Page 69 - Elements of Chemical Reaction Engineering Ebook

40 Conversiori and Reactor Sizing Chap. 2

FA = FA0 - FA0 X (2- 10)

Substituting Equation (2-10) into (2-14) gives the differential fom of the
design equation for 1 plug-flow reactor:

Desinn
-+!--A- (2- 15)
equation
I I
We now separate the variables and integrate with the limit V = 0 when X = 0
to obtain the plug-flew reactor volume necessary to achieve a specified conver-
sion X:

(2-16)

To carry out tbe integrations in the batch and plug-flow reactor design
equations (2-9) and (2-15>, as well as to evaluate the CSTR design equation
(2-13), we need to know how the reaction rate -rA varies with the concentra-
tion (hence conversion) of the reacting species. This relationship between reac-
tion rate and concentration is developed in Chapter 3.

Packed-Bed Reactor. The derivation of the differential and integral forms of
the design equations for a packed-bed reactor are analogous to those for a PFR
[cf. Equations (2-15) and (2-16)]. That is, substituting for FA in Equation
(1-13) gives

PBR design (2- i7)
equation

The differential form of the design equation [i.e., Equation (2-17)] must be
used when analyzing reactors that have a pressure drop along the length of the
reactor. We discuss pressure drop in packed-bed reactors in Chapter 4.
Integrating with the limits W = 0 at X = 0 gives

I I
(2-18)

Equation (2-18) can be used to determine the catalyst weight W necessary to
achieve a conversion X when the total pressure remains constant.

2.3 Applications of the Design Equstions
for Continuous-Flow Reactors

The rate of disappearance of A, -rA, is almost always a function of the con-
centrations of the various species present. When a single reaction is occurring,