Trona Solution Mining: Cavity Growth & Brine Saturation (2D)

Injection & Recovery

Injection rate (Q) 20 m³/hr

Solvent temperature (T) 65°C

Well spacing (L) 30 m

Ore trona grade 65%

Live Readout

Elapsed time

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Cavity radius

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Brine concentration

0 g/L

Saturation limit

0 g/L

Na₂CO₃ recovered

0.0 t

Sweep / phase

Dissolving

How it works

Hot solvent enters through the injection well and dissolves the surrounding trona ore. Dissolution is mass-transfer limited: the rate is proportional to the concentration gradient between saturation and the bulk brine, times the wetted contact area of the growing cavity —

dm/dt  = k(Q)·A(r)·[Csat(T) − C]     A(r) = 2πrH
dV/dt  = (dm/dt) / (ρore·grade)      r = √(V/(πH))
dMsolute/dt = k·A·[Csat − C] − Qprod,eff·C
C = Msolute / (V0 + V(t))

k(Q) rises with injection rate (turbulence thins the boundary layer, k ∝ √Q); Csat(T) is the temperature-dependent solubility ceiling — once C reaches Csat, the bracket [Csat − C] collapses to zero and dissolution halts locally until production pulls saturated brine out and dilutes the cavity. The production well only recovers brine once the dissolution front has swept across the well spacing L: sweep efficiency is modeled as min(1, (r/L)²), so recovery ramps up and reaches full efficiency at breakthrough (r ≥ L).

Cross-section — the growing cavity around the injection well, shaded by local brine concentration; the production well sits at distance L.
Concentration chart — brine concentration C(t) against the saturation ceiling Csat(T).
Cavity/breakthrough chart — cavity radius r(t) against the well-spacing threshold L that triggers breakthrough.

Injection well Production well Dissolution cavity