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

2. 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

3. 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

4. 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

5. 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

6. 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
NF ppm 8
HPMC 50 ppm 9
NF ppm + HPMC 16ppm
Yes 11 12 13 14 15 16 17 18

7. 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

8. 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)

9. 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 %

10. 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 %

11. 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

12. 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

13. 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 %

14. 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

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

16. 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

17. Particle size distribution – Working with the data

18. Particle size distribution – Working with the data

19. What do you do with all this data?

20. Behavorial tendencies from graphs

21. Behavorial tendencies from graphs

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

23. Behavorial tendencies from graphs

24. Thank you!