% of cross-sectional area of feed chamber.

ii) Hydrocyclone Classification

682

342

Variables Affecting Cut Point

683

Parameter Change (Increase) Cut Point Change (coarseness of U/F)

Cyclone Diameter

Vortex Finder Diameter

Apex Diameter

Barrel Length

Cone Angle

Inlet Pressure

F80

Feed SG

Fluid Viscosity

Variables Affecting Capacity

Parameter Change (Increase) Capacity Change

Cyclone Diameter

Vortex Finder Diameter

Apex Diameter

Inlet Pressure

Inlet Area

684

343

iii) Cyclone Selection CriteriaBased on experimental studies and field work, the relationship for cyclone diameter is as follows:

D = 0.02338(1-V/Vm)2.167 (x50c)1.515 (P)0.4242 (s - l)0.7576

whereD is cyclone diameter in cmV is the volume percent solids in the FeedVm is maximum percent solids = 53%x50c is cut size in mP is the inlet pressure in kilopascals (100Kpa = 14.5 PSI)s & l are specific gravity of solid and liquid

685

Cyclone Selection Criteria

The cut size can be estimated from the equation:

X50c = 3.14 (dy) Ln(119.12/yd)where

yd is the cumulative % finer than size dy (m)Example: If target P80 is 150 m, yd = 80, dy = 150 mWe require:1. Water and Solids Balance on Weight and Volume Basis2. Determine Cyclone Diameter3. Determine Number of Cyclones4. Estimate Inlet Area5. Estimate Vortex Finder Diameter6. Estimate Apex Diameter (Spigot Size)

686

344

Cyclone Design Rules of Thumb

Inlet AI = 0.05 Dc2

Vortex Finder Do = 0.35 Dc

(can be 0.2 – 0.45 Dc)Apex Du ≈ 0.2 Dc

Du/Do < 0.45 Rope0.45 < Du/Do < 0.56 Rope or

Spray0.56 < Du/Do < 0.90 Spray

Cone Angle Θ = 10o – 20o

687

iv) Example CalculationProblem: Select cyclones for the following circuit

ROD MILL BALLMILL

PUMPBOX

Solids SG = 3.2

Rod Mill Feed, F = 250 stph

Pt

T

Wt

Pt must be greater than 55% solids by weight

Po, O, Wo80% passing 150 micron in O

Po = 36.5%

CYCLONES

Pu

U

Wu

(U/F) = 4

Water

688

345

Balance Across Cyclone

Feed –

? stph

> 55% solids

F80 =

Overflow –

250 stph solids

36.3% solids

P80 = 150 um

Underflow –

? % solids

? stph

P80?

Determine unknowns for solids and water balance

689

Step 1: Select U/F solid content to prevent roping.Roping – When too high a density of solids reports to the underflow plugging the

apex. This results in coarse material reporting to the overflow

Task #1: Water and Solids Balance

Underflow (U/F) % Solids by Weight

Roping is probable to the right of each curve

Ove

rflo

w (

O/F

) %

Sol

ids

by

Wei

ght

100908070

60

50

40

30

20

15

1075 76 77 78 79 80 81 82 83 84 85 86 87 88

From graph, for O/F solids of 36.5%, the maximum U/F solids is approximately 81%

Select U/F Solids = 80% by weight

690

346

Classifying Cyclone Mass and Volume Balance:Circulating Load: 400%Solid S.G.: 3.2, Water SG.: 1.0Feed = O/FCyclone Feed = O/F + U/FWeight % Solids = 100 x STPH Solids / STPH SlurryVolume % Solids = 100 x USGPM Solids/ USGPM Slurry

Product Solid Liquid Slurry Solids (%)STPH USGPM STPH USGPM STPH USGPM STPH USGPM

Feed 250O/F 250 313 434.9 1740 685 2052 36.5 15.2U/F 1000 1250 250 1000 1250 2250 80.0 55.6Cycl. Feed

1250 1563 684.9 2740 1935 4302 64.6 36.3

Note: USGPM = STPH (4/SG)

Water and Solids Balance

691

Balance Across Cyclone

Feed –

1250 stph

4302 USGPM

64.6% solids

Overflow –

250 stph

2052 USGPM

36.3% solids

F80 = 150 um

Underflow –

1000 stph

2250 USGPM

80% solids

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347

Step 1: Determine Cyclone DiameterD = 0.02338 (1–V/Vm)2.167 (X50c)1.515 (P)0.4242 (–t)0.7576

V = 36.3% Vm = 53% X50c = 3.14(dy) ln(119.12/yd)

where dy = 150 myd = 80%

X50c = 187.5 m P = 8 psi = 8 x (100/14.5) = 55.17 kPa (–t) = 3.2 – 1.0 = 2.2

D = 52.8 cm = 20.8 inchesSince 20 inch is a standard size, select as cyclone

diameter

Task #2: Select Cyclones

693

Step 2: Determine Number of CyclonesTotal flow to cyclones, V = 4,303 USGPMThe estimated capacity for a single cyclone based on water flow is:

Q = 0.7071 D2P = 0.7071 x (20)2 x 8

= 800 USGPMNumber of Cyclones = V/Q = 5.38Say 6 cyclones. For extra capacity, select 7 cyclones

Step 3: Estimate Inlet AreaInlet area = 0.05 D2

= 20 square inches

Step 4: Estimate Vortex Finder DiameterVortex Finder Diameter = 0.35 D = 0.35 x 20

= 7 inches

Determine Number of Cyclones

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348

Step 5: Estimate Apex Diameter (Spigot Size)Minimum diameter below which roping will occur:

S = 4.16 – 16.43 / [2.65 - + (100/Pu)] + 1.10 ln(U/)where = 3.2

Pu = 80%U = 1000 tph / 6 cyclones (ie. assuming 6 cyclones)

S = 3.29 inchesTherefore use a spigot with a diameter of 3.29 inches or greater

(say 4”)

SummarySelect 7 x 20 inch diameter cyclones for cut size of 187.5um at Feed

of 4303 USGPM with 55% solids:

- Inlet area of 20 square inches- Vortex finder diameter of 7 inches- Apex diameter of at least 4 inches

Cyclone Selection

695

Operational Aspects

‒ Correct underflow fan, 20o and hollow centre

‒ Low % solids in feed, high % solids in underflow• Minimise underflow tail (fines in underflow)

• Maintain correct spigot size

‒ Maintain correct feed pressure‒ Low % solids in feed

Roping Conditions

• Du/Do < 0.45 Rope

• 0.45 < Du/Do < 0.56 Rope or Spray

• 0.56 < Du/Do < 0.90 Spray

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349

Optimization• Number of Cyclones ∆ Pressure ∆ d50c

• Apex smaller Du = larger d50c & lower water recovery to UF

• Vortex Finder Larger Do = larger d50c & lower water recovery to UF

• Feed Water Diluting feed slurry reduces fines tail and may improve efficiency (particle-particle interactions)

• Cyclone Diameter larger Dc = Larger d50c (& lower wear & pumping costs)

697

Maintenance Aspects

• Right size apex and vortex finder

• Good liner condition

‒No odd wear patterns, not worn through

‒Liners correctly installed, no steps

• Functional distributor

‒Unbiased flow patterns, clean pressure ports

• Pump well maintained

• Be careful when changing apex / liners

‒Don’t drop parts into the launder!

