Gained Output Ratio (GOR)
GOR is the primary thermal efficiency metric for MED and MSF desalination systems — the kg of distillate produced per kg of steam consumed. Higher GOR means greater efficiency.
ṁ_distillate (kg/hr) = Q_distillate (m³/day) × 1000 / 24
GOR:
GOR = ṁ_distillate (kg/hr) / ṁ_steam (kg/hr)
Latent heat interpolation (saturation):
0.5 bar → 2305 kJ/kg | 1.0 bar → 2257 kJ/kg | 1.5 bar → 2226 kJ/kg
2.0 bar → 2201 kJ/kg | 3.0 bar → 2163 kJ/kg | 5.0 bar → 2108 kJ/kg | 10.0 bar → 2015 kJ/kg
Steam per m³ distillate:
Steam per m³ = 1000 / GOR (kg/m³)
Thermal energy consumption:
E_th (kJ/kg) = h_fg / GOR
E_th (kWh/m³) = E_th (kJ/kg) / 3.6
Performance Ratio (PR)
PR is the IDA-standard thermal efficiency metric, normalized to the latent heat at 100°C / 1 atm (2326 kJ/kg). PR equals GOR when steam is at 100°C; they diverge when steam conditions differ.
h_ref = 2326 kJ/kg (latent heat at 100°C, 1 atm)
Performance Ratio:
PR = GOR × (h_fg_operating / h_ref)
PR = GOR × (h_fg_operating / 2326)
When steam is at 1 atm (1.013 bar), h_fg ≈ 2257 kJ/kg, so PR ≈ GOR × 0.97
Thermal energy input:
Q_steam (kW) = ṁ_steam (kg/hr) × h_fg (kJ/kg) / 3600
IDA benchmarks:
PR < 6: Below industry average
PR 8–12: Typical modern plant
PR > 12: High-performance
Brine Concentration Factor
Calculate reject brine TDS and water recovery from thermal desalination. Enter feed conditions plus either distillate or brine discharge flow — the third stream is calculated from the mass balance.
Q_feed = Q_distillate + Q_brine
Recovery:
R (%) = Q_distillate / Q_feed × 100
Concentration Factor:
CF = Q_feed / Q_brine = 1 / (1 − R/100)
Brine TDS:
TDS_brine = TDS_feed × CF
Density flag:
ρ_brine > 1.04 g/cm³ when TDS > ~60 g/L — check pump sizing
Reference case:
Seawater: 35 ppt feed, 40% recovery → brine ~58 ppt, CF ≈ 1.67
Top Brine Temperature (TBT) Scaling Risk
Assess CaCO₃ (carbonate) and CaSO₄ (anhydrite) scaling risk at the specified Top Brine Temperature, based on concentrated ion activities and temperature-dependent solubility products.
Ksp_CaCO₃(T) = 3.36×10⁻⁹ × exp(−0.0115 × (T − 25)) [mol²/L²]
Ion product (CaCO₃):
Ca_c = Ca_feed × CF; Alk_c = HCO₃_feed × CF
Ca_mol = Ca_c / 40,080; HCO₃_mol = Alk_c / 61,020
CO₃_mol = HCO₃_mol × 10^(pH − pK₂) where pH=8.0, pK₂=10.0
IP_CaCO₃ = Ca_mol × CO₃_mol
SI_CaCO₃ = log₁₀(IP / Ksp_CaCO₃)
CaSO₄ (anhydrite) solubility product:
Ksp_anhydrite(T) = 4.93×10⁻⁵ × exp(−0.02 × (T − 25)) [mol²/L²]
SO₄_mol = SO₄_feed × CF / 96,060
IP_CaSO₄ = Ca_mol × SO₄_mol
SI_CaSO₄ = log₁₀(IP / Ksp_anhydrite)
Industry thresholds (no antiscalant):
MSF: safe to ≤90°C | MED: safe to ≤65°C
With antiscalant:
MSF: safe to ≤120°C | MED: safe to ≤90°C