Holistic Modelling of Mineral Processing Plants –

A practical approach

THE MINERAL PROCESSING INNOVATIONAND OPTIMISATION INTERNATIONAL

CONGRESS: 2013

Applied maths background Simulation of ocean currents PhD Mineral Processing Mathematical Modelling at JKMRC – primarily

the problem of developing a holistic integrated simulator

Background

MLA DPPJKSimFloatJKMultiBalSGS IGSLIMN

Commercial Software

With others:Corescan (Core texture modelling)

Coal Sim (Simulation system for plant design in coal)

Independently (MathsMet)VisioBal1D ( 1D Mass Balancing/ completed)VisioBal2D (2D Mass Balancing/completed)VisioBal3D (3D Mass Balancing/completed)VisioBal2DPlus ( 3D from 2D/completed)VisioSim (finished in a week!)MMVisioOpt (completed – pending VisioSim)

Active Software Development

VisioToAccess VisioToExcel General flowsheet simulator in Excel

Numerous subproducts

For me personally:1. The datastructure must be particle-based2. There had to be compatibility with VisioBal series3. Simulation must be ‘extensible’

Arguably no such system existed – hence no option but DIY

Why the need for yet another simulator?

Prof JP Franzidis (Project Leader) Prof Bill Whiten (Chief Scientist) Dr Andrew Schroder (JKTech simulation

expert) Dr Kym Runge (Flotation expert) Dr Ricardo Pascal (Software Design) Rob Lasker (Software developer) Stephen Gay (Liberation modelling)

JKSimFloat User specification Group

1. It uses all available data. 2. Datahandling is efficient, organised and accessible 3. The steady state simulator (including relevant data and reports) is available to all staff. 4. It is understandable to all staff: • Financial controllers (decision makers) • Technical experts • Operators 5. Reporting is aesthetic, and clear. 6. It is robust 7. It is accurate 8. It is available via the internet. 9. It must show a flowsheet, and the data reporting must be accessible via the flowsheet (as well as separately). 10. It is compatible with other software (such as mineralogical systems, control systems and geometallurgical software)

The perfect simulator

Day 1 Course overview/ Concept of optimisation/ Basics of Excel/ Overview of Modelling methods

Day 2 / Concept of variables/Simulation/Hierarchical Modelling/Difference between a design simulator and operational simulator

Day 3 Fundamental Simulation skills / Flowsheeting (Visio)/Databases (Access)/Understanding the basic of Software development (VBA)/Object Oriented Programming

Day 4: The particle structure for simulation/Information theory/ unit models/Hidden Markov Models

Day 5: /Solver methods/Optimisation Framework/Circuit Optimisation/Operational optimisation/ Presentations of simulators: LIMN, Coal Sim, JKSimFloat, JKSimMet

www.MathMet.com: Courses

Simulation Course (5 days)

Information theory Particle Based Modelling Markov Chain Monte Carlo The future - Hidden Markov Models Hierarchical Modelling ‘Treasures’ that already exist in your

computer

Concepts discussed

We need to differentiate ore properties from unit models.

Hence the same particle going through the same unit will have the same ‘behaviour’

Behaviour means ‘probability’ . Hence there is strong connection between mineral processing simulation and probability theory.

Fundamental advantage of a particle based model

Ball Mill

Product and feed for a ball mill

Particle recovery

75%

10%

Probability Entropy

A measure of disorder Yet the most disordered system is actually

the one which is most regular. The maximum entropy solution is then the

most ‘regular’ solution. Can be applied directly to mass balancing

rather than non-negative least squares Trivial to apply.

Mass Balance Interface

Confidence

TotalFlow Not Used

PercentSolid Not Used

SolidFlow Fixed

WaterFlow Not Used

Size Mass%

Assay in each Size

Fe SiO2 Al2O3 P S TiO2 Mn CaO MgO LOI Remainder

6.00 Fixed Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard

-6+2 Fixed Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard

-2+1 Fixed Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard

-1.00 Fixed Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard

Bulk Assay Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed

In 1877, Ludwig Boltzmann formulated the alternative definition of entropy S defined as:

kB is Boltzmann's constant and Ω is the number of microstates consistent with the

given macrostate. Boltzmann saw entropy as a measure of statistical

"mixedupness" or disorder. This concept was soon refined by J. Willard Gibbs, and is now regarded as one of the cornerstones of the theory of statistical mechanics.