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ReferenceTexts:

• Wills, Barry, 1997, “Mineral Processing Technology, 6th

Ed• Napier-Munn, T., Morrell, S., Morrison, R., Kojovic, T.,

1996, “Mineral Comminution Circuits: Their Operation and Optimization”Papers:

• Timothy Olson and Patrick Turner, “HydrocycloneSelection for Plant Design”, http://www.krebs.com/literature.php/hardrock_mining/

• Richard Arterburn, “The Sizing and Selection of Hydrocyclones”, http://www.krebs.com/literature.php/hardrock_mining/

699

Fine Grinding

351

References:• Mark Adams, Mine 331, ubc, presented on Nov., 2012• www.outotec.com• www.isamill.com• www.metso.com• www.flsmidth.com• Burford and Clark, 2007. IsaMillTM technology used in efficient grinding circuit.• Gao and Forssberg, 1995. Prediction of product size distribution for a stirred ball mill • Kelly and Spottiswood, 1982. Introduction to mineral processing• Hogg and Cho, 2000. A review of breakage behavior in fine grinding by stirred-media milling• Jankovic, 2003. Variables affecting the fine grinding of minerals using stirred mills• Larson, Anderson, Morrison and Young. Regrind mills: challenges of scaleup www.isamill.com• He, Wang, Forssberg, 2004. Slurry rheology in wet ultrafine grinding of industrial minerals: a

review• Parry, 2006. Ultrafine grinding for improved mineral liberation in flotation concentrates• Tong, Klein, Zanin, Skinner, and Robinson, 2012. Stirred milling of siliceous goethitic nickel

laterite – batch grinding study• Drozdiak, Klein, Nadolski, and Bamber, 2011. A pilot-scale examination of a high pressure

grinding roll/stirred mill comminution circuit• Wang, Nadolski, Mejia, Drozdiak, and Klein, 2013. Energy and cost comparisons of HPGR

based circuits with the SABC circuit installed at the Huckleberry mine• Roufail, Klein, and Radziszewski, 2012. Morphological features and discrete element method

(DEM) forces produced in high speed stirred mill

Outline

• Introduction

• Fine Grinding Technologies

• Fine Grinding Flowsheet (IsaMill)

• Grinding Mechanisms and Conditions

• Case Studies

• Sizing and Scale-up

• Selection Criteria

• Conclusion

352

IntroductionEmergence of fine grinding

• Most of the world’s high-grade, coarse-grained deposits have been depleted

• Especially in the latter half of the 20th century, attention has turned to the mining of low-grade, fine-grained deposits

• These fine-grained deposits have necessitated fine grinding to produce the liberation grind sizes required for downstream processes to succeed and to do so efficiently enough to make the process economically viable

IntroductionExample – Necessity Breads Innovation

• In the 1980s, Mt Isa Mines (now Xstrata) owned the McArthur River Pb-Zn ore body, which required a 7 µm grind for liberation

• Existing grinding technologies were tested, but resulted in the orebodybeing uneconomical

- Power consumption too high

- Generally ineffective below 20 µm

- Poor flotation due to negative influence of steel grinding media

• MIM looked outside of mining for a solution and partnered with Netzsch, who manufactured small stirred mills for other industries

• Once scaled-up, this technology was known as the IsaMill and became enabling technology for start-up of McArthur River Mine

353

IntroductionGoal of Grinding

• The goal of a grinding machine is to use electrical energy to do work on ore as efficiently as possible (i.e., with as few losses as possible)

Electrical Energy = Mechanical Energy

+ Sound, Thermal, etc energy Losses

• There is no difference in fine grinding, except that more energy is generally required to break finer ore

IntroductionGrinding Energy Curve

354

Introduction

History of Fine Grinding

• 1870s: Ball mills are first used for grinding on industrial-scale

• 1900s: Fine grinding is practiced extensively in ceramic, paint and pharmaceutical industries using different small-scale mills

• 1953: Tower Mill is developed by Nichitsu Mining Industry in Japan

• 1960s: Stirred Media Detritor (SMD) is developed by English China Clays in UK

• 1980: First Tower Mill is installed in a mining application

• 1980s: Mt Isa Mines (now Xstrata) partners with Netszch in Germany to scale-up their horizontal stirred mill for mining applications

• 1991: Tower Mill license acquired by Svedala (now Metso) and renamed the Vertimill

• 1994: First production-scale horizontal stirred mill installed by Xstrata and renamed the IsaMill

• 1996: First SMD is installed in a mining application when license is acquired by Svedala(now Metso)

• 2000s: Other fine grinding mills are acquired/licensed to FLSmidth and Outotec who bring them into mining industry

Fine Grinding Technologies

Technologies and Typical Grinding Range

Technology Type Typical Grinding Range: µm

Ball Mill 50-10000

Vertimill 20-6000

IsaMill 5-400

SMD 5-100

HIGmill Under development

VXPmill Under development

355


Ball Mill

• First used in mining in the 1870s

• Multiple manufacturers around the world

• Horizontal configuration

• Normally closed-circuit with cyclones

• Cyclone inefficiency (fines bypass) often leads to overgrinding

• Steel media (25-90 mm or 1-3.5″) – up to 45% full

• Power intensity: 20 kW/m3

• Generally accepted as less efficient than stirred milling below 100 µm product sizes ( and ineffective below 20 µm)

http://www.flsmidth.com


Vertimill

• First used in mining in 1980

• Metso has license to market to mining

• Vertical configuration open to atmosphere

• Screw agitated

• Top fed, bottom discharge

• Open or closed circuit with cyclones

• Steel media (12-37 mm or 0.5-1.5″)


• Operating speed: 3 m/s

• Generally considered inefficient below 20 µmObtained from http://www.metso.com

356


Stirred Media Detritor (SMD)


• Metso has license to market to mining


• Pin agitated

• Screens to retain media

• Top fed, top discharge

• Open or closed circuit with cyclones

• Sand or ceramic media (2-5 mm)


• Operating speed: 3 m/shttp://www.metso.com


VXPmill


• Previously named the Deswik Mill

• Manufactured by FLSmidth


• Disc agitated

• Disc spacing and number variable (up to 16 discs)

