# 7.11: Untitled Page 156

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## Chapter 7

unconverted gas is recycled to the reactor through a *mixer*. In order to avoid the buildup of argon in the system, a purge stream is required and this gives rise to a *splitter* as illustrated in Figure 7‐5. If the argon is not removed from the system by the splitter, the concentration of argon will *increase* and the efficiency of the reactor will *decrease*. The characteristics of splitters are discussed in detail in Sec. 7.3.1.

*Figure 7‐4*. Catalytic reactor with recycle

There are several methods for analyzing recycle systems. One approach, which we discuss first, is an extension of the method used previously. A set of control volumes is constructed and Axioms I and II are applied to those control volumes. Because more than one control volume is required, the most appropriate choice of control volumes is not always obvious. In previous chapters, we have discussed a set of rules or guidelines to be used in the construction of control volumes. Here we repeat those rules with the addition of one new rule that is important for the analysis of systems with recycle streams.

**Rule I**. Construct a *primary cut* where information is *required*.

**Rule II**. Construct a *primary cut* where information is *given*.

**Rule III**. Join these cuts with a surface located where **v ** **n ** is *known*.

*A*

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**Rule IV**. When joining the primary cuts to form control volumes, minimize the number of new or *secondary cuts* since these introduce information that is neither given nor required.

**Rule V**. Be sure that the surface specified by Rule III encloses regions in which volumetric information is either *given* or *required*.

**Rule VI**. When joining the primary cuts to form control volumes, minimize the number of *redundant cuts* since they provide no new information.

If one follows these rules carefully and if one pays careful attention to the associated degree‐of‐freedom analysis, the solution of many problems is either easy or impossible.

*Figure 7‐5*. Recycle stream in an ammonia converter

*7.3.1 Mixers and splitters *

Mixers and splitters are a natural part of recycle systems, and one must pay careful attention to their properties. In Figure 7-6 we have illustrated a mixer in which *S* streams

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