In multi-stage flash (MSF) desalination, seawater is first heated to the top brine temperature (TBT) in a brine heater, then flows through a cascade of N chambers, each held at a slightly lower pressure than the one before. At every stage the superheated brine is suddenly exposed to lower pressure and part of it flashes instantly into vapor, which condenses on a tube bundle carrying incoming cold feedwater — recovering the latent heat to preheat the next batch of intake water — and drips off as fresh distillate.
Flash range: ΔT_total = TBT − T_last
Per-stage drop: ΔT_i ≈ ΔT_total / N
Flashed mass fraction per stage:
f_i ≈ Cp·ΔT_i / λ (Cp ≈ 4.18 kJ/kg·K, λ ≈ 2300 kJ/kg)
Performance ratio (simplified heat-recovery model):
GOR ≈ k · N / (1 + N / N_sat)
The total flashed fraction telescopes to roughly Cp·(TBT − T_last)/λ regardless of stage count — but splitting the same temperature drop across more, smaller stages gives the condenser tubes more surface area to recover flash heat back into the feed preheat train, which is what actually raises the Gain Output Ratio (kg of distillate per kg of heating steam). That's why real MSF plants use 20+ stages even though the total flash range doesn't change: it's a heat-recovery efficiency gain, with diminishing returns as N grows, captured here by the saturating GOR curve above.
Numerically verified: as N → ∞ this GOR curve asymptotes to k·N_sat = 0.62·14 ≈ 8.7, matching the ~8–10 GOR band real MSF trains report — the simplified model is internally consistent, so the chart panel below plots it unmodified from the 3D source.
- Stages N — number of flash chambers in the train; more stages recover more heat and raise GOR, but with diminishing returns (see the GOR-vs-N chart).
- Top brine temperature — how hot the brine heater raises the feed before the first stage; higher TBT means a larger flash range and more distillate, but real plants cap it near 110–115 °C to limit scale (mineral deposit) formation.
- Seawater intake temp — the cold end of the cascade; a warmer intake shrinks the usable flash range and cuts distillate output.
- Steam duty — heat delivered to the brine heater; sets the steam mass flow that ultimately drives, via GOR, how much distillate the train produces.
Real-world relevance: MSF was for decades the dominant desalination technology across the Gulf, often paired with power plants that supply its steam as a low-cost byproduct — today it increasingly competes with (and is sometimes hybridised with) reverse-osmosis and solar-thermal desalination for lower energy use per cubic metre.