In this study, a detailed rigorous theoretical model was developed to predict the transmembrane flux of a shell-and-tube type vacuum membrane distillation (VMD) module for seawater desalination. Two modes of operation are used for performing the VMD, namely lumen-side feed (in-out) configuration and shell-side feed (out-in) configuration. In this study, detailed mathematical formulations are derived for an out-in configuration that is commonly used in seawater desalination applications. Experimental results and model predictions for mean permeate flux are compared and shown to be in good agreement. The results indicate that although the simple VMD model that maintains a constant permeate pressure is easy to use, it is likely to significantly overestimate the mean permeate flux when compared to the detailed model that considers the pressure build-up in the fiber lumen. The pressure build-up of water vapor in the fiber lumen is identified as the crucial factor that significantly affects the VMD performance because it directly reduces the driving force for vapor permeation through the membrane pores. Additionally, its effect is more pronounced at longer fiber lengths and higher permeate fluxes, and this is achieved at higher feed temperatures and velocities and at lower feed salinities. In conclusion, the results of the study are extremely important in module design for the practical applications of VMD processes.

在这项研究中，建立了详细的严格理论模型，以预测用于海水淡化的壳管式真空膜蒸馏（VMD）模块的跨膜通量。两种操作模式用于执行VMD，即管腔侧进料（进出）配置和壳侧进料（进出）配置。在这项研究中，针对海水淡化应用中通常使用的外入式配置推导了详细的数学公式。对平均渗透通量的实验结果和模型预测进行了比较，并显示出很好的一致性。结果表明，尽管简单的VMD模型可保持恒定的渗透压易于使用，与考虑纤维管腔内压力累积的详细模型相比，可能会大大高估平均渗透通量。纤维内腔中水蒸气的压力积累被认为是显着影响VMD性能的关键因素，因为它直接降低了水蒸气透过膜孔的驱动力。另外，在更长的纤维长度和更高的渗透通量下，其效果更为显着，这是在更高的进料温度和速度以及更低的进料盐度下实现的。总之，研究结果对于VMD流程的实际应用在模块设计中极为重要。纤维内腔中水蒸气的压力积累被认为是显着影响VMD性能的关键因素，因为它直接降低了水蒸气透过膜孔的驱动力。另外，在更长的纤维长度和更高的渗透通量下，其效果更为显着，这是在更高的进料温度和速度以及更低的进料盐度下实现的。总之，研究结果对于VMD流程的实际应用在模块设计中极为重要。纤维内腔中水蒸气的压力积累被认为是显着影响VMD性能的关键因素，因为它直接降低了水蒸气透过膜孔的驱动力。另外，在更长的纤维长度和更高的渗透通量下，其效果更为显着，这是在更高的进料温度和速度以及更低的进料盐度下实现的。总之，研究结果对于VMD流程的实际应用在模块设计中极为重要。