Page 480 - Elements of Chemical Reaction Engineering Ebook

Sec. 8.3 Nonisothermal Continuous-Flow Reactors 451

The POLYMATH program and solution to Equations (E8-4.13), XM~, and
(E8-5.4), X,,, are given in Table E8-5.1. The exiting temperature and conversion are
103.7"F (563.7 R) and 36.4%, respectively.

8.3.2 Adiabatic Tubular Reactor

The energy balance given by Equation (8-48) relates the conversion at
any point in the reactor to the temperature of the reaction mixture at the same
point (i.e., it gives X as a function of T). Usually, there is a negligible amount
of work done on or by the reacting mixture, so normally, the work term can be
neglected in tubular teactor design. However, unless the reaction is carried out
adiabatically, Equation (8-48) is still difficult to evaluate, because in nonadia-
batic reactors, the heat added to or removed from the system varies along the
length of the reactor. This problem does not occur in adiabatic xeactors, which
are frequently found in industry. Therefore, the adiabatic tbbular reactor will
be analyzed first.
Because Q and Ws are equal to zero for the reasons stated above, Equation
(8-47) reduces to

Energy balance for
adiabatic operation (8-53)
of PFR
I I
This equation cain be combined with the differential mole balance

dX
F*o - = - r*(X, T)
dV
to obtain the temperature, conversion, and concentration profiles along the
length of the reactor. One way of accomplishing this combination is to use
Equation (8-53) 1.0 construct a table of T as a function of X. Once we have T
as a function of X, we can obtain k(T) as a function of X and hence -rA as a
function of X alone. We then use the procedures detailed in Chapter 2 to size
the different types of reactors.
The algorithm for solving PFRs and PBRs operated adiabatically is shown
in Table: 8-2.