Page 86 - Elements of Chemical Reaction Engineering 3rd Edition

5a Conversion and Reactor Sizing Chap. 2

The space velocity (SV), which is defined as

(2-22)

might at first sight be regarded as the reciprocal of the space time. However,
there is a difference in the two quantities' definitions. For the space time, the
entering volumetric flow rate is measured at the entrance condition, while for
the space velocity other conditions are often used. The two space velocities
commonly used in industry are the liquid hourly and gas hourly space veloci-
ties, LHSV and GHSV, respectively. The uO in the LHSV is frequently mea-
sured as that of a liquid at 60 or 75"F, even though the feed to the reactor may
be a vapor at some higher temperature. The uo in the GHSV is normally mea-
sured at standard temperature and pressure (STP).
For reactions in which the rate depends only on the concentration of one
species [i.e., -rA = f(cA)], it is usually convenient to report -rA as a function
of concentration rather than conversion. We can rewrite the design equation for
a plug-flow reactor [Equation (2-16)] in terms of the concentration, CA, rather
than in terms of conversion for the special case when u = uo .

(2-16)

FAO = uO 'A0 (2-23)
Rearranging Equation (2-10) gives us

(2-24)

For the special case when u = uo,

when X = 0, CA = CAO

when X = X, CA = CA
Differentiating yields

-dCA
dX= -
cAO
(2-25)
equation

Valid only if u = uo (2-26)