Page 414 - Chemical process engineering design and economics

394 Chapter 7

volume or the ratio of mass feed flow rate to the catalyst mass. The volumetric
feed-gas flow rate is calculated at a standard temperature and pressure. Thus,
the space velocity is defined by:

GHSV = hourly volumetric feed-gas flow rate/reaction volume
LHSV = hourly volumetric liquid-feed flow rate/reaction volume
WHSV = hourly mass feed flow rate/catalyst mass

The units of space velocity are the reciprocal of time. Usually, the hourly
volumetric feed-gas flow rate is calculated at 60 °F (15.6 °C) and 1.0 arm (1.01
bar). The volumetric liquid-feed flow rate is calculated at 60 °F (15.6 °C). Space
velocity depends on the design of the reactor, reactor inlet conditions, catalyst
type and diameter, and fractional conversion. Walas [7] has tabulated space
velocities for 102 reactions. For example, for the homogeneous conversion of
benzene to toluene in the gas phase, the hourly-volumetric space velocity is 815
1
h" . This means that 815 reactor volumes of benzene at standard conditions will
be converted in one hour. Although space velocity has limited usefulness, it
allows estimating the reaction volume rapidly at specified conditions. Other
conditions require additional space velocities. A kinetic model is more useful
than space velocities, allowing the calculation of the reaction volume' at different
operating conditions, but a model requires more time to develop, and frequently
time is not available.
Table 7.11 lists equations for sizing a reactor using space velocity, and Ta-
ble 7.12 outlines a calculation procedure. First, calculate the reaction volume,
using a space velocity. Then, calculate the reactor cross-sectional area, using a
superficial gas velocity. Ulrich [9] states that the superficial velocity varies
from 0.005 to 1 m/s (0.00164 to 3.29 ft/s). Forment and Bischoff [31] used 1
m/s (3.29 ft/s). Fulton and Fair [27] used 1 ft/s (0.3048 m/s) for a methanation
reactor for the synthesis of phthalic anhydride from o-xylene. We will use about
0.3048 to 1.0 m/s (1.0 to 3.28 ft/s). From the cross-sectional area, calculate the
reactor diameter, which should be rounded off in six-inch increments. Then,
calculate the reactor length by summing up bed length and allowing about three
additional feet for inert ceramic balls at the top and bottom of the bed. Next,
round off reactor length to the nearest three-inch increment. The balls promote a
uniform velocity across the catalyst bed and prevent a dished-shaped depression
from forming at the top because of the jet action of the incoming flow. The bed
itself, however, is the prime flow distributor. Alternatively, or in addition to the
balls, add a baffle plate at the reactor entrance to deflect the jet of incoming
gases. The height of the bed is limited to at least 1/2 D to promote uniform flow
distribution and not more than 25 ft (7.62 m) to avoid crushing the catalyst.

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