Page 459 - Elements of Chemical Reaction Engineering Ebook

430 Steady-State Nonisothermal Reactor Design Chap. 8

Combining Equations (8-5), (8-7), and (8-8), we can now write the energy bal-’
ance in the form

The energy of the system at any instant in time, ksys, is the sum of the
products of the number of moles of each species in the system multiplied by
their respective energies. This term will be discussed in more detail when
unsteady-state reactor operation is considered in Chapter 9.
We shall let the subscript “0” represent the inlet conditions. Unsub-
scripted variables represent the conditions at the outlet of the chosen system
volume.

(8-9)

To put this equation in a more applicable form, there are two items to dissect:

1. The molar flow rates, Fi and Fjo
2. The molar enthalpies, H,, Hio [H, = H, (T), and Hio E Hi (To)]

CD-ROM animation An animated version of what follows for the derivation of the energy bal-
ance can be found in the reaction engineering modules “Heat Effects i” and
“Heat Effects 2” on the CD-ROM.

8.2.3 Dissecting the Steady-State Molar Flow Rates
to Obtain the Heat of Reaction

We will now consider flow systems that are operated at steady state. The
steady-state energy balance is obtained by setting (dh:,,ldt) equal to zero in
Equation (8-9) in order to yield

n n
Steady-state (8-10)
energy balance

To carry out the manipulations to write Equation (8-10) in terms of the heat of
reaction we shall use the generalized reaction

b c d
A+-B ----+ -C+-D ‘(2-2)
a a a
The inlet and outlet terms in Equation (8-10) are expanded, respectively, to: