Optimization of superstructures

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

One of the approaches that can be used in design is to carry out structural and parameter optimization of a superstructure. The structural optimization required can be carried out using mixed integer linear programming in the case of a linear problem or mixed integer nonlinear programming in the case of a nonlinear problem. Stochastic optimization can also be very effective for structural optimization problems. 

When optimizing a superstructure for a multiphase reaction, the rate of mass transfer must be specified. This will, to a large extent, be determined by the design of the equipment. Yet, the objective of the superstructure... 

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. 

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. 

Consider now ways in which the best arrangement of a distillation sequence can be determined more systematically. Given the possibilities for changing the sequence of simple columns or the introduction of prefractionators, side-strippers, side-rectifiers and fully thermally coupled arrangements, the problem is complex with many structural options. The problem can be addressed using the optimization of a superstructure. As discussed in Chapter 1, this approach starts by setting up a grand flowsheet in which all structural features for an optimal solution are embedded. 

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. 

Figure 18.28 Heat exchanger network design from the optimization of a superstructure.

Figure 18.32 If the solution from the optimization of a simplified superstructure features parallel branches, then add additional structural features and re-optimize.

For more complex network designs, especially those involving many constraints, mixed equipment specifications and so on, design methods based on the optimization of a superstructure can be used. 

HEAT-INTEGRATED DISTILLATION SEQUENCES BASED ON THE OPTIMIZATION OF A SUPERSTRUCTURE... 

Thus, the introduction of constraints and complex columns demands a simultaneous solution of the sequencing and heat recovery problems. This can be carried out on the basis of the optimization of a superstructure. 

Targeting and Design for Maximum Water Reuse Based on Optimization of a Superstructure 605... 

To include all of these complexities requires a different approach from the one described so far. The design approach based on the optimization of a superstructure can be used to solve such problems14. Figure 26.36 shows the superstructure for a problem involving two operations and a single source of fresh water14. The superstructure allows for reuse from Operation 1 into Operation 2, reuse from Operation 2 to Operation 1, local recycles around both operations, fresh water supply to both operations and... 

As with the case for water minimization, the graphical methods used for effluent treatment and regeneration have some severe limitations. As before, multiple contaminants are difficult to handle, constraints, piping and sewer costs, multiple treatment processes and retrofit are all difficult to handle. To include all of these complications requires an approach based on the optimization of the superstructure. 

In this way, the analyses for reuse only, regeneration reuse, regeneration recycling and effluent treatment for discharge can all be examined simultaneously by the optimization of the superstructure in Figure 26.55. 

Maximum water reuse can be identified from limiting water profiles. These identify the most contaminated water that is acceptable in an operation. A composite curve of the limiting water profiles can be used to target the minimum water flowrate. While this approach is adequate for simple problems, it has some severe limitations. A more mathematical approach using the optimization of a superstructure allows all of the complexities of multiple contaminants, constraints, enforced matches, capital and operating costs to be included. A review of this area has been given by Mann and Liu21. 

Figure 28.9 Waste minimization projects can be traded off against treatment options by optimization of a superstructure. 

Yeomans, H. and Grossmann, I.E. (1999) A systematic modeling framework of superstructure optimization in process synthesis. Computers el Chemical Engineering, 23, 709. 

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