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

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

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

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 - =

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

System consisting of three reactions ) (dissolved O (gas) 2 ¾ ® H Fe 1 3 4 + - 16H 2SO 15Fe 8H 14Fe FeS Rate expressions: R(), rFe2+, rO2 Rate constants: ks kFe and kLa

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

Fe2+, Fe3+, and O2 Mass Balances V 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 + - = ]) [ ] ([

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)

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

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

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

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

 - 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

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)

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)

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 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

Plant Optimisation CSTR/PFR

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

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) 207-220

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) 275-295

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