The method of McCabe-Thiele is widely used for the design of distillation columns. At a given pressure, this graphical method is only based on 3 equations: (i) the partitioning curve linking the liquid and gas phases for a given component at a given plate thanks to a unique set of thermodynamic data and (ii) two operating lines, each one describing the liquid/gas equilibrium of two consecutive plates either in the enrichment section or in the stripping one. In this paper, the method has been adapted to the membrane separation processes aiming at the easy selection of a first set of appropriate designs of cascades that fulfill given separation targets, especially in the case of a binary mixture of components having both intermediate rejections and very different concentrations. Membrane cascades involving several recyclings of the permeate and retentate streams are proposed according to a similar but more sophisticated methodology than for distillation, since for a selected membrane and for given hydrodynamic conditions (pressure, velocity, temperature), several proposals can be made for each equation mentioned above. In short, a set of operating lines is generated varying with the volume reduction ratio (VRR) either for the permeate or the retentate retreatment sections. The method is applied to the OSN separation of a final synthesis medium of a homogeneous catalyzed reaction, namely olefin hydroformylation achieved in toluene. This example is a typical one dealing with the more general case of a product to be extracted in the permeate and a catalytic system to be recovered in the retentate for further recycling in the synthesis reactor aiming at a greener production process. The initial concentration ratio of the two components to separate in OSN is 1/1000 and both compounds have intermediate rejections of 30% and 88%. Thanks to this method, the design of several membrane cascades is proposed and discussed according to different goals of separation (target product purity or recovery, enrichment of component to be recycled, energy consumption, etc.).

McCabe-Thiele的方法被广泛用于蒸馏塔的设计。在给定压力下，这种图形化方法仅基于3个方程：（i）通过一组独特的热力学数据，将给定板上给定组分的液相和气相链接的分配曲线；以及（ii）两条操作线，每个描述了两个连续塔板在浓缩区或汽提塔中的液/气平衡。在本文中，该方法已适用于膜分离工艺，旨在轻松选择满足给定分离目标的第一组合适的级联设计，特别是在具有中间截留和非常高的组分的二元混合物的情况下不同的浓度。根据与蒸馏相比类似但更复杂的方法，提出了涉及多次渗透液和截留液再循环的膜级联反应，因为对于选定的膜和给定的流体动力学条件（压力，速度，温度），可以针对每种膜提出若干建议上面提到的等式。简而言之，针对渗透物或渗余物再处理段，生成的一组操作线随体积减小率（VRR）的变化而变化。该方法用于均相催化反应的最终合成介质的OSN分离，即在甲苯中实现的烯烃加氢甲酰化。该实例是一个典型的实例，涉及更一般情况下要在渗透物中提取的产物和要在渗余物中回收的催化体系，以便在合成反应器中进一步循环利用，以期实现更绿色的生产工艺。在OSN中分离的两种组分的初始浓度比为1/1000，两种化合物的中间截留率分别为30％和88％。由于这种方法，根据分离的不同目标（目标产品的纯度或回收率，要回收的组分的富集，能耗等），提出并讨论了几种膜级联的设计和讨论。