Global optimization of MSF seawater desalination processes

This article addresses the global optimal design of multi-stage flash desalination processes. The mathematical formulation accounts for non-linear programming (NLP) based process models that are supplemented with the non-deterministic optimization algorithm. MSF-once through, -simple mixture (MSF-M) and -brine recycle (MSF-BR) process configurations have been evaluated for their optimality. While freshwater production cost has been set as the objective function for minimization, mass, energy and enthalpy balances with relevant supplementary equations constitute the equality constraints. Differential evolution algorithm (DE/rand/bin) was adopted to evaluate the global optimal solutions. Further, obtained solutions have been compared with those obtained with MATLAB optimization toolbox solvers such as SQP and MS-SQP. The global optimal solution corresponds to a variable value set of [2794.4 m3/h, 1.0499, 7.62 m, 3.359 kW/m2 ∙ K, 3.297 kW/m2 ∙ K, 3.042 kW/m2 ∙ K and 22] for decision variables [WM, RH, LT, UB, UR, Uj, NR] in the MSF-BR process to yield an optimal freshwater production cost of 1.0785 $/m3. Compared to the literature, the obtained global solution from DE is 2.31% better. Further, inequality constraint resolution has been excellent for DE but not other methods such as MS-SQP, SQP and DE-SQP.