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Efficient Storage and Recall
- f Slag Thermochemical
Properties for Multiphysics Modelling
Dr Johan Zietsman University of Pretoria
May 22-25, 2016 | Seattle, Washington, USA
Background
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Efficient Storage and Recall of Slag Thermochemical Properties for - - PowerPoint PPT Presentation
Efficient Storage and Recall of Slag Thermochemical Properties for - - PowerPoint PPT Presentation
Efficient Storage and Recall of Slag Thermochemical Properties for Multiphysics Modelling Dr Johan Zietsman University of Pretoria May 22-25, 2016 | Seattle, Washington, USA Background 2 Ilmenite Smelting 3 High-titania Slag
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Ilmenite Smelting
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High-titania Slag
Predominantly Single Phase
4 (Pistorius and Coetsee, 2003)
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Combination of Factors
Heat Transfer Fluid Flow Thermochemistry
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Concepts
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Thermochemistry Calculator
(FactSage, ChemApp)
Multiphysics Solver (OpenFOAM) Heat transfer Fluid flow Mass transfer Electromagnetics Equilibrium calculation Heat capacity Enthalpy Viscosity Density
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Comprehensively Describing Pyrometallurgical Processes
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y = 0.0717x4.4821 R² = 0.9132 5 10 15 20 25 30 35 40 45 1 2 3 4 5 Average Equilibrium Calculation Duration (ms) Number of System Components Al2O3-CaO-MgO-SiO2
Computational Cost
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0.001 0.01 0.1 1 10 100 1000 2 4 6 8 10 12 Iteration Duration (h) Number of System Components 1e4 cells 1e5 cells 1e6 cells
Computational Cost
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Thermochemistry Calculator
(FactSage, ChemApp)
Multiphysics Solver (OpenFOAM) Heat transfer Fluid flow Mass transfer Electromagnetics Equilibrium calculation Heat capacity Enthalpy Viscosity Density
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Comprehensively Describing Pyrometallurgical Processes
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Thermochemistry Calculator
(FactSage, ChemApp)
Multiphysics Solver (OpenFOAM) Heat transfer Fluid flow Mass transfer Electromagnetics Equilibrium calculation Heat capacity Enthalpy Viscosity Density Thermochemistry Accelerator (gtc)
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Comprehensively Describing Pyrometallurgical Processes
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Thermochemistry Accelerator (gtc)
Enthalpy Element mole fractions Total amount (mol) Phase fractions Phase element fractions Heat capacity Density Viscosity Temperature (K)
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Previous Work
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- Not a new problem
- Aluminium casting examples
- Up to 4 system components
- Geometric approaches
- Limited use of thermochemistry
theory
- No application to extractive
metallurgy
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Previous Work
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Method
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- Start with binary and ternary systems
- Use a geometric approach
- Apply thermochemistry theory to
– simplify and accelerate calculations; – minimise dimensionality of geometries; and – minimise storage and memory requirements.
- Implement prototype in Python
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Decisions
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- Phase diagrams describe
thermochemical behaviour
– Binary – Ternary
- Phase diagrams are also geometric
systems, consisting of:
– Points – Phase region boundaries (curves, surfaces) – Phase regions (volumes)
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Geometric Approach
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Geometric Approach
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Geometric Approach
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Geometric Approach
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Geometric Approach
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Geometric Approach
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Geometric Approach
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Simplifies the calculation of
- Phase fractions
- Phase compositions
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Geometric Approach
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Thermochemistry Theory
Gibbs Phase Rule 𝑔 = 𝑑 − 𝑞 + 2
At constant pressure:
𝑔′ = 𝑑 − 𝑞 + 1
Classify phase regions
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Thermochemistry Theory
Gibbs Phase Rule
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- Reduce dimensionality
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Thermochemistry Theory
Lever Rule
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Thermochemistry Theory
Lever Rule
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- Reduce dimensionality
- Calculate phase fractions
- Binary systems:
– 2-phase regions
- Ternary systems:
– 2-phase regions, 3-phase regions
- c-component systems:
– 2-phase regions, …, c-phase regions
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Thermochemistry Theory
Lever Rule
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Thermochemistry Theory
Lever Rule
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Thermochemistry Theory
Lever Rule
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- Positive:
– Extensive mathematical and numerical libraries – Simple language – Access to ChemApp – Rapid prototyping
- Negative:
– Computationally slow
- Will transfer algorithms to Fortran
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Implementation
Python
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Thermochemistry Accelerator (gtc) Geometry Calculator (gcalc) Geometry Constructor (gcon) Geometric Representation Database (gdb)
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Thermochemistry Calculator
(FactSage, ChemApp)
Multiphysics Solver (OpenFOAM) gtc gcalc gcon gdb
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- 1. request equilibrium result
- 2. request geometry
- 3. request geometry construction
- 4. request equilibrium results
- 5. do equilibrium calculations
- 6. provide equilibrium results
2 3 4 6 8 10 12 11 7 5
- 7. construct geometry
- 8. provide geometry
- 9. store geometry
10.provide geometry 11.calculate equilibrium 12.provide equilibrium result
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Equilibrium Calculation
New Region
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Thermochemistry Calculator
(FactSage, ChemApp)
Multiphysics Solver (OpenFOAM) gtc gcalc gcon gdb
1
- 1. request equilibrium result
- 2. request geometry
- 3. provide geometry
- 4. calculate equilibrium
- 5. provide equilibrium result
2 3 5 4
Equilibrium Calculation
Stored Region
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Results
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- Binary system (Al2O3-CaO):
– 20x faster ChemApp – Negligible deviations from ChemApp results
- Ternary (Al2O3-CaO-SiO2):
– 15x faster than ChemApp – Negligible deviations
- Fortran implementation
– Can be 10x to 1000x faster than Python – Possible 150x to 20000x acceleration – Multiphysics-thermochemistry integration can become feasible
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Accelerator Performance
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Next Steps
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- Add Cp and H
- Develop generic algorithm for c-
component systems
- Develop multicomponent, multiphase
solver in OpenFOAM
- Develop test cases
– Freeze lining – Slag-alloy reduction interactions
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Future Plans
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