Separation of azeotropic mixtures is common in chemical industry but its optimal flowsheet design still faces many challenges. With the help of useful geometric tools, such as Residue Curve Maps (RCMs), quantities of methods have been proposed for synthesizing azeotropic distillation processes. These methods are mostly based on heuristic rules, and moreover, due to the difficulty of visualization, attention on mixtures with more than four components is much less focused. Rooks et al. (1997) proposed an equation based approach which is able to generalize geometric methods and explore the structure of distillation regions for azeotropic mixtures with arbitrary number of components, but absent of liquid-liquid phase behavior. Feng et al. (2003) proposed a highly efficient algorithm for synthesizing an azeotropic distillation system based on partitioning the composition space and then identifying candidate operating units. However, their method leads to processes lacking flexibility of mixing of multi streams and splitting of streams for different operation units. And actually, it is difficult to be totally automated, for with the number of components increasing, identifying candidate operations cannot be easily handled. Finally, it lacks a proper method to assess the flowsheet.

In this work, a systematic methodology is introduced for the optimal design of azeotropic distillation processes. The proposed methodology involves two main parts, and can be applied to both homogeneous and heterogeneous systems with arbitrary number of components. The first part is a pre-procedure for exploring composition space structure (i.e., distillation regions and liquid-liquid phase regions), identifying candidate operations and detecting limitation of azeotropic distillation. For simplicity of computation with optimization in the second part, distillation boundaries are linearized and therefore distillation boundary crossing (DBC) splits exploiting the curvature of a distillation boundary are neglected. In fact, DBC splits rely on accuracy of thermodynamic models too much and therefore are not always reliable. This pre-procedure is mainly based on the algorithm proposed by Rooks (1997) but extend it to heterogeneous systems. For azeotropic distillation processes, mixing is the main way to jump across distillation boundaries, but it does not work in all cases. Specifically, whether a mixture can achieve perfect separation depends on the topological structure of their distillation regions. That is to say, when an *unchangeable point* (a point which is the intersection of all distillation or compartment boundaries, see Figure 1) is presented, it is impossible to obtain perfect separation via only distillation and mixing, because any mixing cannot make an unchangeable point jump across the distillation boundary validly. In such cases, other technologies, e.g., decanting in heterogeneous systems, pressure swing distillation, extractive distillation, etc., must be used to facilitate the separation. Unfortunately, unchangeable points almost exist in all topological structures. The pre-procedure can detect all unchangeable points before implementing the second part. The second part is a state space superstructure (Bagajewicz, 1998) based algorithm for finding the optimal flowsheet. The employed superstructure, illustrated in Figure 2, consists of a RCMs operator (OP) and a distribution network (DN). The RCMs operator involves candidate operations generated by the pre-procedure, i.e., distillation and mixing in a homogeneous system and additional decanting in a heterogeneous system, for a specific task. The DN deals with mixing and splitting possibilities for each stream in the process network. Column products in low purity, namely located on the distillation boundary, enter the DN to mix with one another, feed streams, entrainer and decanting products (if in a heterogeneous system) for further separation. These recycle streams can improve the flowsheet performance, both in purity and recovery.

Compared with methods available, the present method is believed to be superior in the following aspects. First, the superstructure allows the flowsheet to be more flexible and efficient. Mixing involving multi streams permits a more free way to cross the distillation boundaries, and splitting allows a process stream to go into different operation units for a better efficiency. As demonstrated in Fig. 2, the present method significantly enlarges the feasible area versus Feng et al. (2003) for two reasons. One is that feasible area with only two-stream mixing is the skeleton generated by lines between DN input streams, while feasible area with multi-stream mixing and stream splitting is the whole convex polygon area bounded by lines between DN input streams, as illustrated in Figure 3. The other is that Feng et al. (2003) cannot deal with *isolated points* (Isolated point: lines between a isolated point and other DN input stream point intersect no operation lines after removing self-loop, see Figure 4) and therefore causes unnecessary product loss or purity degradation. Based on above facts, some rules are constructed for the feasibility test of recycle streams from a flowsheet viewpoint. Second, the pre-procedure takes great advantage with large numbers of components involved in the system. Since only distillation and mixing cannot handle perfect separation, which is common in homogeneous systems, detection of unchangeable points before further optimization can determine the recovery limitation of specific component and prepare for using other technologies, such as pressure swing distillation, extractive distillation. Third, A TAC (Total Annualized Cost) objective function is proposed for assessing cost of practical processes and detailed design parameters (i.e., stage number, reflux ratio) can be derived. The TAC is relevant to the stage number and the reflux ratio calculated by a shortcut method proposed by Liu (2004). For simplicity, an alternative linear objective is also used to avoid computational difficulty.

At last, the model results in a mix integer nonlinear program (MINLP). To demonstrate the efficacy of the method, two examples are presented. One is the ethanol-water-toluene system for the purpose of producing anhydrous ethanol (see Figure 5), and the other is the MTBE-methanol-isobutene-butane system for the illustration of multicomponent mixtures (see Figure 6).

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**Literature Cited**

Bagajewicz, M., Pham, R., Manousiouthakis, V. On the state space approach to mass/heat exchanger network design. Chem. Eng. Sci. 1998, 53, 2595.

Gangyi Feng, L. T. Fan, P. A. Seib, Botond Bertok, Levente Kalotai, and Ferenc Friedler. Graph-Theoretic Method for the Algorithmic Synthesis of Azeotropic-Distillation Systems. Ind. Eng. Chem. Res. 2003, 42 (15), 3602¨C3611.

Guilian Liu, Megan Jobson, Robin Smith, and Oliver M. Wahnschafft. Shortcut Design Method for Columns Separating Azeotropic Mixtures. Ind. Eng. Chem. Res. 2004, 43 (14), 3908¨C3923.

Raymond E. Rooks, Vivek Julka, Michael F. Doherty, and Michael F. Malone. Structure of Distillation Regions for Multicomponent Azeotropic Mixtures. AIChE J. 1998, 44 (6), 1382-1391.

Figure 1. An unchangeable point in the topological structure

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Figure 3. Feasible area: (a) Feng et al. (2003); (b) this work

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Figure 4. An isolated point in the flowsheet

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