A brief summary of what one can expect and the concepts discussed in greater detail in a 5 Day Course on Modelling and Simulation of Mineral Processing Plants. Feel free to contact me Basdew Rooplal at rooplalba@yahoo.com for more info.

1. HOLISTIC MODELLING OF
MINERAL PROCESSING PLANTS
– A PRACTICAL APPROACH
THE MINERAL PROCESSING INNOVATION
AND OPTIMISATION INTERNATIONAL
CONGRESS: 2013

2. BACKGROUND
• Applied maths background
• Simulation of ocean currents
• PhD Mineral Processing
• Mathematical Modelling at JKMRC – primarily the problem
of developing a holistic integrated simulator

3. COMMERCIAL SOFTWARE
MLA DPP
JKSimFloat
JKMultiBal
SGS IGS
LIMN

4. ACTIVE SOFTWARE
DEVELOPMENT
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)

5. NUMEROUS
SUBPRODUCTS
• VisioToAccess
• VisioToExcel
• General flowsheet simulator in Excel

6. WHY THE NEED FOR YET
ANOTHER SIMULATOR?
For me personally:
1. The datastructure must be particle-based
2. There had to be compatibility with VisioBal series
3. Simulation must be ‘extensible’
Arguably no such system existed – hence no option but DIY

7. JKSIMFLOAT USER
SPECIFICATION GROUP
• 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)

8. THE PERFECT SIMULATOR
• 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)

9. SIMULATION COURSE (5
DAYS)
• 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

10. CONCEPTS DISCUSSED
• Information theory
• Particle Based Modelling
• Markov Chain Monte Carlo
• The future - Hidden Markov Models
• Hierarchical Modelling
• ‘Treasures’ that already exist in your computer

11. FUNDAMENTAL ADVANTAGE
OF A PARTICLE BASED MODEL
• 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.

12. Ball Mill
PRODUCT AND FEED
FOR A BALL MILL

13. PARTICLE RECOVERY
75%
10%

14. 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.

15. MASS BALANCE
INTERFACE
Confidence
TotalFlow Not Used
PercentSoli
d 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

16. BOLTZMAN
 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.

17. MULTIMINERAL PARTICLE

18. MULTIMINERAL PARTICLE
CONSIDERED AS A BINARY
PARTICLE????

19. 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”

20. KullBack-Liebler divergence (1951))
)ln( *
i
i
i
p
p
p
pi is probability to estimate (i.e. grade)
pi
* is prior probability

21. Phase Diagram (Uniform)
Mineral 1
Mineral 3Mineral 2

22. Markov Chain Monte Carlo
Test Points Starting Point
Mineral 1
Mineral 2Mineral 3

23. Phase Diagram (Low Grade Mineral 1)
Mineral 1
Mineral 2 Mineral 3

24. PARTICLE-BASED
MODELLING ISN’T HARD
• 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

25. PARTICLE DISTRIBUTION
Fitted
TotalFlow 35.57
PercentSolid 0.00
SolidFlow 35.57
WaterFlow
Size Mass%
ParticleType in each Size
P1 P2 P3 P4 P5 P6
6.00 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

26. MASTER TABLEMaster
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 25.58
P2 60.33 3.34 3.04 0.14 0.02 0.08 0.03 0.03 0.05 6.32 26.62
P3 53.54 7.03 6.42 0.16 0.03 0.16 0.03 0.05 0.08 8.98 23.51
P4 58.59 4.26 3.90 0.15 0.02 0.10 0.05 0.04 0.06 7.19 25.64
P5 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09
P6 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 25.66
P2 60.51 3.26 2.96 0.14 0.02 0.07 0.03 0.03 0.05 6.27 26.67
P3 53.52 7.04 6.43 0.15 0.02 0.16 0.03 0.05 0.08 9.04 23.48
P4 58.74 4.18 3.83 0.14 0.02 0.10 0.05 0.04 0.06 7.17 25.68
P5 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09 9.09
P6 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 25.37
P2 61.04 3.18 2.76 0.13 0.02 0.08 0.04 0.04 0.05 6.15 26.51
P3 52.75 7.37 6.81 0.15 0.03 0.17 0.04 0.05 0.08 9.37 23.17
P4 60.00 3.69 3.24 0.14 0.02 0.09 0.03 0.04 0.06 6.76 25.92
P5 57.52 4.80 4.43 0.15 0.02 0.13 0.03 0.04 0.06 7.73 25.10
P6 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 25.11
P2 60.30 3.70 3.37 0.19 0.00 0.17 0.00 0.01 0.03 5.84 26.39
P3 51.74 7.94 7.19 0.17 0.03 0.17 0.08 0.08 0.11 9.80 22.70
P4 60.16 3.66 3.18 0.13 0.03 0.13 0.03 0.02 0.13 6.16 26.36
P5 53.61 7.31 6.16 0.09 0.09 0.07 0.19 0.09 0.10 8.64 23.68
P6 53.10 7.25 6.63 0.01 0.09 0.02 0.02 0.11 0.32 8.95 23.50

27. HIDDEN MARKOV MODEL
• 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.

28. TRADITIONAL MODELLING
Input observable
Ore Properties
Unit Model Output observable
Ore Properties
Operating
Parameters

29. ADVANCED MODELLING
Input Observable
Ore Properties
Unit Model
Output
Observable Ore
Properties
Operating
Parameters
Fixed
Input Hidden Ore
Properties
Hidden Output
Ore Properties

30. CHANGE TO MODELLING (TRADITIONAL)
Input observable
Ore Properties
Unit Model Output observable
Ore Properties
Input observable
Ore Properties
Unit Model Output observable
Ore Properties
Input observable
Ore Properties
Unit Model Output observable
Ore Properties
Input observable
Ore Properties
Unit Model Output observable
Ore Properties

31. 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

32. COST OF SAMPLING
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50
Accuracy %
Sampling Cost (Thousands)
Traditional
Improved

33. WILD HYPOTHESIS!
• 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.

34. HIERARCHICAL
MODELLING

35. TWO WAYS TO
HIERARCHICAL MODEL
• 1. Combine variables
• 2. Combine units.

36. HIERARCHICAL MODELLING
APPLIED TO VARIABLES
• 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

37. UNIT COMBINING
• 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?

38. APPLIED TO UNITS

39. IT IS TOTALLY VALID TO
MODEL THE SAME UNIT
USING DIFFERENT MODELS
• 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

40. EXTENSIBILITY IN VBA
Very easy in VBA
• A class Unit has member variables
m_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

41. ENVISAGED INTERACTIONS

42. ‘TREASURES’ THAT ALREADY
EXIST ON YOUR COMPUTER
• Excel
• Excel/VBA
• Visio
• Access

43. EXCEL
• 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!

44. VISIO
• 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.

46. MICROSOFT ACCESS
• A database system
• Also VBA
• Used by many simulation systems – but often not
‘publicised’ to users.
• Essential for organised handling of data

47. VBA
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

48. 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:

49. OPTIMISATION AND
SIMULATION OF MINERAL
PROCESSING PLANTS
5 Day course.
Available on request.
Further details:
• www.MathsMet.com
• LinkedIn: Stephen Gay (group VisioBal)
• www.MathsMet/Stephen
Looking for case studies for proof of concept.