Fundamentals of mineral processing and recycling Ted Nuorivaara Dept. of Chemical and Metallurgical Engineering Fall 2017

Applying what we have learned on this course in real life examples Week 5 Applying what we have learned on this course in real life examples

Case: Experimental flotation studies Common topics in this course and experimental flotation studies: Composition Mineral composition Chemical composition Particle properties Particle size distribution Density Properties of the separation process Slurry properties Mass pull Recovery Grade Separation efficiency Kinetics

Case: Experimental flotation studies Additional properties to be taken into account: Chemical system Includes the type of chemical and their corresponding concentrations Operating conditions Air flow rate Imppeller speed Special conditions

Introduction to research What is research? A detailed study of a subject in order to discover new information or reach a new understanding Sustainable chemicals Cellulose derivatives Cellulose is a rigid polymer whose properties can be varied Certain cellulose derivatives have similar attribute as surfactants Their macromolecular size affects their behavior

Experimental design Experiment No Chemicals pH Re-grinding 1 NF240 50ppm 5,5 No 2 HPMC 50ppm 3 NF240 30ppm + HPMC 16ppm 4 10 5 6   7 ZnSO4 100 g/t SIBX 100 g/t NF240 50 ppm 8 HPMC 50 ppm 9 NF240 30 ppm + HPMC 16ppm Yes 11 12 13 14 15 16 17 18

Total volume of suspension Experimental design Parameter Value Air flow rate 4 l/min Impeller speed 1300 rpm Flotation time 30 min Solid content 33 w-% Amount of solids 600 g Amount of water 1200 g Total volume of suspension 1,5 l This and the previous slide combined is called the experimental design

Case: Experimental flotation studies What properties can be measured? Mass of fractions Concentration of elements (grade) Particle size distribution What properties can be calculated? Mass pull Recovery Kinetic constant Separation Efficiency Median particle size (a.k.a. d50)

Mathematical relations vs. real life Recovery 𝑹𝒆𝒄𝒐𝒗𝒆𝒓𝒚= 𝑪𝒄 𝑭𝒇 ∗𝟏𝟎𝟎 % C = mass of concentrate c = fraction of valuable mineral in the concentrate F = mass of feed f = fraction of valuable mineral in the feed Mass pull 𝑴𝒂𝒔𝒔 𝒑𝒖𝒍𝒍= 𝑪 𝑭 ∗𝟏𝟎𝟎 %

Mathematical relations vs. real life  Test Fraction 0-3min 3-6min 6-10min 10-14min 14-20min 20-30min Tailings Total Tot. 0-30min 2  Mass (g) - Measured 203,7 16,9 2,6 0,4 0,2 360,4 584,6 224,2 Mass pull of froth fractions (%) - Calculated 34,84 2,89 0,44 0,07 0,03 38,35 Grade of Cu (%) - Measured 0,020 0,042 0,063 0,000 0,110 0,08 Cc (Ff) - Calculated 0,041 0,007 0,0016 0,396 (0,45) 0,049 Recovery - Calculated 9,14 % 1,57 % 0,37 % 0,00 % 88,92 %   11,08 %

Mathematical relations vs. real life Kinetics 𝑹= 𝑹 𝒎𝒂𝒙 [𝟏− 𝒆𝒙𝒑 −𝒌𝒕 ] R = total recovery at a time t Rmax = maximum theoretical recovery k = kinetic constant t = time This is called the first order kinetic equation

Mathematical relations vs. real life  Test Fraction 0-3min 3-6min 6-10min 10-14min 14-20min 20-30min k (s^-1) Rmax (%) Diff^2 2 t (min) 3 6 10 14 20 30  Recovery 9,1 % 10,7 % 11,1 % 0,57845 11,08 0,00002 % Modelled recovery 9,13 % 10,74 % 11,05 % 11,08 % ”This is how you experimentally calculate the value for k” ”by applying the first order kinetic equation to the experimental data we are able to determine the famous k, you used in your assignments” Solved wíth MS-Excel ”Solver” 𝑹= 𝑹 𝒎𝒂𝒙 [𝟏− 𝒆𝒙𝒑 −𝒌𝒕 ] This value is minimized in the solver function

Mathematical relations vs. real life Separation efficiency 𝑆𝐸= 𝑅 𝑚 − 𝑅 𝑔 = 100 𝐶 𝑚 (𝑐−𝑓) 𝑚−𝑓 𝑓 SE = separation efficiency Rm = % recovery of the valuable mineral Rg = % recovery of the gangue into the concentrate C = the fraction of total feed weight that reports to the concentrate f = % of metal in the feed c = % of metal in the concentrate m = % of valuable element in the mineral 𝐶= 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 ∗𝐹𝑒𝑒𝑑 𝐺𝑟𝑎𝑑𝑒 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝐺𝑟𝑎𝑑𝑒 ∗ 100 %

Mathematical relations vs. real life Test Cummulative Recovery of Cu at t = 30 min (%) Cumulative grade of Cu at t = 30 min (%) Feed Grade - Cu (%) 11 35,6 % 0,293 % 0,096% C Cu content in Chalcopyrite (%) Separation Efficiency – in relation to Cu (%) 0,116 34,63 24,03

Particle size distribution One of the most common ways to determine the particle size distribution of the sample is to use laser diffraction

Particle size distribution – Raw data Frequency Undersize Size Classes (μm) Volume Density (%) 0,259261 0,313977 0,294563 6,51E-05 0,35673 0,000653 0,334671 0,007234 0,405303 0,066636 0,380241 0,073965 0,46049 0,146005 0,432016 0,095575 0,523192 0,242499 0,490841 0,116317 0,594431 0,361877 0,557675 0,1439 0,675371 0,511252 0,63361 0,18 0,767332 0,698918 0,719884 0,226027 0,871814 0,934148 0,817906 0,283131 0,990523 1,226744

Particle size distribution – Working with the data

Particle size distribution – Working with the data

What do you do with all this data?

Behavorial tendencies from graphs

Behavorial tendencies from graphs

Behavorial tendencies from graphs SE = 10 % SE = 20 %

Behavorial tendencies from graphs

Thank you!