Solving equations describing the steady-state model of MSF desalination process using Solver Optimization Tool of MATLAB software

Abstract

This work presents an algorithm for solving the large system of non-linear equations describing the steady state model of the two main layouts for the MSF process (the multistage flashing with brine recirculation and the once-through multistage flash desalination (MSF-OT)). The model accounts for the geometry of the stage, the mechanism of heat transfer, and the variation of the thermophysical properties of various fluids with temperature and salinity. In addition, the overall heat transfer coefficient was evaluated at each stage using convective heat transfer coefficient for internal and external flows, tube thermal conductivity and fouling resistance. Furthermore, the model takes into consideration the dependence of thermodynamic losses on stream flow rate, temperature, and the brine salinity. The system of equations was solved through an iterative procedure by using Solver Optimization Tool of MATLAB software. For each stage, the developed model was then used for evaluating the temperatures of the brine, distillate and cooling brine, the flow rates of brine outlet, distillate production, and steam heating. Finally, the resolution method was validated against the simulation results reported in the literature and the actual plant data at MSF-OT installation in Doha, Kuwait. The agreement was found to be good.

Keywords:

• MSF-BR
• MSF-OT
• Steady-state modeling
• System of non-linear equations
• Fsolve