Equivalent batch structure

Figure 7.34 Comparison between continuous and batch reactive equipment. All three continuous reactors required to form the AR share equivalent batch structure. Adapted from Ming et al. (2013).

Observe that we first determine a candidate region with continuous operation in mind. Only after the continuous AR structures have been determined are they converted to equivalent batch reactor structures. 

The optimal continuous reactors for the BTX system are described in Section 7.2.2. Hence, an equivalent optimal batch structure is then... 

To make the above discussion more concrete, consider the example branching structure of Fig. 3. In this structure, we have identified an x and y, which have the same objective function values, and their ancestors, (x, y) which are characterized by the same set of symbols, (i.e., batches). Furthermore, we can see that the children of x,y do indeed satisfy the requirements of Condition-a and Condition-b and hence, (x, y) would be considered as candidates to develop a new equivalence relationship. If we examine the partial schedules (x, y) as depicted in Fig. 6, our knowledge... 

Multiple Steady States We have seen that multiple steady states are often observed in CSTRs, and fed-batch reactors may exhibit the same behavior for an equivalent fixed a policy and sidestream feed composition. Thus, care must be taken in the choice of equilibrium concentration applied, as rather different outcomes in performance may arise, even when the correct optimal structure belonging to the AR is enforced. Additional information on multiple steady states in CSTRs can be found in (Gray and Scott, 1984, 1983 Schlosser and Feinberg, 1994). 

Caprolactam for use as fibers is hydrolytically polymerized in batches as 80%-90% aqueous solutions with 0.2%-0.5% acetic acid and ethylene diamine at 250-280° C. The acetic acid acts as chain stabilizer (see above). The ethylene diamine increases the amine equivalent of PA 6 so that mixed weaves of Perlon and wool can be evenly dyed. The water is removed as steam in the polymerization progresses. Caprolactam is also polymerized continuously by what is known as the VK process (vereinfacht-A ontinuierliche, or simplified continuous, process). This process is carried out without pressure with, for example, 6-amino caproic acid or AH salt as initiator. In contrast to the production of nylon 6,6, this process can proceed continuously the melt can be directly spun from the reactor. Polyamide 6 fibers have good properties but they yellow slowly since pyrrole structures are formed at the chain ends. 

Strictly speaking, the dynamical inverse (Eq. 14) of the batch process has RD s = 2, and its observer-based approximation has primary and secondary components with RD s = 1, or equivalently, the approximated inverse has been passivated with respect to the input-output cascade structure (Eq. 2). 

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