• Bottom fed, top discharge

• Ceramic media (2-2.5 mm) – up to 80% full


Deswik Mill at UBCwww.flsmidth.com

357


HIGmill

• New to mining industry as of 2012

• Outotec has license to market to mining


• Disc agitated

• Disc spacing and number variable (up to 30 discs)

• Bottom fed, top discharge

• Normally open circuit with cyclones

• Ceramic media – up to 70% full

http://www.outotec.com

Fine Grinding TechnologiesIsaMill


• Xstrata Technology has license to market to mining

• Horizontal configuration operating under pressure

• Disc agitated

• Internal classifying system produces “steep” particle size distribution and less overgrinding than others

• Normally open circuit with densifying cyclones (operates at 40-60% solids)

• Ceramic or sand media (1-6 mm) – up to 75% full



http://www.isamill.com

358

Fine Grinding FlowsheetMcArthur River Zinc/lead mine, M3000 IsaMill, Feed: P80 70 µm, Product: P80 7 µm

Burford and Clark, 2007

Fine Grinding FlowsheetSimplified Potgietersrust Platinum mine C-Section (Anglo Platinum) Flowsheet with a M10,000 IsaMill

Media: 3.5 mm MT1, Feed: P80 75 µm, Product, P80 < 53 µm, Energy consumption: 9 kWh/t


359

IsaMill Grinding Mechanism


Product Size vs. Energy Usage

Jankovic, 2003

360

Size Reduction Mechanisms

Kelly and Spottiswood, 1982, Gao and Forssberg, 1995

Hogg and Cho, 2000

Grinding ConditionsIsaMill

• Media Size

• Media Fill

• Stirrer Speed

• Solid Content

• Feed Size

• Flow Rate

• pH Control

• Additive Addition

M20 Stirred mill at the NBK Institute of Mining

361

Grinding Media

• The goal of a grinding machine is to use electrical energy to do work on ore as efficiently as possible (i.e., with as few losses as possible)

• Grinding media’s job is to transfer energy from a grinding machine to the ore for breakage

• The majority of energy losses in grinding occur in the transfer of energy from the machine to the ore

• Since grinding media is the conduit for energy to get from the machine to the ore, it is vitally important

Grinding Conditions

Grinding Media

• Energy Transfer in a Grinding Media

• Media’s Energy

What makes up media’s energy?

• Examples of Grinding Media

Grinding Conditions


362

Cost of Grinding Media

• Grinding media is often the 3rd highest cost in processing behind energy and labour

• Proper media selection can improve economics by:

- Reducing its own cost through price and wear improvements

- Reducing energy usage through more efficient energy transfer from grinding machine to ore

Media Selection

• Type, Size, Supplier and Model, Price

Grinding Conditions

Slurry Rheology

• Slurry rheology significantly influences the grindability of industrial minerals in wet ultrafine grinding

• Parameters: mineralogy, solid concentration, particle size and distribution, particle shape, temperature, rotation, pH, and dispersants

• Rheology optimization to increase throughput, energy efficiency and product size

Grinding Conditions

He et al., 2004

363

Case Study - 1

Ultrafine grinding for Improved Mineral Liberation in Flotation Concentrates

Parry, 2006

• Objectives: Effect of stress intensity on breakage rates for minerals of different hardness; Effect of mill type on grinding energy requirements; Effect of stirred milling on downstream processing in terms of particle size distribution and mineral liberation

• Results: It is possible to target either hard or soft minerals for liberation in stirred milling; Mineral liberation behavior was similar for the horizontal and vertical high-speed stirred mills. The greatest benefit of regrinding using high-speed stirred mills was improved quartz liberation.

Case Study - 1

Netzsch LME4 stirred mill at UBC Laboratory 1.5 L batch SMD at UBC

364

Case Study - 1By varying the stress intensity it is possible to target either hard or soft minerals for liberation – Selective comminution was suggested in stirred milling

Effect of Stress Intensity

Case Study - 1The greatest benefit of regrinding using high-speed stirred mills was improved quartz liberation

Netzsch mill products

365

Case Study - 2

Stirred Milling of Siliceous Goethitic Nickel Laterite to Upgrade Ni

Tong, Klein, Zanin, Skinner, and Robinson, 2012

• Based on the differences in the mechanical properties of mineral components in ores, selective grinding was investigated to update valuable minerals --- properties of mineral

• Previous study indicates an opportunity for selective size reduction of particles of differing hardness’s using a stirred mill --- mill

• At low stirrer speed, soft minerals break faster than hard ones. Breakage of the softer or harder components in an ore can be targeted by adjusting the “stress intensity” in stirred mills --- grinding conditions

• Results: The breakage rates with respect to sample mass for Ni, Mg, and Si indicate that: Mg>Ni>Mass>Si. The optimum grinding time for the highest Ni upgrade was 0.25 min. The Ni grade increased from 0.88% to 1.35%, with 24% Ni recovery

Case Study - 2

Netzsch LME4 stirred mill at UBCBatch grinding tests: Feed size: -2000 µmProduct: 38 µm

366

Case Study - 2

Time

min

0-2000 µm

Grade, %

All - 38 µm product

All + 38 µm product

- 38 µm particles from milling +38

µm feedwt% Grade,

%wt% Grade,

%wt% Grade,

%0 1.14 46.0 1.44 54.0 0.88 0 0

0.25 1.14 54.3 1.43 45.7 0.79 8.3 1.350.5 1.14 57.8 1.43 42.2 0.74 11.8 1.371.0 1.14 63.6 1.39 36.4 0.70 17.6 1.252.0 1.14 70.4 1.36 29.6 0.62 24.4 1.193.0 1.14 74.8 1.33 25.2 0.59 28.8 1.124.0 1.17 78.6 1.33 21.4 0.58 32.6 1.07

Effect of grinding time on the breakage of +38-2000 µm siliceous goethitic nickel laterite particles: 20 wt% solid, 1000 rpm, 50% charge volume

Case Study - 2

Effect of grinding time on the weight fraction remaining on 400 mesh screen and the specific rate of breakage: 20 wt% solid, 1000 rpm, 50% charge volume, siliceous goethitic nickel laterite (38-2000 µm)

367

Case Study - 2

Effect of grinding time on the grade changes and recovery with respect to elements: 20 wt% solid, 1000 rpm, 50% charge volume, siliceous goethitic nickel laterite (38-2000 µm)

Case Study - 3

A Pilot-Scale Examination of a High Pressure Grinding Roll / Stirred Mill Comminution Circuit

Drozdiak, Klein, Nadolski, and Bamber, 2011

• Cone crusher / ball mill, HPGR / ball mill, HPGR / stirred mill circuits were examined on Mesaba copper-nickel deposit, feed size: F80: 21 mm, P80: 75 µm

