Isothermal Operations with Single Reactions

When a single chemical reaction takes place in the reactor, the operation is described by a single design equation, and Eq. 6.1.1 reduces to 

The solution of the design equation, Z(t) versus t, provides the dimensionless reaction operating curve of the reactor. It describes the progress of the chemical reaction with time. Furthermore, once Z(t) is known, we can apply stoichiometric relation (Eq. 6.1.7) to obtain the composition of each species at time t. Also, if one prefers to express the design equation in terms of the actual operating time t, rather than the dimensionless time t, using Eq. 6.1.3, the design equation becomes 

Note that Eq. 6.2.1 has three variables the operating time t, the reaction extent Z, and the reaction rate r. The design equation is applied to determine any one of these variables when the other two are known. A typical design problem involves the determination of the operating time necessary to obtain a specified extent for a given reaction rate. The second application involves the determination of the extent obtained in a specified operating time t for a given reaction rate. The third application involves the determination of the reaction rate when the extent is provided as a function of time. Below, we will consider each of these applications. 

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To solve the design equation, we have to express the reaction rate r in terms of Z and, to do so we relate the species concentrations to the dimensionless extent From Eq. 6.1.11, for isothermal operations with single reactions, and when the reference state is the initial state ... 

Derived the dimensionless design equation for isothermal operation with single reactions and obtained the reaction operating curve. 

We start the analysis of plug-flow reactors by considering isothermal operations with single reactions. For isothermal operations, rf0/rfT = O, and we have to solve only the design equations. The energy balance equation provides the heating (or cooling) load necessary to maintain isothermal conditions. Furthermore, for isothermal operations, the reaction rate depends only on the species concentrations, and Eq. 7.1.5 reduces to... 

In the remainder of the chapter, we discuss how to apply the design equations and the energy balance equations to determine various quantities related to the operations of CSTRs. In Section 8.2 we examine isothermal operations with single reactions to illustrate how the rate expressions are incorporated into the design equation and how rate expressions are determined. In Section 8.3, we expand the analysis to isothermal operations with multiple reactions. In Section... 

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