Optimal multiple reactor system

Dynamic Modeling of Molecular Weight and Particle Size Development and Application to Optimal Multiple Reactor System Design... 

Pollock, M. J., MacGregor, J. F., and Hamielec, A. E. (1981) Continuous poly (vinyl acetate) emulsion polymerization reactors dynamic modeling of molecular weight and particle size development and application to optimal multiple reactor system design. Computer Applications in Applied Polymer Science, (ed. T. Provder), ACS, Washington, pp. 209-20. 

Reactor systems that can be described by a yield matrix are potential candidates for the application of linear programming. In these situations, each reactant is known to produce a certain distribution of products. When multiple reactants are employed, it is desirable to optimize the amounts of each reactant so that the products satisfy flow and demand constraints. Linear programming has become widely adopted in scheduling production in olefin units and catalytic crackers. In this example, we illustrate the use of linear programming to optimize the operation of a thermal cracker sketched in Figure E 14.1. 

There are a number of different reactor systems which can be used to evaluate catalysts and optimize catalytic reactions, but most of the commercially available units are rather large. Reactions run in these systems, because of their size, usually need large amounts of catalyst and substrate so they are not very economical. Further, the time needed for reactor cooling, product removal and recharging for multiple use of the same catalyst can be rather long. It would seem that a more facile approach would be to use smaller reactors for diese purposes. 

These numbers show that the optimal economic steady-state design is the multiple-stage reactor system. The higher the conversion, the larger the economic incentive to have multiple stages. At 95 percent conversion, the capital cost of a three-CSTR process is 67 percent that of a one-CSTR process. At 99 percent conversion, the cost is only 38 percent. Thus, if only steady-state economics is considered, the design of choice in these numerical cases is a process with two or three CSTRs in series. 

There are innumerable industrially significant reactions that involve the formation of a stable intermediate product that is capable of subsequent reaction to form yet another stable product. These include condensation polymerization reactions, partial oxidation reactions, and reactions in which it is possible to effect multiple substitutions of a particular functional group on the parent species. If an intermediate is the desired product, commercial reactors should be designed to optimize the production of this species. This section is devoted to a discussion of this and related topics for reaction systems in which the reactions may be considered as sequential or consecutive in character. 

We noted earlier that chemical engineers are seldom concerned with single-reaction systems because they can always be optimized simply by heating to increase the rate or by finding a suitable catalyst [You don t need to hire a chemical engineer to solve the problems in Chapter 3]. Essentially aU important processes involve multiple reactions where the problem is not to increase the rate but to create a reactor configuration that will maximize the production of desired products while rninirnizing the production of undesired ones. 

As noted in the introduction, a major aim of the current research is the development of "black-box" automated reactors that can produce particles with desired physicochemical properties on demand and without any user intervention. In operation, an ideal reactor would behave in the manner of Figure 12. The user would first specify the required particle properties. The reactor would then evaluate multiple reaction conditions until it eventually identified an appropriate set of reaction conditions that yield particles with the specified properties, and it would then continue to produce particles with exactly these properties until instructed to stop. There are three essential parts to any automated system—(1) physical machinery to perform the process at hand, (2) online detectors for monitoring the output of the process, and (3) decision-making software that repeatedly updates the process parameters until a product with the desired properties is obtained. The effectiveness of the automation procedure is critically dependent on the performance of these three subsystems, each of which must satisfy a number of key criteria the machinery should provide precise reproducible control of the physical process and should carry out the individual process steps as rapidly as possible to enable fast screening the online detectors should provide real-time low-noise information about the end product and the decision-making software should search for the optimal conditions in a way that is both parsimonious in terms of experimental measurements (in order to ensure a fast time-to-solution) and tolerant of noise in the experimental system. 

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. 

Figure 5.4 displays the results of the new objective function. The new objective function may be written as a straight-line equation as a function of c. The line has a gradient of 0.25 and an intercept of 0.15moI/L. Thus, the line intersects the boundary at two points, labeled Xj and x2, respectively, in Figure 5.4. Since these points coincide with the AR boundary and the objective function, they are the optimal operating points. Hence there are multiple optima for the given objective— there are in fact an infinite number of optimal operating points for this system, for all eoncentrations on the mixing line joining Xj and Xj also satisfy the objective function. Point X3 is a representative point that satisfies this relation. The following three optimal reactor structures may be formulated that satisfy the objective function ...

Godorr, S.A., Hildebrandt, D., Glasser, D., 1994. The attainable region for systems with mixing and multiple-rate processes finding optimal reactor structures. Chem. Eng. J. Biochem. Eng. J. 54,175-186. 

The alternative to traditional scale-up, proposed in the context of microreaction technology and coined scale-out or numbering-up , has attracted considerable academic interest. With this approach, the system of interest is studied only on a small scale in so-called microreactors and the final reactor design is simply a multiplication of interconnected small-scale devices. No attempt is made at large-scale optimization. Instead, the optimal functioning point is found for a small-scale device by empirical laboratory studies and then is simply reproduced by replication into the large interconnected structure. 

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