A Hybrid Steady-State Mathematical Model for a Brine-Recycle Multistage Flash Desalination System

Abstract

A steady-state mathematical model for a brine-recycle multistage flash (MSF-BR) desalination system is developed for performance prediction and analysis. The proposed formulation combines the computational simplicity of section-wise steady-state models with selected rigorous thermodynamic features while avoiding the complexity of detailed stage-by stage formulations. The governing model consists of coupled mass, salt, and energy balance equations combined with heat-transfer relations for the recovery section, rejection section, brine heater, and mixing units. The resulting nonlinear algebraic equations are linearized using a modified tridiagonal model (TDM)-based approach and solved iteratively within a FORTRAN computational framework. The model is validated using published benchmark data for a 5 MGD brine-recycle MSF desalination plant reported by Rosso et al. Predicted temperatures, flow rates, salinities, heat-transfer coefficients, distillate production, and gain output ratio (GOR) show good agreement with the reference results, with deviations generally within acceptable engineering limits.  The model also reproduces the effects of steam and seawater temperatures on plant performance. While deviations in distillate production and gain output ratio increase at elevated steam temperatures, the agreement remains satisfactory within the practical operating range of MSF desalination plants. The results demonstrate that the proposed model provides reliable steady-state predictions with moderate computational effort. Owing to its balance between physical realism and numerical simplicity, the model represents a practical tool for simulation, parametric analysis, and preliminary optimization of large-scale MSF desalination systems.