• Results: based solely on the specific energy requirements for comminution, the HPGR / stirred mill circuit achieved a reduction of 9.2% and 16.7% over the HPGR / ball mill and core crusher / ball mill circuits, respectively

368

Case Study - 3

Pilot-scale HPGR installation at UBC M20 stirred mill at UBC

Case Study - 3

HPGR / Stirred Mill flowsheet A

HPGR / Stirred Mill flowsheet B

369

Case Study - 3Summary of results for the first-stage HPGR operating in open (Circuit A) and closed (Circuit B) circuit

Case Study - 3

Stirred mill signature plot results

Summary of stirred mill operating conditions

370

Case Study - 3Summary of specific energy consumption for each circuit

Case Study - 3Proposed layout for an HPGR / stirred mill circuit

371

Case Study - 4Energy and Cost Comparisons of HPGR Circuits with the SABC Circuit Installed at the Huckleberry Mine

Wang, Nadolski, Mejia, Drozdiak, and Klein, 2013

• To summarize a comprehensive energy and cost study comparing an existing SAG-ball mill circuit with HPGR-ball mill and HPGR-stirred mill circuit

• Results:

The HPGR-ball mill circuit achieved a 21% reduction in energy consumption over the existing SAG-ball mill circuit at the same P80 grind size of 160 µm

At a grind of 80% passing 75 µm, the HPGR-stirred mill circuit showed a 34% reduction in energy compared to the base case

The energy reduction for the new flowsheets significantly improved the economics of the Huckleberry comminution duty

Case Study - 4

372

Case Study - 4

Huckleberry SABC circuit – base case

Case Study - 4

HPGR – ball mill circuit

HPGR –stirred mill circuit

373

Case Study - 4Summary of stirred mill test conditions and results

Stirred mill signature plots

Case Study - 5Morphological Features and Discrete Element Method (DEM) Forces Produced in High Speed Stirred Mill

Roufail, Klein, and Radziszewski, 2012

• The effect of different operating parameters of high speed stirred mill on the particle breakage mode is addressed. Morphological features of broken particles is investigated and related to the types of forces generated in the mill using Discrete Element Method (DEM)

• Results: About 60% of total particles that are morphologically analyzed for quartz and galena were rough particles. Such an observation indicates that the fine product are broken via fracture. The agitator speed, mineral type, and residence time would dictate the type and mode of particle breakage

374

Case Study - 5

Roughness

LevelBreakage Mode

R1

Hammered

- Started Abrasion

(Transgranular)

- Then Exposed to Impact

(Indents on Surface)R2

Smoothest

Abrasion

(Transgranular)R3

Semi-Rough

Exposed to both Abrasion and Fracture

(Transgranular and Intergranular)R4

Rougher

Fracture

(Intergranular)R5

Roughest

Fracture

(Intergranular)

Breakage Mode versus Roughness Level

Morphology Roughness Level Definitions and Illustration

Case Study - 5

• The smooth particles increased, and the rough particles decreased with time• The fracture breakage may be the predominant breakage mechanism• For coarse particles, attrition was the main mechanism as residence time increased

375

Case Study - 5

Mineral TypeAgitator Speed

(RPM)

Initial (P1)Morphological Feature

(Skewness Value)Residence

Time (P4/P5)Sphericity Elongation Roughness

Galena Concentrate

1000P1 -0.45 -0.77 -1.26P5 -0.69 -0.78 -1.53

2000P1 0.00 -0.61 -0.55P4 -0.43 -1.22 -1.06

Quartz1000

P1 0.79 -0.13 -0.9P5 -0.18 -0.36 -1.49

2000P1 -0.20 -0.61 -2.00P5 -0.61 -0.91 -3.06

Mixed Quartz & Galena

Concentrate

1000P1 -0.14 -0.55 -1.33P5 -0.30 -0.60 -0.60

2000P1 -0.14 -0.50 -1.36P5 -0.29 -0.77 -1.58

Quantitative Morphological Statistical Analysis (by Clemex)

Case Study - 5

Initial Setting of Particles in the 3 Sections (A, B, and C) at Time Zero

376

Case Study - 5

Agitator Speed (RPM)

Maximum Normal Forces (N)

Maximum Tangential Forces (N)

A B C A B C1000 2.0 1.6 0.8 0.3 0.2 0.11500 2.3 1.9 1.2 0.5 0.4 0.22000 2.7 2.3 1.7 0.4 0.3 0.2

Maximum Normal and Tangential Forces

Agitator Speed (RPM)

Maximum Normal Forces (N)

Maximum Tangential Forces (N)

A B C A B C1500 Media 4.4 3.5 4.7 1.1 0.9 1.11500 Galena 4.7 4.1 4.3 1.6 1.4 1.22000 Media 4.5 4.4 4.1 1.0 1.1 1.02000 Galena 5.4 3.7 5.0 1.8 1.1 1.5

Maximum Normal and Tangential Forces Distribution

Sizing and Scale-UpGeneral

• Fine grinding machines are sized based on throughput (t/h) and energy requirement (kWh/t)

• Energy requirement is generally quantified based on testwork results must be scrutinized

• It is dependent on the following

- Specific ore

- Grinding machine

- Operating conditions (speed, slurry density, etc.)

- Media (type, size, density and quality)

- Feed and target product size

377

Sizing and Scale-Up

Schematic diagram of experimental flow – signature plot study (Roufail, 2011)

Sizing and Scale-Up

The pendulum testing flow circuit Rahal et al., 2011

378

Sizing and Scale-UpIsaMill

• IsaMill is sized using a Signature Plot Test

• Continuous test with 15 kg of ore producing a specific energy graph

• Conducted in 4 L IsaMill identically proportional to full-scale

• Uses identical media to full-scale

• Conducted under same operating conditions as full-scale (density, pressure, media charge level, etc.)

• Published operating vs. scale-up data shows the units scale-up well


Sizing and Scale-UpIsaMill (continued)

• Signature Plots Test: Scale-up of MRM M3000 IsaMill

Barns and Curry, 2006Larson et al.

379

Sizing and Scale-UpIsaMill (continued)

• Sizes presently available

Model Grinding Volume

L

Power

kW

Max Flow rate

m3/h

M100 100 75 12

M500 500 200 30

M1,000 1,000 355 or 500 90

M3,000 3,000 1120 ----

M5,000 5,000 1500 160

M10,000 10,000 3000 250

M50,000 50,000 8000 1000

Selection CriteriaGeneral

• When selecting a technology for fine grinding, the following should be considered:

- Feed and product size required

- Capital cost

- Operating cost (media/power consumption and maintenance)

- Availability

- Operability

- Downstream process requirements (chemistry, density, etc.)

