Page 40 - Elements of Chemical Reaction Engineering Ebook

Sec. 1.4 Continuous-Flow Reactors 11

it takes the familiar form known as the design equation for a CSTR:
*I

(1-6)

The CSTR design equation gives the reactor volume necessary to reduce
the entering flow rate of species,j, 40., to the exit flow rate FJ. Ve note that the
CSTR is modeled such that the conditions in the exit stream (e.g., concentra-
tion, temperature) are identical to those in the tank. The molar flow rate F, is
just the product of the concentration of speciesj and the volumetric flow rate u:
I 1

moles - moles .volume
- -- - -
time volume time
I I
1.4.2 Tubular Reactor

hi addition to the CSTR and batch reactors, another type of reactor com-
monly used in industry is the tubular reuctol: It consists of a cylindrical pipe
and is normally operated at steady state, as is the CSTR. For the purposes of the
material presented here, we consider systems in which the flow is highly turbu-
lent and the flow field may be modeled by that of plug flow. That is, there is no
radial wuiation im concentration and the reactor is referred to as a plug-fow
reactor (PFR), (The laminar flow reactor is discussed in Chapter 13.)
In the tubular reactor, the reactants are continually consumed as they
flow down the length of the reactor. In modeling the tubular reactor, we
assume that the concentration varies continuously in the axial direction
through the reactor. Consequently, the reaction rate, which is a function of con-
centration for all but zero-order reactions, will also vary axially. The general
mole balance equation is given by Equation (1-4):

dt

To develop the PFR design equation we shall divide (conceptually) the reactor
into a number of subvolumes so that within each subvolume AV, the reaction
rate may be considered spatially uniform (Figure 1-5). We now focus our
attention on the subvolume that is located a distance y from the entrance of the
reactor. We let F’(y) represent the molar flow rate of species j into volume AV
at y and F’(y + Ay) the molar flow of species j out of the volume at the loca-
tion (y + Ay). In a spatially uniform subvolume AV,

I *”
rJ dV = rJ AV