This study presents an integrated analytical model for the hydrodynamic behavior of the spiral-wound membrane element considering the curvature of the flow feed and permeate channels. The new model introduces a set of closed-form expressions for the output parameters of the permeate flow rate, fluid recovery fraction, and the permeation flux, which can be a necessary tool for optimization and evaluation of the parameters involved in the problem. Accordingly, the results were set forth for a reverse osmosis water treatment SWM element. The difference in the output parameters for the solutions with flat and curved membranes was investigated, and the consequences of the common assumption of the flat-sheet membrane were examined mathematically. It was found that neglecting the membrane curvature implements a significant impact/error on the prediction of the permeate channel pressure and membrane width with maximum permeation rate, whereas its impacts on feed channel pressure and output parameters are insignificant, especially for the considered reverse osmosis case study. Also, the curvature effect on the solution can be magnified by three parameters of the membrane width: permeate channel permeability, and membrane resistance.

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包括膜曲率在内的螺旋缠绕膜组件的流体动力学模型：反渗透案例研究

本研究提出了一个综合分析模型，用于考虑进料和渗透通道的曲率的螺旋缠绕膜元件的流体动力学行为。新模型为渗透流量、流体回收率和渗透通量的输出参数引入了一组闭式表达式，可以作为优化和评估问题中涉及的参数的必要工具。因此，针对反渗透水处理 SWM 元件列出了结果。研究了具有平坦和弯曲膜的解决方案的输出参数的差异，并从数学上检查了平板膜的共同假设的后果。发现忽略膜曲率对具有最大渗透率的渗透通道压力和膜宽度的预测产生重大影响/误差，而其对进料通道压力和输出参数的影响微不足道，特别是对于考虑的反渗透情况学习。此外，对溶液的曲率效应可以通过膜宽度的三个参数放大：渗透通道渗透率和膜电阻。