Page 42 - Elements of Chemical Reaction Engineering 3rd Edition

14 Mole Balances Chap. 1

doubtful that one would find a reactor of' the shape shown in Figure 1-6, unless
designed by Pablo Picasso. The conclusion drawn from the application of the
design equation is an important one: The extent of reaction achieved in a plug-flow
tubular reactor (PFR) does not depend on its shape, only on its total volume.

1.4.3 Packed-Bed Reactor

The principal difference between reactor design calculations involving
homogeneous reactions and those involving fluid-solid heterogeneous reac-
tions is that for the latter, the reaction rate is based on mass of solid catalyst,
W, rather than on reactor volume, V For a fluid-solid heterogeneous system,
the rate of reaction of a substance A is defined as
- r; = g mol A reacted/s -g catalyst

The mass of solid Is used because the amount of the catalyst is what is impor-
tant to the rate of reaction, The reactor volume that contains the catalyst is of
secondary significance.
h the three idealized types of reactors just discussed [the perfectly mixed
batch reactor, the plug-flow tubular reactor, and the perfectly mixed continu-
ous-stirred tank reactor (CSTR)], the design equations (i.e., mole balances)
were developed based on reactor volume. The derivation of the design equation
for a packed-bed catalytic reactor will be carried out in a manner analogous to
the development of the tubular design equation. To accomplish this derivation,
we simply replace the volume coordinate in Equation (1 -8) with the catalyst
weight coordinate W (Figure 1-7). As with the PFR, the PBR is assumed to have

I I

FA
W W+AW
I I

Figure 1-7 Packed-bed reactor schematic.
no radial gradients in concentration, temperature, or reaction rate. The general-
ized mole balance on species A over catalyst weight AW results in the equation

in - out + generation = accumulation
FA(W) - FA(W+AW) + riAW = 0

The dimensions of the generation term in Equation (1 - 12) are

moles A moles A
time
(ri)AW= * (mass of catalyst) = -
(time) (mass of catalyst)