Reactor superstructure optimization

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). 

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

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. 

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. 

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. 

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

Thus, the design of a batch reactor can be based on the optimization of a temporal superstructure. Given a simulation model with a mathematical formulation, the next step is to determine the optimal values for the control variables of a batch reaction system. 

If the rate of feed addition, rate of product takeoff, temperature and pressure are known in each time interval, a simulation of the reactor can be carried out in that time interval. The problem is that the conditions will change from one time interval to subsequent time intervals. The profile of the dynamic variables (feed addition, product takeoff, temperature and pressure) need to be known through time. In the approach described in Chapter 3 for profile optimization5, a shape can be imposed for a given variable through time and the dynamic variables optimized in conjunction with the temporal superstructure. One profile for each dynamic variable is assigned to the... 

To determine a reactor network that optimizes the performance index (e.g., maximizes yield) out of the many embedded alternatives in the superstructure of Figure 10.2, we define variables for... 

Kokossis and Floudas (1994) extended the MINLP approach so as to handle nonisothermal operation. The nonisothermal superstructure includes alternatives of temperature control for the reactors as well as options for directly or indirectly intercooled or interheated reactors. This approach can be applied to any homogeneous exothermic or endothermic reaction and the solution of the resulting MINLP model provides information about the optimal temperature profile, the type of temperature control, the feeding, recycling, and by-passing strategy, and the optimal type and size of the reactor units. 

While these optimization-based approaches have yielded very useful results for reactor networks, they have a number of limitations. First, proper problem definition for reactor networks is difficult, given the uncertainties in the process and the need to consider the interaction of other process subsystems. Second, all of the above-mentioned studies formulated nonconvex optimization problems for the optimal network structure and relied on local optimization tools to solve them. As a result, only locally optimal solutions could be guaranteed. Given the likelihood of extreme nonlinear behavior, such as bifurcations and multiple steady states, even locally optimal solutions can be quite poor. In addition, superstructure approaches are usually plagued by the question of completeness of the network, as well as the possibility that a better network may have been overlooked by a limited superstructure. This problem is exacerbated by reaction systems with many networks that have identical performance characteristics. (For instance, a single PFR can be approximated by a large train of CSTRs.) In most cases, the simpler network is clearly more desirable. 

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