Page 469 - Elements of Chemical Reaction Engineering Ebook

440 Steady-State Nonisothermal Reactor Design Chap. 8

where a is the heat-exchange area per unit volume of reactor. The variation in
heat added along the reactor length (i.e., volume) is found by differentiating
with respect to V:

Heat transfer to a 1 2 = Ua(T,-T) (8-44)
PFR

For a tubular reactor of diameter D,

4
a= -
D
For a packed-bed reactor, we can write Equation (8-44) in terms of catalyst
weight by simply dividing by the bulk catalyst density

(8-45)

Recalling dW = pb dV then

Heat transfer to a (8-46)
PBR

8.3 Nonisothermal Continuous-Flow Reactors
In this section we apply the general energy balance [Equation (8-22)] to the
CSTR and to the tubular reactor operated at steady state. We then present
example problems showing how the mole and energy balances are combined to
size reactors operating adiabatically.
Substituting Equation (8-26) into Equation (8-22), the steady-state energy
balance becomes

(8-47)
These are the forms [Note: In many calculations the CSTR mole balance (FA& = - rAV) will‘ be
Of *e steadY-state used to replace the term following the brackets in Equation (8-47); that is,
balance we will use
(FAOX) will be replaced by (-rAV).] Rearran@ng #s the steady-state bal-
ance for the case of constant or mean heat capacities in the form
I n