Page 55 - Introduction to chemical reaction engineering and kinetics

2.5 Laminar-Flow Reactor (LFR) 37

L
Length
Figure 2.5 LFR: velocity and concentration (for A + . . . -+ products) profiles (at
steady-state)

(2) The system mass inside the vessel is not necessarily fixed.
(3) There is no axial mixing of fluid inside the vessel.
(4) There is no radial mixing of fluid inside the vessel.
(5) The density of the flowing system is not necessarily constant.
(6) The system may operate at steady-state or at unsteady-state.
(7) There may be heat transfer through the walls of the vessel between the system
and the surroundings.

These seven points correspond to those posed for a PFR in Section 2.4.1. However,
there are important differences in points (1) and (4) relating to the type of flow and to
mixing in the radial direction in a cylindrical tube. These are illustrated in Figure 2.5 (for
a cylindrical vessel). In Figure 2.5, we focus on the laminar-flow region of length L and
radius R ; fluid is shown entering at left by PF and leaving at right by PF, with a transition
region between PF and LF; in other words, regardless of how fluid enters and leaves,
we assume that there is a region in which LF is fully established and maintained; r is the
(variable) radius between the center line (I = 0) and the wall (r = R). For simplicity in
this case, we consider only steady-state behavior, in spite of the more general situation
allowed in points (1) (2), and (6).
Some consequences of the model described in the seven points above are as follows:
[l] From point (l), the velocity profile is parabolic; that is, the linear (axial) velocity
u depends quadratically on radial position r , as described by fluid mechanics (see,
e.g., Kay and Nedderman, 1974, pp. 69-71):

u(r) = u,[l - (T/R)~] (2.5-1)