β-spodumene (LiAlSi₂O₆) reacts with concentrated H₂SO₄ to form soluble Li₂SO₄, which is later water-leached. The forward reaction is treated as a first-order, temperature-activated process (Arrhenius kinetics), scaled by particle surface area:
k(T,d) = A·exp(−Ea/RT) · √(200/d)
conv(t) = min(1, D/100) · (1 − e^(−k·t))
excess = max(0, D − 100·conv)
Li ext. = conv·100 · (1 − 0.002·excess)
Higher temperature and finer grind (smaller d) raise the rate constant k, so conversion climbs faster along the kiln. Acid dosage D (as % of the stoichiometric requirement) caps the maximum possible conversion and also sets how much unreacted acid remains — too little starves the reaction, too much complicates the downstream neutralization and washing, both cutting into final lithium extraction.
- Kiln pane — particles are drawn along the drum's axial length; each particle's local residence time is its position fraction × the residence-time slider, so the color gradient (grey → amber → pale green) shows the real conversion profile from feed to discharge.
- Profile plot — the same three outputs (sulfate formed, acid excess, Li extraction) plotted against residence time from 0 to 90 min at the current temperature/dosage/size, with a marker at the chosen residence time.