Statistical Methods For Mineral Engineers

Many flotation recovery curves follow a sigmoidal shape. The Hill equation (borrowed from biochemistry) models recovery as a function of residence time:

$$ R(t) = R_max \cdot \fract^nK^n + t^n $$ Statistical Methods For Mineral Engineers

Where $K$ is the time to 50% recovery and $n$ is the slope (kinetics). Fitting this using non-linear least squares allows engineers to optimize residence time for maximum throughput. Many flotation recovery curves follow a sigmoidal shape

No statistical method for mineral engineers is complete without addressing the fundamental error of sampling. No statistical method for mineral engineers is complete

Before any processing occurs, the resource must be quantified. Traditional geostatistics (kriging, variograms) is a field unto itself, but here we focus on practical statistical descriptors.

For a flotation circuit, consider four factors: grind size (P80), collector dosage, frother dosage, and pH. A full factorial ( 2^4 ) design requires 16 experiments. A half-fraction ( 2^4-1 ) requires 8 experiments but does not resolve certain higher-order interactions—acceptable for screening.

Case study: A copper-molybdenum plant used a ( 2^3 ) factorial design and discovered that the interaction between collector dosage and pH was statistically significant (p < 0.01), whereas neither factor alone was significant. The optimum was found at a combination previously dismissed by OFAT trials.