Multiobjective Optimization of Cross-Flow Membrane Channel Geometry via Integrated CFD Modeling and RSM-Desirability Function Analysis

Abstract Pressure-driven membrane separation processes are pivotal for seawater desalination and wastewater recovery. However, the geometric configuration of the flow channel strongly influences mass-transfer performance and energy consumption. This study applies an integrated three-dimensional computational fluid dynamics (CFD) and response surface methodology (RSM) framework to optimize length-to-height (L/H) and length-to-width (L/W) ratios of cross-flow membrane channels for concentration polarization (CP) mitigation and hydraulic pressure drop (ΔP) reduction. A 13-point central composite design (CCD) was employed to construct second-order polynomial response-surface models (R2 > 0.95). To address the tradeoff between CP mitigation and energy consumption, a desirability-function multiobjective optimization was performed and validated using the nondominated sorting genetic algorithm II (NSGA-II). Results demonstrate that surface solute concentration exhibits a nonmonotonic, U-shaped dependence on L/H, whereas ΔP increases nonlinearly with vertical confinement. The optimal compromise geometry (L/H = 33 and L/W = 3), achieved a 2.21% reduction in the maximum CP and a 66.86% decrease in ΔP relative to the reference design. Six independent CFD validation simulations confirmed the model’s interpolation accuracy, yielding mean relative errors of 0.134% for CP and 1.050% for ΔP. These findings provide a numerically supported, application-specific physical threshold for scaling highly efficient, low-energy membrane modules.