Compact multi-effect distillation design with low-grade heat: Unified performance, heat-transfer area, and cooling-water demand maps

• PR rises with effects: ≈3.9 at n=4, weakly dependent on steam temperature. • Higher steam T compresses SA toward ∼120 m²·s·kg_D⁻¹ across practical ranges. • SCW drops as effects increase due to deeper internal heat recovery. • Preheaters recover ∼70% of boiler input at n≈12 with ∼100°C steam. • Inter-stage flashing yields ∼25–30% of distillate at n≈12 and ∼110°C. Wherever low-grade heat sources are available, multi-effect distillation (MED) offers a reliable option for seawater desalination. However, the trade-off between motive-steam temperature, number of effects, heat-transfer surface area, and cooling-water demand remains a key factor in system sizing and integration. This study develops a unified steady-state thermodynamic framework for MED systems that links the number of effects and steam temperature to three important design indicators: performance ratio (PR), specific heat-transfer area (SA), and specific cooling-water flow (SCW). The model is based on coupled mass, salt, and energy balances and incorporates realistic correlations for latent heat, seawater enthalpy, and boiling-point elevation. Representative operating conditions are considered (feed salinity 42,000 ppm, brine salinity 70,000 ppm, last-effect temperature 40°C, preheater terminal temperature difference 5°C, condenser temperature difference 10°C). Parametric simulations reveal that PR increases mainly with the number of effects and shows weak sensitivity to steam temperature. In contrast, SA decreases with increasing steam temperature but increases with effect count. The SCW requirement decreases with increasing number of effects due to deeper internal heat recovery. The resulting PR–SA–SCW maps provide practical engineering guidance for MED system sizing and for integration with low-grade heat sources such as industrial waste heat and renewable thermal energy. The developed PR–SA–SCW maps also quantify cooling-water demand across different operating conditions, enabling simultaneous assessment of thermal efficiency and condenser load.