- Accuracy and reliability of sizing

380

ConclusionHighlights

• Fine grinding is becoming more and more of a requirement in effectively processing the fine-grained, low-grade deposits of today

• There are several technologies available on the market today to accomplish fine grinding, each having different attributes

• Accurate determination of the energy requirement of a certain technology and duty is key in its sizing

• Always consider the total cost of ownership and the accuracy and reliability of the sizing

Energy Efficiency in MiningBern Klein

N. Emre Altun

Andrew Bamber

Jeff Drozdiak

Stefan Nadolski

Persio Rosario

Chengtie Wang

AJ Gunson

Trent Weatherwax

Reem Roufail

Jennifer Parry

Libin Tong

Robert Hall

Malcolm Scoble

Mario Morin

Scott Dunbar

381

Energy and MiningMining and non-ferrous metal smelting accounted for

7% of Canada’s industrial energy consumption (2009)

6% of direct industrial GHG emissions of Canada (2009)

Mining is #2 energy consumer in British Columbia accounting for 5% of BC Hydro’s power generation (primarily open pit mining)

Comminution is principal energy consumer (50-70%)

Material handling (haulage) # 2

Water/dewatering #3

Estimates for UG Mining 40% of energy goes to comminution, 40% to ventillation

Source: A Review of Energy Consumption and Related Data: Canadian Mining and Metal Smelting and Refining Industries 1990 to 2009. Nyboeer, J., Rudd, S., March 2011, Canadian Industrial

Energy End-use Data and Analysis Centre, Simon Fraser University, Burnaby, BC, Canada

Motivation for Reducing Energy Usage

Energy usage represents a significant operating cost for mines

Cost of energy will increase in the future

Energy Conservation and GHG Reduction a priority in Canada

Canada GHG Emissions and Intensity Legislation 2013 (potential)

BC Clean Energy Act 2009 - BC Hydro is mandated to save 66% of new load growth

TSM Initiative – GHG and energy efficiency guidance document (MAC)

CMIC – Energy efficiency - The 40% Mine

382

Motivations for Improving Energy Efficiency

Source: A Review of Energy Consumption and Related Data: Canadian Mining and Metal Smelting and Refining Industries 1990 to 2009. Nyboeer, J., Rudd, S., March 2011, Canadian Industrial Energy End-use Data and Analysis Centre, Simon Fraser University, Burnaby, BC, Canada

Energy Intensity Indicators for Metal Mining


Source: A Review of Energy Consumption and Related Data: Canadian Mining and Metal Smelting and Refining Industries 1990 to 2009. Nyboeer, J., Rudd, S., March 2011, Canadian Industrial Energy End-use Data and Analysis Centre, Simon Fraser University, Burnaby, BC, Canada

Energy Intensity Indicators for Non-Metal Mining

383


0

20

40

60

80

100

120

1985 1990 1995 2000 2005 2010 2015Year

Sp

ot

Cru

de

Oil

Pri

ce

($

US

/Bar

rel)

-100

-50

0

50

100

150

Ch

an

ge

in S

po

t C

rud

e O

il P

ric

e (%

)

Price Change

Spot Crude Oil Price 1990-2011

Source: http://www.tradingeconomics.com/canada/inflation-cpi; STCA – Statistics Canada

Electrical energy ~ ½ price of diesel – incentive to electrify

Total Energy and Potential Savings in Metal Mining

0

5

10

15

20

25

30

35

40

45

50

Sp

ecif

ic E

ne

rgy

Req

uir

emen

t (k

Wh

e/t

on

)

Current Best Practice PracticalMinimum

TheoreticalMinimum

Blasting

Diesel Equipment

Drilling

Digging

Ventilation

Dewatering

Crushing

Grinding

Separation & Floatation

Ancillary Operations

Source: Industrial Technologies Program, USDOE, June 2007

384

Emerging and Enabling Technologies

Comminution (HPGR, stirred mills)

Application of sensors, pre-concentration & waste rejection

(sorting technologies)

Hydromet (Galvanox, Electrowinning)

Improved energy efficiency through optimized water usage

Energy recovery

Increasing trend of electrifying technologies

Comminution

385

Energy Efficient Comminution Technologies

High Pressure Grinding Roll (HPGR)’s versus AG/SAG circuits

Stirred Mills versus Ball Mills

Novel circuits

HPGR - ISA Mill Circuit AG HPGR circuit for high clay ores

HPGR’s

Potential Benefits

Energy savings

Improved metallurgy (liberation)

Considered only for hard ores

Other Potential Applications

HPGR of pebble crusher product

High clay ores

Deposits with ores of variable hardness

386

UBC-Koeppern HPGR

High Pressure Grinding Rolls (HPGR)

High Speed Stirred Mills

Potential Benefits

Energy savings

Selective Comminution

Considered primarilly for fine grinding

Other Potential Applications

Primary Grind

387

ISA Mill

Stirred Media Detritor

388

J. Droizdiak MASc

(a)(b)

(c)

Crusher Ball Mill vs HPGR Ball Millvs HPGR ISA Mill

Unit Operation Feed f80 (mm)

Product p80 (mm)

Specific Energy Consumptionwith Dry Screening (kWh/t)

Specific Energy Consumption with Wet Screening (kWh/t)

First Stage HPGR 21 7.68 1.54 1.54

Second Stage HPGR 7.68 0.35 2.91 3.58

Stirred Mill 0.34 0.075 9.73 9.73

TOTAL 14.18 14.85

Comparison of specific energy consumption for each circuit

Energy consumption in the HPGR / stirred mill circuit

Energy Comparison

389

SABC Circuit versus HPGR Circuit

SABC Circuit versus HPGR Circuit

SABC Circuit Power HPGR Circuit Power

P80 = 160 um

Operation Power (kW) Operation Power (kW)

SAG Mill 7435 HPGR 3175

Crusher 149 Crusher 332

Ball Mill 8167 Ball Mill 8839

Material Handling 736 Material Handling 1090.4

Total 16487 13436.4

Energy Savings % 19

390

HPGR – ISA Mill Circuit

SABC vs HPGR vs HPGR-ISA Circuit

SAG Circuit HPGR Circuit HPGR-Stirred Mill

P80 = 75 um

OperationPower (kW) Operation

Power (kW) Operation

Power (kW)

