4308 Ind. Eng. Chem. Res. 2010, 49, 4308–4328 Sequential Approach to Design Batch Distillation Processes for Homogeneous Azeotropic Systems Vincentius Surya Kurnia Adi and Chuei-Tin Chang* Department of Chemical Engineering, National Cheng Kung UniVersity, Tainan 70101, Taiwan, ROC By addressing both flowsheeting and scheduling issues, a systematic approach is developed in this work to design batch azeotropic distillation processes for the homogeneous ternary and quaternary systems. The proposed design strategy is implemented sequentially in three stages. First, an integer program (IP) is formulated for producing the optimal structure of state-task network (STN). A nonlinear program (NLP) is then developed to generate the corresponding material-balance constraints. In the final step, a mixed integer linear programming (MILP) model and a mixed integer nonlinear programming (MINLP) model are constructed for stipulating the optimal short-term and cyclic schedules respectively. The conventional concept of event points is adopted to facilitate the continuous-time representation in these model formulations. The implementation procedure is illustrated with two example systems in this paper. Satisfactory process configurations and production schedules can both be produced in all the cases we have studied so far. 1. Introduction azeotropic distillation processes. Their model was developed with a superstructure called MESH, in which all thermodynami- Distillation is one of the most popular separation methods - cally preferred columns were embedded. Thong and Jobson8 10 used in the chemical process industries. Since it is accomplished proposed a systematic design method to generate not only the mainly by exploiting the difference between the volatilities of azeotropic distillation processes but also their detailed equipment light and heavy keys, it is clearly not possible to break down specifications. A heuristic synthesis procedure was also proposed an azeotrope with a single ordinary distillation operation. In in a later study by Thong et al.11 Feng et al.12 used a graphical practice, this problem may be overcome by using a pressure- technique to identify all possible operations in an azeotropic swing column, or by introducing an entrainer, extracting solvent, or ionic salt, that could change the vapor-liquid equilibrium distillation system by resorting to the first principles and by (VLE) properties. To avoid addressing these diversified issues logically sequencing such units. Additional works were also carried out to combinatorially generate all feasible sequences in one study, the scope of present work is limited to those 13 achieved with entrainers. Furthermore, it is assumed that the via a P-graph-based approach. Finally, advances in the related theories and applications have been thoroughly reviewed by feed and products of a distillation operation are always located 14 within the same region enclosed by distillation boundaries. Doherty and Malone. Notice that this assumption may not hold if one or more Since the aforementioned publications are all concerned with boundary exhibits extreme curvature. However, since the design, the continuous azeotropic distillation processes, it is thus operation and control of the corresponding separation processes desirable to extend the existing design methods for applications can be very difficult, such options are therefore excluded in the in batch systems. To this end, it should be first noted that a present study. large number of generalized scheduling models have already The design of azeotropic distillation processes has always been developed. For example, Papageorgaki and Reklaitis15 been an important research issue. Stichlmair et al.1 evaluated proposed a MINLP model to generate the optimal schedules and developed an entrainer-selection method for any given for multiproduct batch processes; Kondili et al.16 solved this system. Stichlmair and Herguijuela2 later exploited the notion problem with a MILP program; Kim and Moon17 synthesized of preferred separation, which could be used for handling the multipurpose schedules with symbolic model verifier (SMV). mixtures with several azeotropes and complex boundary struc- It is worth noting that the mathematical program reported in tures. It should also be noted that separation techniques other Kondili et al.16 was formulated according to the so-called state- than distillation were also considered in this study. Pham and task network (STN) with discrete-time representation. Ierapet- Doherty3 proposed a framework for synthesizing azeotropic ritou and Floudas18,19 later proposed a STN-based MILP model distillation processes according to estimated minimum reflux for producing an optimal batch schedule. An equivalent resource ratios. Wahnschafft et al.4 