REACTORS: IDEALIZED CHEMICAL REACTORS - Biomass as a Sustainable Energy Source for the Future - page 179

TABLE 6.4 Total conversion of reactant A
t (min)

E exp( − kt) exp( − kt) E Δ t

2 0.033 0.670 0.670 × 0.033 × 2 = 0.044

4 0.133 0.449 0.120

6 0.200 0.301 0.120

8 0.100 0.202 0.040

10 0.033 0.135 0.009

Sum c A /c A0 ≈ 0.33
X A =1− 0.33 ≈ 0.67

6.6.2 Dispersion Model

The plug flow model detailed in Section 6.4 does not consider axial mixing of the
species in the reactor. If this is the case, the shape of a pulse of tracer injected at
the input will be conserved along the reactor. Then, at the exit, the tracer concentration
versus time curve will have exactly the same shape as the injection of the tracer. The
reader can imagine that this situation is unrealistic.
In the reactor, the tracer is spread axially, and this dispersion will be reflected in an
increase of the width of the concentration versus time curve at the exit. However,
sometimes, the dispersion is so small that it can be neglected, and then one may
assume that the fluid flows as plug flow. The dispersion coefficient D (m 2 s −1 ) repre-

sents this spreading process:

￿ Large D means rapid spreading of the tracer curve.

￿ Small D means slow spreading.

￿ D = 0 means no spreading, hence plug flow.

The parameter that measures the extent of axial dispersion is the vessel dispersion

, which is dimensionless. The number can be determined either

D
u L

D
u L

number

experimentally from tracer experiments or using correlations available in the
literature.
Consider a steady-flow tubular reactor of length L through which fluid is flowing
at a constant velocity u and in which material is mixing axially with a dispersion
coefficient D . The molar balance in each slice of the reactor is

Rate of accumulation = 0 ðÞ =

φ n , A −

Rate of supply bulk flow rate of release bulk flow φ n , A +d φ n , A

z z + dz

DS dc A
dL

DS dc A
dL

Rate of supply dispersion − − rate of release dispersion −

+ rate of production dV ð R ð Þ − Þ