Reactor superstructures

Kokossis and Floudas (1994) proposed a superstructure of alternatives for the nonisothermal reactor system and subsequently formulate and solve the synthesis problem according to the proposed general structure. The presented approach is based upon a generalization of the isothermal reactor superstructure by Kokossis and Floudas (1990). The nonisothermal case features altema-... 

Description A popular approach to solving the reactor network synthesis problem is by use of reactor superstructures. A reactor superstructure is a reactor configuration... 

Figure 1.8 (a) A CSTR configuration that approximates a plug flow reactor (PFR). Kauchali et al. (2002). Reproduced with permission of Elsevier, (b) Example of a reactor superstructure. Rooney and Biegler (2000). Reprodnced with permission of Elsevier. 

Two important questions that arise when dealing with the optimization of reactor superstructures thus arise ... 

Superstructure methods. The superstructure approach was briefly mentioned in Chapter 1. A reactor superstructure is designed to approximate the performance characteristics for various scenarios. Combining the superstructure in different arrangements produces a range of outputs that is, in turn, an approximation to the AR. Superstructure methods result in a system of algebraic equations and must be solved using a non-LP method. 

The Total Connectivity Model The connectivity model is a reactor superstructure formulation that attempts to approximate different reactor types using a network of small CSTRs. Combination of CSTRs in series and parallel allows for the approximation of different fundamental reactor types, specificdly ... 

The IDEAS approach is a reactor superstructure method that represents all reactor networks as the combination of two generalized blocks. When the system is viewed in this manner, the resulting equations describing the problem can be made linear. An advantage of this is that traditionally nonlinear reactor network problems may then be solved via an LP technique, such as that described by the LP formulations in Section 8.6.1. And as a result, the solution to the linear system is guaranteed to be globally optimal. 

Basic Idea The IDEAS framework describes a generahzed reactor superstructure that may be used for addressing many reactor network synthesis problems. Construction of a candidate AR occurs by successive solution of a number of LP subproblems for different objective functions. The solution corresponding to each LP problem results in a different point on the AR boundary. Therefore, the computation of candidate ARs is resolved in a point-wise manner. The accuracy of the constraction is determined by the number of unknown variables used in each LP problem, whereas the number of points computed for the AR boundary depends on the number of individual LPs solved. 

Significant recent approaches to chemical reactor network synthesis can be classified into two categories, viz. superstructure optimization and network targeting. In the former, a superstructure is postulated and then an optimal sub-network within it is identified to maximize performance index (Kokossis and Floudas, 1990). 

A reaction is required to be carried out between a gas and a liquid. Two different types of reactor are to be considered an agitated vessel (AV) and a packed column (PC). Devise a superstructure that will allow one of the two options to be chosen. Then describe this as integer constraints for the gas and liquid feeds and products. 

Figure 7.11 Superstructure for two-phase reactions with three reactor compartments in each phase. Mass transfer is only allowed with the corresponding shadow compartment.

Nonisothermal reactors. Nonisothermal operation brings additional complexity to the superstructure approach1112. In the first instance, the optimum temperature... 

Nonisothermal reactors with adiabatic beds. Optimization of the temperature profile described above assumes that heat can be added or removed wherever required and at whatever rate required so that the optimal temperature profile can be achieved. A superstructure can be set up to examine design options involving adiabatic reaction sections. Figure 7.12 shows a superstructure for a reactor with adiabatic sections912 that allows heat to be transferred indirectly or directly through intermediate feed injection. 

As with isothermal reactor design, the optimization of superstructures for nonisothermal reactors can be carried out reliably, using simulated annealing. 

Figure 7.12 Superstructure for a Nonisothermal reactor with adiabatic sections.

The choice of reactor configuration and conditions can also be based on the optimization of a superstructure. Combinations of complexities can be included in the optimization. An added advantage of the approach is that it also allows novel configurations to be identified, as well as standard configurations. 

If a model is available for the reaction chemistry and kinetics, then a temporal superstructure can be developed to represent a batch reactor in the time dimension with a series of reactor compartments that connect to each other sequentially in the time dimension3. This temporal superstructure network, representing a batch reactor, is created... 

Figure 14.2 A temporal superstructure for a well-mixed batch reactor.

Thus, the design equations for a batch reactor for the optimization of a temporal superstructure can be based on differential or algebraic equations. 

Figure 14.3 shows a temporal superstructure for a multiphase batch reactor3. As with the continuous steady state reactors discussed in Chapter 7, mass transfer is only allowed between adjacent reactor compartments. 

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