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- 1. THE MINERAL PROCESSING INNOVATION AND OPTIMISATION INTERNATIONAL CONGRESS: 2013
- 2. Applied maths background Simulation of ocean currents PhD Mineral Processing Mathematical Modelling at JKMRC – primarily the problem of developing a holistic integrated simulator
- 3. MLA DPP JKSimFloat JKMultiBal SGS IGS LIMN
- 4. 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. VisioToAccess VisioToExcel General flowsheet simulator in Excel
- 6. 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. 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. 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. 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. Information theory Particle Based Modelling Markov Chain Monte Carlo The future - Hidden Markov Models Hierarchical Modelling „Treasures‟ that already exist in your computer
- 11. 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
- 13. 75% 10%
- 14. 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. 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. 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. 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”
- 18. KullBack-Liebler divergence (1951)) )ln( * i i i p p p pi is probability to estimate (i.e. grade) pi * is prior probability
- 19. Phase Diagram (Uniform) Mineral 1 Mineral 3Mineral 2
- 20. Markov Chain Monte Carlo Test Points Starting Point Mineral 1 Mineral 2Mineral 3
- 21. Phase Diagram (Low Grade Mineral 1) Mineral 1 Mineral 2 Mineral 3
- 22. 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
- 23. 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
- 24. 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 25.58 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
- 25. 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.
- 26. Input observable Ore Properties Unit Model Output observable Ore Properties Operating Parameters
- 27. Input Observable Ore Properties Unit Model Output Observable Ore Properties Operating Parameters Fixed Input Hidden Ore Properties Hidden Output Ore Properties
- 28. 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
- 29. 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
- 30. 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 Accuracy % Sampling Cost (Thousands) Traditional Improved
- 31. 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.
- 32. 1. Combine variables 2. Combine units.
- 33. 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
- 34. 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?
- 35. 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
- 36. 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
- 37. Excel Excel/VBA Visio Access
- 38. 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!
- 39. 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.
- 40. A database system Also VBA Used by many simulation systems – but often not „publicised‟ to users. Essential for organised handling of data
- 41. 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
- 42. 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:
- 43. 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.

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