Page 111 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 3.i! Present Status of Our Approach to Reactor Sizing and Design 83
- [ mass 1 [ moles 1 (3-22)
-rA = Pb(-rA)

moles -- --
time e volume volume time a mass
In fluidized catalytic beds the bulk density is normally a function of the Bow
rate thirough the bed.

3.2 Present (Status of Our Approach
to Reactor Sizing and Design

In Chapter 2 we showed how it was possible to size CSTRs, PFRs, and PBRs
using the design equations in Table 3-1 if the,.rate of disappearance of '4 is
known as a function of conversion, X:

-rA = g

TABLE 3-1. DESIGN EQUATIONS
Differential Algebraic Integral
Form Form Form

dX dX
Batch NAo .- = -rAV (2-6) t= NAo -
(2-9)
dt io -rAV
Backmix.
The design (CSTR)
equations
dX
V= FA0 1 - (2-16)
o -rA
Packed bed dX w = FA,/ - (2- 18)
dX
-
(PBN FAO - = -ra (2-17) o -ra
dW
In general, information in the form -rA = g(X) is not available. However, we
have seen in Section 3.1 that the rate of disappearance of A, -rA, is normally
expressed in terms of the concentration of the reacting species. This functionality,
-rA = k[fn(C,,C,, ...)I (3- 1)
-rA. = f(C,)
+ is called a rate lmv. In Section 3.3 we show how the concentration of the react-
ing species may be written in terms of the conversion X,
c, = h, (XI
I c, = h, (X)
-'A = g(x)
and then we can With thlese additiional relationships, one observes that if the rate law is given
design isothermal and the concentrations can be expressed as a function of conversion, then in
reactors fact we have -rli as a function of X and this is all that is needed to evaluate
the design equations. One can use either the numerical techniques described in
Chapter 2, or, as we shall see in Chapter 4, a table of integrals.