Mineral Scale Prediction Modelling: Precipitation of CaCO ...
Holistic modelling of mineral processing plants a practical approach
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Holistic Modelling of Mineral Processing Plants –
A practical approach
THE MINERAL PROCESSING INNOVATIONAND OPTIMISATION INTERNATIONAL
CONGRESS: 2013
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Applied maths background Simulation of ocean currents PhD Mineral Processing Mathematical Modelling at JKMRC – primarily
the problem of developing a holistic integrated simulator
Background
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MLA DPPJKSimFloatJKMultiBalSGS IGSLIMN
Commercial Software
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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
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VisioToAccess VisioToExcel General flowsheet simulator in Excel
Numerous subproducts
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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?
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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
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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
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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)
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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
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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
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Ball Mill
Product and feed for a ball mill
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Particle recovery
75%
10%
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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.
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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
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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
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Multimineral Particle
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Multimineral particle considered as a binary particle????
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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”
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Evolution of Entropy
KullBack-Liebler divergence (1951))
)ln(*i
ii
p
pp
pi is probability to estimate (i.e. grade)pi
* is prior probability
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Phase Diagram (Uniform)
Mineral 1
Mineral 3Mineral 2
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Markov Chain Monte Carlo
Test Points Starting Point
Mineral 1
Mineral 2Mineral 3
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Phase Diagram (Low Grade Mineral 1)
Mineral 1
Mineral 2 Mineral 3
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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
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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
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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
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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
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Traditional Modelling
Input observable Ore
PropertiesUnit Model
Output observable Ore
Properties
Operating Parameters
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Advanced Modelling
Input Observable Ore
Properties
Unit Model
Output Observable Ore
Properties
Operating Parameters
Fixed
Input Hidden Ore Properties
Hidden Output Ore Properties
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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
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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
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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 %
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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!
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Hierarchical Modelling
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1. Combine variables 2. Combine units.
Two ways to hierarchical model
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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
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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
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Applied to units
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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
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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
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Envisaged interactions
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Excel Excel/VBA Visio Access
‘Treasures’ that already exist on your computer
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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
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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
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A database system Also VBA Used by many simulation systems – but
often not ‘publicised’ to users. Essential for organised handling of data
Microsoft Access
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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
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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:
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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