Boltzman

Multimineral Particle

Multimineral particle considered as a binary particle????

Boltzman’s rejection

In 1904 at a physics conference in St. Louis most physicists seemed to reject atoms and he was not even invited to the physics section. Rather, he was stuck in a section called "applied mathematics”

Evolution of Entropy

KullBack-Liebler divergence (1951))

)ln(*i

ii

p

pp

pi is probability to estimate (i.e. grade)pi

* is prior probability

Phase Diagram (Uniform)

Mineral 1

Mineral 3Mineral 2

Markov Chain Monte Carlo

Test Points Starting Point

Mineral 1

Mineral 2Mineral 3

Phase Diagram (Low Grade Mineral 1)

Mineral 1

Mineral 2 Mineral 3

The structure for modelling is still 2D. That is the distribution of particle types with

in each size-class. (for each streams) A separate ‘Master Table’ contains the

properties of each particle type. Very consistent with object-oriented

programming

Particle-based modelling isn’t hard

Particle Distribution

FittedTotalFlow 35.57

PercentSolid 0.00 SolidFlow 35.57

WaterFlow

Size Mass%ParticleType in each Size

P1 P2 P3 P4 P5 P66.00 0.06 25.29 25.91 23.33 25.39 0.04 0.04-6+2 58.01 25.16 28.80 20.50 25.42 0.06 0.06-2+1 32.01 22.90 29.03 23.99 24.01 0.04 0.03-1.00 9.92 21.73 29.98 25.08 23.13 0.04 0.04

Bulk ParticleType

Master Table Master

Size ParticleType

Element

Fe SiO2 Al2O3 P S TiO2 Mn CaO MgO LOI Remainder

+6

P1 58.31 4.42 4.04 0.15 0.02 0.10 0.04 0.04 0.06 7.23 25.58P2 60.33 3.34 3.04 0.14 0.02 0.08 0.03 0.03 0.05 6.32 26.62P3 53.54 7.03 6.42 0.16 0.03 0.16 0.03 0.05 0.08 8.98 23.51P4 58.59 4.26 3.90 0.15 0.02 0.10 0.05 0.04 0.06 7.19 25.64P5 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09P6 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09

-6+2

P1 58.44 4.36 3.98 0.14 0.02 0.10 0.03 0.04 0.06 7.16 25.66P2 60.51 3.26 2.96 0.14 0.02 0.07 0.03 0.03 0.05 6.27 26.67P3 53.52 7.04 6.43 0.15 0.02 0.16 0.03 0.05 0.08 9.04 23.48P4 58.74 4.18 3.83 0.14 0.02 0.10 0.05 0.04 0.06 7.17 25.68P5 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09P6 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09

-2+1

P1 58.34 4.54 4.06 0.14 0.02 0.11 0.04 0.04 0.06 7.27 25.37P2 61.04 3.18 2.76 0.13 0.02 0.08 0.04 0.04 0.05 6.15 26.51P3 52.75 7.37 6.81 0.15 0.03 0.17 0.04 0.05 0.08 9.37 23.17P4 60.00 3.69 3.24 0.14 0.02 0.09 0.03 0.04 0.06 6.76 25.92P5 57.52 4.80 4.43 0.15 0.02 0.13 0.03 0.04 0.06 7.73 25.10P6 59.12 4.41 3.71 0.15 0.04 0.10 0.06 0.06 0.08 6.75 25.54

-1

P1 57.15 5.37 5.09 0.06 0.06 0.05 0.11 0.07 0.11 6.81 25.11P2 60.30 3.70 3.37 0.19 0.00 0.17 0.00 0.01 0.03 5.84 26.39P3 51.74 7.94 7.19 0.17 0.03 0.17 0.08 0.08 0.11 9.80 22.70P4 60.16 3.66 3.18 0.13 0.03 0.13 0.03 0.02 0.13 6.16 26.36P5 53.61 7.31 6.16 0.09 0.09 0.07 0.19 0.09 0.10 8.64 23.68P6 53.10 7.25 6.63 0.01 0.09 0.02 0.02 0.11 0.32 8.95 23.50

We try to think beyond what is observable In a hidden Markov model, the state is not

directly visible, but output, dependent on the state, is visible.

