An XRT sorter fires two X-ray energies through each lump and applies the Beer–Lambert attenuation law at each:
T(E) = exp(−μ(E)·ρ·x)
ρ is density and x is the lump's path length — both unknown and different for every lump. But taking the ratio of the two log-transmissions cancels ρ·x exactly:
R = ln T(E_low) / ln T(E_high) = μ(E_low) / μ(E_high)
At the low energy, photoelectric absorption dominates and scales steeply with effective atomic number (μ ∝ Z~3.5&fasl;E³); at the high energy, Compton scattering dominates and is almost Z-independent. So R is (to first order) a pure material signature, independent of how big or thick the lump is — which is exactly why XRT can sort lumps of wildly different sizes on the same criterion. This sim assigns every lump a true R from its simulated composition, adds sensor noise, and fires the ejector only when the noisy reading clears your threshold, so you can see false accepts/rejects appear as the noise or the grade slider changes.
- Recovery — % of the ore atoms actually fed that end up in the concentrate chute.
- Concentrate grade — purity of the concentrate stream (raise the threshold to raise grade, at the cost of recovery).
- Sensor noise — models detector/electronics jitter; push it up to see the recovery/grade trade-off degrade.