Page 197 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.4 Pressure Drop in Reactors 169
of the increase in cross-sectional area, A,, as the fluid enters the sphere, the
superficial velocity, G = riz/A,, will decrease. From the Ergun equation
[Equation (4-%2)],

(4-22)

we how that by decreasing G, the pressure drop will he reduced significantly,
resulting in higher conversions.
Because the cross-sectional area of the reactor is small near the inlet and
outlet, the presence of catalyst there would cause substantial pressure drop;
thereby reducing the efficiency of the spherical reactor. To solve this problem,
screens to hold the catalyst are placed near the reactor entrance and exii. (Fig-
ures 4-9 and 4-10). Were L is the location of the screen from the center of the

Feed I I

talyst
+ L'

'i'

Products +z axis
Figure 4-9 Schematic drawing of the inside Figure 4-10 Coordinate system and
of a sphenca! reactor. variables used with a spherical reactor. The
initial and final integration values are slhown
as zo and z,.

reactor. We can use elementary geometry and integral calculus to derive the
following expressions for cross-sectional area and catalyst weight as a function
of the variables defined in Figure 4-10:
A, =T[R*-(z-L)*] (4-38)

Spherical reactor
catalyst weight

By using these formulas and the standard pressure drop algorithm, one can
solve a variety of spherical reactor prablems. Note that Equations (4-38) and