Hidden Markov Model

Traditional Modelling

Input observable Ore

PropertiesUnit Model

Output observable Ore

Properties

Operating Parameters

Advanced Modelling

Input Observable Ore

Properties

Unit Model

Output Observable Ore

Properties

Operating Parameters

Fixed

Input Hidden Ore Properties

Hidden Output Ore Properties

Change to Modelling (traditional)

Input observable Ore

PropertiesUnit Model

Output observable Ore

Properties

Input observable Ore

PropertiesUnit Model

Output observable Ore

Properties

Input observable Ore

PropertiesUnit Model

Output observable Ore

Properties

Input observable Ore

PropertiesUnit Model

Output observable Ore

Properties

Advanced - concept of ‘similarity’

Input Ore Properties1

Unit Model

Output Ore Properties1

Input Ore Properties2

Output Ore Properties2

Input Ore Properties3

Output Ore Properties3

Input Ore Properties4

Output Ore Properties4

Cost of sampling

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70

80

90

100

TraditionalImproved

Sampling Cost (Thousands)

Accuracy %

Using the methods above can assays within sizes be estimated if only bulk assays and sizes are known?

I am hoping this hypothesis will be the basis of a Research grant. I consider it plausible if a plant is continually monitored.

Wild hypothesis!

Hierarchical Modelling

1. Combine variables 2. Combine units.

Two ways to hierarchical model

Use general variables such as ‘grind-size’ rather than specific operating variables

Often used in mineral processing Not explicitly stated, so not formally used as

a ‘hierarchical’ model

Hierarchical Modelling applied to variables

Used in JKMultiBal/JKSimFloat but purpose is convenience rather than design

Introduces concept of model of the model i.e. if combined con changes, how do each

of the cons change?

Unit combining

Applied to units

Therefore a simulation model MUST be extensible in order to be practical.

VisioSim: A database is used to associate icons with models

A different user with the same dataset can use a different set of models.

A different user with the same dataset can use a different flowsheet! (not developed)

Need feedback between different hierarchical levels

It is totally valid to model the same unit using different models

Very easy in VBA A class Unit has member variablesm_strModel (the Model used for the unit)m_objModel (the VBA Model Addin is made a member of the unit)

Set m_Model=Application.run(m_strModel & “.Create”,me) m_Model.Simulate

Extensibility in VBA

Envisaged interactions

Excel Excel/VBA Visio Access

‘Treasures’ that already exist on your computer

Excellent environment for User Interface Easily transferred Needs disciplined management VBA behind the scenes is very powerful. Avoid many of the Excel functions such as

cell linking!

Excel

A flowsheet system – part of Microsoft Professional Allows ‘hierarchical flowhseet structures’ Has VBA underneath where the flowsheet structure (connection

between streams and units ) can be interrogated. Icons made available to me by David Wiseman (LIMN) Some standardisation between LIMN, VisioBal series, Coal Sim.

Visio

A database system Also VBA Used by many simulation systems – but

often not ‘publicised’ to users. Essential for organised handling of data

Microsoft Access

VBA is not a true object-oriented language.However advantages are: Excel/Access/Visio can all be called from

each other. Can even extend to Outlook, Word and

PowerPoint! All metallurgists should learn Some VBA

VBA

Conclusions

A particle based structure is the ‘real structure for modelling processing plants.

The particle based structure requires advanced mathematical methods

A ‘perfect’ simulator can indeed be a reality.

The cost-savings of applying a perfect simulator is potentially huge.

It is possible for users to develop models that can be easily integrated into a general simulator.

Already existing models only need minor adjustment to be used for a particle-based structure.

If you truly want to understand these concepts, enrol in the course:

5 Day course.Available on request.Further details: www.MathsMet.com LinkedIn: Stephen Gay (group VisioBal) www.MathsMet/StephenLooking for case studies for proof of concept.

Optimisation and Simulation of Mineral Processing Plants