Design Equations and Auxiliary Relations

The differential design equation of an ideal batch reactor, written for the mth-independent reaction, was derived in Section 4.4  

Recall fliat is the dimensionless extent of the mth-independent chemical reaction defined hy 

As discussed in Chapter 4, in order to describe the operation of a reactor with multiple chemical reactions, we have to write the design equation (Eq. 6.1.1) for each independent chemical reaction. Also, to solve the design equations (to obtain relationships between Z s and t), we have to express V/ (t) and the rates of the chemical reactions, r s and r s, in terms of Z s, and t. The auxiliary relations needed to express the design equations explicitly in terms of Z s, and T, are derived next. 

The volume-based rate of the idi chemical reaction, is generally expressed by (see Section 3.3) 

Using Eq. 2.7.3, the molar content of species j in the reactor at operating time t is 

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For convenience, Tables A.3a and A.3b in Appendix A provide the design equations and auxiliary relations used in the design of plug-flow reactors. Table A.4 provides the energy balance equation. 

In this chapter, we anidyze the operation of ideal batch reactors. In Section 6.1, we review how the design equations are utilized and discuss the auxiliary relations that should be incorporated in order to solve the design equations. In the rest of the... 

To solve the design equations, we have to express the rates of a// the chemical reactions in terms of Z s and t. Below, we derive the auxiliary relations that relate the species concentrations to Z s and t. 

The design equations, the energy balanee equation, and the auxiliary relations for species concentrations. 

In this chapter, the analysis of chemical reactors is expanded to additional reactor configurations that are commonly used to improve the yield and selectivity of the desirable products. In Section 9.1, we analyze semibatch reactors. Section 9.2 covers the operation of plug-flow reactors with continuous injection along their length. In Section 9.3, we examine the operation of one-stage distillation reactors, and Section 9.4 covers the operation of recycle reactors. In each section, we first derive the design equations, convert them to dimensionless forms, and then derive the auxiliary relations to express the species concentrations and the energy balance equation. 

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