For the optimized design and application of membrane devices, careful consideration of the complexity of the underlying mass transport mechanism as well as the dependence of device performance on design parameters and operation conditions is critical. In this study, we present a new one-dimensional model, which is straightforward and yet accounts for the major phenomena that could impact the mass transport characteristics of membrane devices. A novel numerical method is subsequently presented to calculate the transport equations. Unlike the conventional method where transport equations for different subdomains, i.e., membrane and the side compartments, are calculated in separated steps and requires repeated iteration to achieve convergence, the presented method treats fluid and solute transport in the whole device as connected flow networks, and deduces the discrete forms of governing equations through Kirchhoff's Laws. By calculating the equations in a coupled implicit manner, whole-field solution can be obtained with improved numerical stability, accuracy, and efficiency. The superiority of the method have been validated by experimental data with respect to different membrane devices. Capable of readily and accurately evaluating their mass transport characteristics under various conditions, the presented method provides an efficient tool for screening the optimal design parameters and operation conditions.

对于膜装置的优化设计和应用，至关重要的是要仔细考虑基础物质传输机制的复杂性以及装置性能对设计参数和操作条件的依赖性。在这项研究中，我们提出了一个新的一维模型，该模型简单明了，却说明了可能影响膜装置传质特性的主要现象。随后提出了一种新颖的数值方法来计算运输方程。与传统方法不同，在传统方法中，不同子域（即膜和侧隔室）的输运方程式是在单独的步骤中计算的，并且需要反复迭代以实现收敛，因此本方法将整个设备中的流体和溶质输运视为连通的流动网络，并通过基尔霍夫定律推导了控制方程的离散形式。通过以耦合的隐式方式计算方程，可以获得具有改善的数值稳定性，准确性和效率的全场解。该方法的优越性已通过针对不同膜装置的实验数据得到验证。该方法能够在各种条件下轻松，准确地评估其传质特性，为筛选最佳设计参数和操作条件提供了有效的工具。通过关于不同膜装置的实验数据已经验证了该方法的优越性。该方法能够在各种条件下轻松，准确地评估其传质特性，为筛选最佳设计参数和操作条件提供了有效的工具。通过关于不同膜装置的实验数据已经验证了该方法的优越性。该方法能够在各种条件下轻松，准确地评估其传质特性，为筛选最佳设计参数和操作条件提供了有效的工具。