SAG Mill 7950 HPGR 3175 HPGR 7141

Crusher 87 Crusher 332 Crusher 332

Ball Mill 9079 Ball Mill 12133 Stirred Mill 4143Material Handling 762.4

Material Handling 1282.4

Material Handling 953.4

Total 17878.4 16922.4 12569.4

Energy Savings % 5 30

391

AG - HPGR Circuit- Soft Ores Containing Clays

To Ball Mills

Crusher Feed Bin

Autogenous Mill/Scrubber

Cone Crusher

Diverter

HPGRTrommel Screen

Washing Screen

Coarse Ore

P. Rosario – PhD Thesis

AG - HPGR Circuit versus SABC Circuit

AG - HPGR SABC TotalFeed SavingsFeed rate ( 1 line / 2 lines) 81,600 69,485 t/dAvailability 85% 94%Fresh Feed / Total w. Rec Solids 4,000 3,080 t/hF80 123 123 mmSub Specific Energy (Fresh/Total) 4.29 7.79 kWh/t 44.9%Trommel&Screen 0Aperture 12.7 15.9 mmTotal U/S - T80 4.880 5.361 mmBond WI 15.0 15.0 kWh/tCyclone O/F P80 200 1 µmHPGR Specific Energy (Fresh/Total) 7.03 7.41 kWh/tSub Specific Energy (Fresh/Total) 11.32 15.21 kWh/t 25.5%

392

Pre-concentration

and

Waste Rejection

Sensing and Sorting Technologies Hand sorting - pre-Roman times

Automated sorting

Uranium radiometric sorting Ontario 1958

Diamonds X-Ray fluorescence W. Australia 1985

Recent large scale examples (est. 300 sorters installations)

Nickel, Kambalda W. Australia

Platinum, Amplats, Rustenburg UG2 Section

Sensors - Surface versus Bulk Properties

Challenges – Better sensors, higher throughput machines

393

Courtesy C. BergmanMintek, 2009

Sensor Technologies

Method Analysis Application

Photometric (reflection, brightness, grey level, RGB, IR, UV, texture)

Surface Coal, sulphides, phosphates, oxides

Radiometric Bulk Uranium, gold

Conductivity, magnetic susceptibility

Bulk Metal sulphides, native metals, iron oxides

X-Ray Fluorescence Surface Diamonds, metal sulphides, limestone, iron

X-Ray Transmission Bulk Coal, sulphides

394

Optical Image Analyzer at UBC

Optical Sorting

CommoDas ‘‘MikroSort’’

Optical Sorter

Conductivity Testing at UBC

Balancing Coil 1 Balancing Coil 2 Balancing Coil 3

Sensing Coil 1 Sensing Coil 2 Sensing Coil 3

PC

A/D Converter: Signal generation

and analysis

Sort Signal

Amplifier Bridge/

Power Supply

Conductivity Sorting

CommoDas ‘‘ROM Secondary EM’’

Conductivity Sorter

395

Sudbury Operations - Energy Assessment

Sudbury Operations - Conductivity Sorting

Deposit Conc. Mass (%) Conc. Grade (%) Recovery (%)Ni Cu Mg Ni Cu Mg Ni Cu Mg

0.83 11.42

0.81 0.36

0.43

1.40

1.29 9.08

0.87

Montcalm West

1.16 0.47

2.10 0.35

0.32 0.15

1.66 0.56

0.68

TL Footwall

TL Zone 2

TL Zone 1

Montcalm East

Craig 8112

Craig LGBX

Fraser Ni

Fraser Cu

5.54 72 1.50 0.57 5.16 93.49 87.40 67.46

2.57 83 2.43 0.37 2.39 95.85 86.70 77.07

4.21 80 0.94 0.40 3.73 92.73 89.43 70.67

1.81 41 1.65 20.92 0.68 81.12 74.89 15.42

1.90 66 1.85 12.05 1.08 94.66 87.88 37.51

3.41 62 2.03 0.87 3.41 90.35 83.84 59.11

40.476.00 44 0.98 0.48

68.224.61 75 2.06 0.63

29.935.97 30 0.64 0.30

Feed Grade (%)

6.05 59.23 57.50

4.17 93.60 85.48

5.58 63.07 48.43

396

McCreedy East Mine – U/G Sorting

McCreedy East Mine - U/G Sorting

397

Operation MontcalmThayer

LindsleyFraser Copper Fraser Nickel Craig Onaping Depth Ni Rim S

Hoisting $399,995 $1,319,625 $505,001 $684,364 $2,391,748 $1,891,163

Haul $786,583 $302,422 $884,600

Pre-con -$1,342,180 -$843,569 -$615,687 -$979,603 -$1,285,380 -$1,285,380 -$1,167,864

Grinding $560,607 $273,248 $236,058 $320,410 $476,930 $476,770 $418,730

Processing $1,397,813 $698,906 $436,817 $873,633 $1,310,450 $1,310,450 $1,135,723

Overall Savings $1,402,823 $831,002 $1,376,812 $719,440 $1,186,364 $2,893,589 $3,162,352

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

9000.00

10000.00

Power (kW)

Montcalm ThayerLindsley

FraserCopper

FraserNickel

Craig OnapingDepth

Ni Rim S Ni Rim SF/W

Base

Precon

Sudbury Operations – Sorting (Bamber Ph.D.)

Overall reduction in energy consumption 20%

Sorting Past – Present - Future?

Proven Technology

Sorting machines exist

Metallurgy proven

Concepts for mine designs developed

Economics demonstrated

Challenges of implementation

Better sensors

Higher capacity sorters

Technology transfer - Risk averse industry

398

Future - How can we make better use of sensors?

Sensors – organic part of mining system

Apply to all aspects from exploration (geophysical, borehole sensors) to mining and processing

Embedded sensors in material handling systems (ore passes, scoops, shovels, bins, chutes, conveyors)

Transmission, recording, analysis technologies

Wireless data transmission (WiFi)

Data available to GEMCOM, MineSight, process control

Intelligent connected mines with active online telemetry

Innovative Use of Sensors

Core logging equipment

Boreholes

Blast hole drill rigs

Face shovel

Belts

Sorter

399

Sensor Based Systems in Surface Mining

Sensor-based technologies and U/G Mining

400

Conventional vs Sensor Based Mining

Conventional mining:

- people-orientated, plan-based, subjective, time consuming

Future mining:

Application of on-line telemetry from in-mine sensors: Production scheduling, grade control,plant process control settings:

- flexible- objective - real-time- simultaneous

ConclusionsThere is significant potential to reduce energy usage in mining by applying several existing technologies

Relatively new, but proven. comminution technologies are more energy efficient than conventional technologies, but industry is slow to adopt these technologies.

The outcomes of sensor-based technologies and sorting are significant in economic and environmental measures – these can be applied to making mining smarter.

Challenges to the application of these technologies relates primarilly to aspects of technology transfer and mining culture rather than technical challenges.

