1. Modelling, Simulation and Optimisation of Leaching Reactors
Frank Crundwell
Billiton Process Research
Randburg, South Africa

2. Modelling and Simulation
Sizing and design of reactors
Simulation and sensitivity analysis
Process Control
Influence of operating conditions
and parameters
Optimisation of reactor, plant and process

3. The Issue: Material and number balances for particulate processes
0.000
0.004
0.008
0.012
0.016
0.020 50
100
150
Particle Size (um)
Size Density (Number)
Inlet
Outlet

4. Amount leached is obtained from the size density
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1 50
100
150
200
250
300
Residence Time  = V/Q
Conversion
Continuous l + = )) ( ) n R V Qn Q 2
FeS in ò - = in 3 d n 1 X l ) ( ) ( X 1
FeS in 2 - =

5. Continuous Reactors for Leaching Sulphides
Pressure Leaching
Bacterial Leaching
Atmospheric Leaching of Finely Milled Material
Differing conditions of operation
Each imposes different constraints
Choice of process based on overall flowsheet cost

6. System consisting of three reactions)
(dissolved O
(gas) 2 H Fe 1 3 4 + -
16H
2SO
15Fe 8H
14Fe
FeS
Rate expressions: R(), rFe2+, rO2
Rate constants: ks kFe and kLa

7. Mass Balances for Leaching Reactors
Slurry in
Fe2+
Fe3+
CuFeS2
Compute
Fe2+
Fe3+
CuFeS2
Air

8. Fe2+, Fe3+, and O2 Mass BalancesV 15 r Fe Q 2
FeS in ) ( ] [ - + = V r 14 Fe Q 2
FeS 3 in ) ( ] [ + - = V 4 r O a k Q 2 Fe
sat L in + - = ]) [ ] ([

9. Sensitivity Analysis Oxygen (ppm) Conversion
kLa  - Dimensionless mass transfer coefficient
0.1
0.2
0.3
0.4
0.5
0.6
0.7
5000
10000
15000
20000
Conversion
0.0
1.0
1.5
2.0
2.5
3.0
3.5
Oxygen (ppm)

10. Only “two states” of operation
0.7 9 8
0.6 7
0.5 6
0.4 5
Conversion
Fe2+ concentration (g/L) 4
0.3 3
0.2 2
0.1 1 5 10 15
kFe - Dimensionless ferrous oxidation rate constant

11. Pressure, Bacterial and Atmospheric Leaching
are related by ks /L
0.7
0.6
0.5
0.4
Conversion
0.3
0.2
0.1
0.2
0.4
0.6
0.8 1
ks /L - Dimensionless Residence Time

12. Leaching strategies can be compared by examining ks /L
Pressure - high temperature
 high ks, low , moderate L
Bacteria - low temperature
 low high , moderate L
Fine grinding - intermediate temp
 med ks, med , low L

13. Performance  - Residence Time Conversion Flow Rate 1.0 0.9 0.8 0.7
0.6
Conversion
0.5
0.4
0.3
0.2
Flow Rate
0.1
0.0 5 10 15 20 25 30
 - Residence Time

14.  - Residence Time 14 12 10 8 Oxidation Rate (kg/m3/d) 6 4 2 5 10 15
Flowrate 12 10 8
Oxidation Rate (kg/m3/d) 6 4 2 5 10 15 20 25 30
 - Residence Time

15. 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 Oxidation Rate (kg/m3/d)
60 % conversion 2 4 6 8 10 12 14
FeS2 Feed rate (t/m3/d)

16. Solids Feed Rate (t/m3/d)35
Ferric g/L 30
Ferrous*100 g/L
Pyrite, g/L 25 20
Exit Concentration 15 10 5 2 4 6 8 10 12 14
Solids Feed Rate (t/m3/d)

17. 16 14 12 10
Oxidation Rate (kg/m3/d) 8 6 4 2
0.0
0.1
0.2
0.3
0.4
0.5
Grade of FeS2 in Solids

18. 18 16 14 12 10
Oxidation rate (kg/m3/d) 8 6 4 2
0.00
0.10
0.20
0.30
0.40
Fraction Solids in Total Feed

19. Plant Optimisation
CSTR/PFR

20. CSTR/PFR approximation
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.0
1.0
2.0
3.0
4.0
5.0
Volume Primary/Volume Secondary
Conversion
2 Tanks
3 Tanks
4 Tanks

21. Predicted vs Measured - Bacterial Leaching
0.2
0.4
0.6
0.8
1.0 5 10 15
Total Residence Time (days)
Conversion
Tank 1
Tank 2
Tank 3
Tank 4
Predicted
Crundwell, Chemical Engineering Journal 54 (1994)

22. Predicted vs Measured - Zinc Pressure Leaching
1.00
0.98
0.96
0.94
Conversion
0.92
0.90
Measured
Predicted
0.88
0.86 1 2 3 4
Compartment number
Crundwell and Bryson Hydrometallurgy 29 (1992)

23. Conclusions Number balance elucidates the relationship between
pressure, bacterial and atmospheric leaching
Sensitivity analysis shows “two state” solution with
respect to Fe2+ oxidation and O2 mass transfer
Comparison with measurements is very good
CSTR/PFR optimises these autocatalytic reactors
(notwithstanding basic ferric sulphate precipitation)
Control on Fe2+ and O2 most accurate