Solution mining dissolves potash ore (sylvinite) by pumping water down an injection well into a salt cavern; the outlet brine concentration is limited by KCl solubility and by how much contact time the water gets with the cavern wall before it is pumped back out:
C_sat (g/L) = 255 + 3.5 · (T−20) [KCl solubility rises with temperature]
A = 2π·r·H [cavern wall contact area, H = 15 m lift]
fraction = 1 − exp(−k_m·A / Q) [residence-time saturation, k_m ∝ reactivity]
C = C_sat · fraction [outlet brine concentration]
dm/dt = C · Q · 1000 [g/h of KCl dissolved]
dV/dt = (dm/dt) / ρ_salt [m³/h of rock dissolved, ρ = 1.99 t/m³]
r = √(V / (π·H)) [cavern radius grows with dissolved volume]
recovery = (r / R_max)², stability = 1 − (r / R_max)^1.6
Raising injection flow pushes more total water through the well, but it also shortens contact time so the outlet brine comes out less concentrated per litre — the classic trade-off in cavern leaching. Raising temperature or rock reactivity increases the achievable concentration and dissolution rate directly. As the cavern grows past its design radius R_max, roof stability falls because the unsupported span-to-height ratio worsens, the same reason real solution-mining operations cap cavern size with well spacing.
- Injection pipe (left, cyan) — fresh/weak brine pumped down to the cavern.
- Cavern — grows outward from the well screen as salt dissolves; fill colour darkens toward gold as brine approaches saturation.
- Extraction pipe (right) — saturated brine pumped back to surface at the computed extraction rate.