What is a theoretical grade-recovery curve? An example.

The theoretical grade-recovery curve for an ore is a definition of the maximum expected recovery by flotation of a mineral or element at a given grade.  This is defined by the surface area liberation of the value minerals and is consequently directly related to the grind size utilised in the process.  The theoretical grade-recovery can be readily used to quickly identify potential recovery increases that can be gained through optimisation of flotation circuits and whether the process is running efficiently.

To establish the theoretical grade-recovery curve for a material a mineralogical liberation study should be undertaken using tools such as QEMSCAN or MLA.  Using these tools in combination with standard flotation tests can quickly and efficiently define the efficiency of a process and where potential improvements may be made.

The following example shows the key aspects of using the theoretical grade-recovery curve for a copper flotation circuit where chalcopyrite is the major copper bearing mineral.  The material in this example was ground to P80 of 125 micron in a closed ball mill circuit prior to flotation.

Figure 1 shows the theoretical grade-recovery curve determined from the liberation characteristics of this material at this grind size.  It should be noted that the modal mineralogical distribution of this material contained 2% w/w chalcopyrite, which can be seen on the curve as the grade value at 100% recovery.  We can also see the proportion of fully liberated chalcopyrite particles was 30% w/w based on the recovery demonstrated for 100% chalcopyrite grade.

Process data for this material showed that a concentrate containing 80% w/w chalcopyrite at a recovery of 60% was achieved.  When compared with the theoretical grade-recovery chart it can be seen that this was significantly under the maximum expected recovery for this grade concentrate and hence an opportunity for flotation optimisation was present.

In this case optimisation of a series of key flotation parameters for this material resulted in an increase in recovery to 71% chalcopyrite while still maintaining a final concentrate grade of 80% w/w chalcopyrite.

Figure 2 shows that this correlated to a more efficient process with the actual plant recovery much closer to the theoretical grade recovery curve defined for that grind size.  A key thing to remember is that the actual achievable recovery can never fall on the right hand side of the theoretical grade-recovery curve as this would contradict the fundamental parameters of the material.

In our example the operators wished to increase recovery further even after optimisation of the flotation circuit.  To achieve this, the basic theoretical grade-recovery curve needed to be moved and to achieve this the liberation of chalcopyrite had to be increased.

The theoretical grade-recovery curve for chalcopyrite when the grind size was reduced to a P80 of 106 micron can be seen in figure 3.  It can be seen that the proportion of fully liberated chalcopyrite increased to 50% w/w and the whole curve was pushed right, giving greater opportunities for recovery improvements to be made.

The increased recovery at finer grind size can be seen in figure 4 to rise from 71% chalcopyrite to 85% chalcopyrite in a concentrate with 80% chalcopyrite grade.  This was a significant recovery increase and although the improved recovery was greater than the original theoretical grade-recovery curve suggested possible a change in the liberation characteristics allowed the operator to see the benefit.

Finally, we should remember that the theoretical grade-recovery curve is generally defined for the value minerals in an ore and not based on the final element/metal to be recovered.  From the example here if we looked at Cu recovery the theoretical grade recovery curve would correspond to figure 5. 

In this case the maximum grade of Cu is restricted by the host mineral, hence to chalcopyrite the Cu grade cannot exceed 34.63% in the concentrate, even assuming 100% recovery of chalcopyrite.  This is a simply a function of the chemical composition of chalcopyrite with 34.63% Cu, 30.42% Fe and 34.94% S.  The grade at 100% chalcopyrite recovery therefore corresponded to the actual Cu head grade (assuming all Cu occurred with chalcopyrite) and was 0.69% Cu. 

Overall, the theoretical grade-recovery curve can be a very powerful tool for metallurgists in defining whether target recoveries and grades are feasible for the grind size of their operation and more importantly where recovery increases may be possible through optimisation.  Used well a simple mineralogical study to define liberation characteristics can offer a fast and easy way to define where efforts in plant optimisation should be directed for maximum benefit.