401

NBK Research Centre

Acknowledgements Natural Sciences and Engineering Research Council of Canada Canada Foundation for Innovation Teck Ltd Inco Falconbridge Xstrata Technology COREM Vale Xstrata Knelson Metso Minerals BC Hydro CSIRO Australia Koeppern CAMIRO Placer Dome Barrick SGS

402

Statistical Experimental Design

The problem of Experimental design is deciding what pattern of design points will reveal aspects of the situation of interest (Box &Hunter 1978)

Outline

• Introduction

• Factorial Design

• Fractional Factorial Design

• Response Surface Designs

• Central Composite Design

403

DefinitionsExperiment: test or series of tests

Experimental domain: the experimental ‘area’ or design region/domain is defined by the variation of the experimental variables and their combinations

Factors: experimental variables that can be changed independently of each other also called independent variables/parameters

Response: measured result of the experiments or performance variable or quality measure

Main Effect: the change in response produced by a change in the level of the factor measured by the difference between the average response at the high level of the factor and the average response at the low level

Introduction

• The validity of the conclusions that are drawn from an experiment depends to a large extent on how the experiment was conducted‐ (When experiments are performed randomly the result will also be random Lundstedt et al 1998)

• Experimental Design aims at maximising information gained from a minimum number of experiments with respect to defined experimental variables and the responses.

The failure of “One variable at a time Approach” An engineer is interested in finding the values of temperature and pressure that maximize yield in a chemical process:

If the one variable at a time approach is applied

By fixing the temperature at 155F (current operating level

And varying the time at incremental levels of 0.5 from

0.5hrs to 2.5. The resultant variation of yield with

time shows the optimum time to be 1.7hrs

Montgomery & Runger (2002)

404

Introduction

.

Why statistical Design Experiments ?

• However, the contour plot of actual process yield as a function of temperature and time with the one factor at a time experiments superimposed on the contours shown below shows that the approach has failed to locate the optimum

One Variable a Time

fails where there are

Interaction effects

Montgomery & Runger (2002)

405

Design Selection Guideline

Number of

Factors

Screening

Objective

Response Surface

Objective

1 ‐ ‐

2‐4 Full or Fractional

Central composite or

Box‐Behnken

5 or more

Fractional or

Plackett ‐ Burman

Screen first to

reduce number of factors

Choice of an experimental design depends on the objectives Screening Objectives: Removing less important factors, normally precedes determination of response surface Response Surface Objectives: Give an indication of the local shape of response surface

Factorial Experimental Design

Definition: Is when experimental trials (or runs) are performed at all combinations of factor levels.

For example,A Metallurgist is interested in investigating the effects of Bowl speed (BS) and Fluidisation (Fw) water on Gravity recovery of gold using a Knelson Concentrator. If two levels of BS (30G and 90G) and two levels of Fw (5gpm and 10gpm) are considered important, a factorial experiment would consist

of making experimental runs at each of the four possible combinations of these levels of BS and Fw.

Useful in screening studies

Full factorial limited to determining linear influence of variables

Fractional Factorial: Allows for evaluation of interactions between variables

406

Two Level 2k full Factorial Design

If the combination of k factors are investigated at 2 levels then the total number of runs is 2k

Factor level are given by (-) for lower level and (+) for high level

Fractional Factorial Designs

As the number of variables to be screened increase, the number of required tests increases dramatically for Full factorial design and most of the experimental runs become redundant, Fractional Factorial design deals with this redundancy

Definitions:

Half Fraction: is a 2k‐1 i.e. k22 1 = k22

1 factorial design

Fractional Factorial design: Consist of 2k fraction of the total full

factorial runs for n variables at 2 levels given by 2n‐k i.e. nk 22 =n

k2

2

1 factorial design

Generator: is the defining relation of the design e.g. If settings for a 25-1 factorial design is constructed such that the 5th variable settings are given by 5 =1234 such that 5x5=1234x5 Or 52=12345, the generator can be written as I = 12345, where I the product of multiplying the elements of any column by a column of identical elements.Contrast: represented by lij is the linear function of the observations which estimate the ij interactions and is the measure between two averages.

Resolution: represented by Roman numerals is the length of the shortest word in the defining relation for example the 25-1 fraction is a resolution V design, it does not confound main effects and two factor interactions with each other, But confound 2 -factor interactions with 3-factor interactions. Resolution R=III does not confound main effects with one another But does confounds main effects with two factor interactions. Whilst resolution R=IV does not confound main effects and 2-Factor interactions But does confound 2-factor interactions with 2-factor interactions

407

Construction of Fractional Factorial Design of Highest resolution

Several Fractional factorial designs exist

For the most basic 2k‐1

Write a full factorial design for the first k‐1 variables

Associate the kth variable with plus or minus interactions column 123...(k‐1).

With Fractional factorial design it is always possible to estimate the effects But they will be confounded (contaminated by higher level interactions)

• Many variables can be investigated without an excessive number of experiments.

• Less information is gained compared to full factorial designs, and the price to be paid for the few experiments is the ‘contamination’ of the main effects by the interaction effects i.e. The main effects are confounded

• Increase in degree of fractionation lowers the resolution of the best fraction and increases confounding between effects of various order

Model matrix X from factorial design is used to define the design matrix in fractional factorial designs and the settings for the remaining variables are defined using the Columns in the matrix.

• variables x4 to x7 are defined by the columns for the interactions between the variables a, b and c

• Columns are orthogonal and thus possible to estimate the main effects independent of each other

Example:Seven variables can be studied in a 27‐4 fractional factorial design. The design is defined by the model matrix 23 = 2‐427

which is 1/16 of the factorial design. A full factorial design would require 128 experiments. The 8 experiments are selected to span the largest possible experimental domain in the 7 dimensional space spanned by the seven variables.

Example of Construction of Fractional Factorial Design

408

Case StudyThe Knelson CVD is a heavy metal continuous gravity concentrator with proven capabilities to recover gold associated with sulfides. Myra Falls (a polymetallic Cu‐Pb‐Zinc Mine is loosing 50% of its gold to the tailings. It is required to asses possible application of the CVD for gold recovery from plant tails. The gold to tails is associated with pyrite which is the main iron mineral for the ore.

To test potential application it is necessary to test the CVD across the experimental domain and determine the parameter levels yielding the optimum metallurgical performance in both grade and recovery. Fe is used as an indicator for Au.

