Page 109 - The engineering of chemical reactions

The Plug-Flow Tubular Reactor 93

Figure 3-2 The plug-flow tubular reactor (PFTR).
The length of the reactor is L, the inlet molar flow
rate of species j is F’,, and the outlet flow rate of

0 Z L
Z--f

We first assume that the tube has constant diameter D and also that the density does
not vary with position (either liquids or gases with no mole number change, pressure drop,
or temperature change with gases). In this case the linear velocity u with which the fluid
flows through the tube is equal to the volumetric flow rate u divided by the cross-sectional
tube area At(At = n D2/4 for a cylindrical tube),
4v
u=2=-
At nD2
at any position.
A steady-state shell balance on species j in the element of length dz between z and
z + dz yields

Fj(z)-Fj(z+dz)+AtdzVjr=O
The molar flow rate of species j is related to these quantities by the relation
Fj = AtUCj
Therefore, the mass balance on species j becomes
Atu[Cj (z) - Cj (z + dz)] + At dz Vjr = 0
We next make a Taylor series expansion of the difference in Cj between z andz+dz
and let dz + 0, keeping only the lead term,
,I~~o[Cj(Z) - Cj(Z + dZ)l = -

[We obtain the same result by just noting that this difference when divided by dz is simply
the definition of a derivative.] Both At and dz can be canceled in each term; so the mass
balance on species j becomes

which is the form of the PFTR equation we will most often use. Note again that this
expression assumes

1. Plug flow,
2. Steady state,
3. Constant density,