Synthesis of Optimal Chemical Reactor Networks

Networks C. A. Schweiger and C. A. Floudas1 Department of Chemical Engineering, Princeton University, Princeton, NJ 08544-5263, USA Abstract{The synthesis of optimal reactor networks using a superstructure based approach is considered. The fundamental units in the superstructure are the continuous stirred tank reactor (CSTR) and a cross ow reactor (CFR). The mathematical modeling leads to an optimal control formulation which is solved using a control parameterization technique. The approach is applicable to general reaction mechanisms and is applied to a complex nonisothermal reaction problem. INTRODUCTION The goal of reactor network synthesis is to determine the types, sizes, and operating conditions of the reactor units as well as the interconnections among them which transform the given raw materials into the desired products. Previous approaches for addressing this problem can be classi ed as either superstructure based methods or targeting methods. The superstructure based methods employ a xed reactor network which includes all the possible networks of interest. This approach was rst introduced by Jackson (1968) who postulated a network of parallel plug ow reactors (PFRs) interconnected with sidestreams. Further developments were made by Achenie and Biegler (1986, 1990) where nonlinear programming techniques were used to solve the problem. A reactor network superstructure incorporating continuous stirred tank reactors (CSTRs) and PFRs with various interconnections was considered by Kokossis and Floudas (1990, 1991, 1994). The PFRs were approximated by a series of equal-sized sub-CSTRS and integer variables were used to represent the existence of the reactor units. The resulting formulation was a large-scale, complex, nonconvex mixed-integer nonlinear program (MINLP). One of the limitations of the superstructure approach is that the solution obtained is only as rich as the proposed superstructure. Increasing the richness comes at the cost of increasing the complexity of the model. To address this issue, targeting approaches were developed based on the attainable region concept rst introduced by Horn (1964). The attainable region is the set of all possible conditions that can be obtained through reaction and mixing. These methods determine a target on the performance index for the reactor network regardless of the reactor types and con guration. These techniques were explored as geometric problems by Glasser et al. (1987), Hildebrandt et al. (1990), and Hildebrandt and Glasser (1990). Mathematical programming techniques for the targeting approach were explored by Balakrishna and Biegler (1992a,b). This work focuses on addressing two disadvantages of the superstructure based approaches: the large, complex formulations and the approximation of the PFR by algebraic models. The PFR is modeled using di erential equations and di erential sidestreams are used to enhance the richness of the superstructure. The mathematical modeling leads to an optimal control problem which is solved using a control parameterization technique. REACTOR NETWORK SUPERSTRUCTURE The reactor network superstructure must be su ciently rich without becoming unnecessarily complicated. Feinberg and Hildebrandt (1997) showed that the only reactor types that are required to achieve all possible compositions for a given reaction are the PFR, CSTR, and di erential sidestream reactor. Thus, the reactor network design is a question of how to incorporate traditional reactors and not a speculation of alternative devices. The fundamental reactor units considered are the CSTR and a cross ow reactor (CFR) unit. The CFR shown in Figure 1 is a PFR with di erential entering and leaving sidestreams. The reactor network superstructure consists of the CSTR and CFR units along with mixers and splitters and is based on the principles discussed in Floudas (1995) and Schweiger and Floudas (1998).