First step is to identify and screen the factors:

McLeavy(2005) identified 8 potential factors that influence CVD performance (Fluidisation, %solids, Feed Grade, Heavies particle size, Bowl speed (BS), Pinch valve open time (PVO), Pinch valve closed time (PVC), solids feed rate

2 level full factorial design would require 256 runs

Redundancy in terms of either or both higher level interactions and excess variables studied as k increases

Fractional Factorial design exploits this redundancy

Variable level using synthetic ores for Factor Screening McLeavy (2005) used sixteen‐run 2IV

8‐4

Prior to screening experiments the limits of factors is determined, the table below shows typical CVD factor levels

Variable High Low Centre point

Heavies (%) 4 1 2.5

Fluidisation (gpm) 14 5 10

PVO (s) 0.05 0.03 0.04

PVC (s) 8 2 5

BS (RPM) 925 725 825

Solids Feed rate (tph) 2 1 1.5

% Solids 45 30 37

Heavies Particle size (p80) microns 425 125 275

Variable Level

409

Fractional Factorial design: A 28-4 Resolution IV design , CVD Results

Fluidisation

% Solids

Feed Grade

Heavies Particle size

BS PVO PVC Solids Feed rate

Grade

run 1 2 3 4 5 6 7 8 Y (%) 1 + + + + + + + + 30.9

2 + + + + + ‐ ‐ ‐ 55 3 + ‐ + + ‐ + ‐ ‐ 18.1

4 ‐ ‐ + + ‐ ‐ + + 69.9 5 + + ‐ + ‐ ‐ ‐ + 26.4

6 ‐ + ‐ + ‐ + + ‐ 11.4

7 + ‐ ‐ + + ‐ ‐ ‐ 24.2 8 ‐ ‐ ‐ + + + + + 3.7

9 + + + ‐ ‐ ‐ ‐ ‐ 28 10 ‐ + + ‐ ‐ + + + 20.5

11 + ‐ + ‐ + ‐ ‐ + 69

12 ‐ ‐ + ‐ + + + ‐ 31.4 13 + + ‐ ‐ + + ‐ ‐ 3.5

14 ‐ + ‐ ‐ + ‐ + + 30.9 15 + ‐ ‐ ‐ ‐ + + + 12.9

16 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 27.1

Calculated Contrasts for CVD Experiments showing main effects & two factor interactions, 3 factor interactions and more are ignored

• Line 9 in the table shows that 12 =37=48=56 and are aliases of each other and the interactions are confounded.

l1 = 1 L2 = 2 L3 = 3 L4 = 4 L5 = 5 L6 = 6 L7 = 7 L8 = 8 l12 = 1‐2 + 3‐7 + 4‐8 + 5‐6l13 = 1‐3 + 2‐7 + 4‐6 + 5‐8l14 = 1‐4 + 2‐8 + 3‐6 + 5‐7l15 = 1‐5 + 2‐6 + 3‐8 + 4‐7l16 = 1‐6 + 2‐5 + 3‐4 + 7‐8l17 = 1‐7 + 2‐3 + 6‐8 + 4‐5l18 = 1‐8 + 2‐4 + 3‐5 + 6‐7

Results for the CVD Fractional Factorial design

410

Factor Screening Results

These results are used to screen out less significant factors

If only 3 factors are to be used for modeling and optimisation: (Solids fee rate, BS & PVC) will be selected based on Grade and (Heavies particle size, PVC and BS) will be selected based on Recovery.

If both Recovery and Grade are to be used as performance measures then the experimenter would opt for (PVC,BS & %Solids).

Rank Grade Effect (%)

1 Solids feed rate ‐8.2

2 BS ‐7.3

3 PVC 6.3

4 %Solids ‐6.2

5 Fluidisation ‐4.6

6 Feed Grade 4.2

7 PVO ‐3.1

8 Heavies particele size 2

Rank Recovery Effect (%)

1 Heavies particele size ‐21.9

2 PVC ‐12.5

3 BS ‐12

4 %Solids ‐5.9

5 Fluidisation 4.8

6 PVO 4

7 Feed Grade ‐3.2

8 Solids feed rate 1.6

Response Surface Designs

• Useful in fitting the second order models to the response with the use of a

minimum number of runs

• Allows estimation of interactions and quadratic effects

• Consist of:

3 level Factorial Design

Central composite:

- Circumscribed Central Composite Design

- Inscribed Central Composite Design

-Face centred Central Composite Design

Box Behnken

Doehlet Designs

411

3 level Full factorial designGiven k factors, each at 3 levels a Full factorial design has 3k

runs.

When the number of factors is greater than 3, a full factorial design requires a large number of runs and is not efficient Best suited for screening out the few important main effects from the less important

Comparison of Response Surface Designs

Full Factorial Design Box- Behnken Design Circumscribe Central Composite Design

a b c

Box Behnken design is economical in selecting points from three level factorial arrangements, which allows the efficient estimation of coefficients for either first or second order models Central Composite design (CCD) is preferred because of its flexibility and allowance for sequential experimentation i.e. Design can build upon factorial design experiments

412

Central Composite Designs

Circumscribed central composite design matrix:CVD example

PVO PVC Bowl Speed Features

-1 -1 -1

23 Factorial design

component

-1 -1 1

-1 1 -1

-1 1 1

1 -1 -1

1 -1 1

1 1 -1

1 1 1

-1.6818 0 0

Star design points1.6818 0 0

0 -1.6818 0

0 1.6818 0

0 0 -1.6818

0 0 1.6818

0 0 0

Repeat centre runs0 0 0

0 0 0

0 0 0

a

Factorial design plus

6, star design points allow for 5 level to be assessed Centre repeat runs for error analysis and to measure significance of change in response due to variation in factor levels.

413

CVD Results for Circumscribed Experimental Design

Repeat centre runs are used to asses curvature and for error analysis

X1 X2 X3 PVO PVC BS Fe Grade Fe Recovery-1 -1 -1 0.2 5 30 15.0 26.0

-1 -1 1 0.2 5 90 24.0 30.4

-1 1 -1 0.2 15 30 33.5 34.0

-1 1 1 0.2 15 90 25.7 30.0

1 -1 -1 0.6 5 30 24.2 19.4

1 -1 1 0.6 15 90 18.0 18.1

1 1 -1 0.6 5 30 15.3 24.0

1 1 1 0.6 15 90 13.0 23.0

-1.6818 0 0 0.1 10 45 26.0 19.4

1.6818 0 0 0.9 10 45 8.0 15.7

0 -1.6818 0 0.4 2 45 15.0 24.0

0 1.6818 0 0.4 25 45 33.5 25.9

0 0 -1.6818 0.4 10 20 25.7 23.0

0 0 1.6818 0.4 10 100 24.2 38.0

0 0 0 0.4 10 45 15.1 19.1

0 0 0 0.4 10 45 13.6 21.0

0 0 0 0.4 10 45 14.0 19.0

Empirical Modeling

• Experimental results are used to model the relationship between the metallurgical performance measures (Grade & Recovery) as a function of the design variables.

• The Response Surface designs allows for strategic exploration of the design space such that a relationship between key variables and response can be defined

• Response Surfaces can be generated and the variables level combination yielding the minimum/maximum response gives the optimum settings

• Various optimisation strategies exist but are beyond the scope of this chapter.

comminution may 21 final 2.0.pdf

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