An 8 t batch of zinc-smelter residue at 300 g/t germanium grade (2.4 kg Ge total) runs through four real stages, each driven by one of the sliders:
k = k0 (acid/60)^0.65 exp[(Ea/R)(1/Tref − 1/T)]
X(t) = Xmax (1 − e^−kt) leach extraction
η_precip = 1 − e^−(dose/Kd) tannin saturation
η_chlor = e^−((Eh−450)/150)² redox selectivity
Ge_recovered = Ge_total·X·η_precip·η_chlor·0.97
Leaching follows first-order kinetics (k0=0.30 h⁻¹ at 60 g/L acid, 45 °C) with an Arrhenius temperature term (Ea=42 kJ/mol) — hotter, more acidic pulp dissolves germanium faster, approaching a 94% ceiling. Precipitation follows Langmuir-type saturation in the tannin dose (Kd=0.9 g/L): more reagent binds more Ge until it saturates. Chlorination converts precipitate to volatile GeCl₄ most efficiently near 450 mV — too reducing or too oxidizing drops the selectivity, modeled here as a Gaussian around the optimum. Calcination hydrolyzes the chloride to GeO₂ at a fixed 97% conversion (molar ratio GeO₂/Ge = 1.44).
- Flow diagram — particles carry dissolved/precipitated germanium between the four vessels; tank fill height tracks each stage's live efficiency.
- Recovery curve — the strip along the bottom plots overall Ge recovery % against process time as the batch runs.