employed a concept called “operation task network (RTN) representation was proposed by Pan- leaves” to check split feasibility on the basis of residue curves telides.20 Zhang and Sargent21,22 provided a unified mathemati- 5 and distillation line maps. Fidkowski et al. developed a cal formulation to determine the optimal operating conditions calculation procedure to determine the equilibrium compositions of RTN in continuous-time representation. The STN-based 6 of azeotropes. Fien and Liu presented a detailed review model later became a popular choice for many scheduling concerning the use of ternary composition diagrams and residue applications due to its capability to capture the equipment- curve maps (RCMs) for heuristic synthesis and shortcut design sharing possibilities. Various other mathematical programs have of the multicomponent separation processes. Bauer and Stichl- also been constructed accordingly, e.g., Shah et al.23 and 7 mair formulated a MINLP model to generate the optimal Maravelias and Grossmann.24 An overview of the continuous- * To whom correspondence should be addressed. Tel.: 886-6-275- time versus discrete-time approaches for scheduling multiproduct 25 7575 ext. 62663. Fax: 886-6-234-4496. E-mail: ctchang@ and/or multipurpose batch processes was presented by Floudas. mail.ncku.edu.tw. Finally, a STN-based cyclic scheduling strategy has also been 10.1021/ie100101w 2010 American Chemical Society Published on Web 04/12/2010 Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010 4309 proposed by Wu and Ierapetritou.26 They essentially modified Table 1. Thermophysical Data of the Acetone (A)-Ethanol the aforementioned short-term model18 with additional con- (E)-Chloroform (C) System straints to accommodate the unique requirements in periodic component name boiling point operations. acetone unstable node (low-boiling) 55.86 °C From the above discussions, it is obvious that a specific state- ethanol stable node (high-boiling) 78.02 °C task network must be created before constructing the schedule- chloroform saddle point (intermediate) 60.75 °C generating models. There are in fact an extremely large number Three Azeotropes Sorted by Temperature of alternative means to break up an azeotrope. Since it is azeotrope number 1 mole-basis mass-basis impractical to incorporate all of them in a mathematical program, a systematic screening procedure is needed to select an ethanol 0.141 0.060 59.10 °C appropriate STN first. To this end, any given azeotrope-entrainer chlf 0.859 0.94 system is divided in this study into a finite number of lumped azeotrope number 2 mole-basis mass-basis materials according to a modified version of the classification ° 12 acetone 0.341 0.236 62.52 C method suggested by Feng et al. On the basis of this ethanol 0.200 0.110 classification scheme, all possible operations can then be chlf 0.459 0.653 identified easily by inspection. Although this classification azeotrope number 3 mole-basis mass-basis approach can be applied to both homogeneous and heteroge- neous systems, the scope in the present paper is limited to the acetone 0.381 0.230 64.24 °C former case for the sake of conciseness. Consequently, there chlf 0.619 0.770 can be only two types of feasible batch operations in each case study discussed in this paper, i.e., distillation and mixing. (a) Approximate the critical surfaces and curves, i.e., the The former operation splits one material into two (or more), distillation boundaries and pseudoboundaries, with flat while the latter combines several into one. In fact, a few heuristic planes and straight lines. search techniques have already been proposed to generate a (b) Divide the ternary or quaternary systems into distinct continuous flowsheet on the basis of these feasible operations, triangular areas or pyramid regions based on the ap- e.g., Friedler et al.27-29 It should be noted that multiple feasible proximated boundaries. (but not optimal) solutions of a given design problem may be (c) Carry out further partition to ensure the uniqueness of produced with these approaches.12 To synthesize the “optimal” intermediate products obtained from separation operations. STN structures for the present applications, the logic-oriented The specific partitioning steps for typical ternary and quaternary approach suggested by Raman and Grossmann30,31 has been systems are described with specific examples in the sequel. adopted. In particular, an integer program has been developed 2.1. Lumped Materials in Ternary Systems. Let us con- to represent the inferential relationship and to determine the sider the homogeneous mixture of acetone (A), ethanol (E), and best process configuration. In addition, a nonlinear programming chloroform (C). The thermophysical data presented in Table 1 model has been formulated