Optimal Design of Multieffect Vacuum Membrane Distillation Modules Based on the Combination of Computational Fluid Dynamics and Design of Experiments

Multieffect membrane distillation (MD) is a process that can effectively reduce the energy consumption of the MD process, and it has broad industrial application prospects in the field of concentration and reduction of wastewater. Therefore, it is crucial to develop optimum membrane modules suitable for the multieffect distillation process. This study introduces a computational fluid dynamics (CFD) and design of experiments (DOE) integrated approach for the multiobjective optimization design of multieffect VMD modules, systematically investigating the interrelationships between structural variables and their coupled effects on module performance. First, a three-dimensional CFD model was established to calculate mass transfer flux (J_v), gain output ratio (GOR), and permeate-to-feed ratio (ϕ_p), and the CFD model was validated experimentally in a lab-scale VMD system. Based on the Box-Behnken response surface method (BBD response surface method), the inlet position, membrane surface length, and channel height of VMD modules were taken as variable factors to perform CFD simulation, and the response values of different variable combinations were obtained. The results show that inlet position and channel height are the main factors influencing J_v, and channel height is the main factor influencing GOR and ϕ_p. Based on these results, regression equations were developed to predict J_v, GOR, and ϕ_p, providing critical guidance for practical VMD module design. By application of the developed models, the structural dimensions of VMD modules were optimized to achieve concurrent improvements in both thermal efficiency and water productivity. These results establish a theoretical basis for deploying the optimized module in industrial-scale multieffect VMD systems.