All of the arguments presented for a single reaction apply to the primary reaction in a multiple reaction system. Besides suffering the losses described for single reactions, multiple reaction systems also form waste by-products in secondary reactions.
The correct type of reactor must be selected. The CPI uses a variety of reactor types, but most emulate one of three ideal models used in reaction kinetic design theory: the ideal-batch, continuous well-mixed, and plug-flow models (see Figure 3.7.2). In ideal-batch and plug-flow reactors, material spends the same time in the reactor. By contrast, in the continuous well-mixed reactor, the residence time is widely distributed. A series of continuous well-mixed reactors approaches the plug-flow reactor in behavior.
The differences in mixing characteristics between ideal-batch and plug-flow reactors and ideal-batch and continuous well-mixed reactors can significantly effect waste minimization in multiple reaction systems.
In the continuous well-mixed reactor, the incoming feed is instantly diluted by the product which has been formed. Thus, an ideal-batch or plug-flow reactor maintains a higher average concentration of feed than a continuous well-mixed reactor.
As shown in the two sets of parallel reactions in Table 3.7.1, the feed material can react either to the PRODUCT or in parallel to the WASTE BY-PRODUCT. By looking at the ratio of the rates of the secondary and primary reactions in Table 3.7.1, the chemical engineer can choose conditions to minimize that ratio.
For some two-feed reaction systems (as shown in Table 3.7.1), semibatch and semiplug-flow processes can be used. In a semibatch process, the reactor is charged with one of the feeds at the start of the reaction, and the other feed is added gradually. The semiplug-flow scheme uses a series of well-mixed reactors, and one of the feeds is charged gradually as the reaction progresses.
Instead of the parallel reactions shown in Table 3.7.1, reactions can also be in series. This reaction system with its corresponding rate equations is as follows:
In this reaction system, the FEED reacts to the PRODUCT without any parallel reactions, but the PRODUCT continues to react in series to the WASTE BY-PRODUCT. If the FEED's residence time in the reactor is too short, insufficient PRODUCT is formed. However, if the FEED remains in the reactor too long, this excess time increases its chances of becoming WASTE BY-PRODUCT. Thus, the FEED should ideally have a fixed, well-defined residence
Rate equations r1 = -MCfeed]31
ri = ki [CFEED i]ai [CFEED 2]bl r2 = k2[ Cfeed i]a2[ CFEED 2]02
Ratio to minimize f = f[CFEED]a2-ai
T2 = kk2[CFEED, i]a2 ai [Cfeed, 2]b2-b' ri ki a2 > ai
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