Course description
Today, data acquisition and mass balancing are increasingly computerized and automated. Mass balancing or accounting is critical to many responsibilities of the metallurgical team of any mineral or metal processing plant: troubleshooting/improving/assessing plant performance, monitoring/controlling plant operation, accounting.
The mass balance made with original data (throughput, assay, size fraction, etc) is generally incoherent and inconsistent due to the errors of the data used (measured or estimated).
Methods for checking of correctness of material balance of separation operations, quality control with correction of errors in operation conditions i.e. flows and chemical assays used on balances need to be minimized to obtained reliable results (as balances are sensitive i.e. to the accuracy of metal assays), therefore adjustment methods are necessary to minimize errors in grades and distribution in the products of a concentration plant and assess its efficiency. Those will be learned during this course.
Professionals working in mineral processing should manage metallurgical accounting techniques and the calculations to make decisions about the operation, sampling, assays. This course prepare participants to use later more advanced techniques and specialized methods such as VBA, MATLAB o Python could be applied.
This course is an introduction to balances that could be done in other circuits of the plant, but the focus is on the flotation circuit and overall balance. The second part of a course will be programmed later for classification and grinding circuits.
Course content
1. Introduction to metallurgical calculation with Microsoft Excel
2. Metallurgical Balances
2.1. Classical or algebraic balance
o for two products (one concentrate and one tailing)
o three products (two concentrates and one tailing)
2.2. Matrixial
o Introduction of matrixial calculations
o Four products (three concentrates and one tailing)
2.3. Balance by nodal method
2.4. Balance from mineral to metal
3. Balances from batch to continuous
3.1 Close Cycle tests
3.2 Split factors form lab to plant
4. Introduction to SOLVER tools
4.1 Kinetic balance: cumulative grades and recoveries
4.2 Adjustment of kinetic models García-Zuñiga, Klimpel, Agar, Kesall with excel and solver
5. Adjustment for metal accounting and control of operational data
5.1 Correction on chemical assays in metallurgical balances with Solver and integration factor
5.2 Method Smith Ichiyen
5.3 Correction on chemical assays in metallurgical balances with residual weight and Lagrange multipliers techniques
Objectives and outcomes
After the course the professional in Mineral Processing and Metallurgical Engineering and / or related will be able to
- Handle the necessary fundamentals to understand the numerical techniques applied to calculate metallurgical balances which is the foundation of today's metallurgical modelling and simulation and specialized software.
- Will apply numerical techniques (algebra, matrixial functions, solver tool from Excel) to calculate mass and material balances
- Get familiar with advanced techniques such as Lagrange multipliers and other correction methods using Excel.
- Use of simple calculation for process assessment
- Develop balances for the total plant, by circuit, by operation unit using data of analysis of results of the operation or survey
