Reaction-Based Design Equations

To analyze and design chemical reactors more effectively and to obtain insight into the operation, we adopt reaction-based design formulation. In this section, we derive the reaction-based design equations for the three ideal reactor models. Reaction-based design equations of other reactor configurations are derived in Chapter 9. 

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Equation 4.3.8 is the reaction-based, differential design equation of an ideal batch reactor, written for the mth-independent reaction. As will be discussed below, to describe the operation of a reactor with multiple chemical reactions, we have to write Eq. 4.3.8 for each of the independent reactions. Note that the reaction-based design equation is invariant of the specific species used in the derivation. For an ideal batch reactor with a single chemical reaction, Eq. 4.3.8 reduces to... 

Equation 4.3.22 is the reaction-based design equation for CSTRs, written for the mth-independent reaction. To describe the operation of the reactor with multiple reactions, we have to write Eq. 4.3.22 for each independent reaction. 

The reaction-based design equations derived in the previous section are expressed in terms of extensive quantities such as reaction extents, reactor volume, molar flow rates, and the like. To describe flie generic behavior of chemical reactors, we would like to express the design equations in terms of intensive, dimensionless variables. This is done in two steps ... 

Equation 4.4.4 is die dimensionless, reaction-based design equation of an ideal batch reactor, written for die mth-independent reaction. The factor ( / Co) is a scaling factor that converts die design equation to dimensionless form. Its physical significance is discussed below (Eqs. 4.4.13-4.4.15). 

To reduce the reaction-based design equation of a plug-flow reactor to dimensionless form, we differentiate Eqs. 4.4.5 and 4.4.8,... 

The formulation of the reaction-based design equations is illustrated in the three examples below. Example 4.1 shows how a case that is conventionally formulated in terms of 4 species-based design equations with 16 terms is formulated here in terms of 3 reaction-based design equations with 6 terms. Example 4.3 illustrates how, by adopting the heuristic rule on selecting a set of independent reactions, we formulate the design by the most robust set of equations. 

Species B is the desired product. Formulate the reaction-based design equations, expressed in terms of the reaction rates, for ... 

Adams et al. (/. Catalysis 3, 379, 1964) investigated these reactions and expressed the rate of each as second order (first order with respect to each reactant). Formulate the dimensionless, reaction-based design equations for an ideal batch reactor, plug-flow reactor, and a CSTR. 

Formulate the dimensionless, reaction-based design equations for ideal batch reactor, plug-flow reactor, and CSTR using the heuristic rule. ... 

We derived the reaction-based design equations for three ideal reactors. 

We converted the reaction-based design equations to dimensionless forms that, upon solution, provide the dimensionless operating curves. 

Equation 5.2.18 is the dimensionless, differential energy balance equation of ideal batch reactors, relating the reactor dimensionless temperature, 0(t), to the dimensionless extents of the independent reactions, Z (t), at dimensionless operating time T. Note that individual dZ /dfr s are expressed by the reaction-based design equations derived in Chapter 4. 

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