Differential reactor, ideal design

As with the batch reactor, the design equations in differential form for the PFR must be integrated to solve engineering problems. The same three possibilities that woe discussed for the batch reactor also exist here, except that the variable of time for the batch reactor is replaced by position in the direction of flow for the ideal PFR. For Case 3, where ttie reactor is either isothermal or adiabatic, Eqns. (3-26) and (3-27) can be integrated symbolically to give... 

To illustrate this idea, consider a reactor that is packed with catalyst particles. A fluid containing the reactant(s) flows through the fixed bed of particles. The reactor could be a differential reactor, as described in Chapter 6, or it could be an integral, ideal plug-flow reactor. Let s consider the PFR. The design equation is... 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

In the inertial microbalance, the mass located at the tip of an oscillating tapered quartz element is detected as a change in its vibrational frequency. The design of this equipment provides a packed bed of catalyst through which all the gas is forced to flow, and the classical methods of testing for differential operation in an ideal plug-flow fixed-bed reactor can therefore be applied. 

For an ideal batch reactor, the differential form of the design equation for... 

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 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. 

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

The design formulation of nonisothermal batch reactors consists of + 1 nonlinear first-order differential equations whose initial values are specified. The solutions of these equations provide Z s and 6 as functions of t. The examples below illustrate the design of nonisothermal ideal batch reactors. 

This is the differential design equation for a distillation reactor, written for the mth-independent chemical reaction. Note that Eq. 9.3.2 is identical to the design equation of an ideal batch reactor. The difference between the two cases is in the variation of the reactor volume and species concentrations during the operation. 

DIFFERENTIAL FORM OF THE DESIGN EQUATION FOR IDEAL PACKED CATALYTIC TUBULAR REACTORS WITHOUT INTERPELLET AXIAL DISPERSION... 

Equation (3-5) is referred to as the design equation for an ideal batch reactor, in differential form. This equation is valid no matter how many reactions are taking place, provided that Eqn. (1-17) is used to express r/, and provided that all of the reactions are homogeneous. 

Equations (3-26)-(3-28) are various forms of the design equation for a homogeneous reaction in an ideal, plug-flow reactor, in differential form. The equivalents of Eqns. (3-26)-(3-28) for a heterogeneous catalytic reaction are given in Appendix 3.Ill A as Eqns. (3-26a), (3-27a), and (3-28a). Be sure that you can derive them. 

Let s begin with reactant A and perform a material balance over a differential element of the reactor, as shown in Figure 7-4. This is the same control volume that we used to derive the design equation for an ideal PFR in Chapter 3. 

The analyses of an ideal batch reactor and an ideal PFR are essentially identical, so let s illustrate with the PFR. The design equation for an ideal PFR in differential form is... 

The problem of evaluating the influence of pore diffusion on an experimental result can be simplified through some transformations of the previous equations. Suppose that a reaction rate has been measured in some kind of experimental reactor, preferably an ideal CSTR or a differential PFR. From the experimental data, a rate of reaction per unit of geometrical catalyst volume, designated —Ra,y, can be calculated. The v in the subscript indicates that this is a volumetric raLtc of reaction. The measured rate (—Ra.v) is not necessarily the same as the intrinsic rate, expressed on a volumetric basis (—rA,v)-The measured rate may reflect internal transport effects, whereas the intrinsic rate does not. 

In this discussion, the design of diagnostic experiments and the analysis of the resulting data have been illustrated for an ideal PFR operating at relatively high conversion. However, the concepts discussed apply equally well to a fixed-bed reactor operating in the differential mode. 

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